title: FerroelectricThin-filmWaveguidesinIntegratedOpticsandOptoelectronics
author: Prokhorov,A.M.;Khachaturian,O.A.publisher: CambridgeInternationalSciencePublishing
isbn10|asin: 189832610Xprintisbn13: 9781898326106ebookisbn13: 9780585119229
language: English
subject Ferroelectricthinfilms,Integratedoptics,Opticalwaveguides.
publicationdate: 1996lcc: TA1520.P761996ebddc: 548.8
subject:Ferroelectricthinfilms,Integratedoptics,Opticalwaveguides.
Pagei
FerroelectricThin-FilmWaveguidesinIntegratedOpticsandOptoelectronics
Pageii
OtherbooksavailablefromCambridgeInternationalSciencePublishing
PlasmaChemistry
CoherentRadiationProcessesinPlasma
ThermalPlasmaandNewMaterialsTechnology
LaserThermochemistry
LuminescenceofMoleculesandCrystals
FerrousPowderMetallurgy
Arc-SlagRemeltingofSteelandAlloys
QuantificationandModellingofHeterogeneousSystems
MetallurgyofArcWelding
BibliographyonMechanicalAlloyingandMilling
Pageiii
FerroelectricThin-FilmWaveguidesinIntegratedOpticsandOptoelectronics
AMProkhorov,YuSKuz'minov,OAKhachaturyan(GeneralPhysicsInstitute,RussianAcademyofSciences,Moscow)
TranslatedfromtheRussianbyMariannaTsaplina
CAMBRIDGEINTERNATIONALSCIENCEPUBLISHING
Pageiv
PublishedbyCambridgeInternationalSciencePublishing7MeadowWalk,GreatAbington.CambridgeCB16AZ,England
FirstpublishedApril1996
©AMProkhorov,YuSKuz'minovandOAKhachaturyan©1996CambridgeInternationalSciencePublishing
ConditionsofsaleAllrightsreserved.Nopartofthispublicationmaybereproducedortransmittedinanyformorbyanymeans,electronicormechanical,includingphotocopy,recording,oranyinformationstorageandretrievalsystem,withoutpermissioninwritingfromthepublisher
BritishLibraryCataloguinginPublicationDataAcataloguerecordforthisbookisavailablefromtheBritishLibrary
ISBN189832610X
ProductionIrinaStupakPrintedbyStEdmundsburyPress,BuryStEdmunds,Suffolk,England
Pagev
ContentsPreface ix
Symbols xi
Introduction xiii
1Epitaxialfilmsofcomplexoxidecompounds
1
1.1Vacuumepitaxy 2
1.2Gas-transportepitaxy 4
1.3Filmsdepositedbyifsputtering 8
1.3.1ThinfilmsofLiNbO3depositedonasapphiresubstrate
9
1.3.2TungstenbronzeferroelectricK3Li2Nb5O15 13
1.3.3KNbO3thinfilms 14
1.3.4KTaxNb1-xO3thinfilms 16
1.3.5.Thinfilmsbypulsedlaserdeposition 17
1.3.6.WaveguidesbyMeVHeionimplantation 20
1.3.7Stripwaveguides 21
1.3.8Doublewaveguide 23
1.4Autodiffusedlayersinlithiumniobateandlithiumtantalate
25
1.4.1Out-diffusionkinetics 27
1.5Thediffusionmethodformetalsandoxides 33
1.5.1Diffusionoftransitionmetals 37
1.5.2Titaniumdiffusion 41
1.5.3Copperdiffusion 49
1.6Proton-exchangedLiNbO3waveguides 51
1.6.1Ion-exchangeprocessesinLiNbO3 53
1.6.2Samplepreparationandexperimentalmethods 54
1.6.3Annealedproton-exchangedwaveguides 56
1.6.4Waveguidesfabricatedusingbufferedmelts 59
1.6.5Protondiffusion 63
1.6.6Waveguidesusingcinnamicacid 64
1.6.7Proton-exchangewaveguidesofMgO-dopedandNd:MgO-dopedLiNbO3
66
1.7Planarion-exchangedKTiOPO4waveguides 69
2Liquid-phaseepitaxyofferrolelectrics
74
2.1Theepitaxialgrowthbymelting(EGM) 74
2.2Thecapillaryliquidepitaxial(CLE)technique 78
2.2.1CLEgrowthprocedure 79
2.2.2.CLEgrowthandcrystalquality 80
2.3Theliquid-phaseepitaxy(LPE)technique 83
2.4Physico-chemicalbasisofcapillaryliquid-phaseepitaxy
87
2.4.1ThephasediagramofLiVO3-LiNbO3 91
2.4.2PhasediagramofLiVO3-Li(Nb,Ta)O3pseudobinarysystem
92
2.4.3Theschemeofthegrowthcell 95
2.5KineticsofepitaxialgrowthofLiNbO3 97
2.5.1Thestationarycrystallizationmodel 97
2.5.2Epitaxyundernon-isothermicconditions 100
2.5.3DeterminationofsupersaturationUanddiffusioncoefficientD
101
2.5.4Epitaxyunderisothermalconditions 106
2.6CrystallizationoffilmsfromLiNb1-yTayO3solidsolutions
109
2.6.1Liquid-phaseepitaxialgrowthofLi(Nb,Ta)O3films
112
2.7ThinfilmsofLiNbO3dopedwithdifferentelements
114
2.8Epitaxialferroelectricfilmswithperovskitestructure
119
2.8.1Liquid-phaseepitaxyofpotassiumniobate 119
Pagevi
2.8.2Growthofpotassiumlithiumniobatefilmsonpotassiumbismuthniobatesinglecrystals
122
2.9Diffusionliquid-phasemethodofgrowingimmersedwaveguidechannels
123
2.9.1Striplinestructures 124
2.9.2Symmetricwaveguides 124
2.10GrowthofepitaxialfilmsintheKTiOPO4familyofcrystals
127
3Influenceofelectriccurrentuponliquid-phaseepitaxyofferroelectrics
131
3.1.Electricfieldandcrystallization 131
3.1.1Bulkcrystallization 131
3.1.2Thinfilms 134
3.1.3Liquid-phaseelectroepitaxy 136
3.2Physicalbasisofliquid-phaseelectroepitaxy(Thetheoryofthemethod)
138
3.2.1Temperaturedistributioninasystemundertheactionofanelectriccurrent
138
3.2.2Filmgrowthrate 141
3.2.3Chemicalcompositioncontrolofthefilm 142
3.2.4Initialstagesofnucleation 143
3.3Theroleofthermoelectriceffectsinthecourseofliquid-phaseelectroepitaxyofferroelectrics
149
3.4Electro-LPEgrowthoflithiumniobate-tantalatefilms
151
3.4.1Epitaxialgrowth 152
3.4.2Electrochemicalprocessesintheliquidphase 152
3.4.3Growthkineticsofelectro-LPEgrownlithiumniobate-tantalatefilms
155
3.5OptimizationofconditionsofepitaxialgrowthoflithiumniobatefilmswithallowanceforJouleheat
158
4Structureandcompositionoflightguidingfilms
165
4.1Structureandphysico-chemicalpropertiesoflithiumniobateandtantalatecrystals
165
4.2X-raydiffractionanalysisoffilms 173
4.2.1Layercomposition 174
4.2.2Monocrystallinityandinterplanardistances 175
4.2.3Measurementofstrainsinthediffusedlayer 178
4.2.4Tidistributionindiffusedlayers 181
4.2.5Thestructureofproton-exchangedLiNbO3 182
4.2.6Orientationrelations 184
4.3Morphologyandperfectionoflayers 185
4.3.1Micromorphologyoffilmsurfacefordifferentcrystallographicorientationsofthesubstrate
186
4.3.2Diffusion-induceddefectsinfilms 188
4.4Substrate-filminterfaceandtransitionregion 190
4.5Dislocationstructure 191
4.6Domainstructure 196
4.6.1Epitaxialfilmonadomainboundaryofthesubstrate
197
4.6.2Domainconfigurationsinfilms 198
4.6.3Microdomainsinsubstratesandinepitaxiallayers
199
4.6.4PeriodicallyinverteddomainstructuresinLiTaO3andLiNbO3usingprotonexchange
200
4.6.5Waveguideperiodicallypoledbyapplyinganexternalfield
203
4.6.6DomaininversioninLiNbO3usingdirectelectron-beamwriting
204
4.7Annealing-inducedvariationofthephasecompositionandcrystallinestructureofthelithiumniobatecrystalsurface
206
4.7.1Annealing-inducedvariationofthecrystallinestructureofthelithiumniobatecrystalsurface
206
4.7.2Annealing-inducedvariationofthephasecompositionofthelithiumniobatecrystalsurface
208
5Physicalpropertiesofwaveguidelayers
215
5.1Opticalpropertiesoflithiumniobateandtantalatesinglecrystals
213
5.2Opticalwaveguidemodesinsingle-crystalfilms 215
5.2.1Waveguideandradiationmodes 216
5.2.2Waveequationandfielddistribution 221
5.2.3OpticalmodesinepitaxialLi(NbTa)O3waveguides
225
5.2.4Characteristicsofout-diffusedwaveguides 229
5.2.5Propertiesofdiffusedwaveguides 234
5.3Secondharmonicgenerationinwaveguides 237
Pagevii
5.3.1Phasematchinginanopticalwaveguide 239
5.3.2Overlapoffieldsofinteractingmodes 240
5.3.3Angularmatching 241
5.3.4Temperaturematching 244
5.3.5Second-harmonicgenerationinawaveguidewithperiodicallydomain-invertedregions
247
5.3.6Effectofprotonexchangeonthenonlinearopticalproperties
249
5.3.7Sum-frequencygenerationinwaveguides 253
5.4SecondharmonicgenerationintheformofCherenkovradiation
255
5.5Electro-opticeffectsinopticalwaveguides 258
5.6Lightresistanceoflightguides 260
5.7Photorefractivepropertiesoflightguides 264
5.7.1Holographicformationofgratingsinopticalwaveguidelayers
265
5.7.2PhotorefractiveeffectinplanarTi-diffusedguides
269
5.7.3Relaxationofindexchange 274
5.7.4Photorefractiveeffectinannealedproton-exchangedLiNbO3waveguides
275
5.8Energylossinwaveguides. 279
5.8.1LossesinTi-diffusedLiNbO3waveguides 279
5.8.2Absorptionlossinstripguides 282
5.8.3Lossinepitaxialwaveguides 284
5.9Ferroelectricpropertiesofwaveguides 285
5.9.1Dielectricproperties 285
5.9.2Pyroelectricproperties 287
5.9.2.1Thelow-frequencysinusoidaltemperaturemodulationmethod
287
5.9.2.2Thethermalpulsemethod 287
5.10Temperaturedependenceofthermoelectriccoefficientsoflithiumniobateandlithiumtantalate
289
6Thin-filmstructureinintegratedoptics
293
6.1Principalcharacteristicsofwaveguidingelectro-opticmodulators
293
6.1.1Controlvoltage 293
6.1.2Bandwidth 295
6.1.3Modulationdepthandinsertionlosses 297
6.2Photoinducedpolarizationconversion 298
6.3WaveguidemodulatorsonthebasisofTi:LiNbO3 300
6.3.1Electro-opticmodulatoroncoupledchannelwaveguideswithavariableDb
300
6.3.2Interferometricandperfectinnerreflectionmodulators
304
6.4Practicalexamplesofwaveguideelectro-opticmodulators
308
6.4.1Opticalwaveguideswitchmodulator 308
6.4.2Thin-filmelectro-opticlightmodulator 311
6.4.3Braggdiffractionmodulator 315
6.4.4Ridgewaveguidemodulator 317
6.4.5Ti-diffuseddiffractionmodulator 320
6.4.6InterferometricMach-Zehndermodulator 326
6.4.7Electro-opticphotorefractivemodulator 328
6.4.8KNbO3inducedwaveguidecut-offmodulator 331
6.5Waveguideelectro-opticpolarizationtransformer 334
6.6Lightbeamscanninganddeflectioninelectro-opticwaveguides
338
6.7Electro-opticallytunablewavelengthfilter 342
6.8Flip-chipcouplingbetweenfibresandchannelwaveguides
345
6.9KTiOPO4waveguidedevicesandapplications 349
6.9.1PhasematchinginperiodicallysegmentedKTiOPO4waveguides
352
Conclusions 356
References 357
Index 371
Pageix
PrefaceThisbookisalogicalcontinuationofthetwopreviousbooksbytheauthors1whichwerepublishedintheAdamHilgerseries.Altogether,thesethreebooksprovideacompleteenoughpictureofapplicationofferroelectriccrystalsandfilmsinlaserradiationcontrol.Thisvolumeisdevotedtoferroelectricthin-filmwaveguidesforintegratedopticsandoptoelectronics.Wedealherewiththemostwell-knownmethodsofobtainingthin-filmstructures.Ourprimeconcernisliquid-phaseepitaxyfromalimitedmeltbulkwithandwithoutapplicationofanelectricfield.Amethodispresentedwhichcombinesliquid-phaseanddiffusiontechniquesforobtainingstructureswithaprescribedconfigurationofwaveguidechannels.Adetainedconsiderationisgiventophysico-chemicalpropertiesofthinferroelectriclayers,suchasmorphology,domainstructureofatransitionlayerandferroelectricproperties.Animportantroleforpracticaluseaselectro-opticmodulators,deflectorsandtransducersisplayedbytheopticalproperties,modecompositionofpropagatingradiation,secondharmonicgeneration,electro-opticproperties,photorefraction,destructionthresholdandlightloss.Alltheseaspectshavefoundreflectioninthebook.Examplesofpracticaluseofopticalwaveguidesaregiven.
Thebookmaybeinstructiveforexpertsinthefieldofintegratedopticsandoptoelectronics,aswellasforstudentsinterestedinthecorrespondingtopics.
A.M.PROKHOROVYU.S.KUZ'MINOVO.A.KHACHATURYANMOSCOW1995
Pagexi
ListofSymbolsAH,CH -latticeparameters
Bij -dielectricimpermeabilitytensorrC -electrodecapacitancec -thermalconductivityc -concentrationd -interelectrodegapdij -nonlinearopticalcoefficientd -thicknessds -elementofthelightpathD -diameterD -diffusioncoefficientD -electricinductivitye -electronchargeE -electricfieldstrengthEx,Ey -electricfieldcomponentsgij -componentsofquadraticelectrooptic
coefficientG -electrodewidthh -heightI -lightintensityj -chargedparticleflowJv -concentrationgradientJ -currentdensityJr -nthorderBesselfunctionk -coefficientofsegregationk=2pn/l.
-propagationconstant
k -thermalconductivity
K(k) -completeellipticintegralKTP -KTiOPO4l -lengthL -pathlengthL -interactionlengthM -molecularweightM -numberofmodesno,ne -ordinaryandextraordinaryrefractive
indicesNi -molarfractionPL -Langmuirvapourpressurep -pressurePo -saturatedvapourpressureP -poweroflightPout -outputpowerPin -inputpowerP -dielectricpolarisationPs -spontaneouspolarisationPijml -photoelastictytensorq -kineticcoefficientQD -activationenergyfordiffusionQv -activationenergyforvaporisationQij -electrostrictivecoefficientr -radiusrij -linearelectroopticcoefficientR -resistanceRi -reflectivitys -distanceS -complianceS -areaSi -principalstrainSAW -surfaceacousticwavest -time
T -temperatureTEi -wavemodesU -supersaturationn -velocityofzonemotionV -voltagebetweenelectrodesW -electrodewidthzef -effectiveparticlechargea -energyofformationofunitsurfacea -coolingratea -insertionlossai -electronicpolarisabilitya -evaporationcoefficienta0 -inverseaccommodationcoefficienta -numberofatomsperunitvolumea -overlapparameterb -propagationconstantintheguidebi -wavevectorsG -normalisedoverlapintegraldij -KroneckersymbolDn -refractiveindexchangeDm -variationofchemicalpotentialDlr -shiftofthecentrewavelengthe -dielectricpermitivitye0 -dielectricpermitivityinavacuumx -appliedelectricfieldh -phasemodulationindexq -diffractedangleqB -Bragganglel -wavelengthl0 -free-spacewavelengthlL.S -heatconductivitiesofsourceandliquidl -specificheatofcrystallisationL -gratingperiodicity
m -mobilityn -molefractionP -Peltiercoefficientr -liquid-phaseresistivity
Pagexii
r -density
s -surfacetensions -supersaturations -stresst -diffusiontimetp -precipitationtimet -switchingtimetT -Thomsoncoefficientt -thicknessj -phaseshiftj -overallphasefactork -couplingconstantw -modefieldwidth
Pagexiii
IntroductionAnincreasednumberofcomplicatedelectronandopticalsystemsstimulatesthedevelopmentofoptoelectronics.Theanalysisoftendenciesinthedevelopmentofappliedphysicspointsouttheimportantrolethedielectricmaterialsand,firstofall,non-centrosymmetricpiezo-andferroelectricsplayintheformationofnewtrendsinelectronics(LinesandGlass1981).
Aninevitableincreaseinthevarietyofthin-filmferroelectricstructuresthatarewidelyusedinthenewtrendsofappliedphysicsbringsaboutimprovementintechnologyanddetailedstudiesofthevariousphysico-chemicalpropertiesofsubstances.Thispromotesfurthercreationofmaterialswithpredeterminedphysicalpropertiesthatareoptimumforconcreteapplicationsinengineering(Miyazawa1980;Tomashpol'sky1984;Khachaturyanetal.1984).
Singlecrystalsofactivedielectricsandferroelectricspossessinganinterestingcombinationofelectro-,acousto-andnonlinearopticalpropertiesarepromisingmaterialsfordesigninghighlyefficientdiscreteelementsofintegratedoptics(modulators,deflectors,switches,etc.)andquick-operatingschemesforcomputation,andcanunderliethecreationofhybridopticalintegratedschemes(Kuz'minov1975;Smolenskyetal.1971;Marcuse1974;BurfootandTaylor1979;Smolenskyetal.1985).
TheprincipalapplicationsofferroelectricmaterialsarepresentedinFig.1.Asisseenfromthefigure,thewidestrangeofapplicationofferroelectricsisoptics.Ferroelectriccrystals,usuallyclearandmeasuringfrom0.35to4mm(ed.byShaskol'sky1982)areappliedasphaseandamplitudemodulatorsoflaserradiation,transducers,deflectors,etc.
Ferroelectricfilmshavebeenintensivelyinvestigatedforthelast15yearsduetothegeneraltendencyofmicrominiaturization,decreaseinpowercapacityandincreaseinthesensitivityofdevices.Anumberofphenomena(e.g.lightswitch-overinstriplinewaveguides)donothavebulkanaloguesatall.Thepossibilityofusingthin-filmstructuresascontrolelementshasledtothedevelopmentofalargenumberofmethodsforobtainingfilmsandcoverings.
Dependingonaconcretedomainofapplicability,thin-filmferroelectricsofdifferentstructuralperfectionareused,forinstance,ferroelectricceramics,polycrystallineandepitaxialsingle-crystalfilms.Forsmall-sizecondensers,polycrystallineferroelectricfilmswithahighdielectricpermittivityandlowdielectricloss(BaTiO3,SrTiO3,(Ba,Sr)TiO3)areused,animportantrolebeingplayedbythedependencesoftheseparametersontemperature,frequencyand
Pagexiv
Fig.1Recentadvancesinmaterialsforcommunicationdevices(Miyazawa1980).
electricfieldstrength(Photonics,editedbyBalkanski1975).Forstoichiometricpolycrystallinefilmscloseto1mminthickness,thelow-frequency(1kHz)dielectricpermittivityexceeds1000andthehigh-frequencydielectricabsorptionleadstoastrongfrequencydependenceofdielectricpermittivityandthelosstangent.Slightviolationsfromstoichiometrycustomarilyinduceadecreaseofdielectricpermittivityandanincreaseoflosses.(Ba,Sr)Nb2O6,(Ba,Sr)TiO3andLiTaO3filmsofsolidsolutionsofPbTiO3andPbZrO3withlanthanum(PLZT)andtriglycinesulphate(TGS)aresuccessfullyusedforhigh-frequencypiezoelectricfilters,transducersandpyroelectricthermaldetectors.Therequirementoftheseapplicationsisahighelectromechanicalcouplingorpyroelectriccoefficient,aswellaslowdielectriclosses.Polycrystallinefilmsaresuitableprovidedthecrystallographicaxesareappropriatelyorientedduringfilmdepositionorsubsequentpolarization.Butthebestcharacteristics
canbeexpectedfromsingle-crystalfilmswithorientedpyroelectricandpiezoelectricaxesbecauseoftheirhighcouplingcoefficientandtheabsenceofinfluenceofpolarisationofintercrystallayersinpolycrystallinefilms.
TheuseofferroelectricfilmsforrecordingIRradiationisofinterest.Severalpapersaredevotedtothestudyofpyroelectriceffectinferroelectricfilms(Okuyamaetal.1981;Nakagama1979;Mukhortovetal.1981;Petrossoetal.1983;Schittetal.1984;Antsyginetal.1986).Okuyamaetal.(1981)described
Pagexv
Fig.2Examplesoftheuseofthin-filmferroelectrics(Okuyama,Hamakawa1986).
athin-filmpyroelectricdetectormadeoftheferroelectricPbTiO3.
Antsyginetal.(1986)investigatedthin-filmstructuresofferroelectricbarium-strontiumniobate.Theexperimentsestablishedthatpyroelectric,electro-opticandelectrophysicalpropertiesofthebarium-strontiumniobate(BSN)filmsarewelldescribedbythephenomenologicalrelationstypicalofbulkferroelectricswithasmearedphasetransition.ItwasfoundthatontheBSN-electrodeboundarythelengthofanon-ferroelectriclayerdoesnotexceedabout3×10-8m.ThestudiesofBSNfilmrepolarisationcausedbyanappliedelectricfield,carriedoutbypyroelectricmeasurementsusingthethermalpulsemethod,repolarizationcurrentsandpulsedelectro-optics,showedthattherepolarizationofBSNfilmsisdeterminedbynucleationnearapositiveelectrode.Quick-operatingandmultielementradiationdetectorsemployingBSNfilmsasanactivepyroelectriclayerwerecreated.
Thus,alreadyearlyworksontheapplicationofthinferroelectricfilms
forIRradiationrecordingindicatedthattheirsensitivityisclosetothatofpyroelectriccrystals,althoughitshouldbenotedthatferroelectricfilmsweremostlypolycrystalline.
Geary(1979)andLemonsetal.(1978)pointedtothepossibilityofemployingferroelectricsPb5Ge3O11andGd2(MoO4)3indeviceswithamovingdomainboundary.Theydescribedopticalshuttersandanalogueelements.Figure2givesexamplesofapplicationofthin-filmferroelectricstructures(OkayamaandHamakawa1986).Inthemetal-ferroelectric-semiconductor(MFES)structure,thesurface
Pagexvi
potentialofthesemiconductorcancontrolthepolarizationoftheferroelectricfilm.WhentheMFESstructureisusedasashutterofafield-effecttransistor(FET),theoutletcurrentofthetransistorcanbemodulatedbythesurfacepotentialduetofilmpolarization.Forexample,PbTiO3filmspossessadielectrichysteresisloopandahighremanentpolarizationandcanthereforebeusedinMFESFET-typememorycellspossessingstablestatesillustratedinFig.2a.
Sinceathinferroelectricfilmhasaveryhighdielectricconstant,theappliedvoltageindevicescanbeloweredappreciablybyusingaferroelectricratherthanadielectricfilm.Thin-filmelectroluminescent(EL)devicestypicallyhaveasandwichstructureconsistingofZnSfilmsanddielectricY2O3films.AnELdeviceusingPbTiO3insteadofY2O3films(Fig.2b)hasalowcontrolvoltage.ThethresholdvoltageofanELdeviceisloweredfrom210to50V.
FilmsofPbTiO3depositedontothinSiO2orSimembranesasstripsseveraltensorhundredmicrometersinlengthwereusedforthefabricationofultrasonictransducers(Fig.2c).Thinmembranesweremadebyseedingboron-dopedsiliconwiththeuseofaqueoussolutionsofethylenediamineandpyrocatecholwhichetchedwellthe(100)and(110)facetsbuthadaweakeffectuponthe(111)facets.Electrodesweredepositedbyphotolithography.Anultrasonicwaveinducedmechanicaloscillationsofthemembraneatseveralresonancefrequencies,theshearstressinthefilmcausedpiezoelectricstress.Inthe300-690mmdevice,thesecondresonanceharmonichadafrequencyof30-150Hz.
VariousIRtransducerscanbemadeinPbTiO3filmsonthebasisofthepyroelectriceffect.MFESFETwithanelectrodeabsorbingIRlightaresensitivetransistors(Fig.2e).InfraredlightincreasesthePbTiO3filmtemperatureandthusmodulatesthesurfacepotentialofSiwhichaffectstheoutletcurrentofthetransistor.Theoutletvoltage
isinverselyproportionaltothelightmodulationfrequency.TheresponsetoIRradiationisveryquickandforaCO2laserthetimeofpulseincreasemakesup3.5ms.Thesensitivityofasiliconmonolithictransducercanbeincreasedbyremovingthesiliconsubstratefromthesensitivearea.
Thepropertiesandthewayofpreparationofthinfilmsusedinopticaldevicesmustsatisfyhigherdemands.
Thefirstexperimentalandtheoreticalstudiesofthin-filmopticalwaveguidesusedinintegratedopticswereperformedinthesixties(Deryuginetal.1967;Goncharenko1967;Goncharenkoetal.1969;Tien1971).Thesepapersinvestigatedthemainpropertiesofthin-filmdielectricwaveguidesofopticalrangeandshowedprospectsoftheirapplication.Someprogressmadeinthisfieldinrecentyearsisindicativeofthenecessityofgrowingthinsinglecrystalepitaxialfilmsforthispurpose.Infilmsofthicknesscomparablewiththewavelength,onecanobtainhighintensitiesevenwithmediumlaserpowers.Furthermore,thephasevelocityofalightwaveinathin-filmwaveguidedependsonthefilmthicknessandtheorderofthewavemode,whichsuggestsnewprospectsforcreationofdevices.
Thetheoryofplanardielectricwaveguides,whichunderliethecreationofthemainelementsforradiationcontrol,isdescribedindetailinanumberofpapersandmonographs(Tien1971;Zolotovetal.1974;Kogelnik1977;Tamir1979;Hunsperger1984;House1988).
Pagexvii
Therequirementsofintegratedopticsinperfectthin-filmstructuresnecessitatedawideuseofvariousmethodsoffabricatinglow-losswaveguidelayers.Alltheknownmethodscanbeconditionallydividedintotwogroups:
1.Refractiveindexincreaseinthenear-surfacelayerofabulkcrystal.
2.Growthofathinfilmwithahigherrefractiveindexonthesubstratesurface.
Thefirstgroupincludesthethermaldiffusionoftransitionmetalions,out-diffusion,ionimplantationandion-exchangeddiffusion.Thesecondinvolvesmainlyepitaxialfilmgrowth.
Untilrecently,theliquid-phaseheteroepitaxyhasbeen,infact,theonlyleaderinproducingheterostructureswithpredeterminedphysicalcharacteristics,whichwasparticularlyclearlyseenonanexampleofawiderangeofA3B5compounds.Foranumberofdevices,thissituationwillremainunchangedinthenearfuture.Amongtheknownliquid-phaseepitaxymethodsthemostpromisingforcomposition,thicknessandstructurecontrolistheliquid-phaseelectroepitaxyoffilms.
Theexistenceofelectro-,piezo-andnonlinearopticalpropertiesoffersnewopportunitiesforpracticaluseofferroelectricfilms.Theuseofepitaxialfilmsofoxideferroelectricsonthebasisofniobatesofalkalinemetalsintheelementalbasisofoptoelectronicsshowstheirnoticeableadvantagesoverbulkanalogues,firstofallfromtheviewpointofminiaturization,loweringofconsumedenergyandintensityofcontrolfields.Lithiumniobateandtantalatearewidelyusedinintegralelectro-opticelementsandincommunicationsystems.Bothpassiveintegro-opticcomponents(polarizers,couplers,filters)andactivecomponents(modulators,switchers,frequencyshift,etc.)havefoundtheirapplicationincommunicationsystems.Theabove-
mentionedferroelectricsposseshighelectro-opticcoefficientsascomparedwithsemiconductingcompoundsoftheA3B5groupwidelyusedforcreatingradiationsourcesanddetectorsaswellasvariouselectronicdevices.Aspecialplaceinintegro-opticdevicesistakenby'dipped'opticalwaveguidechannels.Obtainingsymmetricwaveguidechannelsbythefilmdiffusionmethodprovidesasimpleandconvenientmatchingbetweenthechannelwaveguideandopticalfibres.
Wehaveanalyzedtheepitaxialgrowthofferroelectricsfromaliquidphase,whichmadeitpossibletooptimizetheconditionsforobtainingstructurallyperfectlayersandfilmpropertycontrol.Theperformedstudiesmadeitpossibletoimprovetechnologytosuchanextentthattheproblemsofverticalintegrationofmultilayerferroelectricstructuresforintegro-opticdevicescanbesolvedcompletelyusingliquid-phaseepitaxyandliquid-phaseelectroepitaxy.Thesetechniquescanalsobeappliedtootheroxideferroelectricsandtohigh-temperaturesuperconductors.
Chapter1presentsthemainmethodsoffabricatingopticalwaveguides,exceptliquid-phaseepitaxy,whichisanalyzedinchapter2.
Epitaxialmethods,whichcannowbeusedtoproducelayerswithmaximumproximityintheirstructuralperfectiontobulkcrystals,arediscussedinchapter2.
Attentioninthischapterisalsogiventothecapillarymethodofliquid-phaseepitaxyofferroelectrics,tothegrowthkineticsoflithiumniobate,potassium
Pagexviii
niobateandsolidsolutionsoflithiumniobate-tantalate.Thecrystallizationmodels,describingthenatureofmasstransferintheliquidphaseforisothermalandnon-isothermalepitaxyconditions,areconsidered.Analyticalexpressionsarederivedlinkingthefilmthicknesswiththegrowthsystemparameters.Thefilmdiffusionmethodofgrowingimmersedwaveguidechannelsinferroelectricsisdiscussed.
Chapter3dealswiththeoreticalandexperimentalresultsofinvestigatingtheinfluenceofadirectelectriccurrentontheliquid-phaseepitaxyprocesses.Materialsoftheoriginalstudiesoftheauthorsongrowingthin-filmferroelectricstructuresarepresentedonanexampleoflithiumniobateandsolidsolutionsoflithiumniobate-tantalate.Anappliedelectricfieldinducingelectriccurrentisshowntohaveanappreciableeffectoncrystallizationconditions,whichguaranteescontrolofthepropertiesofthegrowingstructures.
Chapter4isprimarilyconcernedwiththeresultsofinvestigatingepitaxialferroelectricfilms:crystallinestructure,composition,orientation,micromorphologyofthesurfaceandofthesubstrate-filmboundary,domainanddislocationstructures.
Chapter5isdevotedtoinvestigationsoftheferroelectric,opticalandwaveguidepropertiesofepitaxialfilmsoflithiumniobate,lithiumtantalateandsolidsolutionsoflithiumniobate-tantalate.Thedielectricandpyroelectriccharacteristicsoflayersandthetemperaturedependenceofthermoelectriccoefficientsarepresented.Opticalresistancetolaserradiationisexamined.Refractiveindicesandthemodestructureofradiationthroughepitaxialfilmsaredetermined.Lightattenuationunderwaveguidepropagationandtheelectro-opticpropertiesofstructuresareinvestigated.
Thesubjectofchapter6istheapplicationofopticalplanarandchannelwaveguidestolaserradiationcontrol.Theparametersof
variousthin-filmintegro-opticalmodulators,deflectorsandtransducersofradiationarepresented.
Page1
1EpitaxialFilmsofComplexOxideCompoundsThepresent-daydevelopmentofsolidstateelectronicsisassociatedtoagreatextentwiththedevelopmentofthegrowthtechniqueofsinglecrystalsandsingle-crystalfilms.Thisisconnectedwiththefactthatemploymentofsinglecrystalsandsingle-crystallayersexcludestheinfluenceofgrainboundariesandstructuraldefectstypicalofpolycrystalsandthusprovidesamoreeffectiveuseofthephysicalpropertiesinherentinamaterial.
Inrecentyears,increasingattentionhasbeenpaidtotheproblemsoforientedgrowthofasingle-crystalferroelectriclayerontoasingle-crystalsubstrate,epitaxy,sincetheferroelectricpropertiesaremostofallpronouncedinsingle-crystallayers.
Epitaxyofoxideferroelectricsisnowunderparticularlyintensestudy,andinthischapterweexaminethisproblem.Thenumberofknownferroelectricsisincreasinglylarge,reachingnowseveralhundred.Particularlyfruitfulhasbeenthesearchfornewferroelectricsamongtheperovskite-typestructures(LinesandGlass1977).Thegrowthofperfectepitaxialferroelectricfilmsofagiventhickness,withacontrolledcompositionandanecessaryimpurityconcentration,isoneofthemaintasksofthin-filmtechnologyandisstimulatedbytherequirementsofintegratedoptics.
Single-crystalfilmsarecustomarilyobtainedeitherbyepitaxialgrowthontoorientedsubstratesorbystimulatingorientedcrystallizationonnon-orientedinsulatingsubstrates(Chernovetal.1980;Sheftal1983).
Table1.1givesalistofadvantagesanddisadvantagesofthemain
methodsforobtainingfilms(ed.byPoate1978).Comparativeanalysisofthemethodsforobtainingheterostructuresshowstheadvantageofepitaxialmethods.
Thedegreeoffilmperfectionisdetermined,inthefirstplace,bythespecificitiesofeachmethodand,inthesecondplace,byconcretefilmgrowthconditions(thedegreeofvacuum,temperatureregimes,growthrates,impuritycontent).
Therearenowthreebasicwaysofepitaxialgrowthofsingle-crystalfilms:
1.Vacuumepitaxy(involvingmolecularbeam),
2.Gas-transportepitaxy(involvingdecompositionofvolatilecompoundsandtransportchemicalreactions),
Page2
Table1.1Methodsofproducingfilms
Method Advantages Shortcomings
Vacuumdepositionwithresistiveheatingofevaporator
Simpleequipmentforfusiblematerials
Fusionwithevaporatormaterials
Vacuumdepositionwithelectron-beamevaporator
Fitformostofthesingle-elementmetalsandsemiconductors
Refractorymetals,carbonandoxidesaredifficulttoevaporate
Ionsputtering Fitforbothconductingandinsulatingmaterials;compositionisdeterminedbythatofthetarget.Permitsobtainingamorphousfilmsofmetalsandsemiconductors.readilyadmitsbiasfield
Arorotheratomsandmoleculesofsputteredgasereinsertedintosubstrate,substrateistypicallystronglyheated,filmmaterialismixedwithsubstratematerialandsubstratesurfacecanbedamaged
Chemicalprecipitationfromthevapourphase
Giveshigh-qualitydevices,epitaxiallayersforactivedevices,polycrystallinelayerscanbedeposited
Equipmentismoresophisticated.requiresexactprescriptionofgasflowvelocity;highsubstratetemperature
Epitaxial Guaranteeshigh- Sophisticatedequipment
growthfrommolecularbeams
qualityfilmsofcompounds
Electrochemicalprecipitation
Awiderangeoffilms;uniformlythicklargearea
Canonlybeappliedformetalfilms;problemofimpurities
Epitaxialgrowthfromtheliquidphase
High-qualityfilmsofcompounds
Itisdifficulttocontrolconcentrationandguaranteereproducibility
Ion-beammethod
Strictcontroloverprecipitationparameters
Lowprecipitationrateandsophisticatedequipment
3.Crystallizationfromaliquidphaseorliquid-phaseepitaxy.
Weshallnowconsidereachoftheseepitaxymethods.
1.1Vacuumepitaxy
Epitaxyfrommolecularbeamssuggestsgrowthofanepitaxiallayerwhenmolecularbeamsoratomsfallontoaheatedsubstratesurfaceinaultrahighvacuum.Abeamisgeneratedbysourceslocatedintheso-calledeffusivefurnacesinwhichthermalequilibriumismaintained.Thecharacteristicfeatureofthismethodismaintenanceofaconstantcompositionoftheevaporatingsubstanceanditseffusionrate.Theprocesstypicallyproceedsinhighvacuum,whichguaranteesasufficientpurityofepitaxiallayergrowth.Themethodiscommonlycharacterizedbyrelativelylowtemperaturesandgrowthrates.Alayeronasubstrateisformedundercrystallizationofcomponentscomingfromdifferentindependentbeamsand,therefore,thecompositionofthegrowinglayerandthelevelofitsdopingareeasilycontrolled.Thismakesthemethodsuitableforobtainingstructureswithasharpvariationinthecompositionandimpurityconcentration.Alowgrowthrateenablesthelayerthicknesstoberatheraccurately
controlled.Lowgrowthtemperaturessuppresstheinfluenceofthediffusionprocesseswhichlevelupthecompositionsofneighbouringlayers.
Duringcrystallizationfromamolecular(atomic)beam,vacuuminthereactorismaintainedatsuchalevelthatthefreepathofthemolecules(atoms)exceeds
Page3
greatlythedistancefromthesourcetothesubstrate.Supersaturationabovethesubstrateisdeterminedbythepressureofthevapourofthecrystallizingcomponentandbythesubstratetemperature.Regulationofthesourceandsubstratetemperaturescontrolssupersaturationand,therefore,thegrowthrate.
Layergrowthbythismethodproceedsinthefollowingsteps:
1.transportofthecomponentvapourtothesubstratesurface;
2.accommodationofatoms(molecules)onthesubstrate;
3.atommigrationonthesubstratesurface,re-evaporation;
4.building-inofmigratingatomsinactivegrowthcentres,stablenucleation;
5.coalescenceofnuclei.
Amolecular(oratomic)beam,emittedbythesource,isdirectedontoasubstrate.Thevapourpressureabovethesource,Psour,inthecaseofone-componentvapourisequalto
whereP0isthesaturatedvapourpressureatthesourcetemperature,a0istheinverseaccommodationcoefficientequaltotheratioofthenumberofevaporatedatomstothenumberofatomscollidedwiththesourcesurface.
Inthecaseofatwo-component(AandB)vapour,itspressureabovethesourcecontainingbothcomponentsisequalto(accordingtotheRaoultlaw):
wherePAandPBarethevapourpressuresofthecomponentsAandB,a0Aanda0Bareinverseaccommodationcoefficientsofthe
componentsAandB,P0AandP0BaresaturatedvapourpressuresofthecomponentsAandBforTsour,NAandNBaremolarfractionsofthecomponentsAandB(NA+NB=1).
Incrystallizationofatwo-componentvapour,specialmeasuresaretakentopreserveitsconstantcomposition.Sometimes,evaporationiscarriedoutfromseparateone-componentsources.Thevapourpressureofthecrystallizingcomponentiscontrolledbythesourcetemperature.
Itshouldbenotedthatevenasmalldifferenceintheelasticityofvapoursofthecomponentsofdissociatingcompoundscanhaveanappreciableeffectonboththestructureandthepropertiesofthecondensates.Thelatterplaysagreatroleforferroelectricmaterials.Thecondensatecompositionalsodependsonthesubstratetemperature,whichisexplainedbyselectivere-evaporationofcomponents(Shimaoka1985;Tomashpol'sky1982).
Inrecentyears,themethodofpulsedlaserdeposition(PLD)hasbeenintenselydeveloped(GaponovandSalashchenko1976;Firtsaketal.1984;Lushkaetal.1982).Theideaofusinglaserradiationforsubstanceevaporationinavacuumforthepurposeofthin-filmsputteringappearedwiththeconstructionofinitialpowerfullasers.
VariousresearchesusingPLNhavebeencarriedoutforobtainingorientedfilmsofnearlytwentysemiconductingcompounds,suchasgermanium,silicon,galliumarsenidefilms,aswellasfilmsofoxygen-freeferroelectricsofthetype
Page4
ofantimonysulphoiodideandtinthiohypodiphosphate(GaponovandSalashchenko1976;Firtsaketal.1984;Lukshaetal.1982).Insomecases,orientedgrowthoflasercondensatesexhibitsatemperatureloweringascomparedwithwhatweobserveinthermaldepositionmethods.Thisfactcannotbeexplainedconsistentlybythequantitativeanalysisofthelayerformationmechanism.Onthequalitativelevel,thespecificfeaturesofepitaxialfilmgrowthunderQ-modelaserdepositioncanbeexplainedbybombardingthesubstratebyhigh-energyions(102-103eV)oflaser-inducedplasma,whichstrengthenthepotentialreliefofthesurfaceandprovideanorientedgrowthalreadyunderinsignificantatommotions,thatis,atalowersubstratetemperature.
Therelationshipsbetweenmatterandenergytransferprocessesandphaseandintraphasetransformationsinthecondensateallowustodistinguishbetweentwoprincipalcondensationmechanisms:vapour-liquid-amorphousmetastable(glass-like)phaseandvapour-amorphousmetastablephase(withsubdomainsofpolyamorphousmodificationsandtheircondensationthroughamorphouslabilephases)whicharetypicaloflaserdeposition(Firtsaketal.1984).
Vacuumepitaxy,includinghigh-frequencycathodesputtering(Takadaetal.1974),suggestsaneasycontroloftheprocessandenablespurefilmswithaclearlypronouncedinterfacetobeproduced.Butinsomecases,inparticular,forferroelectrics,theseadvantagesareratherdifficulttorealize.Violationsofstoichiometry,occurringwhencomplexoxidefilmscontainingvolatilecomponentsareformedinvacuum,restrictsubstantiallytheefficiencyofthemethod.Thefilmsthusobtainedareasarulepolycrystallineorhaveanimperfectstructure,forexample,filmsofbismuthtitanate(Takeietal.1969),leadtitanate-zirconate(Philips1971),lead-lanthanumtitanate-zirconate(Ishidaetal.1977;Takadaetal.1974),BaTiO3andBaxSr1-xTiO3(Mukhortovetal.1981),lithiumtantalate(D'Amicoetal.
1984)andlithiumniobate(Takadaetal.1974;Meeketal.1986;Postnikovetal.1973;Foster1971;Ninomukaetal.1978).
Lithiumniobatefilmsonasapphiresubstratewereobtainedbysputteringinvacuum(Foster1971;Takadaetal.1974).Films1800Åthickweretransparentandsmoothbutexhibitedhighopticallosses,upto9dB/cm.Itisnoteworthythatthelossesinfilmsincreasedwithincreasingmismatchbetweenthefilmandsubstratelatticeparameters.
Usingvacuumepitaxy,Ninomukaetal.(1978)precipitatedz-LiNbO3filmsontoasubstrateofasingle-crystalMgOorientedalongthe[111]axis.Suchanorientationalrelationshipisduetotheidenticalpositionofoxygenionsintheindicatedplanes(thelatticeparametermismatchwasabout0.2%).Filmswereprecipitatedatarateof0.1mm/hatasubstratetemperatureof620-660°C.Thisexperiomentgavesingle-crystallayers6000Åthickwithasurfaceroughnessof100Å.Nevertheless,lossesinthefilmswereinthiscasealsoanorderofmagnitudelargerthanindiffusionfilms(~10dB/cm).
1.2Gas-transportepitaxy
Epitaxialfilmgrowthviaachemicalreactionincludesprocessesinwhichthecrystallizingphaseisduetoreactionsproceedinginavapour-gasmixture.
Thecrystallizationprocess,asanyphasetransition,isdrivenbythedifferenceinthethermodynamicpotentialsofphasesundergoingtransformations,but
Page5
inthecaseofcrystallizationbymeansofchemicalreactionsthegasphasesupersaturationcannotbedeterminedsincethechemicalreactionproceedsatthecrystallizationfronttheelementaryactsofchemicaltransformationsandtheelementaryactsofcrystallizationarecloselyconnected.
Theepitaxialgrowthrateisdeterminedbytheyieldofthechemicalreactionsresultingintheformationofacrystallizingsubstanceanddepends,therefore,ontheconcentrationofinteractingphasesinthegasmixture,thespeedofgasmixturepassageoverthesubstrate,thecatalyticactivityandthesubstratetemperature.Theseparameterscanbecontrolledintheepitaxialgrowthprocess.Thecatalyticactivityofthesubstrate,whichdependsonthemethodofsurfacetreatment,iscustomarilyassumedtobefixedineachseriesofexperiments.
Filmgrowthbymeansofchemicalreactionsundergoesthefollowingstages:
1.transportofstartingcompoundstothesubstratesurface;
2.chemicalreactionresultingintheformationofmoleculesofthegrowingcrystal;
3.migrationofmoleculesaboutthesubstratesurfaceduetoreactionheatrelease,aswellasspontaneousmigration;
4.desorptionofunreactedmolecules;
5.building-inofmigratingatomsintoactivegrowthcentres,formationofstablenuclei;
6.coalescenceofnuclei.
Oneofthemodificationsoftheprocessesdescribedaboveisthegas-transportreaction.Itsmaindifferencefromthechemicalreactionisthatachemicalcompoundcontainingacrystallizingsubstanceis
formedstraightinthereactorandthentransportedinacertainwayontoaheatedsubstratewhereitisdecomposedandcrystallized.
Thesysteminwhichtheepitaxialfilmgrowthproceedsthroughgas-transportreactionsmusthaveatleasttwotemperaturezones.Inoneofthem,thetransportinggasreactswiththesubstancesourcetoformavolatilecompoundtransportedtothesecondzonewherethesubstrateislocatedandwherethesubstanceorcompoundissegregatedandcrystallized.Thestagesoftheprocessproceedinginthesecondtemperaturezonearesimilartothestagesoffilmgrowthbymeansofchemicalreactions.
Awidespreadandconstructiveversionofthegas-transportepitaxyistheso-called'sandwichmethod'inwhichthesubstrateandthesourceareplatespositionedfractionsofamillimetrefromoneanotherandhavedifferenttemperatures(Dorfman1974).
Inspiteofthedifficultiesincreatingsteeptemperaturegradients,the'sandwichmethod'hasthefollowingadvantages:
a)thespacewherethereactionproceedsisseparatedfromtheremainingspaceofthereactorand,therefore,thepurityoftheprecipitatinglayerisdeterminedbythepurityofthestartingmaterialonly;
b)ahighefficiency(90-98%)ofmasstransfer(theratioofthesubstrateweightgaintothesourceweightloss);
c)ahighcrystallizationrate(hundredsofmicronsperhour).
Thechemicaltransportreactionunderlyingepitaxyfromthegasphasecanberepresentedinthefollowingwayonanexampleofasemiconductingcompound
Page6
AB:
where(AB)solisamaterialsynthesizedinadvance,theso-calledsolid-statesource,whichisinmostcasesmadeofapolycrystallinepowder;Cvapisagaseoussubstance,theso-calledtransporter;(AB)vapandBvaparegaseousproductsofaforwardchemicalreaction.
Substance(AB)solisinthesourcezoneatthetemperatureTsourandthesubstrateisinthecrystallizationzoneatthetemperatureTcryst,whereTcryst<Tsour.Whenthesourceinteractswiththetransporters,gaseousproductsinthedirectreactions(AB)vapandBvapgoovertothecrystallizationzonewherethereversedreaction(fromrighttoleft)proceedsandresultsintheformationofanepitaxialABlayeronthesubstrate.ThetransporterCvaprevealedinthereversereactiongoesovertothesourcezone,whereitisagaininvolvedinaforwardreaction.
Whenepitaxialfilmsaregrownbycrystallizationfromagasphase,uniformlydopedlayerscanbeobtainedquiteeasily.Adopingimpurityisintroducedintotheoperatingspaceeitherintheformofahighlyvolatilecompoundorintheelementalstate.Theimpurityconcentrationinthegasphaseiscontrolledinthiscasebythegasmixturecomposition,andinthecaseofelementaladditionsbythesourcetemperature.
Themethodofchemicalgas-transportreactionshassomeadvantages:theinitialreagentscanbesubjectedtopurification,thecrystallizationprocessisreadilycontrolled,thedevicesusedinthemethodaresimplerthanthoseusedinthemolecularbeammethod(e.g.nodevicesforhighvacuumareneeded).
Theshortcomingsofthemethodareasfollows:
a)difficultiesinmaintainingaconstantconcentrationofgaseousreagentsinthesubstratezone;
b)rapidcompositionmodulationcannotbecarriedoutduetothediffusioncharacterofgaseousreagentmotiontowardsthesubstrate;
c)theabsenceofaclearlypronouncedboundarybetweenlayers.
CurtiesandBrunner(1975)reportedobtainingLiNbO3filmsonaLiTaO3substrateusinggas-transportepitaxy.Thepropagationlossreachedavalueof40dB/cm,whichisexplainedbythepresenceofscatteringcentresinthefilms.Single-crystalfilmsobtainedbythegas-transportepitaxyevenunderoptimumconditionsusuallyhavealowstructuralperfectionwithnumerouspointdefectsofpackageanddislocations(CurtiesandBrunner1975;Aleksandrov1972;Nelson1963).
FushimiandSugh(1974)reportedonastudyofthegrowthofLiNbO3singlecrystalsbytheclosed-tubevapourtransporttechniqueanditsapplicationtotheepitaxialgrowthofthinfilmsofLiNbO3singlecrystals.
ThetransportexperimentsforLiNbO3werecarriedoutusingsealed,evacuatedtransparentquartztubes.LiNbO3powderandatransportagentwereloadedatoneendofthetube,whichwasthenevacuatedto10-5mmHgandsealedwithatorch.Theampouleswithstartingmaterialswereheatedinanelectricfurnace.Thetemperatureofbothendsofeachampoulewascontrolled,and
Page7
theendcontainingthestartingmaterialswasalwaysmaintainedatthehighertemperature.Theheatingtemperaturesexaminedrangedbetween650and1500°C.ThecoolendproductswereexaminedbyX-raydiffractometrywithCuKaradiation.
Transportagentsexaminedinthisstudyincludedsulphur,iodine,andamixtureoftheseelements.LiNbO3couldbetransportedbysulphur,butnotbyiodine.TransportofLiNbO3bysulphurwasretardedbyaddingiodinetothereactionsystem.Thecomparisonwasmadebetweenthestartingcompositionof1.00gLiNbO3and0.40gsulphurandthatof1.00gLiNbO3,0.40gsulphur,and0.40giodineloadedintheampoules12mmindiameterand100mmlong.Thehotandcoolendtemperatureswere1000°Cand910°C,andtheheatingperiodwassevendays.ThetransportratesofLiNbO3were0.125g/dayforsulphurand0.012g/dayforthemixtureofsulphurandiodine.
TherelationsbetweenthetransportrateofLiNbO3andtheamountofthesulphurtransportagentwereexaminedat1000°Chotendand910°CcoolendtemperaturesandaresummarizedinFig.1.1.Althoughthemeasuredtransportratesareslightlyscattered,theresultwasexpressedas
wherebwasfoundtobe2.0-2.5.
LiNbO3transportedbysulphur,accompaniednoby-productsandcrystallizedinfairlywellshapedtinyrhombs,coveredbythefacetsparalleltothe planes,withdimensionsupto0.5×0.5×0.5mm.The
planescorrespondtotheperfectcleavageplaneofLiNbO3.ThecrystalhabitwasexaminedinaprecessioncamerawithMoKaradiation.
Eventhoughthevapourtransporttechniquewasnotsuitablefor
obtainingbulkLiNbO3singlecrystals,thetechniquewasappliedtotheepitaxialgrowthofLiNbO3ontheLiTaO3substrate.Opticallyflat
,(010)and(001)platesofLiTaO3wereusedassubstratesforepitaxialgrowth.TheconditionsforepitaxialgrowtharelistedinTable1.2.Thoughthedepositedlayerthicknesswasnotuniform,2-10mmthickLiNbO3crystallayerswereformedontheLiTaO3substrates.ThesurfacesoftheLiNbO3layersdepositedontheLiTaO3platesweresmooth,whilethosedepositedonthe(010)andthe(001)plateswereroughbecausetheywerecoveredbythefacets.Fairlygoodcrystal
Table1.2ConditionsfortheepitaxialgrowthofLiNbO3(Fushimi,Sugh1974)
Ampoulesize 15mmdiam.,170mmlong,20mmdiam.,210mmlong
Initialcharge LiNbO3:1.00-1.40g,S:0.40-2.00g
Substrate LiTaO3 ,(010),(001)plate
Substrate-sourcedistance
8.3-11.0cm
Sourcetemperature 950-1000°C
Substratetemperature 900-910°C
Heatingperiod 3-17h
Coolingrate Furnacecooling,60°C/h
Page8
Fig.1.1RelationsbetweenthetransportrateofLiNbO3andtheamontofsulphur(FushimiandSugh1974).
Fig.1.2(right)RockingcurveoftheLiNbO3layerdepositedonaLiTaO3(001)plate(FushimiandSugh1974).
qualityoftheLiNbO3layersandtheirexcellentepitaxyontheLiTaO3substratesoverthewholedepositionareawererevealedbyX-raytopography.Figure1.2showsarockingcurveoftheLiNbO3film
depositedonaLiTaO3(001)plate,whereKa1andKa2reflectionsfromLiNbO3andLiTaO3areclearlyseparated.
1.3Filmsdepositedbyrfsputtering
Papershavebeenpublishedonionimplantationfortreatmentoflithiumniobatecrystalsurfaces,inparticular,forproducinglightguidinglayers.Townsend(1984)reportedobtainingplanarlightguidesinlithiumniobatebyimplantingN+,B+,He+andNe+ions.HealsodeterminedthedependenceoftherefractiveindexvariationAnonirradiationdosesforeachoftheseionsandshowedthepossibilityofproducinglightguideswithPn>0.1atlowsubstratetemperaturesandirradiationdosesexceeding1022cm-3.Itisnoteworthythatwaveguidesobtainedbytheion-implantationmethodtypicallyexhibithighlosses.Sampleannealingreducesthelosses,butoverannealingreducesthedifferencebetweentherefractiveindicesofthewaveguideandthesubstrate.Furthermore,underionimplantation,thesurfacelayerofthesinglecrystalbecomesamorphous.Inlithiumniobate,implantationofAr+andNe+leadstodistortionsinthesurfacelayerofthecrystallatticeupto10%.Damageinwaveguidelayersalsoimpairstheelectro-opticalpropertiesofcrystals.Thisessentialshortcomingoftheion-implantationmethodmakesiteffectiveonlyforproducingpassiveelementsofintegratedoptics.
Theadvantagesofthismethodovertheothermethodsofthinfilmprecipitationarewellknown:thepossibilityoffabricatingmulticomponentcompounds
Page9
(thechemicalelementsinthecompoundcompositioncanbequalitativelycharacterizedbyvariousphysicalproperties,forexample,partialvapourpressure);maintenanceofalowgrowthrate(0.01-5Å/s)duringthewholefilmformationprocessunderintensebombardmentbysecondaryelectronsandions,whichisintheendresponsibleforthehighqualityofitsstructure.ButthemainadvantageofHF-sputtering,particularlyimportantforproducingmultilayerstructures,isthesynthesisofgrain-orientedandevensingle-crystalfilmsonanon-orientingsurface.Thiscanberealizedwhenthefilmissynthesizedbythemechanismoffinalgrowthorientation(Bauer1969).Filmcondensationinthiscasewastheresultofcompetinggrowthofdifferentlyorientedcrystalsratherthanofthetendencytoformationofconfigurationswithaminimumoffreeenergy,asisthecasewhentheinitialorientation(e.g.orientationcausedbytheinfluenceofthesubstratenature)determinesnucleationandsubsequentcondensategrowth.Atdifferentcrystalsurfaces,adifferentnumberofmoleculesiscondensedperunittime,whichdeterminesthepredominantgrowthofcrystalswithoneoftheorientations.IthasbeenestablishedthatunderHF-sputteringthedeterminingfactorinthisgrowthmechanismisthedifferenceinthere-evaporationratesofdifferentcrystallinegrainfacetsundertheactionofelectronandionbombardmentofthesamplesurfaceduringferroelectriclayersynthesis(Margolinetal.1983).Naturally,suchmechanismisonlypossibleatlowgrowthratescomparablewiththeratesofparticlere-evaporationfromthecrystalsurface.HF-sputteringprovidestheindicatedrelationbetweenthespeedatwhichthematerialisfedtothecondensationzoneandthecontrolledspeedofitsremoval.Choosingthetarget-substratedistanceandtheoxygenpressurecreatesconditionsforplasmochemicalreactionsforoxidemoleculeformationduetotwo(andmore)vapouratomcollisionsinthepresenceofionizingelectrons.Undersuchconditions,filmthicknessincreaseswithincreasingsubstratetemperatureTs,which
agreeswithexperiment.Samplesthusobtainedhaveahighdegreeofstructureperfectionandpreserveinitialstoichiometry.
Sapphireandsiliconwereusedassubstratesinsuchexperiments.Theferroelectricfilmswere1-9mmthick.Thesubstratetemperaturemaintainedinthecourseofgrain-orientedfilmsynthesiswasestablishedtodeterminethegrainsize,whichproducesaqualitativeeffectontheprincipalelectrophysicalpropertiesofsamples.Forexample,agrainsizeof~3mmsuggeststheoccurrenceofferroelectricproperties.
1.3.1ThinfilmsofLiNbO3depositedonasapphiresubstrate
Takadaetal.(1974)werethefirsttosucceedinfeedingalaserbeamintoasingle-crystalLiNbO3thinfilmdepositedonasapphiresubstratebytherfsputteringmethod.Theauthorsbelievethatthesuccessisduetotheuseofanextremelylowsputteringrate.Itshouldbeemphasizedthat,intheirwork,theabove-mentionedpolishingprocesswasnotessentialtotherf-sputteredthinfilm,andthelightbeamcouldbeeasilyfedintothefilm.
Anrfdiodesputteringapparatuswasusedtofabricatethethinfilm.Thetargetusedintheexperimentwaspreparedinthefollowingway:First,lithium-enrichedpulledLiNbO3singlecrystalswerecrashedintograins.Then,adisc9cmindiameterand8mmthickwasformedbythegrains.Finally,thedisc
Page10
Table1.3LatticeparametersandordinaryandextraordinaryrefractiveindicesofLiNbO3andsapphireatroomtemperatures(Takadaetal.1974)
Crystal aH(Å) cH(Å) no ne
(l=6328Å)
LiNbO3* 5.149 13.862 2.289 2.201
Sapphire** 4.758 12.991 1.766 1.758
*KNassau,HJLevinsteinandGMLoiacono,J.Phys.ChemSolids,27,989(1966);
**AMyronandJJeppesen,J.Opt.Sec.Am.,48,629(1958).
Table1.4Atypicalsputteringadoptedintheexperiment(Takadaetal.1974)
Target-substratespacing 4cm
Gascontents Ar(60%)+O2(40%)
Gaspressure 2×10-2Torr
rfpower 50W
Magneticfield 100G
Substratetemperature 500°C
Fig.1.3(a)Laserbeaminasingle-crystalLiNbO3filmdepositedbytherfsputteringmethod,and(b)correspondingsample
configuration(Takadaetal.1974).
Page11
wassintered.Thec-planeofsapphirewasusedassubstrate.Table1.3showsthelatticeparametersandordinaryandextraordinaryrefractiveindicesofLiNbO3andsapphire.
AtypicalgrowthconditionofthefilmisshowninTable1.4.ThedepositionrateundertheconditionofTable1.4is250Å/h,whichisextremelylowcomparedwiththevalueusedintheusualsputteringprocess.Filmsobtainedaretransparentandsmooth,andshowahomogeneousinterferencecolour.
Figure1.3showsaphotographofafilmwithathicknessof1800Åandatraceofthe6328ÅHe-Nelaserbeamfedintothefilmbyarutileprismcouplerattheleft-handside.Thelossofthefilmislessthan9dB/cm,whichiscomparablewiththelossmeasuredinanepitaxialZnOfilm.Theexperimentalvaluewasobtainedbyusinganopticalfibrewithadiameterof0.5ram.Oneendofthefibrewasplacednearthefilmsurfaceandtheotherendwasconnectedwithaphotodiodeinordertomeasurethelightintensityscatteredbythesurface.AnexampleofexperimentalresultsisshowninFig.1.4.ThemodeusedinthisexperimentwasTM0.Intheexperiment,thelossoftheTE0modewasusuallylargerthanthatoftheTM0mode.
TheordinaryandextraordinaryrefractiveindicesofthefilmwereobtainedfromthemeasuredvaluesofthecouplinganglesfortheTE0andTM0modesandthethicknessofthefilmbyusingtheformulasfromthepaperbyP.K.Tien.Theresultsare andwherenoandnearetheordinaryandextraordinaryrefractiveindices,respectively.ThesevaluesareclosetothoseofthebulkLiNbO3showninTable1.3.
Itisverydifficulttoidentifythefilmthicknesslessthan1umtobeasingle-crystalLiNbO3filmbecausethefilmistoothintobeinvestigatedbymeansofX-rayanalysis.Thefilmswerethereforemadethickerthan1um,andthefollowingpatternsfromthefilms
wereanalyzed:(i)electrondiffractionpattern,(ii)X-raydiffractionpatternbyadiffractometer,(iii)X-rayLauepattern,and(iv)pseudo-KosselpatternbyadivergentX-raybeam.Analysisshowedthat
Fig.1.4Surface-scatteredlightintensityasafunctionofdistancealongthelaserbeaminthefilm.Theslopeindicates
thatthelossofthefilmat6328Åislessthan9dB/cm.Thethicknessofthefilmis1800ÅTM0modeisused
(Takadaetal.1974).
Fig.1.5(right)Propagationlossoflight
asafunctionofthelatticeconstantcHofdepositedfilms(Takadaetal.1974).
Page12
single-crystalLiNbO3wasreallydepositedepitaxiallyonthesapphiresubstrateoverawideareasothatthec-planeofthefilmwasparalleltothec-planeofthesubstrate.
Figure1.5showsthepropagationlossasafunctionofthelatticeconstantofdepositedfilms.Itcanbeseenthatthepropagationlossoflightinthefilmisstronglyrelatedtotheincreaseofthediscrepancyinthelatticeconstantofthefilmfromthatofthesubstrate.
Theoriginofthepropagationlossoflightisnotclearinthegivensample.Itis,however,expectedthatthelosscouldbedecreaseduptoaboutone-tenthofthatofthepresentsamplesbypurifyingthetargetmaterialandsputteringgasesandbyfindingoutamoreadequatesputteringcondition,eventhoughtheinternalstressinthefilmcausedbymisfitinthelatticeconstantbetweenthefilmandthesubstratecouldnotbecompletelyeliminated.
IntheworkbyN.F.Foster(1969),lithiumniobatewasdepositedbytriodesputteringinanargon-oxygengasmixturecontaining5-10%oxygen.TheapparatususedisshowninFig.1.6.Thesubstrateholderassemblywasmountedsothatthesubstratecouldbelocatedabovepositionsfortheevaporationofmetalfilmsorforthesputteringoflithiumniobatewithoutbreakingvacuum.
Thesubstratesusedwere1/4in.squareby1/2in.longbarsoffusedquartz,orsapphirewiththec-axiscoincidentwiththebaraxis.Afterchemicalcleaning,thebarswereclampedinthesubstrateholder,heatedto~150°Cinvacuum,andplatedwithathinchromiumunderlayerfollowedbyabout1000Åofgold.Thesubstratetemperaturewasthenincreasedtotheinitialdepositiontemperature,thesputteringgaswasadmittedatadynamicpressureofabout2m,andtheprimarydischargewasstruckandadjustedto1.5Aat60V.Thetargetvoltagewasappliedandthesubstrateswungintoplaceoverthetarget.Withatargetvoltageof1kV,thetargetcurrentwas12
mA.Amagneticfieldparalleltotheprimarybeamwasproducedbypassingacurrentof2Athroughthe100turncoilsmountedonthefilamentandanodehousings.Undertheseconditions,thesubstratetemperatureincreasedduringdepositionto30-50°Cabovetheinitialtemperature.Topermitopticalratemonitoring,thesubstratewastiltedat45°tothetarget,andundertheseconditionsthefilmgrowthratewasapproximately3/4m/h.Films2-4umthickweredeposited.Thelithiumniobatetargetwasmadeofapowderpressedintoa2.5cmdiameterx3mmthickdiscand
Fig.1.6Triodesputteringunit(Forster1971).
Page13
subsequentlyfiredinairat1200°C.Initially,thediscwaswhiteandhighlyinsulatingandsputteringwasveryslow.Asthetargetbecameheated,however,itdarkened,presumablythroughthelossofoxygen,andbecamesufficientlyconductingforthedcsputteringprocesstoproceedreadily.Theoxygenpresentinthesputteringgasassuredthatthedepositedfilmswereinsulating.
14filmsweredepositedduringthisstudy.Forthefirstfourdepositionstheinitialsubstratetemperatureswerebetween100and300°C.ThesefilmswereclearandadherentbutshowednoX-raystructureorpiezoelectricactivity.Theremainingtenfilmsweregrownatinitialsubstratetemperaturesof325-380°C.TheseexhibitedwelldefinedX-raypatternscorrespondingtotrigonallithiumniobate.AtypicalX-rayDebye-Scherrerpatternshowsthatthefilmispartiallyoriented.Althoughthedegreeandthetypeoforientationvariedfromfilmtofilm,the(00.1)and/or(01.2)planesshowedsometendencytoalignparalleltothesubstratesurface.
1.3.2TungstenbronzeferroelectricK3Li2Nb5O15
Amongvariousfamiliesofferroelectricmaterials,thetungstenbronzefamilyisofinterestforopticalwaveguidesandSAWapplications.K3Li2Nb5O15(KLN)isatetragonalcrystalwiththepointgroup4mmandistypicalofcompletelyfilledtungstenbronzeferroelectrics.Single-crystalKLNhasalargeelectromechanicalcouplingfactor
, andk33=0.52andalsohasreducedzero-temperaturecoefficientsofdelayforSAWs.However,itisverydifficulttoobtainhighqualityandlargeKLNcrystals.AnapproachtothesolutionofthisproblemistogrowepitaxialKLNfilms(ProkhorovandKuz'minov,1990).
Anrfsputteringapparatus(ANELVAFP-21)wasusedbyShiosakietal.(1982)tofabricateKLNthinfilms.Thetargetusedintheexperimentwaspreparedbysinteringthepressedpowderwitha
potassium-andlithium-enrichedcompositionof33mol.%K2CO3,22mol.%K2CO3and45mol.%Nb2O5.Theoptimumgrowthconditionsforhigh-qualityKLNsingle-crystalthinfilmssputteredonbothK3Bi2Nb5O15(KBN)andsapphiresubstratesarea50%Ar-50%O2atmosphereatapressureof9.0×10-2torr,anrfpowerinputbelow150Wand500-630°Csubstratetemperature.Thedepositionrateundertheseconditionsis~800Åh-1atanrfpowerof100W.
BoththeKLNfilmsepitaxiallygrownonKBNandthosegrownonsapphiresubstratesweretransparentandtheirsurfacesweresmooth.AnalysisoftheseKLNfilmsbyX-raydiffractionandREDmeasurementsshowedthattheKLNfilmsobtainedweresinglecrystalsoffairlygoodquality.
AHe-NelaserbeamwassuccessfullyfedintoKLNfilmssputteredontheKBN(001)andsapphire substrates,usingaprismcoupler.BymeasuringcouplinganglesforthreedifferentTEmodes,theeffectiverefractiveindexb/k0inaKLNfilm2.1mmthicksputteredontheKBN(001)substratewasdeterminedtobe2.26,2.25and2.23fortheTE0,TE1andTE2modes,respectively.TherefractiveindexnointhisKLNfilmwascalculatedtobe2.27fromtheeffectiverefractiveindicesgivenabove.MeasurementsoftheopticalpropagationlossintheKLNfilmgrownontheKBNsubstratewerenotattempted.TherefractiveindexnoinaKLNfilm~2.7mmthicksputteredonasapphire
Page14
substratewasalsodeterminedtobe2.27bymeasuringthecouplinganglesforelevenTEmodes.Thevalueof2.27obtainedaboveisclosetothatforabulkKLNcrystal.Furthermore,theTE0modepropagationlossintheKLNfilmonsapphirewasmeasuredbytheopticalfibreprobemethod.Theopticalpropagationlossinthisfilmwasdeterminedtobe7.8dBcm-1.
SomeexperimentswerecarriedoutontheSAWpropertiesofthelayeredKLN/sapphirestructure.ThesampleusedinthisstudywasaKLNfilm9mmthicksputteredonasapphire substrateatasubstratetemperatureof520±C.Interdigitaltransducers(IDTs)werenormalelectrodeswith25fingerpairsanda100mmspatialperiod,whichwereevaporatedonthefilmsurface.Thecentre-to-centrepropagationpathlengthwas12.5mm.Accordingly,thevalueofKHforthissamplewas0.6.SincethedelaytimeofSAWpropagationis2.3ms,theSAWvelocityonthisKLNfilmwasdeterminedtobe5430ms-1whichisincloseagreementwiththecalculatedvalue,5500ms-1atKH=0.6.
1.3.3KNbO3thinfilms
TheKNbO3filmsweregrowninarf-diodesputteringsysteminwhichthecathodeformsthebottomelectrode.Thesystem,describedindetailbyS.SchwynandH.W.Lehmann(1992),isequippedwithaload-lockandheatedsubstrateplatform(mountedonthetopplateofthesystem),whichallowssubstratesurfacetemperaturesupto700°C(Thonyetal.1992).Thissputterupdesignturnedouttoberatherusefulsincethisconfigurationalsoallowstheuseofhomemadetargetswhichdonotalwayshavethedesiredhighdensityandcohesion.
Themostimportantparameterintheseexperimentsisthecompositionofthetarget.SputteringfrompureKNbO3targetresultedinfilmswhichwereseverelydeficientinpotassium.Inordertoevaluate
whichcompositionisappropriatetoobtainstoichiometricfilms,K2CO3andKNbO3powdersweremixedindifferentmolarratios.Subsequently,thepowderwaspressedatroomtemperatureatapressureof5.6×107N/m2.Thediscsobtainedweresolidenoughtobetransferredintoavacuumchamber.Althoughoutgassingismuchstrongercomparedtosinteredmaterial,thehomemadetargetsprovedtobeusefuliftheyarepumpedandpresputteredforasufficientlylongperiodoftime(approximately10h).Atargetcompositionof1:1moleK2CO3andKNbO3finallyyieldedstoichiometricfilms.Thismeansthatthepotassiumconcentrationinthetargetwasthreetimeshigherthanthefinalconcentrationinthesputteredfilms.Table1.5summarizestheparameterswithwhichcrystallinestoichiometricKNbO3filmsweregrown.
Theopticalpropertiesarestronglyrelatedtothecrystalstructureandthecrystallinityofthelayers.Toprovidefavourableconditionsforthegrowthofhighlyorderedfilms,arelativelyhighsubstratetemperature(610°C)andaverylowdepositionrate(6Å/min)werechosen.Thetypicalthicknessofthelayersobtainedusingtheseparametersis200nm.
Furthermore,lattice-matchedsubstrateshadtobefoundinordertoobtaincrystallinefilms.Thetwocrystallinematerials(MgO)(A12O3)2.5spinelandMgOwereconsideredtobewellsuitedassubstratesforthinfilmsofKNbO3bulkcrystals.Moreover,therefractiveindexofthesematerialsisconsiderablylower
Page15
thanthatofKNbO3allowingmonomodewaveguidinginlayersofonly100nmthickness.TheMgOsubstrateshadatomiclayerpolishedsurfacesandbothsubstrateswerenotspeciallycleanedpriortouse.
ThecompositionofthelayerswasdeterminedbyRBSusingHe4+ionswithanenergyof2MeV.Thesemeasurementsshowedthatstoichiometricfilmscouldbegrownfroma(KNbO3)(K2CO3)targetsputteredinpureargon(Fig.1.7).Theadditionofoxygenresultsinapotassiumdeficiencyofthefilms.Ascanbeseen,themeasurementresultsareinexcellentagreementwiththesolidlineofthesimulatedspectrumofastoichiometricfilmwithathicknessof190nm.Furthermore,theprofileisflattoppedindicatingconstantcompositionacrossthefilmthickness.Theoxygenstoichiometrywasinvestigatedusingnuclearreactionanalysisanddidnotshowanyoxygendeficiency.
TheX-raydiffractionspectrastronglydependonthecompositionofthefilmsanddepositiontemperature.Layerswithapproximatelystoichiometriccomposition(19.2-20at%)depositedonMgOatatemperatureof500°Corbelowonlyshowweaklinesinthex-rayspectrum.Someofthesmallpeakscouldbeidentifiedasthe(110)and(220)reflectionoforthorhombicKNbO3,whereasitwasnotpossibletoidentifytheothersunambiguously.
Whenthetemperaturewasincreasedto580-610°C,thefilmbecamesinglecrystallineandonbothsubstratestwolineswereobtainedwhichwereclosetothe(0001)and(002)reflectionsoftetragonalKNbO3(Fig.1.8).Thelatticeconstantsobtainedfromthex-raydiffractionmeasurementsforallthethreelatticedirectionsyieldeda=b=4.16parallelandc=4.10perpendiculartothesubstrateplaneforlayersdepositedonMgO.Thismeansthatthefilmistetragonalwithinthemeasurementaccuracy.Therefore,thetetragonalcoordinatesystemwillbeusedinthefollowing.Comparedwiththelattice
constantsofthetetragonalphase(extrapolatedtoroomtemperature)ofa=b=3.985Åandc=4.075Åthisindicatedalatticemismatchof4%and0.7%,respectively.Tetragonalsymmetrywhichinbulkmaterialisassignedtothestructuralphaseinthetemperaturerange22-440°Ccanbeexplainedbythefactthatthesubstrateiscubicand,therefore,forcesthegrowinglayerinbothdirectionsoftheinterfaceplanetothesamelatticeconstant.Thex-raydatashowedthatthereisaclosecorrelationbetweenfilmstoichiometryandx-rayintensity:asthestoichiometryimproves,thediffractedlinesbecomenarrowerandtheirintensityincreases.
Table1.5rf-sputteringparametersforgrowingstoichiometriccrystallineKNbO3films(Thonyetal.1992)
Targetcomposition
K2CO3:KNbO3 1:1 mol
Gas 100% Ar
Temperature 610 °C
Power 50 W
Processpressure 2×10-2 mbar
Gasflow 20 cm/min
Page16
Fig.1.7RBSspectrumofaKNbO3thinfilmofthicknessd=188nmdepositedonMgOsubstratefrom
targetcompositionof(KNbO3)(K2CO3)at610°C(Schwynetal.1992).
1.3.4KTaxNb1-xO3thinfilms
APerkinElmer4400sputteringmachinewasusedforfilmdeposition.A4in.diametersputteringtarget(nominalcomposition:KTa0.5Nb0.5O3)witha15at%excessKandpressedto90%oftheoreticaldensity,waspreparedbystandardceramicprocedures.Substratesusedforfilmdeopositionwere(a)Ptcoated(3000Åsputteredlayer)Siwaferswitha1500AthickintermediatelayerofSiO2and(b)GaAs(100)waferswithaheavilydoped(n=1018-1019/cm2)surfacelayer.Anexcellentlatticematch,within0.3%,existsbetweenKTNandGaAssurfacesublattice(Sashitaletal.1993).
Underanychosensetofsputteringconditions,filmsweresimultaneouslydepositedonPt/SiO2/Si,GaAsandsapphiresubstrates.TheKTNsynthesisconditionsaresimilartothoseforKNbO3,seeTable1.5.Filmsthussputteredwerecompletelycolourlessandtransparent.CompositionofaKTNfilmonsapphirewasdeterminedbyRutherfordbackscatteringspectroscopy(RBS).RBSsimulationspectrayieldedafilmcompositionofK0.94Ta0.68Nb0.4O3.X-raydiffractionanalysisoftheKTNfilmon
sapphireshowsonlyasingle(100)peakanditstwohigherorders.Thepeaksharpness,referredtothatofthe(1012)sapphiresubstrate,indicatesnearlysinglecrystalepitaxialgrowthoftheKTNlayer.BraggpeaksfromaKTNfilmonGaAsshowonlyasinglenarrow(200)KTNreflection,indicativeoflargegrainswithahigh(100)preferredorientation.Thetwoweakpeaksonthelow20sideoftheGaAsreflectioncouldnotbeattributedtoanyoftheKTNrelatedreflections.
TheCurietemperatureplot(evsT)foraKTNfilmonaPt/SiO2/Sisubstrate(measuredat1kHz,Fig.1.9a)peakssharplyat6°Cwithamaximumeof2090,indicatingalmostabulksinglecrystal-likebehaviour.Figure1.9bshowsthecapacitance(at1kHz)versustemperaturebehaviourofaPt/KTNfilm/GaAstestcapacitor.Again,thesharppeakat3°Cexhibitsabulksinglecrystal-likeCurie-Weissbehaviour.ReflectancespectraofKTNfilmsyieldedrefractiveindicesfrom2.06at0.6mmto1.975at1.1mmandlowabsorptioncharacteristics.ThesearesmallerthanbulkKTNrefractiveindices,from2.15to2.3.ThequadraticEOeffectinKTNfilmsonSiandGaAssubstrateswasmeasuredasthechangeinreflectanceunderanappliedelectricfieldatnearly5°CaboveTc.Thelock-insignal,correspondingtotheelectricfieldinducedreflectivity
Page17
Fig.1.8X-raydiffractionspectrumofsingle-crystalline
filmdepositedonMgOshowingthe(001)and(002)reflectionoftetragonalKNbO3(Schwynetal.1992).
changeversusappliedfield,isshowninFig.1.10.ThedifferencesintheplotsforGaAsandSisubstratesareapparentlyduetothoseofcrystallinityandstoichiometrydeviationsofthetwofilms.
Thepeakeforthesefilms(~2090)issignificantlylowerthanthatofbulksinglecrystalvalues.ForameasuredTc=3°C,thecorrespondingfilmcompositionshouldbeKTa0.63Nb0.37O3.
1.3.5.Thinfilmsbypulsedlaserdeposition
ThelasersputteringmethodisdemonstratedonanexampleofLiTaO3(J.A.Agostinelli,G.H.Braunstein1993).Thefilmswereproducedon(0001)-sapphiresubstratesbypulsedlaserdeposition(PLD)usingKrFexcimerlaserradiationat248nm.Typicalpulseenergieswere400mJwithpulsedurationsofabout30ns.Thebeamwasweaklyfocusedontoarotatingtarget,givingafluencebetween1.0and2.0J/cm2.ThetargetwasasinteredpolycrystallinebulkceramicdiscofLiTaO3preparedfrommixedpowdersofLiOH.H2OandTa2O5.ThetargetwasproducedwithanexcessLicontentsuchthattheLi/Taatomicratiowas1.1/1.Thediscwasmountedhavingthenormaltoitssurfaceatanangleof10°withrespecttotherotationaxisinordertoimprovetheuniformityofdepositedfilmthickness.Theanglewas
chosensothatthenormaltothetargetsurfacesweepsoutacircleatthesubstanceplanetogiveanoptimumuniformityfortheselectedsubstrate-to-targetdistance,whichwas6cm.Thesubstratewasmountedontheheaterblockusingsilverpainttoprovidegoodthermalcontact.Areactiveambientof85mtorrofO2wasused.Thethicknessofdepositedfilmsrangedfromabout100to800Åbutmostfilmswerepreparedwithathicknessof4000Å.Filmdepositionratesinthevicinityof1A/pulsewerefoundandlaserrepratesof4Hzwerecommonlyused.
Filmsgrownatsubstrate-heatertemperaturesof500°Cwerefoundtobeamorphouswhereasthosegrownat525°Candabovewerecrystalline.Filmswerefoundtoimprovewithincreasingtemperatureandsubstrate-heatertemperatureintherange650-700°C,theproducedfilmshavingexcellentcrystallineproperties.Figure1.11isacoupledXRDscanofaLiTaO3filmdepositedon(0001)sapphireat650°C.Thedataindicatethatthefilmissingle-phase,single-orientationLiTaO3.Thepresenceofonlythe(001)linesofLiTaO3showsthattheentirefilmisc-oriented,allowingeasyuseofthed33coefficient.
Page18
Fig.1.9a)Curie-WeissbehaviourofKTNonPt/SiO2/Siandb)Curie-WeissbehaviourofKTNonGaAs(Sashital
etal.1993).
Fig.1.10Electro-opticeffectofKTNfilms(Sashital
etal.1993).
Fig.1.11(right)Coupledx-raydiffractionscanofa4000
AthinfilmofLiTiO3on(0001)sapphirepreparedat650°C(AgostinelliandBrainstein1993).
Suchanorientationisequivalentto'z-cut'LiTaO3inthebulk.Themeasuredc-latticeconstantof13.73isclosetothevalueof13.755Å
forbulkLiTaO3.ICPanalysisofthesefilmsindicatedaLi/Taatomicratioof48.5/51.5withanuncertaintyofabout2at%.In-planeorientationwasstudiedbyx-raypolefigureanalysisusingthe(012)planeofLiTaO3.Forallsubstratetemperaturesusedbetween525and750°C,thefilmswerefoundtobetwinned.Atthelowertemperatures,roughlyequalproportionsofeachorientationwereobserved.Forsubstrate-heatertemperaturesof650°Candabove,amajororientation(>90%)inexactalignmentwiththesubstratewasobserved.
Thedegreeofcrystallineperfectionwasexaminedusingionchannelling.Fromtheseinvestigationsitfollowsthatthequalityofthefilmimprovesasafunctionofheightabovetheinterface.Thelowerqualityofthenear-interfaceregionislikelytoberelatedtoahighdensityofmisfitdislocationsarisingfromaratherlargelatticemismatchofabout8%.
Althoughafilmthatisstrictlysinglecrystalwouldbedesirable,itissufficientfornonlinearopticalapplicationsthattheLiTaO3filmbec-oriented.Becausethec-axisdirectionistheopticalaxisdirectioninthisbirefringentmaterial,theeffectiveindexforlightthatispropagatinginsuchathin-filmwaveguideaseitheratransversemagnetic(TM)waveoratransverseelectric(TE)wavewillbeindependentofthepropagationdirectionintheplanarwaveguide.Thus,
Page19
ac-orientedfilmofLiTaO3withnoin-planeorientationcaninprinciplegiveanopticalwaveguidehavinglowscatteringloss.Itisalsoofinterestthattheconditionofc-orientationissufficienttogiveasingled33coefficientfortheentirefilm.Thus,thewell-orientedbutsomewhattwinedfilmsofLiTaO3meetthecriteriaforcrystallinequalityrequiredfornonlinearoptical/electro-opticaldevices.Althoughsinglecrystallinityisnotanecessaryrequirementfortheseapplications,asingleorcontrolledferroelectricdomainstructureisessential.Someeffortwasmadetoelucidatetheas-growndomainstructureofthefilmsbyetchinginhotHF:HNO3withasubsequentexaminationbyscanningelectronmicroscopy.Thefilmsappearedtoetchuniformly,whichsuggeststhatthefilmsaresingledomainasgrown.
MeasurementsoftheopticalpropagationlossforaLiTaO3film,~3400Åthick,grownat650°C,areshowninFig.1.12.Abeamof633nmradiationwascoupledintothefilmusingarutileprism.ThedatacorrespondtoscatteredlightintensityfortheTM0mode.Thebestfitlinethroughthedataindicatesalossofabout0.6dB/cm.However,thelargescatterinthedataplacesaconsiderableuncertaintyinthelossfactor.Itisbelievedthatthelargedeviationsfromthelinearfitaretheresultofpoorsamplingstatisticsfromasmallnumberofstrongscatteringcentresthataresamplingthewaveguideintensity.Thesecentresarelikelytobetheparticulatefeaturesdiscussedabove.Itis,however,apparentthatthesecentresdonotproduceanyseriouswaveguideloss.
Moreover,therearesignificantobstaclesforthegrowthofepitaxialLiNbO3andLiTaO3filmsonGaAsforthebluelightgeneration,becauseofthefollowingreasons:(a)GaAshasthezincblendestructurewithalatticeparameterof0.5673nm,whileLiTaO3hasthetrigonalstructurewitha=0.5153nmandc=1.3755nm,(b)LiTaO3isreactivewithGaAsandproducedundesirablephasesatinterfaces,
and(c)anintermediateoxidelayerwithlowrefractiveindexisrequiredtoformawaveguide.
L.S.Hungetal.(1993)reportepitaxialgrowthofaLiTaO3layeronaGaAswithaMgObufferlayer.TheMgOlayeractsasadiffusionbarriertoimpedefilm-substrateinteractions,andformsawaveguidestructurewiththeoverlyingLiTaO3.
(NH4)2Sx-treated(111)GaAswaferswereusedassubstratesforepitaxialgrowthofMgOfilms.MgOwasdepositeddirectlyonGaAsbyelectron-beamevaporation.Thedepositionprocesswascarriedoutat3×10-8torrwithoutintroducingadditionaloxygenintothesystem,ensuringanundisturbedGaAssurfacetothegrowthofepitaxialMgOfilms.Thesubstratewasheatedbyaradiativeheater.Thegrowthtemperaturewas450-550°Candmonitoredbyaninfraredpyrometer.Thedepositionratewas0.05-0.15nm/s,andthethicknessoftheMgOfilmswasabout100-500nm.
LiTaO3filmsweregrownbypulsedlaserdeposition.Theparametersofthesputteringlaserarepresentedabove.Depositionwascarriedoutatarateof0.1nm/pulse,thesamplewascooledtoroomtemperatureinoxygenatapressureof150torr.
ThethicknessandcompositionoftheresultingMgOandLiTaO3filmsweredeterminedbyRutherfordbackscatteringspectrometry.Thespectrumcanbebestfittedbyasimulationofabilayeredstructurewiththestoichiometricratio
Page20
ofMg:O=1.0:1.0andLi:Ta:O=1.15:0.97:3.TherearedgeoftheTaprofileandthefrontedgeoftheGaAsprofileareabrupt,indicatinglimitedinterfacialreaction.
Thestandard0-20diffractionpatterntakenfromaMgOfilmonGaAsrevealsonlytheMgO(111)andGaAs(111)diffractionpeaks.ThefullwidthathalfmaximumoftheMgO(111)rockingcurvemeasuredatabout1.8°,indicatingahighly[111]-axisorientedfilm.EpitaxialgrowthofMgOonGaAswasverifiedbyx-raypolefigureanalysis.AcomparisonoftheresultsobtainedfromMgOandthatfromtheunderlyingGaAsindicatesthatasingle-crystal[111]-orientedMgOfilmisgrownon(111)GaAs,andthattheMgOlatticeisrotatedby180°aboutthe[111]surfacenormalwithrespecttotheGaAssubstrate.
ThecrystalqualityofLiTaO3canbesubstantiallyimprovedbyincreasingthegrowthtemperatureof600-650°C.
1.3.6.WaveguidesbyMeVHeionimplantation
PlanarwaveguidesinKNbO3byMeVHeionimplantationforopticalwaveswithpolarizationparalleltothecrystallographicb-axiswereproducedbyF.P.Strohkendletal.(1991).Theseguidesconsistedoftheessentiallyundamagedsurfacelayerwhichisseparatedfromthebulkbyaburiedlayerofareducedrefractiveindex.TheionicendofthedamagerangeoftheincidentHeionswasfoundtopartiallyamorphizethecrystallattice(R.Irmscheretal.1991).Thewaveguidesareleaky,aslightwhichispropagatingintheundamagedsurfacelayercantunnelthroughthebarrierwithaloweredindexintothesubstrate.Thewaveguidesshowedaminimumpropagationlossforanimplantationdoseof5×1014cm-2.ThisdosewasatleastoneorderofmagnitudebelowthedoseswhichhavebeenusedsofartoproducewaveguidesinKNbO3(T.Bremeretal.1988andL.Zhangetal.1988).
F.P.Strohkendletal.(1991)reportedonacriterionofplanarwaveguidesforopticalwaveswithpolarizationparalleltothecrystallographicc-axiswithevenlowerimplantationdoses,thatis,withdosesofabout1014cm-2.Prismcoupling,aswellasend-firecouplingofaHeNelaserbeamwithawavelengthof632.8nmwasusedtocharacterizetheTEmodespropagatingalongthea-axisintheionimplantedplanarwaveguides.
KNbO3crystalsampleswerecutperpendiculartotheb-axisandhaddimen-
Fig.1.12IntensityasafunctionofpropagationdistanceforlightscatteredoutoftheTM0modeLiTaO3thinfilmwaveguideonsapphire(Agostinelliand
Braunstein1993).
Page21
sionsoftypically7×2×9mm3.ThesampleswereirradiatedatroomtemperaturewithHeionsofeither1or2MeVanddosesintherange5×1013to5×1014cm-2.TheangleofincidenceoftheHeionswasslightlyoffnormaltoavoidchannelling.Thecrystalsampleswereheatsinkedandtheionfluxwaskeptbelow5×1015cm-2h-1topreventthecrystalsfromheating.ThedoseswerekeptdeliberatelylowbecauseionimplantationisaninherentlydestructiveprocessandleadsinKNbO3alreadyatdosesoftheorderof2×1015cm-2tostrongwaveguidelosses.
Afterimplantation,thesamplesexhibitedplanarwaveguiding.PrismcouplingofanHe-Nelaserwithawavelengthof632.8nmwasusedtomeasurethemodespectraoftheplanarwaveguidesbydarklineandbrightlinespectroscopy.Figure1.13showstwoexamplesofdarklinespectrawhichweretakenbymeasuringthebeampowerreflectedfromtheright-anglecouplingprismasafunctionofthemodeeffectiveindexNeffnpcosa,whereistherefractiveindexofthecouplingprismatawavelengthof632.8nm.Thepronouncedreflectivitydipinthedarklinespectrumofthesampleirradiatedwith1MeVHeionsandadoseof5×1013cm-2indicatesthesuccessfulproductionofawaveguidingstructureandoccursduetoresonantexcitationofthelowestmode.Thedeeperthemediainthedarklinespectrathelesslightisreflectedbackfromthecouplingpoint,andhence,thebetteristhecouplingofthelaserbeamtothewaveguidemode.FromthenormalizedintensityinthedipoftheTE0modeofthe1MeVwaveguide,Strohkendletal.(1991)calculatedacouplingefficiencyof~33%.TheTE0modeofthe2MeVguidewasonlydetectedinthebrigthlinespectrumthatistakenbymeasuringthepoweratthewaveguideexitasafunctionofthecouplingangle.Theabsenceofapronouncedreflectivitydipinthecorrespondingdarklinespectrum(Fig.1.13)indicatesthatthecouplingefficiencyoftheincidentlaserbeamtotheTE0modewaslessthan~1%.
Thedarklineandbrightlinespectraofthewaveguidesimplantedwithdoseshigherthan1×1014cm-2exhibitedseveralreflectivitydips.
Notethatforadoseofuptol×1014cm-2nonleakymonomodewaveguideswereproducedinKNbO3.Themuchweakercouplingefficiencyforthe2MeVguidegivesevidencethatthewaveguidinglayerwithanincreasedrefractiveindexislocateddeeperbelowthecrystalsurfacethanforthe1MeVguide.Therefore,Strohkendletal.(1991)havefoundthationimplantationcreatesalayerofincreasedrefractiveindexburiedbelowthecrystalsurface.Therehavebeenseveralreportsonso-called'anomalous'increasesoftheextraordinaryrefractiveindexinbirefringentcrystals(L.Changetal.1988).
1.3.7Stripwaveguides
Integratedopticsapplications,suchasmodulatorsorfrequencydoublers,whichwouldbenefitfromthehighfiguresofmeritofKNbO3demandforthefabricationofstripwaveguides.Baumertetal.(1985)havereportedforthefirsttimeonstripwaveguidesinKNbO3.Theyachievedopticalwaveguidingandcut-offmodulationbyusingtheelectro-opticeffectforwaveguideformationandmodulation.
Flucketal.(1991)reportedforthefirsttimeonpermanentopticalstrip
Page22
waveguidesinKNbO3.Theone-dimensionalwaveguidingstructureswereproducedbyMeVionimplantationandappropriatemasking.
TheKNbO3crystalswerecutperpendiculartothecrystallographicb-axis.Thesizeofthecrystalsampleswas9.95×l.97×8.04mm3.Thesurfaceandthetwoend-facesperpendiculartothea-axiswerecarefullypolishedinordertoallowefficientend-firecouplingofalaserbeam.ThefabricationofstripwaveguidesusingHeionimplantationwascarriedoutbyfirstproducingaplanarguideandthenapplyinganimplantationmasktoformtheverticalsidewalls(Fig.1.14).Theplanarwaveguidewasformedbyirradiatingthesamplesatroomtemperaturewith3.2MeVHeionsandadoseof7.5×1014cm-2.Theincidenceoftheionswasslightlyoffnormaltoavoidchanneling.Thedosewaschosendeliberatelylowbecausefortheseconditionslowattenuationplanarwaveguideshavebeenproduced.Thethicknessoftheplanarwaveguidesisgivenbytheaverageionpenetrationdepth,whichwascalculatedwiththeMonteCarlomethodtobe7.7mmfor3.2MeVHeionsinKNbO3.
Toformone-dimensionalwaveguides,Flucketal.(1991)maskedthesamplesforfurtherimplantationbyasetofparalleltungstenwires13mmindiameterandwithaspacingof400mm(Fig.1.14).ThewireswereusedasasimplemaskofsufficientthicknesstocompletelyshieldstripsoftheplanarwaveguidesfromfurtherHeionbombardment,hencefromfurtherrefractiveindexmodification.TheverticalsidewallswereformedwithHeionsof2.9MeVandvaryingangleimplantation,respectively.Ideally,theimplantationmaskwouldpossessverticalwallsanduniformthickness.Butbecauseofusingwires,thereareionswhichpassthroughtheouterthinnerpartofthewires,thereforereducingtheeffectivewidthofthestrips.Becausetheseionslosepartoftheirenergybeforereachingthecrystalsurface,theypenetratelessdeeplyintothecrystal,hencethesidewalldamagelayerswillcontinuouslyrisetothesurface,reducingthewaveguide
widthespeciallynearthesurface.Thelateralstragglingoftheincidentionswhichisduetotheinteractionwiththetargetionsleadsalsotonarrowingofthewidthofthestripguides.Theactualwidthofthestripwaveguidesformedbyusingtungstenwires13mmindiameterasanimplantationmaskisreducedto11.4mm.
Fig.1.13ReflectivityasafunctionofeffectiverefractiveindexNeffforwaveguidescreatedwith1and2MeVionsandadoseof5×1013cm-2.
(Strohkendletal.1991).
Page23
Fig.1.14a)Creationofaplanarwaveguidinglayer,
b)formationoftheopticalstripwaveguidesbyfurtherimplantationwithappropriatemaskingof
thesamplewhichproducesthesidewalls(Flucketal.1991).
TheopticalcharacteristicsofthestripwaveguidesfabricatedbytheionimplantationprocessasdescribedabovearegiveninTable1.6.
1.3.8Doublewaveguide
Planarburieddoublewaveguideswereproducedincrystallinequartzandtheirconvolutedprofilesweredeterminedbymodeindexmeasurements(Chandleretal.1988).LiNbO3isofmuchgreaterinterestandapplicationthanquartzandionimplantationisquiteabletoproducelow-lossguidesinthismaterial(Al-Chalabi1985).Itisimportant,however,nottoassumeasimpleprofilesummationprocessinLiNbO3.Astheiondamagehasbeenshowntoannealatalowertemperature(<400°C)(Glavasetal.1988),itisquitelikelytosufferpartialannealingduringsuccessiveirradiations,duetotheirthermalorionizationeffects.Anassessmentoftheseriousnessofthisproblemisanimportantprerequisitetotheconsiderationofanymultiplewaveguideconstruction.
Themethodofdeterminingthedouble-waveguideprofileisnotimmediatelyobvious.Simplewaveguidesarenormallycharacterizedbythespacingoftheirresonantmodespectra(brightordarklines)usingaquantummechanicalanalogysuchasperturbationtheory,aphase-integralapproximation,(Wentzel-Kramers-Brillouin),orafiniteelementmethod.Onlythelatterwouldbeapplicabletoadoubleguide,anditsimplementationwouldbelaborious.
Chandleretal.(1989)usedLiNbO3samplesobtainedfrom1mmthicky-cutwafers.Theywereclampedingoodthermalcontactwithanaluminiumblockheldattherequiredtemperature.Beamheatingwasminimizedbyrestrictingthecurrenttoabout0.5mAandthiswasscannedoveranareaofnearly0.5cm2(foruniformityofdose).Theshallowbarrierwasproducedwith1.1MeVHe+toadoseof1.5×1016ion/cm2andthedeepbarrierwith2.2MeVHe+toadoseof3.0×1016ion/cm2.Theenergyratiogaveopticalwellsofapproximatelyequalwidthsandthedoseratiowasnecessaryforequalheightbarriers,becauseofthehigherdamageefficiencyfortheshallowerimplant.Theimplantareasforthetwoenergieswereoverlappingbutdisplacedfromeachotherbyseveral
Page24
Table1.6CharacteristicsoftheopticalstripwaveguidesinKNbO3formedbyHeionimplantation(Flucketal.1991)
Planarimplantation
Energy 3.2MeV
Dose 7.5×1014cm-2
Sidewallimplantation
Energy 2.9MeV
Angie 5/22/34/45°
Totaldose 3.5×1015cm-2
Sizeofstripwaveguide(mm)
Width 11.4
Depth 7.7
Propagationlosses(dB/cm),wavelengthinnm
514.5 4.3
632.8 1.4
860.1 2.9
millimetresinordertogivethreedistinctregionsforprofilemeasurements-shallowbarrier,deepbarrier,andthecompositeguide.Foreachregion,darkmodepositionsweremeasuredwithTEpolarizationusingthezdirectionofpropagationforbothred(0.6328mm)andblue(0.488mm)light.Allvisiblemodesweremeasured-thesharpguidingmodeswithinthewells,andthebroad'substratemodes'notconfinedbytheguides.Thesewereallusedbythecomputerreflectivitysimulationprogramtogivetherefractiveindexprofilesinthedifferentcases.Theanalyticfunctionchosentodescribe
eachrefractiveindexbarrierconsistedofanexponential/Gaussiannucleardamagepeaksuperimposedonaflatelectronicplateau.Thisfunctionischaracterizedbyfourvariableparametersandhasbeenfoundtodescribeadequatelytheexperimentalresultsforsingle-barrierprofilesinLiNbO3(Glavasetal.1988).Forsingle-barrierimplantsthemodeswerespacedfairlyevenly,butinthecaseofthedoubleguidesthespacingwasveryuneven,andalsothelineintensitiesvariedconsiderably.Theuseoftwowavelengthshadtheadvantageofactingasacheckagainstmissinganyoftheveryfaintmodes.
Thefirstsamplewasimplantedwithahigh-energydose(2.2MeV,3.0×1016ions/cm2)followedbythelow-energydose(1.1MeV,1.5×1016ions/cm2)bothat300K(Chandleretal.1989).
Figure1.15showsthecompositeindexprofilesforthissamplemeasuredat0.488and0.6238mmtogetherwiththerealmodevalue.Bothbarriersarerepresentedfunctionallybyexponential/Gaussiannucleardamagepeaksonflatplateaux.Itappearsthat,ingeneral,adirectsummationofthedamagehasoccurredfromthetwoimplants,withafewexceptions.Thehigh-energypeak(whichwasimplantedfirst)hasbeenreduced,possiblybyannealingduringthesecondimplant:thelowenergypeakheightisnotasummationbecauseitisclosetosaturationandthelow-energypeakpositionhasbeenshiftedtogreaterdepth.Thislattereffectmaybeattributedtoanincreasedionrange
Page25
Fig.1.15Fittedprofilesofexperimentaldatameasuredat0.488mm(upper)and0.6328mm(lower).Themodelevelsandnormalizedmodecurves
areshown(0.488mmdotted)(Chandleretal.1989).
(~4%)forthesecondimplant(lowenergy)duetoanoverallreductionindensityoftheregionduringthefirstimplant(highenergy).
LiNbO3hasbeenshowntobeagoodsubstrateforion-implanteddoublewaveguides.Theprofilesofthenucleardamagebarriersareessentiallyadditive,providedthataccountistakenofpossibleannealingduringirradiationandionrangemodificationduetodensitychanges.Forbarriersofequalheight,itmustalsoberememberedthatthedamageefficiencyfallsalmostinverselywiththeionrange.
1.4Autodiffusedlayersinlithiumniobateandlithiumtantalate
KaminowandCarruthers(1974)developedanovelandsimpleout-diffusiontechniqueforachievingthinpositiveindexlayersinLiNbO3orLiTaO3withoutdegradingtheoriginalsurface.Theauthorsuseddiffusionofcomponentsoutofacrystal.Inthismethod,stoichiometricdeparturesnearthesurfaceoflithiumniobateandlithiumtantalatecrystalswereachievedbyvacuumheatingthecrystalscausingout-diffusionofLi2O.Itisknownfromprevious
workonbulkmaterialsthatextraordinaryrefractiveindexneincreasesasLi2Oisremovedfromthecrystalbuttheordinaryindexisnotaffected(Carruthersetal.1974).For
inthe0.48<n<0.50range;andfor
wherethemolarfractionv=0.5forastoichiometriccrystal.Thus,theout-diffusionproducesarefractiveindexgradientthathasamaximumpositiveindexchangeatthesurfaceandgraduallyapproachesthebulkindexintheinteriorofthespecimen.Theseout-diffusedlayersserveasexcellentlow-loss
Page26
opticalwaveguidesthatpossessallthecharacteristicsofthebulkcrystal.
Theout-diffusedlayershavethefollowingadvantagesoverepitaxiallayers:(a)theprocessingismuchsimpler;(b)thesurfaceremainssmoothandneednotberefinished;(c)theopticalqualityandpropertiesofthelayerareidenticalwiththoseofthebulkcrystal;(d)thereisnoabruptlatticemismatchorimperfectionatthefilm-substrateboundarytoproducescattering;and(e)forout-diffusionbelowCurietemperature,thelayersneednotbepoled.However,theout-diffusedlayersmaybedisadvantageousinsomeapplicationsunlesstheindexprofileparameterscanbecontrolledindependently.Thus,thepeakindexchangeatthesurface,a,andthecharacteristicdiffusiondepth,b,determinethenumberofmodestheguidewillsupportandthedegreeofconfinementofopticalenergytothesurface.
Thetransmissioninterferencemicroscopemethodwasemployedtomeasuretheout-diffusionindexprofilesonalargenumberofspecimenspreparedundervariousconditions.
Refractive-indexprofilesnormaltothesurfacesweremeasuredwithaLeitzinterferencemicroscope.Withthisinstrument,interferencefringes,inpolarizedlight,canbeobservedwitharesolutionofabout2mm.Interferogramsthroughthe(a,c)facetof(1,2)areshowninFig.1.16.TheedgeinFig.1.16aisnormaltotheaxis,andthelight(aHglamp)isanordinarywave.OnlyaverysmallordinaryindexchangeDnoisobserved.TheindexchangeDnisgivenbyDn=pl/d,wherepisthenumberoffringesbywhichtheinterferencepatterninthegradedregionisshiftedfromtheunperturbedpattern,listhewavelength(0.546mm),anddisthesamethickness(2000mm).Thefringeshiftdepictstheindexprofiledirectly.AsubstantialpositiveindexchangeisobservedwithextraordinarylightasinFig.1.16b,
wheretheedgeisagainnormaltothec-axiscorrespondingtoout-diffusionalongthec-axis.TheextraordinaryindexchangeisgreaterthaninFig.1.16c,wheretheedgeisparalleltothec-axiscorrespondingtoout-diffusionnormaltothec-axis.TheinterferogramofFig.1.16d
Fig.1.16Interferograms:a)ordinarywave,diffusionalongc,
b)extraordinarywave,diffusionalongc,c)extraordinarywave,diffusionnormaltoc,d)extraordinarywave,diffusionnormaltoc(KaminovandCarruthers1973).
Page27
illustratesthestillgreaterout-diffusionexperiencedby(1-3)underobservationconditionscomparabletothoseinFig.1.16cfor(1-2).
1.4.1Out-diffusionkinetics
Theout-diffusioncomponentsfromthesurfaceofasolidcrystalinvolvethreebasicreactionsteps:(i)diffusionofgaseousmoleculesawayfromthesurface;(ii)desorptionofmoleculesfromthecrystalsurface;and(iii)diffusionofmoleculesthroughthecrystaltothesurface.Thesimpleerrorfunctioncomplement(erfc)solutiontothediffusionequationtowhichtheextraordinaryindexcurveswerefittedintheworkbyKaminowandCarruthers(1973)isonlyvalidforaconstantsurfaceconcentration.Morerefinedboundaryconditionscanbeusedtoexaminethenatureoftheseapproximations.
Inthecrystal,Fick'ssecondlawgoverningthediffusionis
andisvalidforcaseswherethediffusioncoefficientDisindependentoftandx.HereCistheconcentrationdeficitofLi2Oingcm-3atadistancexintothesurfaceafterdiffusiontimet.
Theunitsofconcentrationarerelatedtonby
whereMisthemolecularweightandpthedensity(whichvariesslightlywithnitself).Theinitialconditionis
ThediffusionconstantvarieswithT
whereQDistheactivationenergyfordiffusion,R=1.99calK-1mol-1.
Theboundaryconditionatthecrystalsurfaceequatesthevaporizationflux,Jv,totheconcentrationgradientatthesurfaceas
Thisassumesimplicitlythatthesolid-vapourinterfaceisstationarywithrespecttothediffusiondistance(i.e.thereisnovapouretchingofthecrystalsurface)andthattheflux,Jv,doesnotchangewithsurfaceconcentration.Fortheout-diffusionproblem,thesurfaceconcentrationchangesbyverysmallamounts,soboththeseassumptionsarevalid,andthesolutiontoequation(1.5)is(CarslawandJaeger,1971)
Page28
whereierfcistheintegraloftheerrorfunctioncomplementandisevaluatedbyCarslawandJaeger(1971)andCrank(1970).Thesurfaceconcentrationcanbewrittenas
Thenormalizedfunctionserfc(x/b')andp1/2erfc(x/b)areplottedinFig.1.17andcanbeseentobesimilar.Theexponentialfunctionexp(-x/b'')isalsoincludedforcomparison.
ThequantitiesDneandCarerelatedbyequation(1.5)andequation(1.7)sothatforLiNbO3:
Thenequation(1.11)canberewrittenas
where
ThevaporizationfluxisrelatedtotheequilibriumvapourpressureofLi2Oover(Li2O)v(Nb2O5)(1-v)bytheLangmuirrelation
orforcomputationalpurposes,
Fig.1.17Diffusionprofiles-analyticalcurvesforp½ierfc(x/b),erfc(x/b')andexp(x/b'').Atypicalsetofexperimentaldataisfitted
asshownwitha=a'=a"andb=1.36b'=1.97b"(Carruthersetal.1974).
Page29
wheretheLangmuirvapourpressurePLisrelatedtotheequilibriumsaturationvapourpressurePeqby
and
whereQvistheactivationenergyforvaporization.Heretheevaporationcoefficient,a,mayvaryfromunity,whenmoleculesevaporateintoavacuumattheequilibriumrate,tonearzero,whenmoleculesevaporateatakineticallydeterminedratewithsignificantenergyorentropybarriers.Experimentally,theevaporatinggeometry,totalpressureandpumpingspeedinfluenceJvbecauseofthepartialconfinementofthespecimensurfacebythefurnacetube.Thisdeparturefromidealfreeevaporationwillinfluencethevalueofainanundeterminedmannerthatdoesnotdependontemperature.Consequently,thistemperaturedependenceofaisignoredhere,andtheassumptionwillbejustifiedlater.Thetotalsurfaceconcentrationchangesby (seeCarruthersandPeterson,1971),sowemayregardJvasconstantatanygiventemperature.
Theout-diffusedspecimensareobservedbyKaminowandCarruthers(1973)undertheinterferencemicroscopeandthefringedisplacementsyielded ThedataarefittedtotheierfcdistributionatDne(0),Vand InFig.1.17itcanbeseenthatDn(0)=aandDn(x)=0.5awhenx=0.36b,whichyieldsvaluesforaandb.Atypicalsetofdata,measuredbytheintersectionofeachfringewithalinenormaltothesurface,isplottedinFig.1.17usingthecalculatednormalizationparametersaandbtoobtainacomparisonwiththeanalyticalcurveforierfc.Tocomparethesamedatawiththeerfcandexpfunctions,newparametersa',b'anda",b",respectively,arecalculatedtoobtain
afitat , and asbefore.Then
ItcanbeseeninFig.1.17thatthedataarebestrepresentedbytheierfccurveasexpectedbutthattheerfcandexpcurvesgivefairapproximationstothedata.Theexpfunctionisaconvenientapproximationfordeterminingthewaveguidingpropertiesofthesegradedindexlayers.Whenthecharacteristicdepth,b,obtainedfromsuchcurvefittingisplottedagainstt1/2,theslopeis2(D)1/2,allowinganaccuratedeterminationofD(T)forthetemperatureatwhichthespecimenwastreated.
Thevaporizationfluxcanbecomputedfromtherefractiveindexgradientatthesurface.Fromequations(1.5a),(1.7)and(1.10)wehave
Page30
Itmaybeseenfromequation(1.14)that
Thus,Jvmaybecomputedfromtheparametersaandborfromthegradientitself.Notefromequations(1.15),(1.16)and(1.22)thatthesurfacerefractiveindexgradientisindependentoft.
Fromequations(1.9),(1.17)and(1.20)wehave
where Takingthelogarithmofequation(1.23)anddifferentiatingwithrespecttol/T,wecometo
WehaveignoredtheslighttemperaturedependenceofG0overtherangeofTemployed.Itcanthenbeseenthatthedifferencebetweentheactivationenergiesforvaporizationandsolidstatediffusiondeterminesthetemperaturedependenceoftherefractiveindexgradientatthesurface.
Theactualvaporizationflux,Jv,canbecalculatedfromequation(1.21)andprovidesacheckagainstthemeasuredweightloss.
ThediffusioncoefficientsfoundexperimentallybyCarruthers(1974)areplottedagainstl/TinFig.1.18fordiffusionnormalandparalleltothec-axis.
Fig.1.18Variationofdiffusioncoefficientswithtemperatureas1/Tinlithiumniobatefordiffusionnormalandparalleltothec-axis.Straightlineshavebeenfittedbyleast
squaresregressionanalysis-seeTable1.7(Carruthersetal.1974).
Page31
Table1.7Diffusionequationparameters(Carruthers,Kaminow,Stulz,1974)
D0,cm2s-1 QD,kcalmol-1
LiNbO3
^c-axis (3.21±0.44)×102 68.21±0.48
||c-axis (3.32±1.19)×102 68.17±1.24
LiTaO3
^c-axis (2.8^0.8)×10-2 50.1±4.3
||c-axis (6.6±2.5)×10-2 52.1±7.0
Table1.8Refractiveindexgradientequationparametersfromregressionanalysis(Carruthers,KaminowandStulz,1974)
G0(m-1) (Qv-QD)(kcal/mol) Qv(kcal/mol)
LiNbO3
^c-axis 3.69×10-5 2.38 70.6
||c-axis 2.2×10-7 9.15 59.0
LiTaO3
^c-axis 3.0^10-3 13.6 64
||c-axis 1.5×10-3 11.2 63
Thestraightlineswerecalculatedbytheleastsquaresregressionanalysis.TheresidualvariancesareshownasparallellinesandcanbeseentoencompassthecentroidoftheD-valuesbutnottheerrorrangeinallcases.AlsotheresidualvarianceismuchlargerforD||thanforD^fornotquiteclearreasons.ThecalculatedvaluesofD0andQDare
showninTable1.7.Itcanbeseenthatboththepre-exponentialfactorsandtheactivationenergiesaresimilartoeachother,withinexperimentalerror,fordiffusionnormal.
Thegradientoftherefractiveindexchangeatthesurface(givenbyp1/2a/b)maybeverysensitivetoanumberofexperimentalvariablessuchassurfacecondition,pumpingspeed,andpressure.
Thegradientswereaveragedateachtemperatureandplottedagainst1/TinFig.1.19.Thestraightlinesweredrawnfromaleastsquaresregressionanalysisoftheaveragevaluesoftherefractiveindexgradientsateachtemperature.ThepertinentparametersareshowninTable1.8.
ThevaluesoftheactivationenergyforvaporizationinTable1.7canbecomparedwiththevaluesobtainedforthevaporizationofLi2O.(Berkowizetal.1959;NesmeyanovandBelykh,1969).Forthereaction
avaluefor ofabout155kcal/(moleLi2O)hasbeenestimated.Thisgivesanactivationenergyforvaporizationofabout74kcal/(moleLiNbO3),
Page32
Fig.1.19Variationofthegradientoftherefractiveindexchangeatthesurfaceoflithiumniobategiven
asp1/2a/bwithtemperatureas1/T,seeTable1.8(Carruthersetal.1974).
whichisquiteclosedtothemeasuredvaluesinTable1.8forv=0.48andconfirmsthisreactionasaprobablerealizationmechanism.
TherehavebeennoequilibriumvapourpressuremeasurementsofLi2Ooverlithiumniobate,soitisnotpossibletodetermineaatthistime.However,acomparisonofthevaluesofPLcalculatedfromequations(1.15)and(1.18)andshowninTable1.9withtherangeofequilibriumvapourpressuresofpureLi2Ooverthesametemperaturerange(Berkowizetal.1959;NesmeyanovandBelykh,1960)suggeststhat andthat Suchanisotropicandlowvaluesoftheevaporationcoefficientsuggestthatevaporationoccursatakineticallydeterminedratewithsignificantsurfaceenergyorentropybarriers.
Thediffusiondataforlithiumtantalatewereobtainedbyout-diffusingonespecimenateachofninetemperaturesrangingfrom930°Cto1400°C.Thediffusioncoefficientswerecalculatedfromtheslopesofthebversust1/2relationshipsasbefore.
Sincefewerspecimenswereused,thesedataarenotasaccurateasthoseforlithiumniobate.Asinthecaseoflithiumniobate,thedatafordiffusionnormaltothec-axisshowlessscatterthanthosefordiffusionparalleltothec-axis.Thediffusioncoefficientsareplotted
againstl/TinFig.1.20fordiffusionnormalandparalleltothec-axis.Thestraightlineswerecalculatedbyleastsquaresregressionanalyses,andtheresultingvaluesofD0andQDaregiveninTable1.7.Asforlithiumniobate,thepre-exponentialfactorsandactivationenergiesaresimilar,withinexperimentalerror,fordiffusionnormalandparalleltothec-axis.However,thedifferencesbetweenlithiumniobateandlithiumtantalatearesignificant;thevaluesofD0arelowerbyfourordersofmagnitudeandQDisslightlysmallerforlithiumtantalate.Thegreaterdifficultyofdiffusioninlithiumtantalatemaybeassociatedwiththemorecovalentnatureofthebonding(asreflected,forexample,inthehighermeltingpoint).
Thegradientoftherefractive-indexchangeatthesurface(givenbyD½a/b)isshowninFig.1.21.Thescatterisquitelarge,especiallyfordiffusionparalleltothec-axis.Thestraightlineswerecalculatedbyleastsquaresregressionanalyses,andtheresultingvaluesofG0andQv-QDareshowninTable1.8.Thecomputedactivationenergiesforvaporizationarequitesimilartothoseforlithiumniobateandagainsuggestthatthesamevaporizationreactionisoccurring.Unlikelithiumniobate,however,thegradientofthesurfacerefractive-indexchangebecomeshigherathighertemperatures.Thisisadesirable
Page33
Table1.9ulatedevaporationfluxesandkineticvapourpressureforLiNbO3(Carruthers,Kaminow,Stulz,1974)
Jv(gcm-2s) PL(atm)
T(°C) ^c-axis ||c-axis ^c-axis ^c-axis
930 1.95×10-11 0.828×10-11 0.279×10-11 0.118×10-11
1000 6.04×l0-11 2.42×10-11 0.888×10-11 0.356×10-11
1050 1.24×10-10 2.57×10-11 1.86×10-11 0.385×10-11
1100 2.01×10-10 5.18×10-11 3.07×10-11 0.791×10-11
1125 4.04×10-10 2.63×10-10 6.22×l0-11 4.05×10-11
Fig.1.20Variationofdiffusioncoefficientswith
temperatureas1/Tinlithiumtantalatefordiffusionnormalandparalleltothec-axis.Straightlineshavebeenfittedbyleast
squaresregressionanalysis,seeTable1.7(Carruthersetal.1974).
Fig.1.21(right)Variationofthegradientoftherefractiveindex
changeatthesurfaceoflithiumtantalategivenasp1/2a/bwithtemperatureas1/T,seeTable1.7(Carruthersetal.1974).
featureforobtainingsteeperindexprofilesandthinnerwaveguidinglayers,providedtherequireddiffusiontimesat1400°Ccanbekeptsufficientlyshort.
Theevaporationcoefficients,º,arecomparablewiththoseforlithiumniobate andagainsuggestthatevaporationisthekineticallyrate-limitingreaction.
1.5Thediffusionmethodformetalsandoxides
Amongthemostthoroughlyinvestigatedmethodsisnowthediffusionmethodwhichiswidelyusedforfabricationofplanarandchannellightguidesonlithiumniobateandlithiumtantalateplates.However,thisonlyrefersinfullmeasuretotitaniumdiffusion.Themethodconsistsindepositingafilmorastripofmetaloritsoxideontothesubstratesurface,afterwhichthecrystalisdiffusionallydistilledordopedinoneorseveralstages.Thecharacteristicdiffusiontimerangesbetween1and10h,thetemperaturebeing800-1100°Cforlithium
Page34
niobateand800-1300°Cforlithiumtantalate.Thediffusiontypicallyproceedsinamediumofinertgasesargonandhydrogenandinsomecasesintheair,inanoxygenfluxorinitsmixturewithargon.Inthepresenceofoxygen,processestypicallyproceedintwostageswithapreliminarymetaloxidation.Transitionmetalsaremostoftenemployedasdopingimpurities.
Thestudiesofmetaldiffusionmethodcarriedoutinrecentyearsinthetechnologyoflightguidefabricationinvolvinglithiumniobateandlithiumtantalatehaveshownthatinpractice,titaniumdiffusionismoresuccessfulasbeingmoreintensiveandprovidinghigherDnoandDnevaluesascomparedtoothermetals.
Whenthismethodisappliedtocreatingchannelandsingle-modeplanarstructuresinlithiumniobateandtantalate,allowanceshouldbemadeforLi2Oout-diffusionintheregionsadjoiningthoseofchannelformation.Theout-diffusionprocessisknowntocauseanincreaseinne.Electro-opticdevicesaremostoftenintendedformodesofjustthispolarizationsincetheelementr33(associatedwithne)ofthetensorofelectro-opticcoefficientsoflithiumniobateandtantalatecrystalsisthelargest.Li2Oout-diffusionmayleadtoincreasinglossesandtonon-reproducibilityofthemodecompositioninthechannelstructureandisthereforeundesirable.
Thespecificfeaturesofbackgroundout-diffusionintheformationofTi:LiNbO3lightguidesandthewaysofitssuppressionaredescribedbyChenandPastor(1977),Jackeletal.(1981)andNodaetal.(1980).ChenandPastorshowthatasaresultoftitaniumdiffusion(themetalfilmthickness20mm,preliminaryoxidationtime1hatatemperatureof600°C,andthediffusionproperlastssixhoursat900°C)one'titanium'mode(theeffectivelightguidedepthis4mm)andtwo'out-diffusion'modes(15mm)areexcited.Thelattermodeswerethenremovedbysampleannealinginthepowdermixtureof
Li2CO3+Nb205.Componentsofthemixturewith99%ofthemainsubstanceweretakeninproportioncorrespondingtoLiNbO3compositionwithaccounttakenoflithiumcarbonate.Sampleswereannealedat900°Cfor1-4hours,andthe'titanium'modewasnotsuppressed.
Weshallpointouttwowaysofout-diffusionsuppression:metaldiffusionfromfilmsinamediumoflithiumoxideorcorrespondingchemicalcompoundsandlight-guidechannelformationinagasfluxcontainingwatervapour.
TheefficiencyofthistechniquewasprovedbyJackeletal.(1981)usingIRspectroscopyintheregionof3480cm-1(bond-O-H-)ofspecimenswhichhadundergonedifferenttreatment.Titaniumdiffusioninwetargonleadstoarelativeincreaseofhydrogenconcentrationinthesurfacelayerofsubstratesascomparedtotheoriginalcrystal.TheauthorsbelievethatthisinducesLi+ionmigrationsuppressioninthecrystalandpromotesthedecreaseoftheout-diffusionrate.
Zilingetal.(1980)showedthatassoonasTi4+issubstitutedforNb5+,thereoccurschargenonequilibriumwhichcanbecompensatedbypositioningtheLiionintheinterstice.RefractiveindexvariationinaLiNbO3crystaluponthesubstitutionoftitaniumforniobiumcan,dependingontheconcentrationofthelatter,becausedbythedifferenceinionreactionsandinnerstressesduetodiffusion.TakingintoaccountalimitedplasticityofLiNbO3crystalsatthediffusiontemperature,wecanexpectthattheinnerstresseswillcausemicrocrackingandrelaxpartiallywithincreasingdislocationdensityinthe
Page35
near-surfacelayer.Bothtypesofdefectswereobservedexperimentallyandarelikelytobethemainfactordeterminingopticallossesofwaveguidinglayers.SimilarresultswereobtainedbyGolubenkoetal.(1980)andZolotovetal.(1989)inthestudyofTidiffusionintoz-cutLiNbO3crystalsinAratmospherewithacompensationofthebackLi2Odiffusion.
AtthesametimeitshouldbenotedthatoneofthemostessentialdefectsofTi:LiNbO3-waveguidesistheirliabilitytolaser-induceddamageknownas'optical'(HolmanandCressman,1982).
Animportantroleisplayedbythediscussionofpossiblemechanismsoftherefractiveindexincreaseonthecrystalsurfaceduetodiffusion.Zilingetal.(1980),Sugiietal.(1978),Canalietal.(1986)andFejeretal.(1986)pointoutthreemechanismsofrefractiveindexincrease:
1.duetothephotoelasticeffect;
2.duetoincreaseofelectronpolarizability;
3.duetodecreaseofspontaneouspolarizationinthedopingregion.
Mechanism1
Therelativedielectricimpermittivitytensor andthestraintensorareknowntoberelatedthroughthephotoelasticitytensor
Thecomponentsofthedielectricimpermittivitytensorareequalto
Thecomponentsofthetensors and arerelatedas
where istheKroneckersymbol.
Differentiatingtheexpression(1.27),multiplyingtheresultby andmakinguseof(1.26),wecometo
InthecaseofthinlayersitturnsouttobesufficientonlytoconsiderthemainstrainsSx,SyandSzalongthex-,y-andz-axes,respectively.Makingallowanceforthisandalsofortheestimate
weobtain
Page36
wherePimisanabbreviatednotationofthecoefficientsPijmm.
Sugiietal.(1978)carriedoutadetailedcalculationandreportedDn0andDnotobeatleasthalftheobservedvaluesand,besides,toexhibitastrongertemperaturedependence.
Mechanism2
Herethedirectcauseoftherefractiveindexincreaseisarelativelyhighpolarizabilityoftheimpurityionsimplantedintothecompositionofthemedium.TherelationbetweenelectronpolarizabilityandtherefractiveindexofthesubstanceisgivenbytheLorentz-Lorenzformula
whereNiisthenumberofi-typeatomsinaunitvolumeandaiistheelectronpolarizabilityoftheseatoms.
AccordingtoZilingetal.(1980),HolmanandCressman(1982)andSugiietal.(1978),titaniumiondiffusioninlithiumniobateproceedsmostlythroughLi+andNb+5sitesofthecrystallattice.ThecrystallochemicalradiiofTi4+,Li+andNb5+ionsarerespectivelyequalto0.061,0.068and0.064nm(HolmanandCressman1982),andtheircoordinationnumberinlithiumniobateisequalto6.Theconcentrationofsubstitutionaltitaniumionsunderusualdiffusionconditionsamountstoapproximately1021cm-3.Toprovidetherefractiveindexincreaseoftheorderof0.001forsuchconcentrations,theai,valuesofTi4+ionsmustexceedthecorrespondingvaluesforthesubstitutedionsbyapproximately0.0410-24cm3.Thisrequirementisinprinciplemetbythesubstitution .AsfarastheNb5+ionisconcerned,itsai,valuesarehigherthanthoseofTi4+
sinceithasanadditionaloccupiedelectronshellanditsradiusexceedsthatoftheTi4+ion.Inthequalitativerespect,theactionofthismechanismshouldobviouslybethoughtofasdisputable.
Mechanism3
Thismechanismreflectstherelationbetweenspontaneouspolarizationofadielectricanditsrefractiveindex(theKerreffect).Thisrelationcanbeexpressedintheform(Sugiietal.1978)
whereDPsisvariationofthequantityPsduetoimpuritydiffusion,g13andg33aretensorcomponentsofthequadraticelectro-opticeffect.
Calculationsshow(Sugiietal.1978)that and .
Ontheotherhand,itshouldbetakenintoconsiderationthatpolarizationreversalinthebulkcrystalinducesdeformationsalongthex-,y-andz-axesduetotheelectrostrictioneffect
Page37
whereQyareelectrostrictioncoefficients.
AnincreaseofneandnoisonlypossibleprovidedthatDPs<0,andasaresultofsuchpolarizationreversalwehave
Thesignsoftherequireddeformationsareoppositetothoseobservedinexperiment.
Thus,theonlysatisfactorydescriptionofthefactorsresponsiblefortherefractiveindexincreaseinthesurfacelayeroflithiumniobateduetotitaniumdiffusioncanbegivenexclusivelyintheframeworkofmechanism1.
1.5.1DiffusionofTransitionMetals
ThreedifferenttransitionmetalionshavebeendiffusedintocrystalsofLiNbO3toformlow-lossTEandTMmodeopticalwaveguidesthatconfinethelighttowithinafewmicronsofthesurface.AthinlayerofmetalofthicknesstisfirstevaporatedontoasurfaceofthecrystalandthenthecrystalisheatedattemperatureTinanonreactiveatmosphereforatimet.Theimportantwaveguideparameters-thenumberofmodesM,themaximumindexchangea,andtheeffectiveguidethicknessbcanbeindependentlycontrolledbythediffusionparameterst,T,andt.
SchmidtandKaminow(1974)haveshownthatawidevarietyofmetalsmaybediffusedintoLiNbO3andLiTaO3toformguidinglayers.Onepromisingclassofmetals,whichtheystudied,wasthetransitionelements.Theyareknown(McClure,1959)tocontaind-electronorbitalsthatarepolarizableinthevisiblespectrum.RepresentativemembersareTi,V,andNicontainingrespectively2,3,and8electronsintheunfilleddshellsoftheatoms.Thenumberofd
electronsinaniondependsuponitsvalencestate.
Thinlayers(200-800Å)ofthemetalswereevaporatedontothe(010)or(001)facetsofLiNbO3fordiffusionperpendicularorparalleltothec-axis,respectively.ThesampleswereheatedinflowingAr(topreventoxidationofthemetal)totemperaturesintherange850-1000°C(belowtheCurietemperature)inatimelessthan1h,andthediffusiontimetwasmeasuredfromthatpoint.Aftertimet,flowingoxygenwasadmitted(toreoxidizeLiNbO3)andtheovenswitchedoff.Forsufficientlylongdiffusiontimes,allthemetaldisappearsfromthesurface.Ifthediffusionisstoppedbeforeallthemetalentersthecrystal,anoxideresidueformsonthesurfacewhichisremovedbyverylightlyhandpolishingthesurface.
Observationsoftheindexprofilebytheinterferencemicroscopeindicatethepresenceofpositive-indexlayersforbothnoandnefordiffusionofeachofthethreemetals.Mostofthelayers,however,aretoothin(1-3mm)topermitmeasurementsofthefunctionalfromtheindexprofile.Electronmicroprobemeasurementsalsolacktheresolutiontomeasurethemetalconcentrationprofilesofthethinlayers.However,themicroprobewasemployedtomeasuretherelativeconcentrationprofilefortwothickNi-diffusedguides(Fig.1.22).
Page38
Fig.1.22Electronmicroprobemeasurementofwaveguidesformedbydiffusionofa400Å,Nifilm:Ni/Nb
countratiovsdepthx.aremeasuredpointsfor6hdiffusionat850°C.aremeasuredpointsfor6hdiffusionat950°C.ThesolidlineisfitoftheGaussianfunction.Thedashedlineisfitof
theerfcfunction(SchmidtandKaminow,1974).
Fordiffusiontimeslongcomparedtothetimerequiredforthemetalfilmtocompletelyenterthecrystal,theconcentrationprofileshouldapproachtheGaussianfunction(Shewmon1963)
wherexisthedepthbelowthesurface,athenumberofatomsperunitvolumeinthedepositedfilmofthicknesst,
andthediffusionconstant
(Strictlyspeaking,tin(1.35)shouldincludeacorrectionforthewarm-uptime.)Forshortdiffusiontimes,wherethemetalisnotcompletelydiffusedintothecrystal,theconcentrationprofileshould
beacomplementaryerrorfunction(erfc)withthesurfaceconcentrationindependentoftime(Shewmon1963).Fordiffusiontimescomparablewiththetimerequiredforallthemetaltoenterthecrystal,theconcentrationprofilewillbeintermediatebetweentheGaussiananderfcprofiles.
ThisbehaviourisillustratedinFig.1.22wheretheNi/Nbcountratiosareplottedasfunctionsofdepthfordiffusionperpendiculartothec-axisintwowaveguides.TheactualNi/Nbconcentrationratioisproportionaltothecountratiowithaproportionalityfactorgreaterthanunity.Thedatawereobtainedbyprobingpointsonaplanenormaltotheplaneoftheevaporatedlayer.Measurements
Page39
ofsurfaceconcentrationc(0,t)weremadeontheevaporatedfacetitself.GaussiananderfcprofilesarefittedtothedataatDn(x)=aand(1/2)ainFig.l.22.Thewaveguideformedbyheatinga400Åthickfilmat850°Cfor6hhasafunctionalshapewelldescribedboyacomplementaryerrorfunction.Thewaveguideformedbyheatinga400Åthickfilmat950°Cfor6hhasthelong-tailcharacteristicofacomplementaryerrorfunctionbutitalsohasthebell-likeshapenearthesurfacecharacteristicofaGaussianfunction.Inbothcasesthemetalfilmappearedtobecompletelydiffusedintothecrystal,butthediffusionrateismuchgreateratthehighertemperature.
ThevaluesofbobtainedforthetwoGaussianprofilesinFig.1.22showthatthesurfaceconcentrationc(0,t)isqualitativelyproportionaltot/b,asrequiredby(1.34).Inaddition,thesurfacecountratioforathirdsamplewitht=250Å,whichwastreatedfor6hat950°C,wasalsoinagreementwiththeexpectedt/bdependence.
Itisreasonabletoassumethattherefractive-indexchangeDn(t)isproportionaltoc(x)forsmallDn.ThenmakingallowancefortheGaussianprofile(1.34),wehave
Itisclearfrom(1.37)thatacanbecontrolledbyadjustingtandfrom(1.35)and(1.36)thatbcanbecontrolledbyvaryingtandT.Byanalogywithaslaborexponentialguide,thenumberofmodesMshouldbeproportionalto(CarruthersandKaminow1974)
Thus,asingle-modeguidecanbefabricatedwithb/aand,hence,theopticalmodedepthquitesmall.Incontrast,theb/aratioforout-diffusedguideswasfoundtoberelativelyinsensitivetotheavailablediffusionparameterstandT(CarruthersandKaminow,1974).
Severalmetal-diffusedwaveguideshavebeenexamined.Thenumberofmodesandtheirprismcouplinganglesweremeasuredand,fromthesemeasurements,thediffusiondepthbandtheindexchangeatthesurfacetn(O)wereestimatedbycomparingtheeffectiveindicesofthemodeswiththoseexpectedforanexponentialwaveguide(CarruthersandKaminow1974;Conwell1973).TheaverageresultsofthesemeasurementsforanumberofTi-,V-,andNi-diffusedsamplesaregiveninTable1.10.Itshouldbeemphasizedthatsincetheprofileisnotexponential,alltheeffectivemodeindicesinanexperimentalmultimodeguidecouldnotbemadecoincidentwiththosewithanexponentialguideforanysetofa,bparameters.Thehighest-andlowest-ordermodeswerematchedfortheestimatesofTable1.10,anditwasassumedthatbisaboutthesameforTEandTMmodes.Itmaybeseenthataisaslargeas0.04andbassmallas1mmfortheTiguides.ThediffusiondepthsbarelargerandtheindexchangesaaresmallerforNiandVthanforTiforgiventandT;however,reducingtand/orTwouldbringaandbforNiandVmoreintothelinewiththevaluesfor
Page40
Ti.ThechangeinrefractiveindexwithconcentrationmaybecalculatedusingthedataofTable1.10,equation(1.37)andthestandarddensitiesofthemetals:forexample,forTi,dno/dc=l.6×10-23cm3;forV,dno/dc=0.8×10-23cm3;andforNi,dno/dc=0.6×10-23cm3.
Thedominantsourcesofwaveguidelossarescatteringfromcrystalsurfaceimperfectionsand,possibly,absorptionbythemetalions.Thelossesat0.63mmareestimatedtobeabout1dB/cm.
Thewaveguidesaresuperiortoout-diffusedguidesinthataandbcanbecontrolledseparatelytoyieldverythinsingle-modelayers.TheyhavetheadvantageoverguidesformedbydiffusionofNbintoLiTaO3at1100°CthatthecrystalsarenotdepoledsincetheCurietemperatureofLiNbO31125°Ccomparedto600°CforLiTaO3.DiffusionintoLiTaO3attemperaturesbelow600°Cisfeasiblebutveryslow.
Itseemslikelythatmanyothermetalswillproduceeffectiveguideswhendiffusedintoavarietyofinsulatingcrystals.SchmidtandKaminow(1974)havemadepreliminarytestsusingvariousotherelementsondifferentsubstrates.
Table1.10Averageresultsformetal-diffusedguides(SchmidtandKaminow,1974)
MetalThicknesst(Å)
Timet(h)
Temperat.T(°C)
Diffusiondirection
Numberofmodes(M)
Effectiveb(mm)
EffectiveDn0(0)
EffectiveDne
Ti 500 6 960 1TM 1.1 0.01 ...
4TE 1.1 ... 0.04
1TE 1.6 0.006 ...
5TM 1.6 ... 0.025
V 250 6 950 1TM 6.5 0.0005 ...
4TE 6.5 ... 0.002
V 500 6 970 1TM 6.2 0.0005 ...
4TE 6.2 ... 0.004
Ni 270 6 800 2TM 2.9 0.007 ...
2TE 2.9 ... 0.004
2TE 2.6 0.007 ...
2TM 2.6 ... 0.006
Ni 270 6 960 3TM 6.6 0.002 ...
0TE 6.6 ... ...
2TE 5.5 0.0015 ...
0TM 5.5 ... ...
Ni 500 6 800 3TM 2.8 0.0095 ...
2TE 2.8 ... 0.006
3TE 3.1 0.0085 ...
2TM 3.1 ... 0.0045
Ni 500 6 960 7TM 11.6 0.0025 ...
0TE 11.6 ... ...
4TE 4.5 0.0045 ...
0TM 4.5 ... ...
Page41
Ithasbeenfound,forexample,thatAu-,Ag-,Fe-,Co-,Nb-,andGe-diffusedLiNbO3andTi-diffusedLiTaO3allyieldgoodwaveguides.Apparently,anyvalenceelectronscontributedbytheseelementsincreasetheopticalpolarizabilitywithoutacompensatingincreaseinthelatticevolume.Then,ifthemetalionsdonotintroduceexcessiveabsorptionattheoperatingwavelength,asatisfactorywaveguideisproduced.
1.5.2Titaniumdiffusion
Inthepaperscitedabove,thebackdiffusionofLi2Ohasnotbeenused.Butthisdiffusionisnecessaryforcreatingactiveelementsofintegratedoptics(modulators,switches,etc.)onthebasisofstriplinewaveguidessincealongwithstriplinewaveguidesthebackdiffusionprovidesthecreationofaplanarwaveguideforanextraordinarywave.ThedataonthereversediffusioncompensationisduetoBurnsetal.(1978),RanganathandWang(1973)andChenandPastor(1977)andMiyasawaetal.(1977).Theseauthorsmainlyconsidereddiffusioniny-cutcrystals.Atpresent,z-cutLiNbO3crystalsareofincreasingimportanceforintegratedoptics,firstofallbecausethiscutallowsaparticularlysimple'Cobra'typeelectrodeconfigurationtobeusedformodulatorsandswitches(PapuchonandCombemale1975)and,second,becausetheTidiffusionrateintheAratmospherealongthez-axisofaLiNbO3crystalisseveraltimesgreaterthantheratealongthey-axis(Fukudaetal.1978).Inviewofthis,z-cutLiNbO3crystalsareveryconvenientforcreatingdevicesonthebasisofstriplinewaveguides.
Golubenkoetal.(1980)investigatedTidiffusioninz-cutLiNbO3crystalsinanargonatmospherewithabackLi2Odiffusioncompensation.Themethodsofsamplepreparationareofpracticalinterest.Polishedz-cutLiNbO3sampleswerepreliminarilyannealedat1000°Cinanoxygenatmospheretoremovethesurfacelayer
damagedundermechanicalpolishingofcrystals.Titaniumlayersofdifferentthickness(200-600Å)weredepositedontoannealedplatesbymagnetronsputtering.ThespecimenswereplacedintoaplatinumcruciblefilledwithLiNbO3powderpreparedfromshavingsofthesamecrystals.TheconcentrationofLi2Ovapoursformedbythepowderandthesampleisinequilibrium,andthusthereisnoneedchoosingthetimewhenthebackdiffusioncompensationmuststart.Diffusionwascarriedoutinafurnacewithanargonatmosphere.Theheatingratewas50°C/min.Assoonasthenecessarytemperaturewasestablished,theamountofArwasdecreasedlestthefluxshouldcarryawayLi2Ovapours.Whenthediffusionwasover,thespecimenswerecooledinthesameArfluxatarateof5°C/min.Thewaveguidesobtainedinthisprocesshadlosseslessthan1dB/cmanditwasnotnecessarytocoolthespecimensinanoxygenatmosphere.
TheEPRstudiescarriedoutbyZilingetal.(1980)showedthatLiNbO3specimensthatwerenotspeciallydopedwithtitaniumexhibitedFe+3andMn+2ionspectra.Afterthespecimenswereannealedinavacuumat1000°Cfor2h,theFe+3linedisappearedwhiletheMn+2lineremainedunaltered.Intheregion thereappearedasinglelinewithananisotropicg-factor.AnalysisoftheorientationaldependenceofthespectrumrevealedthattheparamagneticcentreobservedhassymmetryC3v.
Inspecimenscoveredwithatitaniumlayer100nmthick,forwhichthediffusionannealingwascarriedoutinvacuuminregimesprovidingaTiconcentration
Page42
Fig.1.23EPRspectraof(1)Ti-dopedand(2)originalvacuum-annealedcrystals(Zilingetal.1980).
of(0.5-2)×10-2cm-3,thelineintensityincreasesbymorethananorderofmagnitude(Fig.l.23)andcorrespondstothenumberofcentres,6.5×1015.TheparamagneticcentreresponsiblefortheappearanceofthislinehasanelectronspinS=1/2andg-factorstypicalofthe3d-ionwhichinthiscaseistitaniuminthestateTi3+.EPRspectraofpairwiseTi3+ionswerenotobserved.
Whenspecimensareannealedintheair,thenumberofTi3+centresdecreasesrapidlywithincreasingtemperature.Att>600°Cthecorrespondinglinedisappears.NonewlinesexceptthosebelongingtoFe3+wereobserved,whichsuggeststitaniumtransitiontothenon-paramagneticstateTi4+.ThesymmetryC3visindicativeofthefactthataTiioncanbeinthepositionofeitherlithiumorniobium,butthevalenceoftheTiionandthechangeofthisvalencetestifyinfavourofniobiumsubstitution.Forconcentrationslessthanabout6×1019cm-3,theconclusionofthepositionofTiintheLiNbO3latticeisconfirmedbytheresultsreportedbyPearsalletal.(1976).
Thesesubstitutionalatomsalsohaveactivationenergiesofabout3.7eVwhicharemuchhigherthanthoseofinterstitialatoms,suchasLiandCu,ofabout1eV.Therefore,boththemarkedlatticecontraction
andthehighactivationenergyfoundintheTidiffusionintoLiNbO3implythatTidiffusessubstitutionallyintotheLiNbO3crystal.Recently,ithasbeenshownthatTidiffusedintoLiNbO3isall+4valenceandTiionssitnotonvacanciesordefectsbutonwelldefinedsites(Pearsalletal.1976).InLiNbO3,twopossiblesitesremainforsubstitutionalimpurities,aLisiteandaNbsite.ThelatticecontractionwouldoccurifTiionsreplacedeithertheLisiteortheNbsite,sincetheeffectiveionicradiusofTi+4,0.605Å,issmallerthanthoseofLi+1andNb+5of0.68and0.64Å,respectively,whenthecoordinationnumberofallofthemissix.However,thereplacementofNbionsbyTiionsismorefavourablefromthepointofviewofchargecompensation,soitisassumedthatTiisdiffusedassubstitutionalionsfortheNbsiteinLiNbO3.
Page43
Armeniseetal.(1983)discussedthefirststepoftheinteractionbetweenTiandLiNbO3,occurringbefore,andsubsequentlyleadingtotheformationofthe(Ti0.65Nb0.35)O2compoundlayer.Inparticular,theystartedwiththestresseseventuallyinducedbyTideposition,thendescribedthekineticsoftheTioxidationanditsinteractionwiththeOatomsoftheannealingatmosphereandofthesubstrate.So,theyshowedtheformationofLiNb3O8and(Ti0.65Nb035)O2compoundsandthedissolutionofTiO2andLiNb3O8phases,leadingtoacompleteformationofthe(Ti0.65Nb0.35)O2layer.
Opticalgradeandopticallypolishedy-andz-cutLiNbO3single-crystalsubstrateswereused.Tifilmswiththicknessesrangingfrom150to600Å,weredcsputterdepositedonsubstratesfromapure(99.99%purity)TitargetinapureAratmosphere(10-3torr)withadepositionrateofabout80Å/min.BeforeTidepositiontheTitargetwassputteretched,whilenosputteretchingwasperformedonthecrystalsubstrates.Onfewsamples,Tiwasdepositedinanevaporatorequippedwithanelectrongun.Sampleswerethenannealedinaflowing(120litre/h)dryoxygenatmosphereatdifferenttemperaturesandtimes.Theheatingandcoolingratewas30°C/min.
Samplemorphology,compoundformation,atomiccompositionprofiles,andstructuralcharacterizationoftheformedphaseswereanalyzedbyascanningelectronmicroscope(SEM),equippedwithanenergydispersiveX-rayanalysis,Rutherfordback-scatteringspectroscopy(RBS),byusinga1.8-MeV4He+beam,Augerelectronspectroscopy(AES),secondaryionmassspectrometry(SIMS),andglancingangleX-raydiffractionperformedwithaWallace-Wardcylindricaltexturecamera.ThepeculiaritiesandthereasonsforthechoiceofthesemicroanalyticaltechniqueswerediscussedbyArmeniseetal.(1982).NondestructiveRBSanddestructiveAESandSIMSin-depthatomiccompositionprofilingtechniqueswereusedtoobtaincomplementaryinformationandtoensurethatmeasured
compositionswithAESandSIMSwerenotfalsifiedbytheeventualdriftofmobilespecies,inducedinthesampleduringtheionmilling.Inparticular,toavoidelectricalchargeupduringanalyses,sampleswerecoatedwithabout50-100Åofcarbonorgold.
TheTioxidationprocessstartsattemperatureshigherthan300°Candmaybedirectlyobservedfromthecolourofthespecimensurfacelayerwhichchangesfrommetallic-gray(300°C,4h)towhitetranslucentin500°C,4hannealedsamples.Microanalyticaltechniquescanhelptounderstandtheoxidationmechanismsandkinetics.
Withincreasesintheannealingtemperature,thecompleteformationofTiO2,whichoccursat500°C,4h,isfollowedfirstbythegrowthoftheLiNb3O8phase,andthenbytheformationofthe(Ti0.65Nb0.35)O2phase.
TheLiNb3O8compoundcanbeclearlydetectedandidentifiedbyglancingangleX-raydiffractionpatternstakenwiththeWallace-Wardcylindricaltexturecamera.
Thesurfacemorphologyofthesampleannealedat750°Cfor2hwasexaminedinaSEM,operatingwithsecondaryelectrons.Onthesurface,manywhitezonesmorethan100mmindiameterappearandcoverabout10%ofthewholesurface.TheirtypicalshapesandmorphologiesareshowninthemicrographinFig.1.24.
Asalreadymentionedabove,thegrowthofLiNb3O8isfollowedbythe
Page44
Fig.1.24SEMmicrographsofwhitezonesappearingonaz-cutsample,coatedwitha400ÅthickTifilmandannealed
indryO2at750°Cfor2h(Armeniseetal.1983).
appearanceoftheternarycompound(Ti0.65Nb0.35)O2whosespotsbecomeevidentinglancingangleX-raydiffractionpatterntakenwiththeWallace-Wardcylindricaltexturecameraforannealingtemperatureshigherthan700°Candincreasecontinuouslyinintensityupto950°Cfor30minthermalannealing,whentheLiNb3O8phaseisalreadycompletelyconsumedanddecomposed.
Armeniseetal.(1983)fullycharacterizedthisternarycompoundandidentifieditastherealsourceforTidiffusioninLiNbO3.Itgrowsepitaxiallyonbothy-andz-cutsubstrates.
DifferentmicroanalyticaltechniqueswerethusemployedtostudythefirststepsoftheinteractionbetweenTiandLiNbO3crystalsoccurringduringthefabricationofTiindiffusedopticalwaveguides.Theresultsobtainedcanbesummarizedasfollows.
TisputteredorevaporatedfilmsgroworientedontheplanesoftheLiNbO3substrateforallobservedcrystallineorientations.The
crystallinequalityofboththefilmandthesubstratedoesnotdependonthedepositiontechniques(evaporationorsputtering)iflowvoltageandsputteringrateareused.
ThestressesinducedbytheTifilmarethusfoundtobeindependentofthedepositiontechnique.
Forlow-temperaturethermaltreatments(300-500°C)theTifilmwillformanamorphousTioxidelayer.TheoxidationmechanismwasclearlydeterminedasacaptureofOatomsbothfromthesurroundingatmosphereandfromtheLiNbO3substrate.ThislasteffectgivesrisetoanaccumulationofNbattheTi/LiNbO3boundarywhile,duetoitshighionicability,LidoesnotaccumulatebutdiffusesthroughtheTiorTi-oxidefilm.Thechangeoftheoxygenconcentrationintheannealingatmosphere(dryO2ordryAr)willonlyproduceanincreaseordecreaseintheamountoftheOatomscapturedbyTifrom
Page45
thebulk.Therefore,thefirststepofTiin-diffusedopticalwaveguidefabricationconsistsoftheformationofaTiO2layeratabout500°C.TheseresultscanalsoexplaintheformationofwaveguidesobtainedbydiffusingTiatabout1000°CfromdepositedTiO2films(Nodaetal.1975).
Atincreasingannealingtemperature(greaterthanorequalto600°C),theformationoftheLiNb3O8phasewasobservedonbothTicoatedanduncoatedLiNbO3substrates.AssketchedinFig.1.25,ontheTicoatedsamplesthiscompoundgrowsaslargecrystallitescharacterizedbyawell-definedorientationrelationshipwithrespecttotheunderlyingy-andz-cutsubstrates.FromRBSspectratheepitaxialqualityoftheLiNb3O8phaseshowsupbetteronTiuncoatedsamples.
TheLiNb3O8compoundcontinuestogrowwithincreasingannealingtemperatureupto750°C,whileforhigherannealingtemperatureitdecomposesandfinallyvanishes(T>900°C).Fukumaetal.(1978)didnotdetectthepresenceoftheLiNb3O8compoundinsamplesannealedathightemperatures.Thiscompoundisstillpresentandclearlydetectablealsoinrapidly(>30°C/min)cooledsamples,whenannealedattemperatureslessthanorequalto800°C;nevertheless,thepresenceofflowingoxygencannotinhibitthephaseseparationandtheLiNb3O8growth.Moreover,LiNb3O8formationanddissolutionappearnottobeaffectedbythepresenceofTi.Armeniseetal.(1983)attributetheformationofthiscompoundtoLiorLi2Oout-diffusionandtotheconsequentgrowthofaLi-deficienttoplayer.LiNb3O8isreportedtobeproblematic:infact,wheneverthisphasewasdetectedtheamountoftheopticaldamageinwaveguidesincreaseddramatically(Holmanetal.1978).Thisphasewasnolongerdetectedinsamplesannealedattemperatureshigherthan850°C,itsformationinduceslargestressandmicrofracturesinTiO2films(seeFig.l.25)andmaybeasourceofTiprofileinhomogeneitiesinthediffusedlayers.
ThegrowthofLiNb3O8isfollowedbytheappearanceofthe(Ti0.65Nb0.35)O2compoundwhichgrowscontinuouslyupto900-950°C,leadingtoacompleteconsumptionoftheTiO2layer(Fig.1.25).Thisternarycompoundistheonlyphasepresentat900-950°C;itformsauniformlayerontopoftheLiNbO3substrateandconstitutestherealsourceforTiin-diffusionwhichtakesplaceforlongerannealing,asreportedbyArmeniseetal.(1983).ItshouldbepointedoutthatadecompositionofLiNb3O8occursalsoinTiuncoatedsamples,andconsequentlyitappearsasanintrinsicstepoftheLiNbO3annealingprocess.
ResultssimilartothosediscussedaboveforannealinginadryO2atmospherewereobtainedinLiNbO3samplesannealedindryN,Ar,andstaticair.ExperimentsareinprogressonthepresenceandgrowthkineticsoftheLiNb3O8phaseinsamplesthermallytreatedwithprocessessuchasannealinginanatmosphererichinLiorinagasflowingthroughH2O,whichwereallreportedascapableofpreventingLiout-diffusion(Jackel,1982).
Sugiietal.(1978)investigatedthemechanismforgenerationofmisfitdislocationsandcracks.ThediffusionofTiintoLiNbO3createdstressessufficienttogeneratebothmisfitdislocationsandcrackswithinthediffusedlayer.Inevaluatingstresses,apositivesignfortensilestressandanegativeoneforcompressivestresswereused.Byassumingthatthestresssyonthediffusedlayerinthedirectionnormaltothesurfaceplaneiszero,themaximumimpurity-inducedstressesalongthecrystalsurfaceinsidethediffusedlayer
Page46
Fig.1.25SchematicofLiNb3O8and(Ti065Nb035)O2growthinLiNbO3aftertheformationoftheTiO2toplayer.
Temperaturesandtimesareonlyindicativefora400ÅthickoriginalTifilm(Armeniseetal.1983).
canbeexpressedasfollows:
whereSisthecomplianceofLiNbO3(Warneretal.1967)andeisthestressalongthex-,y-andx-axes.ThecalculatedstressesforthesamplesaregiveninTable4.3.Thesestresseswerepartiallyrelievedbythegenerationofmisfitdislocationsneartheboundarybetweenthediffusedandsubstrateregions,butthepresenceofcracksindicates
thatthedensityofthemisfitdislocationswasmuchlowerthantheoneneededforcompleteaccommodationoftheimpurity-inducedstresses.Anisotropyofstresses,(sx)max>(sz)max,resultedinpreferentialgenerationofcracks.
Thesameauthorsalsoconsideredthemechanismcausingrefractive-indexchangesinthediffusedlayer.Thereareatleastthreepossiblemechanismsforrefractive-indexchangesinthediffusedlayer:(i)duetoaphotoelasticeffect
Page47
bydiffusion-inducedstrains,(ii)duetoanincreaseoftheelectronicpolarizabilitybythein-diffusionofTi,(iii)duetoadecreaseofthespontaneouspolarizationofLiNbO3,Pdp,byTidiffusion.
Therefractiveindexofacrystalisspecifiedbytheindicatrix,thatis,anellipsoidwhosecoefficientsarethecomponentsoftherelativedielectricimpermittivitytensorBij,namely,
StrainsSndeformtheindicatrixthroughthephotoelectriceffect,andthechangeinBijisgivenby
wherepijisthephotoelasticcoefficient.
Inthecaseofathindiffusionlayer,itissufficienttoconsideronlyprincipalstrainsS1,S2,andS3,inthex-,y-,andz-axes,respectively.Thenequation(1.42)turnsinto
whereallthesuffixesareabbreviatedinthematrixform(Nye1957).Withallowancefor ,thechangesintherefractiveindicesatthesurfaceareapproximatedby
Forno=2.306,ne=2.220(refractiveindicesforNaD-lines)(Midwinter1968),andp11=0.034,p12=0.072andp13=0.178(O'Brienetal.1970),thecalculatedvaluesforthesampleswerecomparedwiththevaluesobservedbyNodaetal.(1975).Itwasfoundthattherefractiveindexchangesduetothephotoelasticeffectcontributetoabouthalfoftheobservedchanges.
Thesecondpossiblemechanismforindexchangesisbydiffusionofimpurityionshavinglargerelectronicpolarizabilitythanthatofthehostionstobesubstituted.Asinmostsolids,therefractiveindexofaferroelectriccrystalshouldoriginatefromelectronicpolarization.Therelationbetweentherefractiveindex,n,andelectronicpolarizability,a,isgivenas
Page48
whereN1isthenumberofionsoftypeiperunitvolumeandatistheelectronicpolarizabilityoftheion.ItwasfoundthatTiionsreplacedNbionsofatomicfractionofabout1021cm-3intheLiNbO3crystal.InordertoproducearefractiveindexchangeDn=10-3,theelectronicpolarizabilityofTiion,a(Ti),shouldbelargerby0.04×10-24cm3thanthatoftheNbion,a(Nb).However,itisunreasonablesincetheelectronicpolarizabilityofionshasatendencytodecreaseastheionicradiusbecomessmall(Kittel1956).
Thepossibilityofathirdmechanismisnowdiscussed.IntheferroelectricphaseinLiNbO3,oneofthecharacteristicfeaturesisthemarkeddecreaseintherefractiveindexduetospontaneouspolarizationPsthroughtheKerreffect.Theyaregivenby
fortherefractiveindicesnoandne,respectively,wheregoisthequadraticelectro-opticcoefficient.IfTi-diffusionintoLiNbO3changedthespontaneouspolarizationbyDps,Dpswouldproducerefractive-indexchangesgivenas
wheng13=0.043m4C-2,g33--0.16m4C-2(Ivasakietal.1966)andPs=0.50Cm-2(Savage,1966),DPsof-0.005Cm-2willcauserefractive-indexchangesof and Ontheotherhand,achangeofthespontaneouspolarizationwillatthesametimecauselatticestrainsinthea-andc-axesthroughtheelectrostrictiveeffect.Then,thestrainsduetoDPs,Snaregivenby
and
whereQ31=-0.0036m4C-2,andQ33=0.067m4C-2istheelectrostrictivecoefficientforLiNbO3(Iwasakietal.1968).IfDPs<0asrequiredtoincreasetherefractiveindices,itshouldproducestrainsS2>0andS3<0.ThesignsofS2andS3are,however,oppositetothoseoftheobservedstrainseyandez'respectively.Thus,itisunlikelythattherefractiveindexincrementsarecausedbydecreasingthespontaneouspolarization.
Itisconcludedthatthefirstmechanismproposedforrefractive-indexchangesismorelikelythanthesecondandthird.
Page49
1.5.3Copperdiffusion
Nodaetal.(1974)attemptedtodiffusemanykindsofmetals,suchasCu,A1,Ge,Cr,Fe,Nb,andTiintoLiTaO3.Amongthem,Cuwaseasilydiffusedatrelativelylowtemperatures,andasaresultalargerefractiveindexchangewasobservedintheCu-diffusedlayer.TheauthorsreportedtheexperimentalresultsonCudiffusioninLiTaO3.
Twokindsofdiffusionprocesseswereexamined:thermaldiffusion,anddiffusionunderanelectricfield(electrodiffusion).
PolishedLiTaO3Y-platesweredepositedwithCuabout5000ÅthickandwereheatedinairandinanAratmosphere.Forthespecimenstreatedinair,thedepositedCuwasoxidizedduringtheheattreatment,anddiffusionproceededremarkably,whileforthespecimentreatedinanAratmospherediffusionscarcelyoccurred.TheseresultsindicatethatCumustbeionizedinordertodiffuseintothespecimenandthationizationfromthecopperoxideiseasierthanthatfromthepuremetal.
AninterferencefringeprofileoftheCu-diffusedlayerobservedalongthex-axisisshowninFig.1.26.Diffusiontookplaceat800°Cfor10hinair.Theedgewasnormaltothey-axisandthelight(aNalamp)wasanordinarywave.Themaximumincreaseinnois3×10-3andthediffusiondepthisabout120mm.Theprofilefortheextraordinarywavewasthesameasthatfortheordinarywave,andthediffusedlayersupportedbothTEandTMmodes.Apeakoftherefractiveindexwasalwaysobservedbeneaththesurfaceforallspecimensdiffusedunderdifferentconditions.Thereasonforthephenomenonisnotclearyet.Inthethermaldiffusionmethod,itisdifficulttocontroltherefractiveindexchangeandthediffusiondepth.Moreover,therequiredtemperatureishigherthantheCurietemperatureofLiNbO3.Therefore,thermaldiffusionisnotsuitableforfabricatingtheactiveandthinsingle-modewaveguidinglayer.
TheauthorsthenexaminedthediffusionofCuintoLiTaO3underanelectricfieldusingthedepositedCuorCuOaselectrodes.Byapplyinganelectricfield,Cuiondiffusedeasilyfromtheanodesideinthelower-temperatureregion,thatis,500°C,atwhichnothermaldiffusionwasobserved.Figure1.27showsan
Fig.1.26InterferencefringepatternontheCu-diffused
layer,indicatingthechangeoftherefractiveindexn0.CuwasthermallydiffusedintoaLiTaO3Y-plate
at800°Cfor10h(Nodaetal.1974).
Fig.1.27(right)InterferencefringepatternoftheCu
electrodiffusedlayerinLiTaO3indicatingthechangeofrefractiveindexn0.Diffusionwascarriedoutat500°Cfor1hinairandan
electricfieldof10V/mmwasapplied(Nodaetal.1974).
Page50
interferencestructurefortheY-platespecimendiffusedat550°Cfor1hunderanelectricfieldof10V/mm.Thestructurewasobservedalongthex-axisusingtheordinarilypolarizedlight.Theprofilefornewasalmostthesameasthatfornointhiscasealso.Therefractiveindexatthesurfaceincreasesbyabout5×10-3,andthediffusiondepthis25mm.Theincreaseintherefractiveindexwasfoundtobeproportionaltotheappliedfield.Withelectricfieldsstrongerthan30V/mm,microcracksoccurredatthesurfaceofthediffusedlayer,andsuchalayerwasnotsuitableforthewaveguide.
Figure1.28showstherelationbetweenthediffusiondepthandthediffusiontimeforthespecimensdiffusedinairat550°Cunderanelectricfieldof10V/mm.Thechangesintherefractiveindexwerealmostconstantforthevariationofthediffusiontime.Whenthediffusiontimewaslongerthan1h,thecrystallinityofLiTaO3wasdegraded.TheelectrodiffusioninanAratmospherewasalsoexaminedforthespecimensdepositedwithCuO,anddiffusionwasfoundtoproceedmoreslowlythanthatmadeinair.
Nodaetal.fabricatedsuccessfullythewaveguidinglayersupportingonlythefundamentalmodesTE0andTM0bythefollowingconditions:temperature550°C,electricfield10V/mm,diffusiontime10rain,andinanArgasflow.Thethicknessofthediffusedlayerwasabout4mm.AHe-Nelaserbeamwasfedintothelayerwithaprismcouplerandpropagatedalongthex-axisofLiTaO3.AphotographoftheoutputspotsofTE0andTM0modesdecoupledwithagasprismisshowninFig.1.29.Thephotographshowsthatthespotshavewell-definedshapesandthemlinespassingthroughthespotsarefaint.Furthermore,onlyaslightdecaywasobservedinthestrengthofthescatteredlightoverthe1cmlengthofalightstreakalongthelayer,anditcanbeconcludedthattheopticalqualityofthelayerwassatisfactoryat0.633mm.However,aweakabsorptionpeakwasobservedatawavelengthof1mm,andtheuseofthelayerinthis
wavelengthregionmaybesomewhatlimited.
Fig.1.28RelationbetweendiffusiondepthanddiffusiontimeinCu-diffusedLiTaO3.Diffusionwascarriedoutat500°Cinairunderanelectricfieldof10V/mm
(Nodaetal.1974).
Fig.1.29(right)Outputspotswithfaintmline
decoupledwithaGaPprismforTE0andTM0modes.AHe-NelaserbeamisfedintotheCuelectrodiffusedlayerwiththeprism
coupler,andispropagatedalongthex-axisofLiTaO3(Nodaetal.1974).
Page51
1.6Proton-exchangedLiNbO3waveguides
Theionexchangemethodisbasedontreatmentofaspecimeninasaltmeltorsaltmixturesothatasaresultofchemicaldiffusionthereoccursapartialreplacementofmobileionsfromthesurfaceregionofthespecimenbyionsfromthemelt.Themostintensiveion-exchangeprocessesproceedamongunivalentionsofalkalinemetalsLi+,Na+,K+,Cs+,Rb+,aswellasTi4+,Ag+,Cu+and,possibly,Cu2+ions.Theprincipalfactorsaffectingtheion-exchangeprocessaretemperature,time,thestateofthesamplesurface,thechemicalcompositionandthemeltproperties.Toformalightguide,itisnecessarytoprovidearefractiveindexincreaseonthesamplesurface,andthereforethechoiceofappropriateion-exchangedpairsistypicallycarriedoutbycomparingtheelectronpolarizabilitiesofionsorbyestablishingtheratioofelectronpolarizabilitiestothecubesoftheirradii.Thehigherthevaluesofelectronpolarizability,thelargertherefractiveindexincrease.Thisisinmostcasesvalidfortheionexchangeprocessinglasses.Wealsonotethatindevelopingthismethodoneshouldnotneglectapossibleoccurrenceofsomebackgroundprocesses,suchassamplesurfaceseeding,phaseseparationandothers.
Lithiumniobateandtantalatearethefirstcrystallineobjectsforwhichion-exchangeddopingwasfirstrealized.SubstitutionalionsintheseprocessesareofcourseLi+ions.
Manyrecentreportsaredevotedtofabricationandinvestigationofthepropertiesoflightguidesformedbythe exchangemethod.AsthesourceofH+ions,Jackeletal.(1982)usedameltofbenzoicacidC6H5COOHat160-250°C.Toavoidacidevaporationanddecomposition,x-andz-cutlithiumniobateplatesweredopedinaclosedvesselwithoutreachofair.ThelightguidesamplesexhibitedpropagationofTE-modesonly,thedistributionfunctionofthe
refractiveindexofthelightguidebeingastepfunctionwithDne=0.12.Thevaluesoftheioninterdiffusioncoefficientswere3.8×10-12and1.0×10-12cm-2/sat244and217°C,respectively.Theproton-lithiumexchangewasobservedtoproceedsomewhatsloweralongzthanalongxdirection.Thelightlossinlightguideswasapproximately0.5dB/cm.Channellightguidesfabricatedusingmasks(chromiumfilms10nmthickandgoldfilms50nmthick)were1-20mmthick(Jackeletal.1982).Attemptstodopey-cutLiNbO3platefailedduetoastrongdestructionofthesurface.
Thepossibilityofobtainingwaveguidelayersonaz-cutLiTaO3usingtheion-exchangereactioninabenzoicacidmeltwasreportedbyAtuginandZakharyan(1984)andKopylovetal.(1983).Theprofileoftherefractiveindexincreasen(x)atelevatedtemperatureswasinvestigatedbyanumericalmethod(Kolosovskyetal.1981)whichallowedtheauthorstoreconstructtheprofilefromalimitedsetofdatabothforasharp(exponential)andasmooth(Gaussian)profilevariation.SurfaceopticalvariationsshowedthattheinvestigatedinteractionofLiTaO3withbenzoicacidstimulatesanincreaseoftheextraordinaryrefractiveindexonly.TheprofilesofDn(x)areclosetostep-likeones,thedepthofthewaveguideregionmakesupabout2.5mm.TheobservedjumpintherefractiveindexvariationislikelytobecausedbythephasetransitioninLi1-xHxTaO3typecompoundsduetoanincreaseoftheorderparameterx(RiceandJackel1982).
Page52
Theexperimentalresults(Reachetal.1985;Boikoetal.1985;Bashkirovetal.1985;Gan'shinetal.1985)suggestthefollowingschemeofproton-exchangeddoping:
1.Proton-lithiumexchangecausestheformationonacrystalsurfaceofanearlyconstanthydrogenconcentration,whichisapparentlyduetoastrongdependenceoftheinterdiffusioncoefficientDonionconcentrationinthesurfacelayer.
2.Experimentalstudiesshowthattonucleationandafurtherannealing-stimulateddevelopmentinannealingthecrystallinephasesn-Nb2O5andLiNb3O8therecorrespondsadefiniteH+-to-Li+concentrationratiointhedopedregion.Thisratiocanbeattainedwiththehighestprobabilityattheionexchangefront.Theformationoftheindicatedphasesisinevitablyassociatedwiththeoccurrenceofsignificantstructuraldistortions.Thisaccounts,inparticular,fortheloweringoftherefractiveindexDno=0.04whichislargerthanintherestoftheproton-exchangeregion.
3.Mismatchofthelatticeparametersofn-Nb2O5,LiNb3O8andLiNbO3leadstoconsiderablestresses,andthesurfaceregiongoesovertoametastablestate.
Reportshaveappearedonthedevelopmentandsuccessfulapplicationofacombinedwayoflightguidefabricationonthebasisoflithiumniobate-theso-calledTIPE(titanium-in-diffused-proton-exchange)process(Becker1983).Theprocessproceedsasfollows:titaniumdiffusionformsaTi:LiNbO3lightguideinwhichmodesofbothordinaryandextraordinaryrayscanbeexcited.Afterthis,thesampleistreatedinabenzoic-acidorinsomeothermeltsuitableforaproton-lithiumexchange.TheTIPEpromotestheformationofstructureswithahighnonx-,y-andz-cutsofacrystal(aftertitaniumdiffusiontheLiNbO3(Y)surfaceisnotpronetodestructionundertheactionofbenzoicacid).TIPElightguidesmayhave,dependingonthe
preparationconditions,rathercomplicatedrefractiveindexprofiles.Obviously,theTidiffusioninTIPEstructuresshouldonlybecarriedoutattemperatureshigherthan950°C.DiffusionatlowertemperaturesisfraughtwithariskofformationonthecrystalsurfaceofachemicalcompoundcontainingTiandNboxideswhichblocklithiumdiffusionthroughtheinterface.Thismayresultinblockingasubsequentproton-lithiumexchange.
Beingresistanttoinducedlaserradiation,proton-exchangedwaveguidesexhibittheloweringoftheelectro-opticeffectandahighinstabilityoftherefractiveindex.Ti-diffusedwaveguidesdegradewithtime,whileproton-exchangedwaveguidesage.Moreover,theypossessatypicalshortcoming-aweakrestrictionofthelightwave,whichisduetoanessentialimpossibilityofobtainingasharprefractiveindexvariationatthesubstrate-layerboundary.
1.6.1Ion-exchangeprocessesinLiNbO3
Theproton-exchangetechniqueinvolveschemicalreactionbetweensinglecrystallithiumniobate(LiNbO3)andasuitableprotonicsource,mostcommonlybenzoicacid(C6H5CO2H,m.p.=122°C),attemperaturesfrom150°Cto300°C(Jackeletal.1982).Theoverallreactioncanberepresentedbytheequation
Hydrogenisincorporatedwithinthecrystalintheformofhydroxylgroups
Page53
astheresultofbondingbetweenH+andO2-inthelattice.Theextentofprotonexchangedependsonthereactiontimeandtemperature,andonlypartialexchangeisnecessaryforwaveguideformation(Jackeletal.1983;Rice1986;RiceandJackel1984).AcompleteexchangecanbeobservedinLiNbO3powderandresultsintheformationofthecompoundLiNbO3,causingastructural(hexagonaltocubic)transformation(RiceandJackel1982;Fourquetetal.1983;WellerandDickens1985).Itisonlytheextraordinaryrefractiveindexthatisincreasedbyprotonexchange,whiletheordinaryindexisslightlydecreased(Jackeletal.1982).ThenatureofthesinglepolarizationmeansthatTEmodesaresupportedinx-andy-cutwaveguidesandTMmodesaresupportedinz-cutwaveguides.
Theopticalpropertiesofprotonexchangewaveguideshavebeendeterminedfromprism-couplingdata(Clarketal.1983;Wongetal.1986)andinfraredspectroscopyhasbeenusedtofollowtheincorporationofhydrogenashydroxylgroups(JackelandRice1981;Lonietal.1987).ThisapproachhasbeenextendedtodeterminerelationshipsbetweentheextentofformationofOHgroupsandwaveguidedepthsforx-andz-cutsingle-crystallithiumniobate.Improvedopticalpropertiesforannealedwaveguidesandwaveguidesproducedusingbufferedmeltswerereportedmanytimes(Jackeletal.1983;JackelandRice1984;Wong1985;Minakata1986),theterm'buffered'referringtypicallytobenzoicacidcontainingsmallamountsoflithiumbenzonate.Asystematicstudyofannealedandbufferedmeltwaveguideswascarriedoutinordertounderstandwhythepropertiesareimproved.Theroom-temperaturehydrogenisotopicexchangewasshowntooccurinproton-exchangeswaveguides(DeLaRueetal.1987;Lonietal.1987)indicatingthatthesewaveguidesreactwithatmosphericwatervapour.Theisotopicexchangetechniquewasusedtoinvestigatethebehaviourofbothannealedandbufferedmeltproton-exchangedwaveguidestowardsatmosphericwatervapour
attemperaturesupto375°C.
High-indexchanges(Dn=0.12)werereportedforionexchangeofLiNbO3inmeltsofAgNO3(ManharandShah1975)andTlNO3(Jackel1980)Unfortunately,thehigh-indexchangeisnotconsistentlyreproducibleandwasfoundtobedisconnectedwiththeintroductionoftheheavyAg+andTl3.4+ions(Griffiths1981;Chenetal.1982).RatheritresultsfromaprotonexchangeprocesssimilartothatreportedbyJackeletal.(1982),withwaterimpuritiesinthemeltactingasthesourceofhydrogen(JackelandRice1982).Sincetheseprocessescannotgiveconsistentresults,theyarenotasusefulashadpreviouslybeenhoped.Thus,protonexchangeinbenzoicacidfillstheneedforameansofproducinglargeindexchangesinLiNbO3.
JackelandRice(1982)showedthatimmersionofLiNbO3inhotacids,orincertainhydratemelts,resultsinprotonexchange,inwhichlithiumionsarelostfromthecrystalandaresubstitutedbyanequalnumberofprotons(JackelandRice,1981;RiceandJackel,1982).Instrongacids,suchasHNO3orH2SO4,thesubstitutioniscompleteandthenewcompoundHNbO3isacubicperovskite.ThelargestructuralandbulkchangefromthetwistedperovskiteLiNbO3structureprecludestheformationofasurfacelayerontheLiNbO3substrate.However,inlessacidicenvironments,suchasMg(NO3)26H2OorbenzoicacidC6H5COOH),anincompleteexchangeoccurs.Studiesofsingle-phasepowdersamplesshowthatatleastasmuchas50%ofthelithiumcanbereplacedby
Page54
protonswithoutamajorstructuralchange.OnmacroscopicLiNbO3crystals,partiallyexchangedlayersthickerthan10mmhavebeenformedusingbenzoicacid.
JackelandRice(1982)choosebenzoicacidasthemostpromisingoftheprotonsourceswhichproducepartialexchange,primarilybecauseofitshighboilingpoint(249°C)andstabilitythroughoutitsliquidrange.Thehighboilingpointpermittedworkingattemperaturesforwhichdiffusionwasrapid.Stabilityofthecompoundpermittedobtainingconsistentresults.Secondaryargumentsinfavourofbenzoicacidwereitslowtoxicityandlowprice.
Benzoicaciddoesnotattackmostmetals,sometalmaskscanbeusedtodefinechannelwaveguidesorothersmallfeatures,suchasgratings.Usingamaskofapproximately100ÅCrand500ÅAu,Jackeletal.(1982)havemadeaseriesofchannelwaveguides1-20S0109>mwide.Theuseofasimilarmaskingtechniqueformakinghigh-efficiencygratingsisnowunderinvestigation.
Clarketal.(1983)confirmedthattheuseofy-cutsubstratesrendersthesurfaceofthesubstrateliabletosevereetching.However,theproblemcanbeovercomebyusingprotonexchangeinconjunctionwithTiin-diffusiontoproducewaveguidesony-cutsubstrateswhichguidebothTEandTMmodes(DeMichellietal.1982).Bothactiveandpassiveopticalwaveguidedevicescanbefabricatedusingthistechnique;highefficiencybeamdeflectors(Punetal.1982),opticalfrequencytranslators(Wongetal.1982),andsecondharmonicgenerators(DeMichellietal.1983)havebeendemonstrated(seechapters5and6).
1.6.2Samplepreparationandexperimentalmethods
Lonietal.(1989)proposedthefollowingwayofpreparationoflight-guidinglayers.Nominallyidenticalcongruent-compositionx-andz-
cutlithiumniobatesubstrates(dimensions:1cm×1.5cm×0.1cm)werepolishedonbothfacetsforIRspectroscopicexperiments.Thesamplesinholderswereplacedinindividualcoveredsilicaglassbeakerswhichcontainedaccuratelyweighedquantitiesofmoltenbenzoicacid.Theheatingsourcewasahigh-temperatureoilbathwhichwascontrolledto±0.25°C.TemperaturesweremeasuredusingaPt-13%Rh/Ptthermocouple.The'neatmelt'x-andz-cutwaveguideswerefabricatedattemperaturesbetween167°Cand211°C,fortimesrangingfrom0.12to6h.Thefabricationprocedureforthex-cutbufferedmeltproton-exchangedwaveguideswasidentical,exceptthatthewaveguideswerefabricatedat215°Cand135°Cfortimesrangingfrom1to8.5h.ThequantityoflithiumbenzoateaddedtothebenzoicacidmeltswasdefinedintermsoftheLi+molarfraction,thatis,[molesoflithiumbenzoate]/([molesoflithiumbenzoate]+[molesofbenzoicacid]).Themolarfractionsoflithiumbenzoate,forfabricationofthebufferedmeltwaveguides,werebetween0.28×10-2and1.12×10-2.
SampleswereannealedinaPyrextubemountedinafurnacewhosetemperaturewascontrolledto±2°C.Theatmosphereusedwasdioxygensaturatedwithwater,obtainedbybubblingO2throughacolumnofwarm(60°C)water.Thewaveguidesweremountedinastainlesssteelboatthatallowedauniformflowofgasoverthesurfaceofeachwaveguide.Toavoidthermalshockatinletandoutlet,thewaveguidesweremovedslowlyalongthefurnacetubeoveraperiodofapproximatelyoneminute.Theannealingtimewasdefinedastheintervalbetween
Page55
thesamplereachingthefurnacehotspotanditssubsequentremoval.ThewetO2flowwasmaintainedthroughouttheentranceandremovalperiods.
Afterprocessing,thewaveguidesweremountedinevacuablePyrexinfraredcellsfittedwithcalciumfluoridewindowsforH/Dhydrogenisotopicexchangestudies.High-temperaturehydrogenisotopicexchangewascarriedoutbyannealingthewaveguidesasabove,exceptthatD2O(99.8percent)wasusedinsteadofH2O.Theinfraredspectrawererecordedusingaspectrometeranddatastation.Theopticalpropertiesoftheplanarwaveguideswereassessedat)l=0.6328mmusingtheprismcouplingtechniqueandassumingnormalizedstep-indexequations(TienandUlrich1970).TherefractiveindexprofilesoftheannealedwaveguideswerecalculatedusingtheIWKBmethod(Finaketal.1982),amethodparticularlyusefulforwaveguideswithagraded-indexprofile.
ProtondiffusionwascontrolledbytheIRspectra.Thex-cutspectraconsistoftwooverlappingbandsintheOHstretchingregion:abroad-bandatvmax=3250cm-1duetohydrogen-bondedOHgroups,andasharpbandatvmax=3505cm-1dueto'free'OHgroups.PolarizationmeasurementsindicatethatfreeOHisconstrainedtovibrateinthe(x,y)-planeofthewaveguide.Abandatvmax=3505cm-1isalsoobservedinthespectraofz-cutwaveguides.However,theabsorptionduetohydrogen-bondedOHgroupsisdiscernibleonlyasashoulderonthelow-frequencysiteofthesharpbandatvmax=3505cm-1.
Thedifferentspectraarepresumablyduetothedifferentcrystalorientation.
Thex-andz-cutinfraredspectra,Fig.1.30(a,b),indicatethattheOHabsorbanceincreaseswiththewaveguidefabricationtime.Itwasreported(Wongetal.1986)thatforx-cutlithiumniobate,therelationshipbetweentheOHabsorbanceat3505cm-1wasnonlinear
withtemperatureandtime.TheresultsduetoLonietal.(1989)wereinagreementwiththeseobservations.However,todeterminetheextentofproton-exchange,theareaoftheOHbandsshouldbeused.Therelationshipbetweentheabsorptionbandareaandwaveguidefabricationtemperatureislinear,asdepictedinFig.1.31(a,b)forx-andz-cutproton-exchangedwaveguides,respectively.Theobservedtemperaturedependenceindicatedthatthereisaminimumtemperaturerequiredforproton-exchange,thevaluesbeingT=(140.6±3.3)°Cforz-cutmaterialsandT=(131±8.3)°Cforx-cutmaterials.Correspondingvaluesobtainedbyplottingthewaveguidedepth(determinedfromprismcouplingdata)asafunctionoftemperaturewereT=(148.5±7.5)°Cforz-cutmaterialsandT=(145.4±3.4)°Cforx-cutmaterials.Thedatasuggestthattheminimumexchangetemperatureisslightlyhigherforz-cutmaterials.
TherelationshipbetweentheOHabsorptionbandareaand(time)1/2forx-andz-cutproton-exchangedwaveguidesislinear(thez-cutcaseinFig.1.32(a)),whichisconsistentwithaprocessinwhichtheextentofOHgroupformationinthewaveguidelayerisgovernedbydiffusion.Thenaturallogarithmoftheslopeofeachline(areaversust1/2)wasplottedasafunctionof1/TandtheobservedArrheniusbehaviourenabledapparentactivationenergiesfortheproton-exchangeprocesstobecalculated.ThevaluesobtainedwereQx=60.4kJmol-1andQz=81.2kJmol-1.
Sinceboththeabsorptionbandareaandwaveguidedepthshowat1/2dependence,thetwoquantitiescanbelinearlyrelated.Thiswasverifiedbyplottingthebandareaasafunctionofdepthforthex-andz-cutwaveguides,illustrated
Page56
inFig.1.32(b)forthez-cutwaveguides.Therefore,thedepthofaproton-exchangedwaveguidecanbeestimatedbycalculatingtheareaundertheinfraredabsorptionbands.Withsuitablerecalibration,themethodcanalsobeusedforwaveguidesproducedusingbufferedmelts.Themethodisparticularlysuitedforsingle-modeproton-exchangedwaveguides,wheretheusualIWKBandstep-indexmethodscannotbeused.
1.6.3Annealedproton-exchangedwaveguides
Theeffectofannealingontherefractiveindexprofileofanx-cutproton-exchangedwaveguide(Table1.11)isshowninFig.l.33a.Althoughtheinitialstep-likeindexprofileissubstantiallypreservedafterashortannealingtime,ataileventuallyformsatthewaveguide-substrateboundary,indicatingachangetoamoregraded-indexprofile.Thewaveguide(surface)indexofthesampledecreasedby0.04(atl=0.6328mm)afterannealingat320°Cfor3h11min(Fig.1.33a),andthedepthoftheguidingregionincreasedby1.30°m(Table1.11).Asaconsequence,thenumberofmodessupportedincreasedfromthreebeforeannealing,tofive.Afterfurtherannealingat400°Cfor30min,thetailonthestep-likerefractiveindexprofilewasmoreprominent.
Theeffectofannealingontheeffectivemodeindices(at)l=0.6328mm)andwaveguidedepthofthesamesampleisillustratedinFig.1.33b.Thesecond-ordermode(m=1)andthethird-ordermode(m=2)hadmaximumeffectiveindicesafterannealingtimesofapproximately10and15rain,respectively.Thefourth-ordermode(m=3)reachedamaximumafterapproximately1h.Afterthis,theeffectivemodeindicesalldecreasedgraduallywithincreasingannealingtime.Noinitialincreasewasobservedforthefundamentalmode(m=0).TheresultsobtainedforthesamplesinTable1.11indicatethatmostofthechangesintherefractiveindexprofileoccur,
approximately,withinthe
Fig.1.30infraredspectraofproton-exchangedwaveguides.a)x-cut,T=198°C:i)4.42h,ii)3h,iii)2h,iv)1h,
v)0.25h.b)z-cut,T=211°C:i)6h,ii)4.42h,iii)3h,iv)2h,v)1h,vi)0.42h,vii)0.12h
(Lonietal.1989).
Page57
Fig.1.31Absorbancebandareavstemperature:a)x-cut,b)z-cut(Lonietal.1989).
firsthalftoonehourofannealingandthesmallervariationsareobservedafterannealingformuchlongerperiods.
Afterannealingthex-cutproton-exchangedwaveguideat250°Cfor0.5h,therewasasignificantdecreaseintheintensityoftheinfraredabsorptionbandduetothehydrogen-bondedOHgroupsinthesample,butthebandat3505cm-1wasunchanged.Aprolongedannealingatthesametemperatureproducedfurther,butsmaller,variationsinthebroad-band.Thisbehaviourcanbecorrelatedwiththeobservationthatthemajorchangesintherefractiveindex
Fig.1.32a)Absorbancebandvst1/2(z-cutproton-exchangedwaveguides).b)Absorbancebandareavsdepth
(z-cutproton-exchangedwaveguides)(Lonietal.1989).
Page58
profileofsampleX3occurredwithinthefirst0.5hofannealing.Nodecreaseintheeffectivemodeindiceswasobservedatroomtemperature(afterannealing)overameasurementperiodofoneyear,inagreementwithJackelandRice(1984).
Thehydrogenisotopicexchangetechniquewasusedtotestwhetherannealedproton-exchangewaveguidesreactwithatmosphericwatervapourinasimilarmannertoannealedwaveguides,atroomtemperature.Theinfraredabsorptionspectraindicatedthat,unlikeinunannealedproton-exchangewaveguides,nohydrogenisotopicexchangetookplaceinthematerial.However,whenthex-cutwaveguidesweresubsequentlyannealedat320°Cfor0.5hinawet(D2O)/O2atmosphere,therewasanuptakeofdeuterium.Fromtheinfraredabsorptionspectrumofthesampleitcanbeseenthatthehydrogen-bondedOHwasmarkedlyreducedbyannealing.Thesharpbandatvmax=3505cm-1decreasedsignificantly,withthegrowthofanODcounterpartatvmax=2590cm-1.Thespectraoftheabsorptionbandstructuresindicatedthat,afterannealing,thewaveguides
Table1.11Opticalwaveguidemeasurements(l=0.6328mm)andannealingconditionsfor'neatmelt'x-cutproton-exchangedwaveguides(Loni,Hay,DeLaRue,Winfield,1989)
Diffusiontime,h
Annealingtemperature,°C
Annealingtime,h
Waveguide(surface)index
Depth(mm)
1 - - 2.3281 0.40
250 0.5 2.3082 0.70
250 1 2.3081 0.70
250 2.62 2.3036 0.72
3 - - 2.3295 0.73
250 0.5 2.3168 1.14
250 1 2.3151 1.19
250 2.62 2.3098 1.27
6(T=168°C)
- - 2.3307 1.09
250 0.5 2.3231 1.41
250 1 2.3168 1.61
250 2.62 2.3153 1.63
1 - - 2.3244 0.63
320 0.25 2.3072 1.02
320 1 2.2862 1.34
320 3.18 2.2763 1.50
3 - - 2.3286 1.12
320 0.25 2.3137 1.85
320 1 2.3026 2.02
320 3.18 2.2882 2.42
6(T=175°C)
- - 2.3281 1.60
320 0.25 2.3191 2.35
320 1 2.3021 2.72
320 3.18 2.2992 2.54
Page59
Fig.1.33a)Refractiveindexprofile(l=0.6328mm)asafunctionofwaveguideannealing;thesamesamplewasproton-exchangedat175°Cfor3h.b)Variationineffective
modeindiceswithannealingtime(thesamplewasannealedat320°c)(Lonietal.1989).
didnotreactwithatmosphericwateratroomtemperature.Similarresultswereobservedwhenpreviouslyannealed(O2/H2atmosphere)waveguideswerereannealedusingD2Oatahighertemperatureof375°C,althoughhydrogenisotopicexchangewasnotobservedinthesewaveguides(beforereannealing)atroomtemperature.
1.6.4Waveguidesfabricatedusingbufferedmelts
Theopticalpropertiesofwaveguidespreparedinbenzoicacidwithaddedlithiumbenzoateweredeterminedfromprismcouplingdata,viamodeanglemeasurementsandcalculationsusingthestep-indexmodel.Theresultingwaveguidedepthswerelinearlyrelatedtothesquarerootofthefabricationtime.Asthemolarfractionoflithiumbenzoateincreases,theeffectivediffusioncoefficient(estimatedfromthedepthversust1/2curves)decreases(Fig.1.34)indicatingthattheextenttowhichproton-exchangeoccursdependsstronglyonthepresenceoflithiuminthemelt.Asimilareffectmightbeexpected,intheabsenceoflithiumbenzoate,duetothepresenceoflithiuminthemeltresultingfromtheLi+-H+exchangeprocess.
However,thelithiumconcentrationsinbenzoicaciddeterminedbyatomicabsorptionspectroscopyafterprotonexchange,aresufficientlysmall(Lonietal.1987)andtheequivalentlithiumbenzoatemolarfractionisoftheorderof0.02×10-1.Therefore,theeffectivediffusioncoefficientremainsapproximatelyconstantthroughouttheexchangeperiod.
Thedegreeofopticalstabilityinaproton-exchangedwaveguidedependsonthemolarfractionoftheaddedlithiumion(Fig.l.35a,x-cut).Forexample,thedecreaseinthefundamentalmode(m=0)indexoveraperiodof410hwas0.0045forasamplecontainingLi+molarfraction=0.09×10-2,and0.001forasamplecontainingLi+molarfraction=1.10×10-2.JackelandRice(1984)showedthatnomeasurabledecreaseintheeffectivemodeindexcanbeobservedforwaveguidesproducedfrommeltscontainingmolarfractionsoflithiumiongreaterthan3.40×10-2.
Althoughtherefractiveindexprofilesarestep-like,thevalueofDne
Page60
decreasesasthelithiumbenzoatemolarfractionincreases(Fig.l.35b).ThelowestvaluemeasuredbyLonietal.(1989)wasDne=0.085forawaveguideproducedusingLi+molarfractionequalto2.42×10-2.InfraredspectraofwaveguidespreparedinbenzoicacidwithaddedlithiumbenzoateareshowninFig.l.36.AlthoughtheOHabsorptionbandsatvmax=3505cm-1andvmax=3250cm-1arebothpresent,therelativeintensityofthelatterbandismuchsmallerthanthatforwaveguidesproducedusingbenzoicacidaloneundernormallyidenticalconditions.ThelargerLi+molarfraction,thesmallertherelativemagnitudeoftheabsorptionatvmax=3250cm-1,indicatingthatthehydrogen-bondedOHgroupsarepresenttoalesserextent.Noroomtemperaturehydrogenisotopicexchangewasobservedinthewaveguideswhichwerefabricatedusingbufferedmelts(uptoLi+molarfraction=1.04×10-2),indicatingthat,likeannealedproton-exchangedwaveguides,theydonotreactwithatmosphericwatervapour.
Annealingthebufferedmeltwaveguidesinawet(H2O)dioxygenatmospherehadrelativelylittleeffect.Forexample,nomeasurablechangesintheinfraredabsorptionspectrawereobservedafterthebufferedmeltwaveguideswereannealed.Smallchangeswere,however,observedintherefractiveindexprofiles,butthesewereofthesamemagnitudeastheonesobservedduringthelaterstagesofannealingneatmeltproton-exchangedwaveguides.
Sincethepresenceofhydrogen-bondedOHinbufferedmeltwaveguidesisverymuchreduced,thechangesintherefractiveindexprofilesasaconsequenceofannealingmustarise,inthemain,fromthediffusionofprotonsoriginatingfrom'free'OHintothesubstrate.Itisunlikelythat'free'OHout-diffusesintotheatmospheresincetherewouldbeanassociatedreductionintheabsorptionband.
Thelossofhydrogenduringtheannealingprocesscouldariseby
migrationofthehydrogen-bondedOHtothesurfaceoftheguidingregionfollowedbyreactionofsurfacehydroxylgroupstogivesurfaceoxidesandwater.Thelatterprocesscaneithertakeplaceviaroute2,orviaroute4followedbyroute5,inthescheme:
Fig.1.34Effectivediffusioncoefficientsat215°Cand235°CversusLi+molefraction(x-cut)(Lonietal1989).
Page61
Fig.1.35a)VariationineffectivemodeindexwithtimefordifferentLi+molefractions(x-cut).b)Stepindexchange versusLi+mole
fraction(x-cut)(Lonietal.1989).
(where representshydrogen-bondedOH).Theprocessisreversible,sinceithasbeenshownthatDisincorporatedintoproton-exchangedwaveguidesfromD2Oduringannealing.Thiscouldoccureitherdirectly,viaroute6,orviaroute1followedbyroute4.Thelatterrouterequireshydrogen-bondedOHtobepresentandislikelytobeimportantonlyduringtheearlystagesofannealing.Lonietal.(1989)demonstratedreversibleHDexchangeatroomtemperature.However,thisisnotobservedwithannealedorbufferedmeltwaveguides,arguingthatHDroomtemperatureexchangeinvolvesroute1thenroute4androute3thenroute2,ratherthanthedirectroutes5or6.Thedirectroutes5and6dooccurathightemperaturessince,asmentionedabove,Dcanbeincorporatedathightemperatureswithoutthepresenceofhydrogen-bondedhydroxylgroups( ).Itis
Fig.1.36Infraredabsorptionspectraofx-cutprotonexchangedwaveguidesfabricatedusingbufferedmelts,at215°C:i)neatbenzoicacid,ii)Li+molefraction=0.28×10-2,iii)Li+molefraction=1.04×10-2(Lonietal.1989).
Page62
suggestedthattheannealingprocesscanberepresentedbythefollowingreactionsteps:
Theremovalofhydrogen-bondedOHgroupsasH2Opreservedchargeneutralityinthecrystalandcantakeplaceviareaction(1.54)followedbyreaction(1.55).Reaction(1.55)wasfirstsuggestedbyBollmann(1987),althoughforadifferentsituation.
Lonietal.(1989)believethathydrogen-bondedOHgroupsarelikelytoberesponsible,toasubstantialdegree,fortheundesirableeffectsassociatedwithproton-exchangedwaveguides;forexample,deviceinstabilities,suchasdcdrift(Wongetal.1982).Wongetal.(1982)reportedthatapplyingadcvoltageofapproximately5V(eitherpolarity)toaproton-exchangedstripwaveguidephasemodulatorresultedintheextinctionoftheguidedmode,withatime-constantoftheorderof1min.Removingthedcvoltageledtoaslowrecoverywhereasvoltagereversalledtoamuchmorerapidrecovery.Suchaneffectmaywellbecausedbythemovementofhydrogen-bondedOH(protons)undertheinfluenceofanappliedelectricfield.Thedistributionofhydrogen-bondedOHis,initially,likelytobeapproximatelyuniformwithintheguidinglayer.However,onapplyinganelectricfieldtheelectrostaticforceswouldredistributetheprotons.Protonswhicharehydrogen-bondedwillbemorestronglyattractedbyanegativepotential,sincetheyarethemoremobilehydroxylgroups.Theconsequentredistributionoftheprotonscouldresultinamajormodificationinthewaveguiderefractiveindexprofile.Removaloftheelectricfieldwouldgiveachargeimbalanceandtheprotonswouldtendtomigratebacktomorefavourablesites,recoveringtheoriginalwaveguiderefractiveindexprofile.
Inadditiontotheremovalofhydrogen-bondedOHandthediffusion
of'free'OHintothesubstrate,theannealingprocessmayalsoinvolvemigrationoflithiumionsfromadjacentregionsofthesubstrateintothewaveguideregion.Inthissituation,thedistortedunitcellstructureinthewaveguidemaytendtochangebacktothatofvirginLiNbO3.Asaconsequence,theelectro-opticeffectwouldberestoredandpropagationlossesreduced.Itiswidelyacceptedthatthediamond(parallelogram)whichappearsinthe(012)plane,basedontherhombicsystem,isrelatedtothestrongelectro-opticeffectintheLiNbO3crystal,asshowninFig.1.37.Aftertheexchange,thefigureisslightlyclosetothesquare(perovskite,thecubicsystem)causedbythestrainDc/c.Sincethesquarehasthecentreofsymmetry,thelinearelectro-opticconstantdoesnotgenerallyexist.Thus,itisestimatedthatr33reducesbecauseofthedeformationofthediamond.However,inspiteofnophasetransitionintheexchangedlayer,thevalueofr33seemstobeverysmall.ItissuggestedthattheHNbO3(system)compositionoftheexchangedlayershouldhaveapoorelectro-opticeffect.
1.6.5Protondiffusion
Usingtheprismcouplingtechnique,Clarketal.(1983)calculatedtheeffective
Page63
refractiveindexofeachobservedmode.ThevaluesofeffectiverefractiveindiceswerethenusedastheinputforacomputerprogrambasedonnormalizedstepindexequationsgivenbyKogel'nikandRomaswamy(1974),tocalculatethesurfacerefractiveindexandthedepthoftheplanarwaveguide.Thestep-indexassumptionwasverifiedbymodellingthediffusionprofileoftheplanarwaveguidebyafinitedifferencesolutionoftheone-dimensionalionexchange(equation(1.56))(WilkinsonandWalker1979)
where ;Daisthein-diffusioncoefficientforprotons,Dbtheout-diffusioncoefficientforLi+ions,andutheconcentrationofprotonstothetotalconcentrationofions.
Theequationtakesintoaccounttheratioofthediffusioncoefficientsofthespeciesdiffusinginandoutofthesubstrate.Itwasfoundthattherateofprotonsdiffusinginwasverymuchsmallerthanthatofthelithiumionsdiffusingout.Fromthemodel,theoreticalvaluesofthediffusioncoefficientsforlithiumandprotonionswerefoundtobe1.62and0.08mm-2/hat200°C,respectively.Clarketal.(1983)usedtheabovemodelinconjunctionwithavariationalsolutionofthewaveequation(Walker1981)tocalculatemodeeffectiveindices.Theparameterainequation(1.56)wassystematicallyvariedtoobtainabestfittomeasuredeffectiveindexvalues.Thebest-fitprofileoccurredwhen indicatingthatthesolutionofequation(1.56)wasastepfunction.
Plotsofthediffusiondepthversus(time)1/2forvarioustemperaturesareshowninFig.1.32(b).Fromthegradientofthecurves,thevaluesforthediffusioncoefficientwerecalculatedassumingthattheprotonsourceconcentrationdidnotvaryduringtheexchangeprocess.ThisgivesvaluesofthediffusioncoefficientD(T),asshowninTable1.12.
Thevalueswerecalculatedassumingthediffusiondepthdtovaryasfollows(Crank1970):
Fig.1.37Deformationofdiamondappearsinthe planeofLiNbO3
beforeandafterexchange(Minakataetal.1986).
Page64
wheretistheexchangetime.Inequation(1.57),thetemperaturedependenceofDisgivenbytheArrheniuslaw:
whereD0isaconstantfortheprotonexchangeprocessinz-cutLiNbO3,Rtheuniversalgasconstant,Ttheabsolutemelttemperature,andQtheactivationenergyfortheexchangeprocess.Figure1.38illustratestherelationshipbetween1/TandInD(T).Fromthisplot,theQandD0valueshavebeenobtained:Q=94kJ/mol,D0=1.84×109mm2/h.Equation(1.57)canthereforeberewrittenas(1.59) exp(-5.65×103T)mm.FromFig.1.38onecanreadoffthevalueofthediffusioncoefficientwithintheworkingrangeforbenzoicacid(150-230°C).
1.6.6Waveguidesusingcinnamicacid
Punetal.(1991)havedemonstratedtheuseofcinnamicacid(C6H5CH:CHCOOH)andinparticulartranscinnamicacid,asanewprotonsourceforthefabricationofhigh-indexproton-exchanged(PE)waveguidesinz-cutLiNbO3.TherefractiveindexprofileofthePEwaveguidesusingthisacidisagradedindexfunctionandisdifferentfromthoseobtainedusingorganicacidswhichhavestepindexprofiles.
Z-cuty-propagatingPEplanarwaveguideswerefabricatedinintegratedopticsgradeLiNbO3substratesthatwerepolishedononeface.Thesubstrateswereprecleanedthoroughlyusingaseriesoforganicsolventsandpreheatedbeforeimmersingintotheacidmelt.Theanalyticalgradetranscinnamicacidwascontainedinacoveredquartzcrucibleandmaintainedatthesettemperatureforfabrication.Aftertheexchangeprocess,anyresidualacidwasrinsedawaywithacetone.Forannealingexperiments,thewaveguideswerepostbakedinahorizontalfurnaceat350°Cfortimesbetween6minand5h.A
dryoxygenatmosphereflowingat500ml/minwasusedtopreventdeoxidizationofthewaveguides.
Thewaveguidedepthsandindexprofileswerecomputedfromthemeasureddatausingthecontinuouseffectiveindexfunctionmethod(Chiang1985).
Figure1.39showsthevariationofwaveguidedepthdwithexchangetimetfordifferentfabricationtemperaturesT.Assuming ,theeffectivediffusioncoefficientD(T)canbecalculatedforeachfabricationtemperature.ThetemperaturedependenceofD(T)followstheArrheniuslaw,thatis, ,whereD0isthediffusionconstant,Qistheactivation
Table1.12Diffusioncoefficientswithrespecttotemperature(Clarc,Nutt,Wongetal.1985)
T D(T)
(°C) mm2/h
180 0.027
200 0.081
220 0.207
Page65
Fig.1.38PlotofInD(T)versus1/T(gradientofline=Q/R)(Clark,etal.1983).
energyandRistheuniversalgasconstant.FromtheArrheniusplot,thatis,In[D(T)]versus1/T,thevaluesofD0andQwerefoundtobe9.78×107mm2/hand77.15kJ/mol,respectively.HencethediffusiondepthofaPEwaveguideusingtranscinnamicacidcanbeexpressedas
Figure1.40showsatypicalvariationoftheindexprofileofthePEwaveguidewithannealingtimeasaparameter.Thewaveguidewasinitiallyexchangedat235°Cfor2h.Theindexprofilechangesfromatruncated-parabolicfunctiontoastepfunctionafterannealingfor16min.Withfurtherannealing,anindextailformsattheguidesubstrateboundaryandtheprofileisGaussian-like.Figure1.41showstheeffectofannealingonthesurfaceindexchangeDnandthewaveguidedepthincrease ,whered0istheinitialwaveguidedepthbeforeannealing.ThelineardependenceindicatesthatbothDnandDdfollowapower-lawrelationshipwithannealingtimeta,andcouldbegivenby
wherec1andc2areconstants.Fromthemeasureddata,c1andc2havevaluesof0.082and1.81respectively.Otherwaveguidespreparedusingdifferentinitialexchangetimesandtemperatureshavesimilarcurvesafterannealing,butwithdifferentvaluesofc1andc2.Annealedsingle-modewaveguidesalsoexhibitalowerpropagationloss(0.33dB/cm)comparedtothatoftheunannealedcounterpart(0.81dB/cm).
1.6.7Proton-exchangewaveguidesofMgO-dopedandNd:MgO-dopedLiNbO3
Ithasbeenreportedthatproton-exchangewaveguidesformedinMgO-doped
Page66
Fig.1.39Waveguidedepthdasafunctionofexchange
timetusingtranscinnamicacid(Punetal.1991).
LiNbO3haveahigherdamagethresholdthanwaveguidesfabricatedinundopedmaterial(Digonnetetal.1985).Inordertousehigherpumppowerswhileavoidingeffectsassociatedwithphotorefractivedamage,LiNbO3substratesdopedwithbothneodymium(toprovidethelasingmedium)andmagnesiumoxide(tosuppressphotorefractiveeffects)canbeused.
BothJackelandDigoneetetal.(1985)haveindependentlycharacterizedproton-exchangewaveguidesfabricatedinx-(DigonnetM.etal.1985;JackelJ.L.1985)andy-cut(DigonnetM.etal.1985)LiNbO3dopedwith5%MgO,whilstLietal.(1988)characterizedwaveguidesfabricatedinx-cutLiNbO3dopedwithapproximately1%Nd.Jackelusedneatbenzoicacidmeltsforwaveguidefabricationat150and250°CandDigonnettetal.usedneatandbufferedbenzoic-acidmelts(1and2mol.%lithiumbenzoate)at249°C,whereasLietal.useda'double-exchange'technique(requiring1mol%followedby3mol%lithiumbenzoate)at300°C.Lonietal.(1990)reportedthefirstcharacterizationofneat-melt,proton-exchangedwaveguidesinthex-cutsubstratedopedsimultaneouslywithMgOandNd.
Planarwaveguideswerefabricatedonx-cutNdMgO-doped(0.1-0.2%:4.5%)LiNbO3andonx-andz-cutMgO-doped(4.5%)LiNbO3.PlanarwaveguideswerealsoproducedincongruentLiNbO3andwereusedasareferenceforthewaveguidesfabricatedinthedopedsubstrates.Thewaveguideswerefabricatedbyimmersioninneatbenzoicacidattemperatureswithintherangeof182-235°C,withfabricationtimesrangingbetween1and12.5h.Allthewaveguidesweremultimode.Lightpropagationwasalongthey-direction.
ThecharacteristicOHabsorptionbandswereobservedintheinfraredspectraofalltheMgO-dopedand(Nd:Mg)-dopedsubstratesandproton-exchangedwaveguides.Therelativeintensititesofthebandsweredependentonthewaveguidefabricationparameters,inamannersimilartothatobservedforwaveguidesproducedincongruentsubstrates,andtheinfraredspectraofwaveguidesproducedinbothtypesofdopedsubstrateswereidentical.Theonlyobviousdif-
Page67
Fig.1.40IndexprofileofPEwaveguideasafunctionof
annealingtime(T=235°C,t=2.0h,Tc=350°c)(Punetal.1991).
Fig.1.41SurfaceindexchangeDnandwaveguide
depthincreaseDdasafunctionofannealingtimeta(Punetal.1991).
ferencesintheinfraredabsorptionspectra,comparedtothoseofwaveguidesformedbyprotonexchangeincongruentLiNbO3,wereinthepositionsoftheOHpeaksbeforeandafterprotonexchange.
InagreementwiththeresultsreportedbyJackel(1985),theslightlydifferentOHenvironmentsandbehaviourbeforeandafterprotonexchangemaybeindicativeofslightlydifferentwaveguidematerialstructures.
Byplottingtheexponentialrelationshipbetweenwaveguidedepthand
,andassuming ,effectivediffusioncoefficients,D(T),fortheproton-exchangeprocesswereestimated.Figure1.42showstherelationship
Table1.13Diffusionparameters(QandD0)forprotonexchangeindoped(d)andundoped(c)LiNbO3(Lonietal1990)
Sampledescription Diffusionparameters
Q(kJmol-1) D0(mm2h-1)×109
x-cut,H+:LiNbO3(c) 81.24 0.234
x-cut,H+:LiNbO3(d) 91.54 1.41
(H+:Nd:MgO:LiNbO3)(d)
z-cut,H+:LiNbO3(c) 90.40 1.472
z-cut,H+:MgO:LiNbO3(d) 99.36 5.037
H+:Nd.MgO:LiNbO3(d)
Page68
obtainedbetweentheeffectivediffusioncoefficientsandtemperatureforproton-exchangedwaveguidesfabricatedinboththedopedandundopedsubstrates.ItcanbeseenfromtherelationshipsdepictedinFig.1.42thatthediffusionprocessincongruentLiNbO3isslowerforz-cutsubstratesthanforx-cutsubstrates.ThisrelativeslownessisalsothecasefortheMgO-dopedsubstratesand,presumably,fortheNd:MgO-dopedsubstrates.
AlthoughaccordingtoFig.1.42,theprotonexchangeprocessproceedsmoreslowlyinMgO:LiNbO3thanincongruentmaterialofthesameorientation,inagreementwiththeresultsofJackel(1985),thereappeartobenomeasurabledifferencesbetweentheeffectivediffusioncoefficientsforproton-exchangeinNd:MgO:LiNbO3andMgO:LiNbO3.ThepresenceofMgOandNd:MgOLiNbO3singlecrystalshasalsobeenshowntoreducethediffusioncoefficientsfortitaniumin-diffusion(Bulmer1984).ForprotonexchangeincongruentLiNbO3dopedwith5%MgO,theeffectivediffusioncoefficientestimatedbyJackel(1985)forawaveguidefabricationtemperatureof250°Cwas0.81m2h-1.Extrapolatingthecurveforthex-cutproton-exchangewaveguidesinMgO:LiNbO3to250°C,Fig.1.42,yieldsasapproximatelyidenticaldiffusioncoefficientof0.80m2h-1.Thissimilarityisreasonable,giventheprobablelevelofprecisioninobtaininguniformMgOdopantconcentrationsinthesolid.TakingtheeffectivediffusioncoefficientsforprotonexchangeinMgO:LiNbO3(Nd:MgO:LiNbO3)asapercentageofthecorrespondingvaluesforcongruent,onefindsthatthereductionisoftheorderof50±5%forx-cutwaveguidesand37±4%forz-cutwaveguides(Table1.13).
TheobservedArrhenius-typerelationshipsbetweenD(T)andT(Fig.1.42),aretypicaloftheproton-exchangeprocess.ByplottingInD(T)asafunctionofT-1,acomparisonofboththeactivationenergyandpreexponentialfactorwasobtainedforthewaveguidesfabricated
inthedopedandundopedsubstrates,Table1.13.IncongruentLiNbO3,boththeactivationenergyandthepreexponentialfactorarelowerforx-cutsubstratesthanforz-cutsubstratesandhighereffectivediffusioncoefficientsareevidentforx-cutsubstrates(Lonietal.1989,Clarketal.1983).ThisrelationshipalsoappliesforNd:MgO-dopedandMgO-dopedsubstratesofx-andz-cutorientations.Comparingthewaveguidesproducedindopedandundopedsubstrates(Table1.13),onefindsthatlowereffectivediffusioncoefficientsareobtainedforprotonexchangeindopedsubstrates.Inaddition,theactivationenergyandpreexponentialfactorarehigherforMgO-doped(Nd:MgO-doped)substrates.ThesedifferencesareprobablyrelatedtoslightdifferencesbetweenthebulkandwaveguidecrystallinestructuresofcongruentandMgO-doped(Nd:MgO-doped)LiNbO3.
1.7Planarion-exchangedKTiOPO4waveguides
Potassiumtitanylphosphate(KTiOPO4,abbreviatedasKTPbelow)haslongbeenrecognizedasanoutstandingmaterialformanyimportantopticalandelectro-opticalapplications(Zumstegetal.1976,Liuetal.1984,Liuetal.1986).Itshighdamagethreshold,goodmechanicalandthermalstability,largeopticalnonlinearity,andbroadtemperaturebandwidthhavemadeitarguablythebestmaterialforfrequencyconversioninthevisibleandnearinfraredranges.KTPalsoshowsgreatpromiseinelectro-opticapplicationsduetoits
Page69
Fig.1.42Relationshipsbetweeneffectivediffusioncoefficientandtemperatureforaseriesofx-andc-cutproton
exchangedwaveguidesfabricatedindopedandundopedLiNbO3(Lonietal.1990).
lowdielectricconstantsandlargePockelscoefficients(BierleinandArweiler1986).
Despitetheinitialsuccesses,theion-exchangeprocesshasitsdrawbacks.Specifically,theionicconductivityvariessignificantlywithcrystalgrowthmethodsandwithimpurities,makingthedevicefabricationprocessdifficultandwithpooryields.Thisinherentlydiffusiveandstronglyanisotropicion-exchangeprocessoftenproduces (whereMisT1orRb)guideswithabroadpoorlydefinedrefractiveindexprofilealongthec-axis,andwasbelievedtoberesponsiblefortheobservedvariationsintheperformanceofthesedevices.BetterunderstandingofthemechanismofionicconductionandtheunderlyingdefectsinKTPpromisestoreducethisproblem(Morrisetal.1991).
TheionexchangeconditionsandwaveguidingresultsaresummarizedinTable1.14,wheredisthediffusiondepthandDntheincreaseinthesurfacerefractiveindex.Anerrorfunctiondistributionisassumed
fortherefractiveindexprofilesintheionexchangedregions,adistributionwhichagreeswellwiththeionconcentrationprofileandisshowninFig.1.43foratypicalRb-exchangedsample.Themaximumincreaseinthesurfacerefractiveindexobservedforrubidium(Dn=0.02)isclosetothevaluethatwouldresultinnearlycompleteionexchangeformingaRbTiOPO4surfaceonaKTPsubstrate(Zumstegetal.1976).Theincreaseinthesurfacerefractiveindexforalltheseionexchangedguidesgenerallyscaleswiththeelectronicpolarizabilitiesoftheexchangedionsrelativetopotassium.
Theionexchangedwaveguidesarestablebothatroomtemperatureand,providedthediffusiontemperatureremainsbelowabout450°C,theexchangeprocessdoesnotintroduceanynoticeablesurfacedefects.Nearandabove450°C,slightsurfaceetchingoccursinsomesamplesduringtheexchange.
TheresultsgiveninTable1.14showtheiondiffusioninKTPtobehighlyanisotropic,beingmuchgreateralongthez-axis(corpolardirection)andbeing
Page70
Fig.1.43DepthprofileforRbionexchangeinKTP
(BierleinandFerretti1987).
higheronanegativez-surface(positivepyroelectriccoefficient)thanonapositivez-surface.Thediffusionanisotropycorrelateswellwiththelargeanisotropyofionicconductivitiesanddielectricproperties(BierleinandArweiler1986).Thevariationsindiffusionintothedifferentpolarsurfacesresultfromdifferencesinsurfaceadsorptionandreactivities.Additionalvariationsindiffusionkineticsareobservedalongthez-axisfromchangesinlocalionicproperties.Somecrystalshadregionsofvaryingpyroelectricanddielectricpropertiesdependingoncrystaldefects,incorporatedO-H,etc.Thediffusionrategenerallyscaleswithionicconductivity,aresultwhichisexpectedsinceionicconductivityanddiffusionarecloselyrelated.
DiffusionconstantsandactivationenergiesindicatethattheRb-K-exchangeprocessdoesnotobeysimplediffusionkinetics.TheeffectivewaveguidethicknessandDnwerefoundtobenearlyindependentofdiffusiontimefrom0.25to4hatatypicaldiffusiontemperatureof350°Candalsonearlyindependentofdiffusion
temperaturefrom350to400°C.Also,post-annealingaRb-exchangedguideinairfrom300to350°Cfor30minto2hdidnotsignificantlychangedorDn.TheseresultsindicatethattheeffectiveexchangeorthediffusionratefortheRbKsystemisinitiallyhighandthendecreasessignificantlyaftersomepointintheexchangeprocess.ThislargechangeinexchangeordiffusionratecanbeexplainedbyassumingaverylowdiffusionconstantforRbandKinRb-rich
andahighconstantinKTP.Single-crystalRbTiOPO4(RTP)showsamuchlower(~100times)ionicconductivitythanKTPandhenceionicdiffusionisalsoexpectedtobemuchlower.ExchangingKwiththelargerRbioninaKTPsurfacelayerwillalsotendtoblockconductionchannelswhichfurtherlowersionicconductivity.Hence,duringionexchange,asthe
Page71
Table1.14KTPwaveguidecharacteristics(Bierlein,Ferretti,Brixner,Hsu1987)
Ion Surfacetype
Temperature(°C)
Time(h)
Numberofmodes
Modetype
d(mm) Dn
Rb x 450 3.3 0 TE
1 TM 1.3 0.02
Rb z(+) 350 4 3 TE 4 0.019
3 TM 4 0.018
Rb z(-) 350 4 3 TE 6.5 0.008
2 TM 6.5 0.008
Cs z 450 4 11 TE 13 0.028
8 TM 13 0.019
T1 z 335 4 4 TE 1.6 0.23
4 TM 1.6 0.18
surfacerubidiumconcentrationincreases,thediffusionconstantsatthesurfacedecreasewhichwillsuppressfurtherionexchangeandresultintheequilibriumiondistributionshowninFig.1.43.Althoughsuchanequilibriumdistributionisunusual,itisconsistentwithdiffusiontheory.Thistypeofbehaviourisanadvantageforopticalwaveguidedevicessinceitallowstospeedupwaveguidefabricationatrelativelylowtemperaturesandalsopermitsthermallystableproperties.
Planarwaveguideswerefabricatedonthez-surfaces(crystallographiccdirection)ofhydrothermallygrownKTPcrystalsbyimmersingtheminamoltenmixtureofRbNO3(80mol%)andBa(NO3)2(20mol%).Diffusiontimesrangedfrom2to20minat350°C.
Followingdiffusion,633nmlightfromahelium-neonlaserwascoupledintothewaveguideusingaprism.Theeffectiveindicesofthewaveguidemodestravellingalongthey-axisoftheKTPcrystalweremeasuredandtherefractiveindexprofileofthewaveguidewasobtainedbytheinverseWKBmethod(Risk1991).
AtypicalrefractiveindexprofileobtainedinthismannerisshowninFig.1.44forTEmodes.ThesolidcurvesinFig.1.44arethebestfitsoftherefractiveindexprofile,n(z)=ns+Dnerfc(z/d),wherensistherefractiveindexoftheKTPsubstrate,Dnistherefractiveindexchangeatthesurface(z=0)ofthesubstrate,erfcisthecomplementaryerrorfunction,anddisthedepthofthewaveguide.Theexperimentallymeasuredrefractiveindexdistributioniswelldescribedbyanerfcprofile,asmightbeexpectedforsimplediffusion,andthisagreeswiththemicroprobemeasurementsofRb-ionconcentrationreportedbyBierleinetal.(1987).IthasbeenmentionedabovethatDnanddaremarkedlydifferentdependingonwhetherthe+cor-csideofthesubstrateisused(Bierleinetal.1987).WiththeadditionofBaions,thewaveguidepropertiesareessentiallythesameonboththe+cand-csides.
ThewaveguidedepthdandsurfacerefractiveindexchangeDnweremeasuredforseveraldiffusiontimes.Thedepthofthewaveguidewasfoundtodepend
Page72
Fig.1.44RefractiveindexprofileofKTPwaveguideformedbyionexchange.PointswereobtainedbyinverseWKBfrommeasuredmodeindices.Thesolid
curvesarebestfitsoftheprofilen(z)=Dns+Dnerfc(z/d)(Risk1991).
Fig.1.45EffectofpostbakingtheKTPcrystal.Solid
curveshowsrefractiveindexprofileofwaveguidefabricatedaccordingtotemperaturecycledescribed.
Dashedcurveshowsrefractiveindexprofileofthesamewaveguideafterheatinginairto350°C
for10min(Risk1991).
ondiffusiontimetas .ThedepthobtainedforagivendiffusiontimewassimilarforbothTEandTMmodes.ThesurfaceindexchangeDnobtainedforTMmodeswassomewhathigherthanforTEmodes.ThisispossiblyaconsequenceofinferringDnfromthemode
indicesusingasimpleWKBmodelthatdoesnotincludetheeffectofthebiaxialnatureofthesubstrateontheTMmodes.However,theTMmodeindicesareaccuratelymodelledusingthissimpleWKBapproachwiththevaluesofDnanddgiven,andthissufficesforpredictingthephase-matchingcharacteristicsforfrequencydoubling.
ItisimportanttocontrolthetemperatureoftheKTPcrystalbeforeandafterdiffusiontopreventcrackingofthesubstrateandunwantedmigrationoftheRbions.ItwasfoundthatimmersingtheKTPcrystalsdirectlyintothemeltfromroomtemperaturecausedthemtocrack,sothesubstrateswerefirstgraduallyheatedinairtonearthetemperatureofthemeltbeforebeingimmersed.ThisphenomenonisaresultoftheparticularthermalandmechanicalpropertiesofKTP.TheKTPcrystalwasheldinapreheatingfurnaceforabout1h,toensurethatthetemperatureofthecrystalhadequilibratedtothefurnacetemperature.Thenthecrystalwasdippedinthemelt.Aftertheprescribeddiffusiontime,theKTPcrystalwasremovedfromthemeltandallowedtocoolrapidlydowntoroomtemperature.BecausethediffusionoftheRbionsissofastforthisRb/Baprocess,unwantedmigrationoftheRbionsfurtherintotheKTPcrystal
Page73
canoccurifthesubstrateisnotcooledrapidly,resultinginchangesintherefractiveindexprofile.ThisisillustratedinFig.1.45,whichshowstherefractiveindexprofileofaplanarKTPwaveguideimmediatelyafterthediffusionprocessandafteranadditional10minofbakinginairat350°C.Itisevidentthattheadditionalheattreatmenthasresultedinasignificantdecreaseinsurfaceindexchangeandanincreaseinthedepthofthewaveguide,andthattherefractiveindexdistributionnolongerhasanerfcprofile.
Page74
2Liquid-PhaseEpitaxyofFerroelectricsThemethodofliquid-phaseepitaxyfromthefluxisbasedonthefollowingprocedure(Nelson1963;Andreevetal.1975).Thedissolvedsubstancecancrystallizeonthesubstrateimmersedinasupersaturatedconstant-temperatureflux.Inthecourseofcrystallization,supersaturationofthesolutiondecreasesandthegrowthratetendstozero.Themaximumamountofthecrystallizedsubstanceisproportionaltothemassofsolutionandthemagnitudeofsupersaturation.
Theliquid-phaseepitaxyhassomeadvantagesoverothermethods.Stoichiometryneednotbemaintainedduringgrowthfromthemelt,whichpermitsanycombinationoftemperaturesandcompositionsneartheliquiduslineofthephasediagram.Inmanycases,acorrectchoiceofthesolventallowscrystallizationatatemperaturelowerbyseveraldegreesthanthemeltingpointofthecompound.Thishelpstolowertheconcentrationofchemicalandstructuraldefectsascomparedtothatinacrystalgrownfromanearlystoichiometricmelt.Thelowerthetemperature,thelessthepossibilityofcontaminationofthefluxbyimpuritiesfromthecontainer(Alferov1976;Dolginoveta1.1976).
Thereareseveralmodificationsoftheliquid-phaseepitaxyofferroelectrics,themostpopularofwhichareepitaxialgrowthbymelting(Miyazawa1973;Adachietal.1979),liquid-phaseepitaxyfromtheflux(Kondoetal.1975;Baudrantetal.1978(a);Baudrantetal.1978(b);Ballmanetal.1975);KhachaturyanandMadoyan1978;Miyazawaetal.1978;Kondoetal.1979;KhachaturyanandMadoyan1980),capillaryliquid-phaseepitaxy(Khachaturyanetal.
1984;FukudaandHirano1976;FukudaandHirano1980),andliquid-phaseepitaxyfromalimitedvolume(Madoyanetal.1983;Madoyanetal.1985).
Theapplicationofliquid-phaseepitaxymethodsprovidesaclearlypronouncedsubstratefilmboundarywithstep-likerefractiveindicesandarelativelysmoothsurfaceofthestructure.
2.1Theepitaxialgrowthbymelting(EGM)
ToobtainferroelectricsinglecrystalLiNbO3films,Miyazawa(1973)proposedthemethodofepitaxialgrowthbymeltingonLiTaO3substrates.Forsubstrates,LiTaO3singlecrystalswereusedbecausethepointgroupofLiNbO3and
Page75
LiTaO3hasthesameclass, ,andthemeltingpointofLiTaO3ishigherbyabout300°CthanthatofLiNbO3.ThisdifferenceinthemeltingpointisthekeypointfortheEGMmethod,wherethemeltingpointofthesubstratehastobehigherthanthatofthefilmmaterial,aswillbedescribedlater.
Fortunately,itisobviousfrommanypreviousinvestigationsontherefractiveindicesofLiNbO3singlecrystals(Tien1972)thatrefractiveindicesforordinaryandextraordinaryraysofLiNbO3singlecrystalswithanysolid-solutioncompositionarelargerthanthoseofLiTaO3atroomtemperature.TherefractiveindicesofLiNbO3andLiTaO3aregiveninchapter5,indicatingthataLiNbO3filmonaLiTaO3substrateactsasadielectriclightwaveguide.
TheLiTaO3substrate,whichwaspreparedfromasingle-crystalboulegrownbypullingfromameltwithacongruentmeltingcompositionofLi/Ta=0.951inmoleratio(Miyazawa1971)was10×15×4mminsizeinthex,y,andcdirections,respectively.Thec-planewaslappedandpolishedoptically,andLiNbO3ceramicscrushedintopowderwerelaidonthepolishedc-planeofthesubstrate.Thesubstratewiththepowderonitstopsurfacewasheatedto~1300°CinaresistancefurnaceinordertomelttheLiNbO3crushedpowderalone,anditwasthencooledslowlyat~20°C/hthroughthemeltingpointofLiNbO3(1250°C).Inthisway,aLiNbO3filmcrystallizedepitaxiallyontheLiTaO3substrate.Asamatterofcourse,thesubstrateisnotinasingleferroelectricdomain.(ThenameEGMoriginatesfromtheprocessdescribedabove.)ForthecompositionoftheLiNbO3ceramicsacongruentmeltingcompositionofLi/Nb=0.942inmoleratio(Lerneretal.1968)wasused,sinceacompositionalfluctuationdidnotoccurduringthegrowthrun.Consequently,afluctuationoftherefractiveindexdoesnotexistinthegrownfilm.TherefractiveindicesofcongruentLiNbO3are and at6328Å.
ThelatticeparametersofcongruentLiNbO3andLiTaO3singlecrystalsatroomtemperaturearegiveninchapter4.ThemismatchofthelatticeparametersatroomtemperaturebetweentheLiNbO3filmandtheLiTaO3substrateisabout0.08%and0.57%foraHandcH,respectively.ThefilmthicknesswasmeasuredbylineanalysisusinganX-raymicroanalyzer.AnintensitydistributionprofileofcharacteristicX-rayspectraforNbandTa,asshowninFig.2.1,wasobtainedbyscanningtheelectronbeamperpendiculartothefilmsubstrateboundaryoverthecrosssectionofthespecimen.FromFig.2.1thefilmthicknesswasmeasuredtobeabout6mm.Thec-planeofthefilmwasetchedwithasolutionofaHF+2HNO3mixtureatitsboilingpointfor2mintodeterminewhethertheLiNbO3single-crystalfilmwasgrownornot.
TheferroelectricdomainofaLiNbO3singlecrystalisrevealedmoreeasilybychemicaletchingthanthatofLiTaO3.Theetchedtopsurface,showninFig.2.2,indicatestheferroelectricmultidomainstructure,whichisveryclosetothatofaLiNbO3singlecrystalwheretheareaswithtrigonalhillocks(blackincolour)areatthenegativeendofspontaneouspolarizationandthosewithouthillocksareatthepositiveone.ItwasconcludedthattheLiNbO3single-crystalfilmwasgrownontheLiTaO3substrate,sinceitiswellknownthattheferroelectricdomainstructure,asshowninFig.2.2,isnotrevealedinaLiTaO3singlecrystalunderthesameetchingcondition.X-rayexaminationresults
Page76
Fig.2.1Intensitydistributionprofileof
characteristicsX-rayspectraforNbandTa,perpendiculartothefilmsubstrate
boundary(Miyazawa1973).
Fig.2.2(right)Etchfigureofthefilmsurface,indicating
theferroelectricmodulationpattern(Miyazawa1973).
indicatethattheLiNbO3single-crystalfilmwasepitaxiallygrownonthesubstrate.
Asthetopsurfaceoftheas-grownfilmwasrelativelyrough,itwashandpolishedfirstwithdiamondpasteandthenwith0.05mmA12O3powderinordertodemonstratelightwavepropagationinthe
epitaxiallygrownfilm.Figure2.3showsa6328-ÅHeNelaserbeamwhichwasfedintothefilmattheright-handsidebyaprismcoupler.Arutileprismwasusedastheinputcoupler.Thelightbeampropagatedthroughtheentirelengthinsidethefilmandthenradiatedintofreespaceattheleft-handedgeofthespecimen,leavingabrightareawhichindicatesthenear-fieldstructure.Afewspecksoflightareobservedalongthelightstreak,andalargespotisobservedneartheleft-handedge.Inotherexperiments,thesingle-crystalfilmwasgrownonthex-andy-planesofthesubstrate.Thefilmgrownonthex-planeincludedseveralcracksrunningalongtheperfectcleavageplane ofLiNbO3,Fromdetailedobservationsofthefilmsurfaceunderadifferentialmicroscope,itwasfoundthatweaklyobservedscatteringalongthepropagatinglightbeamwascausedbytheroughnessofthefilmsurface.
Ballmanetal.(1975)havemodifiedthemethoddevelopedbyMiyazawa.EvidenceispresentedwhichsuggeststhattheepitaxialgrowthbymeltinginvolvesadiffusionmechanismbetweenthemeltingliquidandtheLiTaO3substrate.AlthoughthegrowthprocessinvolvessimplemeltingofLiNbO3powderonthesurfaceofLiTaO3substrates,thesuccessfulproductionofahighqualityfilmisespeciallydependentuponthemannerinwhichthepowderisappliedtothesubstrate.
Ifthepowderedlayeristoothickorifthethicknessvariesappreciablyoverthesurfacearea,puddlesofLiNbO3formduringthemeltingprocess.Theyproduceaveryunevensurfaceafterrecrystallizationandmakethefabricationofanopticalwaveguidequitedifficult.
Page77
Fig.2.3Lightbeampropagatinginthefilmgrownontothec-plane,whichwas
fedbyaprismcouplerattheright-handside(Miyazawa1973).
LiNbO3powdersofabout30mmparticlesizeweresuspendedinalacquer.ThisLiNbO3-lacquersuspensionwasthen'painted'ontheLiTaO3substrates.Thesepaintedlayerswerepracticallyflat,andwhendry,thesuspendedpowderswerefirmlyfixedtothesubstrate.Thespecimenswerethenbroughtuptothedesiredfiringtemperature(1260°Cand1320°C)inaresistancefurnace.Duringthewarm-upperiod,theorganiclacqueriscompletelydecomposedandleavesaveryuniformlayerofLiNbO3powderreadyforthemeltphaseepitaxialreaction.Aftera30minsoakperiodatthefiringtemperaturethesampleswerecooleddowntoroomtemperatureatarateof20deg/h.
ThefilmthicknesscanbecontrolledbyvaryingtheconcentrationoftheLiNbO3-lacquersuspension.Similarly,thicknesscanbebuiltupbyadditionalpaintingandfirings.Thefilmsrequiredlightsurfacepolishorbuffinginordertocouplelaserlightinoroutviaarutileprism-filmcoupler.Figure2.4showsthephasediagramforLiNbO3(film)andLiTaO3(substrate)astothetwoendmembers(Petersonetal.1967).Theshadedarearepresentsthetemperaturerangecoveredinthisstudyanditincludesthereactiontemperature(1300°C)
reportedbyMiyazawainhiswork.
Fig.2.4LiNbO3-LiTaO3phasediagram
(Petersonetal.1970).
Page78
Itisevidentthatinameltphaseepitaxialprocessseveralfactorscombinetodeterminethefinalcompositionofthefilm.Thephasediagramitselfpredictsthefilmcompositiononecouldobtainasafunctionofthereactiontemperature.Anadditional,andimportantconsiderationistherateatwhichLiTaO3-lacquerwilldissolveinthemoltenLiNbO3-lacquerduringthesoakperiod.Afurthercompositionalgradingcanoccurduetosegregationwhichtakesplaceasthemoltenlayercrystallizesinaccordancewiththephasediagram.Thereisthenthesolidsoliddiffusionprocesswhichoccursasthegrownfilmisslowlycooledtoroomtemperature.
Thefilmthicknessmeasurementswereobtainedbyusinganelectronmicroprobeandtrackingacrossthecleavededgeofaspecimen.Theelectronbeamtrackedacrossthesurfaceofthefilmandcontinuedacrossthefilmsubstrateboundary.Asthebeamfirstentersthefilm,boththeniobiumandtantalumcountsriseandthisisindicativeofthesolidsolutionnatureofthefilm.Asthebeamleavesthefilmandentersthesubstrateregion,theniobiumintensitydiminishes.Thedistancetrackedwhiletheniobiumintensityiselevatedisequaltothefilmthickness.Figure2.5showstheeffectinafilm~3mmthick.
TheroleofsolidsoliddiffusionandhowitmaybeusedtoalterthepropertiesofagrownfilmisshowninFig.2.6.CurveArepresentstheindexoftherefractionprofileforasolidsolutionfilm.CurveBrepresentstheindexprofileforthesamecrystallinefilmafterithasundergoneanannealat1200°Cfor48h.Itisclearfromtheloweringoftherefractionindexandtheincreasedfilmthickness(3.7mmto~10mm)thatextensivediffusionhasoccurredinthesolidstateduringtheanneal.
Thelossofthefundamental(m=0)waveguidemodewasdeterminedbymeasuringthelightlostintransmissionbetweentheinputandtheoutputcoupler.Solidsolutionfilmsofthetypeshownheregavelosses
ofabout5dB/cm.Thesamemethodwasalsousedtoobtain(K,Li)LiNbO3films(Adachietal.1979)uptoseveralmicronsthick.Thequalityofthefilmdependsonthechoiceofsubstratesandthewayinwhichtheceramicpowderisdepositedontothesubstratesurface.
2.2Thecapillaryliquidepitaxial(CLE)technique
Thecapillaryliquidepitaxialtechniqueisoneofthenewmethodsforobtaining
Fig.2.5Nb+andTa+intensityaselectronbeamtracksoffilmsurfaceandfilmsubstrate
interface(Ballmanetal.1975).
Page79
ferroelectricfilms.Themethodisamodificationofthewell-knownStepanov'stechnique(Stepanov1963;Maslov1977)whichgivessinglecrystalsintheformofthinfilms(FukudaandHirano1976;FukudaandHirano1980).
2.2.1CLEgrowthprocedure
ThegrowthsetupusedforCLEgrowthisthesameasusedinthepreparationofLiNbO3ribboncrystals(FukudaandHirano1975).Thegrowthsetupcomprisesa50mmdiameter×30mmlongPtcrucible,agap-shapedPtcapillarywitha0.5mmwidthand30-50mmheight,aconicalPtafterheater,ceramicinsulatorsandasubstratepullingmechanism.ThegrowthgeometryisshowninFig.2.7.Growthisinitiatedwhenthetipofthesubstratetouchestheliquidinthecrucible,withabout0.5mmseparationbetweenthesubstrateandthecapillaryplate.Whenthesubstrateispulled,thesolutionismixedwiththatinthecapillarygap,onthetopofthedie.Therefore,thecapillarydieisusedasareservoirtofeedthelayerofliquidbetweentheexteriorofthedieandanadjacentsubstrate.Temperatureadjustmentisaccomplishedbymonitoringtheliquidtemperature.
Figure2.8showsthegeometryforanimprovedCLEtechniqueandamultilayergrowthtechnique,proposedbyFukudaandHirano(1980).IntheimprovedCLEtechnique,thecapillarydiecomprisestwoparallelverticalplatesofdifferentlengthsuitablyspacedtoprovidethecapillaryaction(seeFig.2.8a).Theliquidrisesthroughthecapillarydietopandgrowthistheninitiated.Thesubstrateplateconstitutesthediewallcomplementingthelowerendportionoftheshortercapillaryplate.Figure2.8bshowsthatafilm(LiNbO3)oraribbon(LiTaO3)crystalcanbegrownusingtheimprovedCLEandEFGtechniquessimultaneously.
LiNbO3thinfilmsweregrownfromaLiNbO3-LiVO3moltensolution.Amixtureof50mol%Li2CO3,10mol%Nb2O5and40
mol%V2O5wasusedasastartingmaterial.ThemixturewasheatedinaPtcruciblebyrfheatingandthesolutiontemperaturewasadjustedtoavaluesuitableforgrowth(850-900°C).Thefilmthicknesswascontrolledbysolutiontemperatureandpullingspeed.Afterterminatinggrowth,thefurnacewascooledtoroomtemperatureatarateofabout200°C/h.ForLiTaO3substratesmirror-polishedplates(typicaldimensions15×30×2mm)werefabricatedfromCzochralskigrownboules.Thefollowingorientationswereused:(001)<100>,(100),<210>,(130°rotatedYplate)<210>and(170°rotatedYplate)<210>,where()and<>showtheplateplaneandpullingdirection,respectively.
LiTaO3thinfilmsweregrownfromaLiTaO3-LiVO3moltensolution,aswereLiNbO3filmsfromaLiNbO3-LiVO3moltensolution.Forsubstrates,LiNbO3platecrystalswerefabricatedfromCzochralskigrownboules.Orientationswere(001)<100>,(131°rotatedYplate)<210>,and(210)<112.1°rotatedY>.
Forseveraladvancedexperiments,basedontheCLEtechnique,multiple-layerstructurefilmsorstripedfilmsonsubstratesandmultipleribbonsweregrown.Thefollowingsubstrateswereused:LiNbO3filmson(001)<100>LiTaO3plates,LiTaO3filmson(001)<100>LiNbO3plates,and(001)<100>LiTaO3substrateswith200or25mmwidthand0.75mmdepthalong<100>
Page80
Fig.2.6Indexofrefractionprofileversusthicknessforafilmbeforeandafter1200°anneal(Ballman
etal.1975).
Fig.2.7(right)GeometryofCLEgrowth(Fukuda
andHirano1980).
direction,asshowninFig.2.9(madebyionbeametching).LiNbO3thickfilmsweregrownon(001)<100>LiTaO3platesoras-grownribbons,fromaLiNbO3meltinsteadofaLiNbO3-LiVO3solution.ThefilmgrowthconditionsarepresentedinTable2.1.
2.2.2.CLEgrowthandcrystalquality
LiNbO3epitaxialthinfilmshavebeensuccessfullygrownontoLiTaO3substrates.Thefilmthickness,whengrownat970°Canda3mm/minpullingrate,wasabout2mmandalmostconstant,exceptnearthefilmedge.Thefilmsurfacewassmooth,clearandmirror-polished.Thesideviewofthefilmsubstrateboundaryobservedbyopticalmicroscopywasverysharp.AnX-rayrockingcurvefromthe
(006)reflectionshowedclearlyseparatedfourpeaksofCuKalandCuKa2radiationfromthefilmandsubstrate(FukudaandHirano1976).
Fig.2.8GeometryforimprovedvariationsoftheCLEtechnique(a)andmultiple-layergrowthtechnique(b)(Fukudaand
Hirano1980).
Page81
Table2.1LiTaO3andLiNbO3thin-filmgrowthconditions(Fukuda,Hirano1976)
Film Substrate Solutiontemperature
(°C)
Pullingrate(mm/min)
Filmthickness(mm)
LiTaO3 LiNbO3 1026 2 2
LiNbO3 LiTaO3 995 1.8 0
LiNbO3 LiTaO3 975 2.3 3.5
LiNbO3 LiTaO3 970 3 3
LiNbO3 LiTaO3 965 2.3 4.5
Fig.2.9A(001)<100>LiTaO3substratewith20mmwideand0.75mmdeepgroovesetchedwithanionbeam,alongthe<100>direction(FukudaandHirano1980).
Theseresultssuggestthatthefilmsobtainedwereofhighquality.
Thethicknessofthefilmisafunctionofthesolutiontemperatureandpullingrate,ashasbeenreportedindetail(FukudaandHirano1976).Thelowerthesolutiontemperature,thethickerthefilmobtained.But
asthetemperaturebecamelower,manysmallhillocksappearedonthefilmsurfaceandslipboundariesweredetectedneartheedge.Rapidpullingproducedagradualdecreaseinthicknesswithinthecrystal,whileslowerpullingproducedagradualincreaseinthickness.
LiNbO3films,whichweregrownontothe(100)<210>,(131°rotatedYplate)<210>,and(170°rotatedYplate)<210>usingthesamegrowthconditionsasemployedonthe(001)<100>plates,wereofpoorqualityhavingroughsurfacesandmanydefects.Thefilmqualitywasremarkablyimprovedbyadjustingtheinitiatedtemperatureusingdiesofdifferentlengths.Itisassumedthattheappropriategrowthtemperaturewasachievedaftercarvingquicklythesolutionontothesubstrateusingcapillaryactionsothatthefilmdidnotsufferbadeffectsoflargesupercoolingbyloweringthesolutiontemperature.
Page82
Theimprovementwasobservedastheresultofchangingthedielength(l)(wherelmeansthepartofagap-shapedcapillary0.5mmwide)forgrowthonthe(170°rotatedYplate)<210>plate.
Figure2.10showstypicaletchpatternsforLiNbO3filmsgrownonplates(+Z)LiNbO3platesand(+Z)LiTaO3plate
crystals,respectively.Etchingwascarriedoutfor15minutesattheboilingpointoftheetchant(HF:HNO3=2:1).Forthecrystalsexamined,itwasobservedthatthefilmsurfacesidewasalways(-Z)planeoverthewholeplateirrespectiveofsubstrateorientation.ItissuggestedthatthefilmgrownbytheCLEtechniqueisofthesingledomaintype.Thismaybeattributedtothefactthatgrowthisinitiatedintheferroelectricphase.
Thelatticeconstantc0ofa filmona(001)<100>LiTaO3plate,whichwasgrownusingthemixtureofLiNbO3(10mol%),LiTaO3(10mol%)andV2O5(80mol%),wasmeasuredbyX-raydiffraction.Thevalueofcowas13.80Å,whichwasnearlythesameasthatofthebulk crystal(Swartzetal.1975).Thissuggeststhat oftheCLEgrownfilmfromthesesystemsapproachedunity,asisindicatedinEFGgrowth(FukudaandHirano1975).
LiTaO3thinfilmscouldbealsogrownwithgoodepitaxyontoLiNbO3substrates,whosemeltingpointwasabout400°Clowerthanthatofthefilm
Fig.2.10TypicaletchpatternsforaLiNbO3film(a)(-Z)LiNbO3plate(b)(+Z)
LiNbO3plateand(c)(-Z)LiTaO3plate,respectively(FukudaandHirano1980).
Page83
material.Thethicknessofthefilmsgrownat1026°Catapullingrateof2mm/min,wasabout2mm.ThefilmsurfaceandqualityobservedandmeasuredbyopticalmicroscopyandX-raydiffractionwerenearlythesameasthatofLiNbO3filmsonLiTaO3substrates.
Figure2.11showstheas-grownfilmsurfaceandsideviewofLiTaO3andLiNbO3multiple-layerstructurefilmson(001)<100>LiTaO3substrates.Thefilmsurfaceflatnessisalmostthesameasthatofthesinglelayerfilmsusedasasubstrate(seethedottedlineinFig.2.11).Thefilmareabout5mmthick.Inparticular,itischaracteristicthatthefilm-to-filmboundaryobservedbyapolarizedmicroscopeisverysharp.
LiNbO3filmsweregrownonto(001)<100>LiTaO3substratesinwhichstripedditches200or25mminwidthand0.75mmindepthalongthepullingdirectionhadbeenprepared(seeFig.2.9).Itshouldbenotedthatstripedditcheswerecompletelyburiedunderfilmsandthatthefilmsurfacewasalmostflat.
FromtheconsiderationoftheCLEcharacteristicsmentionedaboveitissuggestedthataburiedfilmorlayerstructurefilm,asdepictedinFig.2.12,canbegrownbycombiningtheCLEtechniquewithetchingandpolishing.Shapedfilmscanalsobegrownusingashapeddie.
UsingthedieasshowninFig.2.8,LiNbO3thinfilmsandLiNbO3thickfilmsweregrownon(001)<100>LiTaO3substrates.ThinfilmsgrownfromtheLiNbO3-LiVO3systemwereessentiallythesameasthosegrownusingthedieshowninFig.2.7.ThefilmgrownfromaLiNbO3meltwas200mmthick.(001)<100>LiNbO3onLiTaO3multipleribbonswerealsogrown.WhengrownfromtheLiNbO3melt,thesurfacewasnotsmoothandcontainedstriationsandripples,aswasseenintheEFGgrownribbon(FukudaandHirano1975).ThecompositionprofilesperpendiculartothefilmsubstrateboundaryweredeterminedusinganX-rayprobemicroanalyzer.Asshownin
Fig.2.13,thereisasharptransitionfromtheNb-totheTa-containinglayer.
CapillaryliquidepitaxywasusedtogrowferroelectricfilmsofLiNbO3(Khachaturyanetal.1984;FukudaandHirano1976;FukudaandHirano1980),Li(Nb,Ta)O3andLiTaO3(FukudaandHirano1976;FukudaandHirano1980),andKNbO3(KhachaturyanandMadoyan1980;KhachaturyanandMadoyan1984).Thecapillaryliquidepitaxymethodhasthefollowingadvantages:thepossibilityofobtainingfilmsfromahigh-temperaturematerialonsubstratesfrommaterialswithalowermeltingtemperature,asmoothfilmsurfaceandaclearlypronouncedfilmsubstrateboundary.
2.3Theliquid-phaseepitaxy(LPE)technique
Analysisofexperimentalstudiesofthegrowthofthin-filmferroelectricstructuresshowsthatthemostperfectepitaxiallayersofLiNbO3,Li(Nb,Ta)O3,KNbO3wereobtainedbytheliquid-phaseepitaxytechnique.Theopticallossesinlightpropagationthroughtheindicatedstructuresliewithintherange0.5-3dB/cm.
Thelowgrowthratetypicalofliquid-phaseepitaxymakesitpossibletocontrolthesizeofepitaxiallayerstoanaccuracymuchhigherthanthatattained
Page84
Fig.2.11As-grownfilmsurfaceflatnessandsideviewofaLiTaO3
andLiNbO3multiple-layerstructurefilmona(001)<100>LiTaO3substrate(FukudaandHirano1980).
indiffusionprocesses.
Kondoetal.(1975)appliedtheliquid-phaseepitaxymethodtogrowingLiNbO3films.Amixtureof50mol%Li2O,10mol%Nb2O5and40mol%V2O5waschosenasastartingcompositionforLPEgrowth.Thecompositionisequivalentto20mol%LiNbO3inthepseudobinarysystem.AfterweighingtheappropriateamountofLi2CO3,Nb2O5,andV2O5,themixturewasheatedat1200-1250°Cformorethan3hinaresistancefurnace.APtcrucible50mmindiameter,40mminheight,and1mminwallthicknesswasused.Thefurnacewasdividedintothreeheatingzones.Eachzonewascontrolledindependentlywithinanaccuracyof±0.5°C,sothattheverticaltemperaturedistributionwasalmostuniformupto200mmabovethecruciblebase.
Afterachievingcompletemelthomogeneity,themoltensolutionwascooledtoabout850°Catarateof30°C/h,andwasheldmorethan3hatthistemperature.
Ac-cutLiTaO3substrate,positionedslightlyabovethemoltensolutiontobeequilibratedwiththesolutiontemperature,wasdippedinthemoltensolution.Anappropriatedippingtemperaturewas825-850°C.Thesubstratewasthenremovedfromthemoltensolutionandslowlybroughttoroomtemperature.
Fig.2.12Aburiedfilmorlayeredstructurefilmareshown,
whichcanbegrownbycombiningtheCLEtechnique,etchingandpolishing(FukudaandHirano1980).
Page85
Fig.2.13CompositionprofilesdeterminedbyX-ray
probemicroanalyser(FukudaandHirano1980).
Thegrowthrateoftheepifilmwasexaminedbychangingthedippingtime,anditwasestimatedtobeapproximately0.1mm/min.Oneendofthesubstratewascutobliquelyinordertodraintheflux,andthefluxwasfoundtodrainfromthespecimenuponremovalfromthemoltensolution.Theresidueofthefluxadheringtotheas-grownspecimenwaswashedawaywithwater.
Theas-grownspecimenthusobtainedisshowninFig.2.14a.Thesurfaceappearsclearandsmooth,andthefilmseemstransparentandcolourless.Figure2.14bindicatesacross-sectionalprofileofthespecimennearthefilmsubstrateboundary.Thefilmthicknesswasmeasuredtobe~3.1mm,exceptneartheboundary.Protuberanceattheboundarymaybecausedby'wetting'ofthemoltensolutionontothesubstrate.
Theroughnessoftheas-grownsurfacedependsonthefilmthickness.Smallhillocks,whichappearonthesurface,aresurroundedbyfacetsofLiNbO3.Thehillocksonthegrowingsurfaceareadjacenttoaconstitutionalsupercooledsolution,andapreferentialgrowthofthehillocksoccurs.Asaresult,theymaybecomelargerandgrowfasterasthegrowthproceeds.Consequently,thefilmsurfacebecomesrougher.
Fig.2.14a)As-grownLiNbO3filmontheLiTaO3substrate.b)cross-sectionalprofilenearthefilmsubstrateedge.Film
thicknesswasabout3.1mm(Kondoetal.1975).
Page86
Fig.2.15X-rayrockingcurvetakenfor(006)reflection(Kondoetal.1975).
ThecrystallinityofthefilmwasinvestigatedbytakingX-rayrockingcurves.Figure2.15showsa(006)rockingcurve.Thefourpeaks,correspondingtoCuKa1andCuKa2radiationsfromthefilmandthesubstrate,arewellseparated.Thischaracteristicfeatureindicatesthatthefilmhasahighsinglecrystallinitywithgoodepitaxy.
Thefilmwasalsogrownontothey-platesubstrate.Thegrowthratewas3-5timesfasterthanontothec-plane.However,thefilmsurfacewasroughercomparedtothec-plane,andanX-rayrockingcurverevealedthatthefilmhadpoorepitaxywithmanymicrocracks.ThismaybecloselyrelatedtothelatticeparametermismatchbetweenLiNbO3andLiTaO3.Themismatchforthec-anda-axeswasabout0.7and0.1%,respectively.Theanisotropyofthelatticemismatchinthey-planeresultsinthenonuniformgrowthofthefilmcausedbymismatchdislocations.
Baudrantetal.(1978)hasalsousedLiTaO3substratesforliquid-phaseepitaxyoflithiumniobate.
LiTaO3waferswerepolishedtoahighdegreeofperfection,mounted
horizontallyonaplatinumsubstrate-holderandslowlyintroducedintotheverticalfurnaceforepitaxy.Asolutionobtainedfromatypicalchargeof27wt%Li2CO3-20wt%Nb205-53wt%V2O5hadasaturationtemperatureofabout950ºC.Growthtemperatureswerechosebetween940and945ºC.Undertheseconditions,thegrowthratewasabout0.5mm/min.
Inordertoobtainsmoothmonolayer-typeepitaxialfilmsratherthanisland-typefilms,severalcrystallographicorientationsofthesubstrateweretested.Symmetryconsiderationsandagoodfitbetweentheparameterssuggestedanattempttotryfirstepitaxialgrowthonthe(00.1)basalplanes.
SeveralLiNbO3filmswereisothermicallygrownfromundercooledsolutionsduringdifferentgrowthperiodsinordertofollowthesuccessivegrowthstepsofanepitaxiallayer.The[00.1]orientedfilmsbecomerapidlycontinuous
Page87
andfromthicknessofabout2mmareperfectlysmoothanddirectlyusableforlightpropagationexperiments.
Infact,theprofileofthetransitionlayercouldbedeterminedboyionicanalyserchemicalcontrol.Thisprofileshowstheexistenceofan~2000Åthicktransientlayer.Thiscanbeexplainedeitherbyaninterdiffusion ontheLiTaO3matrixor,moreprobably,byaslightdissolutionofthesubstratebeforegrowth.Thus,thefirstgrowinglayerswillhavecompositionofthetypeLiTaxNb1-xO3varyingrapidlyfrom1to0.
Fromanopticalpointofview,thisLPEfilmprofilecan,however,beconsideredasastepinterfacecomparedtothemeltphaseepitaxialfilmprofilewhichexhibitsagradedindex(Takadaetal.1974).Itshouldbenotedthattoofastacoolingrateafterepitaxyinvolvedcrackformationbothinthefilmandinthesubstrateparalleltothecleavageplanes(01.2).
Intheirearlierpaper,Baudrantetal.(1975)usedasubstrateoflithiumniobatecrystalswithorientation^c.Thepreparationandtechnologyofepitaxiallayerswereidenticalwiththosedescribedabove.
Themethodofliquid-phaseepitaxyfromalimitedvolumeofsolutioninamelthasbeenproposedrecentlybyMadoyanetal.(1983)andMadoyanetal.(1985).Crystallizationproceedsherefromalimitedvolumeofflux(solutioninmelt)containedinacapillaryformedbytwoparallelsubstrates.Whenthegapbetweenthesubstratesissmall,theliquid-phaseconvectionisabsentandthegrowingsurfaceisfedbydiffusionofthedissolvedcomponent.Thefilmthicknessdependsonthedistancebetweenthesubstrates(thecapillarywidth),epitaxytemperatureregime,materialandsubstrateorientation.Lowcoolingratesprovideprecipitationofthelayerontothesubstratesurfacewithoutcrystallizationintheflux.
Theliquid-phaseepitaxymethodiseconomicalowingtothepossibilityofusingthesolventmaterialrepeatedly.Thebasicshortcomingofthemethod,whenappliedtolithiumniobate,iscomplicatedcontrolofobtaininglayerswithprescribedparameters.Thetendencyofthesolutioninmelttosuper-cooling(to70-80ºC)hampersapreciselocationoftheliquiduscurve(theinitialepitaxytemperature).Chemicalactivityoftheliquidphaserestrictsstronglythechoiceofconstructionalmaterialforcruciblesandsubstrate-holders.
2.4Physico-chemicalbasisofcapillaryliquid-phaseepitaxy
Crystallizationfromabufferedmeltexhibitsfunctionsofboththesolutionandmeltmethods,whichaccountsforthewiderangeofcompositionsemployed,includingthemajorityofmeltingcompounds.Liquid-phaseepitaxyisdeterminedbythermodynamics,kineticsandtechnology(Andreevetal.1975).Thefirstofthesefactorsisresponsibleforthecharacterofphaseequilibriuminthesubstrate-bufferedmelt-vapoursystem.Thesefactorscompletelydeterminetheprocessunderequilibriumconditionsonly.Thekineticfactorshaveasubstantialeffectupontheepitaxyprocessundernonequilibriumconditions.Thegrowthkineticsaredeterminedbythefeedofthegrowingsurfaceandbytheactivationenergyoftheprocessatthephaseboundaries.Themethodicalfactorsincludethoseconnectedwithprocesstechnology.
Page88
Phaseequilibriuminthesubstrate-solutionsystemdeterminesthenatureofcrystallization.Asaturatedliquidphase(i.e.asaturatedsolutionofthecompoundundercrystallizationinameltofanothermaterial)isbroughtincontactwiththesubstrate,andundersubsequentsupersaturation(duetocoolingoradditionalfeedfromthesolidorgasphase)theepitaxiallayerprecipitatesontothesubstrate.Theliquid-phasecompositionandtheslopeoftheliquiduscurvedeterminethecomposition,growthrateandthicknessofthefilm.Inreality,theprocessproceedsinnonequilibriumconditionsforasimplereasonthatcrystallizationrequiressupersaturation,whichinitselfisadeviationfromequilibrium.Thisexplainswhythecrystallizationprocessandtheepitaxiallayerparametersarecharacterizedbyotherfactors,namely,byalimitedspeedatwhichcomponentsapproachthegrowingsurface(typically,inanon-mixingandisothermicsolution),bysupersaturationofthesolutionduringgrowth,bynucleationandthegrowthmechanismonthesurfaceandbyconvectionduetotemperatureandcompositiongradients.Inaddition,atanearlystageofanewheterostructurallayer,thatis,intheheterotransitionphase,therealwaysexistsathermodynamicinstabilitybetweenthesolutionandthecrystalsurface.
Thermodynamicinstabilitybetweenthecrystalsurfaceandtheliquidphasemustexistprovidedthesolidstatecomposition,wheninequilibriumwiththeliquidphase,differsfromthecompositionofthecrystalwhichisincontactwiththesolution(BolkhovityanovandChikichev1982).Furthermore,thecrystallizationprocessdependsontherelationbetweenthecrystallizationrateofagivensubstanceandthecoolingrateofthesolutionforadefinitestateofthesubstratesurface,ontheinitiallevelofsolutionsaturationandonotherfactors.Thefollowingversionsofthisrelationshiparepossible.Ifthecrystallizationrateexceedsappreciablythefeedrate,theactsofcrystallizationandsolutioncanalternateduetoinsignificantthermal
fluctuations.Thus,theepitaxyprocesswillhaveafluctuationalcharacter,whichcancauseadistortionofthecrystallizationfrontshape.Thiseffectisobservedatminimumratesofinducedcoolingofthesystem.
Underepitaxy,thesolutioninmeltisincontactwiththesubstrateontowhichthelayeriscrystallized.Theepitaxyprocessandthepropertiesoftheprecipitatedlayerarethereforealsodeterminedbythepropertiesofthesubstrate.Thesubstrateonlyhasadirecteffectuponthecrystallizationofthefirstlayer(withthethicknessofseverallatticeconstants),whentheepitaxyprocessisdeterminedbythecharacterofphaseequilibriumatthesubstrate-solutionboundaryandbythekineticsofsurfaceprocesses.Althoughthefurthergrowthproceedsontheepitaxiallayer,partofthesubstrateparametersaffectthecrystallizationduringthewholeprocess(e.g.thesubstrateorientation).Inthisconnection,inthechoiceofmaterialforasubstrate,alongwithphysicalparameters,suchastherefractiveindex,opticalcoefficients,etc.,thecrystallochemicalspecificitiesshouldbetakenintoaccount.Themostimportantconditionforobtainingperfectlayersisuniformityofthecrystallinestructureofthefilmandsubstratewithadifferencebetweenthelatticeconstantsnothigherthan1%.Thesubstratemustbechemicallyneutralwithrespecttotheliquidphaseanditssolubilityinthemeltinsignificant.Finally,substrate-filmpairsshouldbechosentohaveclosethermalcoefficientsofexpansionlesttemperature
Page89
variationsshouldinducestrongtensionsalongtheinterface.
Theclosevaluesofthefeedratesandcrystallizationpromoteconditionsofapproximateconstancyofthebufferedmeltsupersaturation.Thisprovidesahigheruniformityofcrystallizationlayers.Whenthesubstanceapproachesthecrystallizationfrontatarateexceedingthecrystallizationrate,thesupersaturationofthesolutioninthemeltgraduallyincreases.Undertheseconditions,thevariousactivecentreshaveanincreasingeffectuponthelayergrowth.Theroleofsuchcentresismostoftenplayedbydefectsofthesubstratesurfaceandatomsofimpuritiesinthesolution.Whentheinducedcoolingrateofthesystemdiffersonlyslightlyfromtheoptimumepitaxyconditions,thepredominantsubstancecrystallizationonthesecentrescanbeseenasaslightworseningofthestructuralperfectionofthelayers.Afastercoolingofthesystemleadstoastrongerpredominantroleofdefectsoftheorientingsurfaceinthecrystallizationprocess.Theextrememanifestationofthiseffectisthepolycrystallinelayergrowthwhichtakesplaceatconsiderableratesofinducedcoolingofthesystem.Thus,forthegrowthoflayerswithaperfectenoughstructureandmorphologyofthesurface,thesolution-substratesystemshouldbesocooledthatastrictlydefiniteandconstantamountofsubstanceisfedtothecrystallizationfrontperunittime.
Thebasicrequirementsonsolventsusedinliquid-phaseepitaxyareasfollows(Andreevetal.1975):
1.alowmeltingtemperatureofthesolventandalowvapourpressureattheepitaxytemperature;
2.ahighsolubilityofmaterialundercrystallization,whichmakesitpossibletoobtainepitaxiallayersatlowtemperatures;
3.stabilityofthesolidphaseofthedissolvingsubstanceundergrowth
conditions;
4.solventneutralitytothecruciblematerial;
5.alowsolventsolubilityinthecrystallizedlayer(thesolventcontaminatesthefilmlessifthefilmandsolventmaterialhaveidenticalions).
UnderLPEofferroelectrics,theconstituentliquidofthesolutionismostoftenoneofthebasiccomponentsofthesolidstate,andphaseequilibriumsaresuchthattheliquidsolutionfromwhichprecipitationoccursisdilutewithrespecttoallthecomponentsexceptone.
Forinstance,forgrowingferroelectricfilmsoflithiumniobatefromasolutioninmelt,thesolventshouldbenonvolatileandnonviscous,withawiderangeofsupercooling,andmustnotformcompoundsandsolidsolutionswiththedissolvedsubstance.Thethermalcoefficientofsolubilitymusthavevaluesoftheorderof0.1%g/gradinorderthatthesolutioninmeltcouldbecooledslowly.Toobtainfilmsofhighopticalqualityandstructuralperfection,itisnecessarytooptimizesimultaneouslyallthetechnologicalparameters,namely,supersaturationandviscosityofthesolution,saturationtemperature,etc.
Foranadequatechoiceofsolvent,thesolubilityoflithiumniobatewasinvestigatedinvariousinorganiclayers:PbO-PbF2,Li2O-MoO3,Li2O-V2O5(Kondoetal.1975;Baudrantetal.1975),Li2O-B2O3,Li2O-WO3(Kondoetal.1975;Ballmanetal.1975),LiF,LiCl(Kondoetal.1975),KCl(Baudrantetal.1975),K2WO4andWO3(KhachaturyanandMadoyan1978).Thepossibility
Page90
ofLiNbO3precipitationfrombufferedmeltsLi2O-V2O5,Li2O-B2O3andLi2O-WO3wasrevealed.Allthethreesystemsexhibitedprecipitationoflithiumniobatewithouttheformationofotherphasesinawiderangeofconcentrations.
Beforeanyliquid-phaseepitaxialtechniquewasappliedtofilmgrowth,severalsystemsofinterest,K2WO4-LiNbO3,KVO3-LiNbO3,NaVO3-LiNbO3andLi1-xNaxVO3-LiNbO3,wereinvestigated(Neurgaonkaretal.1980)andthetemperatureandcompositionalboundariesoverwhichLiNbO3crystallizeswereestablishedbythedifferentialthermalanalysistechnique.
ExaminationofthephasediagramsinFig.2.16showsthattheLiNbO3phasecrystallizesinallthethreesystemswhentheconcentrationofLiNbO3isabove50mol%and,hence,thedippingtemperaturehadtobeinthe1100to1150ºCrange.TheLPEgrowthoftheNb-richfilmswassuccessfulontheY-cutLiNbO3substratesfromtheK2WO4-LiNbO3andKVO3-LiNbO3systems,andtheunitcellavariedfrom5.148ÅforLiNbO3substrateto5.153ÅfortheNb-richLiNbO3films.Ballmanetal.(1975)alsostudiedtheK2WO4-LiNbO3system,andtheirresultswereinexcellentagreementwiththoseofNeurgaonkarandStaples(1981).AccordingtoNeurgaonkaretal.(1978),K+doesnotpreferthesixfoldcoordinatedLi+-siteintheLiNbO3structure;thechangesintheunitcellaarethereforeconsideredtobeduetochangesintheLi:Nbratio.
Inthethirdsystem,NaVO3-LiNbO3,thesituationiscompletelydifferent.Crystalchemistry(Neurgaonkaretal.1980)showsthatabout7mol%sodiumdissolvesintheLiNbO3structureand,forthisadditionofsodium,theunitcellachangedfrom5.148ÅforLiNbO3to5.179ÅforLi0.93Na0.07NbO3.This
Fig.2.16Partialphasediagram:a)K2WO4-LiNbO3;b)KVO3-LiNbO3;c)NaVO3-LiNbO3
(NeurgaonkarandStaples1981).
Page91
createdalargelatticemismatchbetweentheLiNbO3orLiTaO3substrateandthefilm,andtheLPEgrowthwasthereforeunsuccessful.
2.4.1ThephasediagramofLiVO3-LiNbO3
Theanalysisoftheresultspresentedaboveshowsthatobtainingfilmsismuchmoredifficultfromtheborateandtungstensystemsthanfromthevanadiumone.ThemostsuitablesolventforLiNbO3appearedtobethecompositionLi2O-V2O5whichsatisfiestheabove-mentionedrequirements.Theexcessivesolventiseasilyremovedfromtheepitaxialstructuresurfacebyboilingindistilledwater.
Tochooseoptimumgrowthconditionsandtostudythegrowthkinetics,exactdataarerequiredonthephasediagramofthesolvent-precipitatesystem.Sincethedataintheliteratureareverydiverse,itbecamenecessarytocarryoutsystematicphysico-chemicalstudiesofthepseudobinarysystemLiVO3-LiNbO3.
ThecharacteroftheinteractionbetweenLiNbO3andthefluxLi2O-V2O5waspreliminarilyinvestigated.Coolingthemeltedmixturewith10to100mol%LiNbO3atarateofabout1grad/minresultedintheformationofsmallcrystalswhichcouldbeeasilyseparatedfromtherestofthebufferedmeltbywashingindistilledwater.X-raydiffractionexaminationshowedthattheprecipitatedcrystalpowdercorrespondedtolithiumniobate.Itshouldbenotedthat,insomecases(LiNbO3concentrationfrom30to50mol%),thecrystalsizereached5mm.So,thepossibilityofLiNbO3crystalgrowthbythespontaneouscrystallizationmethodhasbeenshown.
Figure2.17ashowstheusefulpartofthepseudobinaryphasediagraminvestigatedbydifferentialthermalanalysis(DTA),directobservationsofthemeltandX-rayanalysis(Baudrantetal.1978).
Usingheatingandcoolingratesof10or5ºC/min,thermaleffectsdue
todissolutionandcrystallizationcanbedetected.Thus,theappearanceoftheLiNbO3solidphasefromvariousconcentratedsolutionsiseasilydetectableandisrepresentedbythedarkline2inFig.2.17awhichis,infact,thecriticalnucleationcurve.Endothermalphenomenaduetodissolutionarelessdiscernibleatalowsolutionconcentrationandmustoftenbecompletedbymicroscopicandweighingobservationsduringliquid-phaseepitaxyexperiments.ItisthuspossibletodrawthedottedlineinFig.2.17awhichrepresentstheliquiduscurve.
Theeutecticpointhasbeenlocalizedatabout4mol%ofLiNbO3byaccurateX-rayinvestigationsoftheprimarylargestcrystalsfoundinthebulksolid'residue'.TheprimarycrystalshavebeenidentifiedasLiVO3ononesideoftheeutecticpointandLiNbO3,ontheotherside.ThisdiagramshowsthatLiNbO3canbecrystallizedoverawidecompositionrange.Finally,Baudrantetal.(1978)pointoutthatthedomainoftheslowgrowthrateisverynarrow,extendingnomorethan10ºCundertheliquiduscurve.
TheliquiduscurvewascalculatedusingtheSchröderequation:
Page92
Fig.2.17a)PseudobinaryLiNbO3-LiVO3phasediagram,(1)-liquiduscurve.(2)-criticalnucleationcurve(Baudrantetal.1978);b)Dependence
ofthemolefractionlogarithmoninversetemperature(Madoyanetal.1979).
whereN1isthemolarfractionofthedissolvedcomponent.Thelineardependenceofthelogarithmofthemolarfractionontheinversetemperature(Fig.2.17b)suggestsanidealnatureofthesystemsolutions.ThemeltingheatofanindividualLiNbO3,determinedfromtheslopeangle,isequalto13.2kcal/mole.
Analysisofthephasediagramshowsthepossibilityofobtainingfilmsandcrystalsoflithiumniobatewithinawidetemperaturerangeof700to1200ºC.Withintherangeof750-950ºC(15-30mol%LiNbO3),theslopeoftheliquiduscurvepermitsaneasygrowthcontrolsinceaslighttemperaturevariationdoesnotentailavariationofthesolutioncomposition.Thegrowthrateofthelayercanbeestimatedfromthevariationofthesolutionconcentrationatagivencoolingrate.
2.4.2PhasediagramofLiVO3-Li(Nb,Ta)O3pseudobinarysystem
PhasediagramsoftheLiVO3-Li(Nb1-xTax)O3pseudobinarysystem,rangingfrom0to1,wereinvestigated,wherexisthemoleratioofTa2O5/(Ta2O5+Nb2O5)(Kondoetal.1979).Thetemperature-compositionrange,inwhichLi(Nb,Ta)O3solidsolutioncrystallizes,wasdeterminedbydifferentialthermalanalysis(DTA).Phase
diagramsforLi2O-Nb2O5,Li2O-V2O5andV2O5-Nb2O5pseudobinarysystemswerereportedonbyReismanandHolzberg(1965),ReismanandMineo(1962)andWaringandRoth(1965),respectively.
SamplesforDTAexperimentswerepreparedbymixingchemicalreagentgradeLiCO3,Nb2O5,Ta2O5andV2O5powderinthedesiredratios.Themixtureswereplacedinaplatinumcell.DTAmeasurementswereconductedinahigh-temperaturethermoanalyzerusinga-Al2O3asareference.Heating-coolingcycleswerecarriedoutatarateof20ºC/min,andwererepeatedseveraltimes.Heatingorcoolingratesbelow20ºC/minoftenresultedinaveryweakresponsecorrespondingtothermaleffectsduetodissolutionandcrystallization.ThetemperaturecorrectionofDTAmeasurementswasmadebyusingLiVO3(616ºC),NaCl(800ºC)andLiNbO3(1250ºC)asreferencesatthesameheating-coolingrate.Liquidustemperaturesweredeterminedfromtheheatingcurves,because
Page93
theheatingcurvesdidnotindicatesignificantoverheatingeffects,whilethecoolingcurvesoftenindicatedlargesupercoolingeffects.Furthermore,liquidustemperatureswerealsorecognizedbysaturationtemperatures.Thesaturationtemperatureisdeterminedasthetemperaturewhereneitherdissolutionnorcrystallizationoccurswhenasubstrateisdippedinthesolution.Theliquidustemperaturefromtheheatingcycleagreedwiththesaturationtemperaturewithin±10ºC.
TheresultsaregiveninFig.2.18,wheretheendmembersarestoichiometricLiVO3andspecificsolid-solutioncompositionsofthepseudobinarysystemLi(Nb1-xTax)O3,andliquidustemperaturesforseveralvaluesofxareshown.OnthephasediagramoftheLiVO3-LiNbO3pseudobinarysystem,x=0.0intheFig.2.18,theliquidustemperaturedecreasesfrom1250ºC,themeltingpointofLiNbO3to960ºCat20mol%LiNbO3.Apseudoeutecticoccursatabout3mol%LiNbO3.
Theliquiduslinesbecomehigherandtheirslopessteeperastheparameterxincreases.Figure2.18showsthattheprimaryphaseLi(Nb,Ta)O3cancrystallizeatpercentageshigherthan3mol%Li(Nb1-xTax)O3foreachxvalue.
Tamadaetal.(1991)reportedaLiNbO3thin-filmopticalwaveguidegrownbyliquidphaseepitaxy(LPE)usingLi2O-V2O5fluxanda5mol%MgO-dopedZ-plateLiNbO3substrate.Unfortunately,therewasalargeopticallossatblue-greenwavelengthsinspiteofitshighcrystallinityandgoodsurfacemorphology.Thisopticalabsorptionwhichcouldnotbecompletelyremovedbytheheattreatmentinaflowingoxygenwithlessthanafewvol.%ozoneafterfabrication,wasduetothe crystalfieldtransitionofV3+ionswhichwereincorporatedintotheLiNbO3filmfromtheLi2O-V2O5flux.Therefore,inordertorealizeaLi2O-V2O5thinfilmopticalwaveguideforbluewave-
Fig.2.18PhasediagramofLiVO3-Li(Nb1-xTax)O3pseudobinarysystem(Kondoetal.1979).
Page94
lengths,anotherfluxsystemwhichisfreefromtransitionmetalsmustbedeveloped.
Li2O-B2O5wastargetedasalikelycandidateforthisfluxsystemforseveralreasons.First,itdoesnotcontaintransitionmetals,sothatopticalabsorptioncentresmightnotbeintroducedevenifboronwereincorporatedintothefilm.Second,thereportedeutecticreactiontemperatureof800ºContheLiNbO3-LiBO2pseudobinarysystem(Ballmanetal.1975)issufficientlylowascomparedwiththeCurietemperatureofLiNbO3(1050-1200ºC).Moreover,MgO-dopedLiNbO3wasconsideredtobemoresuitableasasubstrateforobtainingaLiNbO3thinfilmwithhighcrystallinity,becausefilmpropertiesweredrasticallyimprovedwhenaMgO-dopedLiNbO3substratewasusedwithLi2O-V2O5flux(Tamadaetal.1991).
YamadaandTamada(1992)reportedLPEgrowthofLiNbO3thinfilmsona5mol%MgO-dopedZ-plateLiNbO3substrateusingLi2O-B2O3fluxandpresentedadetailedcharacterizationofthefilmproperties.
LPEgrowthwastriedfrommetalsofvariouscompositionsintheLiNbO3-LiBO2pseudobinarysystem.Meltcompositionsappropriateforobtainingfilmswithaperfectmirrorsurfacewerearound20mol%LiNbO3intheLiNbO3-LiBO2pseudobinarysystemwhichcorrespondstothepointof50mol%Li2O,10mol%Nb2O5and40mol%B2O3intheternarysystem.Thus,theLi2O/Nb2O5compositionwasalsovariedalongtheB2O340mol%fixedlineintheternarysystem.Thegrowthtemperaturewaschosentobeabout5ºClowerthanthesaturationtemperature,whichresultsinagrowthrateof1mm/min.Inthisway,aLiNbOsingle-crystalthinfilmwithasuitablethicknessforanopticalwaveguidecanbeobtainedbydippingthesubstrateintothemeltfor3-4min.
Thefilmcrystallinitywasinvestigatedbythex-raydoublecrystal
method.Afilmgrownfrom52mol%Li2O,8mol%Nb2O5and40mol%B2O3meltwasused.Thefullwidthathalf-maximumof11.4arcsecforapeakcorrespondingtothefilmiscomparableto10.2arcsecforthesubstratepeak,whichindicatesthatthisfilmhasextremelyhighcrystallinity.Thedifferenceofthediffractionanglebetweenthefilmandthesubstratewas249arcsec.Thelatticemismatchalongtheaaxis,Da,calculatedfromthisvalue,is41.4×10-5nm,whereYamadaandTamada(1992)definedthesubstratelatticeconstantminusthefilmlatticeconstant.ThevalueofDawassomewhatlargerthanthatoffilmsgrownfromLi2O-V2O5flux(3.7×10-5-40.3×10-5nm),whichsuggeststhatthisfilmhasacompositionricherinLi.Thereexistsanapproximately400nmthicktransientlayerformedbyMgdiffusionfromthesubstratetothefilm.However,ifthethicknessofapracticalopticalwaveguide(typically4-5mm)istakenintoaccount,itcanbesaidthattheprofileofthisLPEfilmisalmoststep-shaped.Thoughboroncouldnotbedetectedatallinthismeasurement,averysmallamountmightbeincluded.
Theferroelectricdomainstructurewasalsoinvestigatedusingaconventionaletchingmethod.Thecross-section,whichcorrespondstothe-Ysurfaceofthesubstrate,wasopticallypolishedandthenetchedina1HF+4HNO3solutionat90ºCfor1min.Polishedsurfaceswereexaminedusingadifferentialinterferencemicroscope.Thisshowedthatsingle-poledfilmsweregrownonboththe+Zand-Zsurfaceofthesubstrate.Butthedirectionofspontaneouspolarizationofthefilmgrownonthe-Zsurfaceisoppositetothatofthe
Page95
substrate,whereasfilmsgrownonthe+Zsurfaceweresingle-poledalongthesamedirectionasthesubstrate.Thesephenomenaformastrikingcontrasttothedomaininversionatthe+ZsurfacewhentheLi2O-V2O5fluxisused(TamadaandYamada,1991)andcanbeexplainedbyaninternalself-polingfieldproducedbythedifferenceofthespontaneouspolarizationbetweenafilmandasubstrate(Miyazawa,1979;PeuzinandMiyazawa,1986).Thatistosay,duetotheLi-richcompositionofthefilm,therelationshipofthespontaneouspolarizationofasubstrateandafilmatthegrowthtemperatureiscontrarytothatofthecaseusingLi2O-V2O5flux.
2.4.3Theschemeofthegrowthcell
FourbasicwaysoffilmcrystallizationfromafluxontoasubstrateareillustratedinFig.2.19onanexampleoftheLiVO3-LiNbO3system:
1.growthbyaslowsolutioncooling(thestraightlineA-B);
2.growthonasubstratelocatedinthecoldpartofthecrucibleatatemperatureTcold,theexcessivecrystallizingsubstancebeingincontactwiththesolventinahotterzoneatatemperatureThot.
Convectionanddiffusionthattakeplaceinthismethodcausemassexchangewhichallowsanexcessivedissolvedsubstanceprecipitateonthesubstrate.Inthefilmgrowthregion,theconditionsaredeterminedbythevalueoftheconstanttemperaturegradientandbythesubstrategrowthregime(thestraightlineC-E);
3.growthundertheconditionofsupersaturationduetosolventevaporation(thestraightlineA-D);
4.filmgrowthbymeansofspontaneouscrystallizationfromasupersaturatedsolutionataconstanttemperature.
Solutionsaturationisachievedbypreliminaryslowsaturationofthesolution.Themethodisbasedontheabilityofthesolutionofsome
compoundstoreachastableandstrongsupersaturationwithinawidetemperaturerangeandwithalowtemperaturegradient,whichpermitsrapidgrowthofepitaxial
Fig.2.19Phasediagramillustratingthemethods
ofgrowingsingle-crystalfilmsfromsolutioninmelt(onanexampleoftheLiVO3-LiNbO3
system).
Page96
filmsbyspontaneouscrystallizationfromasupersaturatedsolution.
TheadvantagesofLPEareclearlyseenonanexampleofobtainingalargeseriesofsemiconductorA3B5typecompounds.Togrowoxideferroelectricfilms,thismethodshouldbemodified.
Themostpromisingisthemethodofcapillaryliquid-phaseepitaxialgrowthofferroelectrics,proposedbyKhachaturyanandMadoyan(1985),whichprovidesimprovementofplanarityandthequalityoflayersurfacesgrownfromathinplane-parallelvolumeofameltandpermitssomecontroloverthegrowthparameters.Thismethodalsomakesitpossibletodefinewithahighaccuracytheparametersdeterminingthefilmthicknessandgrowthrate.CombinationofthewideoperationallatitudeofthecapillarytechniquewiththegeneralproceduralmeritsofLPEmakesitthemostpromisingmethodofobtainingintegro-opticalelements.
Inageneralcase,theliquid-phasecapillary(LPC)technique(PanishandSumski1971;Bolkhovityanov1977;MalininandNevski1978)suggestsfilmgrowthfromabufferedmeltlimitedtotwoparallelsubstrates.
Figure2.20givestheschemeofsubstratepositionsandthetemperatureregimefortheliquidcapillaryepitaxymethod.
Substratesaremoundedverticallyoveracruciblefilledwithaliquid,andatastartingepitaxytemperatureT0areimmersedinthebufferedmeltwhichispulledintothegapbetweenthesubstratesduetotheactionofcapillaryforces.Thewettedsubstratesarethenmoundedhorizontallyintheoperatingzoneofthereactionvessel,andthetemperatureinthecrystallizationcellstartstodecrease.Filmsgrowontheinnersurfacesofthesubstrates,asshowninFig.2.20.Aftertheepitaxialthin-filmstructureisformed,theliquidphaseissuckedofffromthecapillarygapbymeansofaliquid-phaseabsorber(Dudkin
andKhachaturyan1988).Theliquid-phaseabsorberwasmadeofmicrochannelslabsorkaolincotton.
Thetemperatureregimeoftheprocessisdeterminedbytheslopeoftheliquiduscurve.Forprecipitationofperfectlayersatahigh-temperaturecoefficientofsolubility,thecoolingrateshouldbeverylow.
Fig,2.20Temperatureregimeduringtheepitaxyprocess(left)
andtemperaturedistributionundercapillarytechnology(right)(KhachaturyanandMadoyan1984).
Page97
Animportantadvantageoftheliquid-phasecapillary(LPC)techniqueisaconstantthicknessoftheliquidzoneoverthewholesubstratesurface.Thismakesitpossibletoremovethewedgeshapeandobtainequallythicklayers.Themaximumgapisdeterminedbythefluxviscosityandbythewettingofthesubstratesurface.
TheLPCtechniquepermitseasycontrolofthegrowthrateandthelayercomposition:theprecipitationrateisdeterminedbysupersaturationnearthefront,whichdependsondiffusionandthetemperaturevariationrate.
2.5KineticsofepitaxialgrowthofLiNbO3
Masstransferplaysanimportantroleinthecrystalandfilmgrowth.Havingadirecteffectuponthethicknessandgrowthrate,theseprocessesdeterminethestructuralperfectionandpropertiesofthegrowncrystalsandfilms.Thestudyoftheregularitiesofprocessesintheliquidphaseandattheinterfacesuggestsoptimumversionsofcontrolovergrowthandobtainingepitaxiallayerswithprescribedproperties.
Themajorityofpapersdevotedtokineticsofepitaxialfilmgrowthfromabufferedmeltarebasedonthediffusionapproximationinwhichthefilmgrowthrateislimitedbythediffusionmasstransferofthedissolvedcomponenttothecrystallizationfront.
WehavealsoconsideredthegrowthkineticsofLiNbO3filmsinthediffusionapproximationandestablishedthedomainofitsapplicabilitywithinwhichtheinfluenceofconvectiveprocessesisinessential.Calculationshavebeencarriedoutwithallowanceforspecificitiesofagrowingsystemforthecapillaryversionofepitaxy,whichpermitsahighlyaccuratereproductionofthecalculatedconditionsofepitaxy(MadoyanandKhachaturyan1983).
2.5.1Thestationarycrystallizationmodel
Weshallconsideracrystallizationsystemintheformoftwoparallelsubstrateswithabufferedmeltbetweenthem.Thegapbetweenthesubstratesismuchlessthantheirsize,whichcorrespondstotherealconditionsandallowsustoproceedtoaone-dimensionalproblem.Thesystemisassumedtobeisothermalwithoutlocalsupercooling,andtheinitialconcentrationC0isthesamethroughouttheentirethicknessofthesolution.
Inrealsystems,phaseandchemicalequilibriumaredisplacedinorientedcrystallization.Thesolutionconcentrationdiffersfromtheequilibriumvalue,variesfromonecrystallographicfacetorientationtoanother,andisconnectedwiththepropertiesofthisfacet.So,inourmodeltheconcentrationnearthesubstratesurfacemustbehigherthantheequilibriumonebyacertainquantityUdependentonthematerialandsubstrateorientation.
Weshallexaminetheconcentrationvariationinacapillaryconsistinginthegeneralcaseofdifferentsubstrates(Fig.2.21).Coolingofthesystemleadstotheformationofaconcentrationprofileandtolayerprecipitationontothesubstrates.Atapointx=0,whichcorrespondstothemaximumsupersaturationofthesolution,theconcentrationgradientisequaltozeroand,therefore,theparticleflowsthroughtheplanex=0areequalonbothsides.Then,fortheliquid-phaseregiontrappedbetweentheplanex=0andthefirstsubstrate,
Page98
Fig.2.21Schematicofdistributionofconcentrationsinacapillarysystem:a)precipitationontodifferentsubstrates;b)precipitationonto
identicalsubstrates;c)concentrationvariationduringcrystallizationinthebulk;d)dependenceoftheeffectivethickness
oftheliquidphaseonthesizeoftheopeninginacapillary.
theconcentrationdistributionsatisfiesthediffusionequationwiththeboundaryconditions
whereC0istheinitialsolutionconcentration,C1(x,t)istheconcentrationofthecomponentbetweenthefirstsubstrateandtheplanex=0,mistheslopeoftheliquiduscurve,tistime,aisthecoolingrate,U1issupersaturationnearthesubstratesurface,(m=tanj)istheslopeangleoftheliquiduscurve.
Introductionofsupersaturationdoesnotalterthecharacterofdistributionbutonlyleadstoitsdisplacementintime(retardation)byu1m/a.Thesolutionofthediffusionequationgivestheexpressionforconcentrationvariation(Moon1974):
where ,Disthediffusioncoefficient.
Underquasistationaryconditions(for ),integratingtheexpression(2.2),weobtainthevalueofthemaximumrelativesupersaturationDCm1:
Page99
WesimilarlyobtainexpressionsfordC2/dxandDCm2intheregionbetweentheplanex=0andthesecondsubstrate.Theresultingsupersaturationinthesolutionisequaltothesumoftherelativesupersaturationandthesupersaturationatthesubstratesurface.Sincethetemperaturesofbothsubstratesarethesame,itfollowsthatintheabsenceofnucleationintheliquid-phasevolume,theremustholdthecondition
From(2.4)wecanreadilyderivetheexpressionfor and :
whereU21=U2-U1and isthegapbetweenthesubstrates.Thus,filmprecipitationontodifferentsubstratesinacapillarycomesfromtheliquidlayerwhosethicknessisdeterminedbytheexpressions(2.5)and(2.6).
Nowweshallconsiderprecipitationontosimilarsubstrates,whenU1=U2.IftheresultingsupersaturationexceedsthecriticalsupersaturationDCm0underwhichcrystallizationoccursinthebulk,precipitationintoeachsubstratecomesfromalayerthickness(Fig.2.21(b)).Supersaturationintheliquidphaseincreases,DCm+U,withincreasinggapsizeanddappearstobeequaltothecriticalvalue.From(2.3)itfollowsthat
Undersuchconditionsnucleationoccursinthemiddleofthecapillary,andanewcrystallizationfrontthereappears.Atthisfront,thesupersaturationUcanbeassumedequaltozerosincespontaneousnon-orientedcrystallizationproceeds.Inthecentreofthecapillarythe
concentrationbecomesequaltotheequilibriumoneatagiventemperature,andanewconcentrationdistributionoccurs(Fig.2.21c).Precipitationontothesubstratecomesfromthelayer
Afurtherincreaseofdleadstoanincreaseof uptothecriticalvalueatwhichintheregionbetweenthesubstrateandthemiddleofthegapacrystallizationfrontoccursagain.Figure2.21dshowsthethicknessvariationoftheliquid-phaselayerfromwhichincreasedprecipitationcomesontothesubstrate.Thus,intheabsenceofconvectiveflowsandaninducedmixtureofthe
Page100
solution,precipitationofthelayercomesfromalimitedvolumeoftheliquidphase.
2.5.2Epitaxyundernon-isothermicconditions
Animportanttaskoftheoreticalestimationsisfindingtheepitaxialfilmthicknesssincethisis,infact,theonlymeasurableparameterofthefilms.Typically,thethicknessisevaluatedfromtheamountofprecipitateusingthephasediagramanddisregardingmasstransfer.
Underthecondition (Fig.2.20),thelayerthicknesshisdefinedbytheexpression(Moon1974)
Ifwesubstituteheretheexpressionforconcentrationvariation(Madoyanetal.1988)
and ,whereCsisthedissolvedcomponentconcentrationinthesolidphaseandkisthesegregationcoefficient,thenreplacingtby
weobtain
Thewholecrystallizationprocesscanbedividedintotwostages:nonstationarywhichformstheconcentrationprofile,andstationaryunderwhichtheprofileremainsunchanged(ZhovnirandMaronchuk
1980).Theefficiencydeterminedastheexperimental-to-calculatedthicknessratioincreaseswithincreasingcoolingtimeorwithdecreasinggapsize.ToobtainLiNbO3filmswithathicknesscorrespondingtotheequilibriumone,wecanincreasethesoakingtimeataconstanttemperatureafterthecoolingprocessisover.TheconcentrationinthesolutionlevelsupandbecomesequaltoU+Ck,whereUissupersaturationatthecrystallizationfrontandCkisthesaturationconcentrationcorresponding,accordingtotheliquiduscurve,tothefinalepitaxytemperature.Intheformula
Page101
C1=U1+Ck,andinsteadofd/2wehaveusedthe valuefromEq.(2.5).
2.5.3DeterminationofsupersaturationUanddiffusioncoefficientD
LetacapillarywithagapdconsistoftwosimilarsubstrateswithacharacteristicsupersaturationU.
Theexpression(2.9)determinesthedependenceofthefilmthicknessonthefinalsolutionconcentration.Substitutingexperimentalfilmthicknessvalues,wecanfindthefinalconcentrationvalueCk+U.Thedifferencebetweenthevalueobtainedand isequaltothecharacteristicsupersaturation.
ForanexactdeterminationoftheUvalueitisnecessary,asmentionedabove,toproceedtosoakingaftercoolingisover.Asthesoakingtimeincreases,thethicknessincrementmustdecreaseduetoconcentrationlevelling.
Inanumberofpapers,diffusionwasinvestigatedonsingle-crystalsampleswithinclusionsofdropsfromthemotherliquor(Timofeeva1978).
Wehaveevaluatedthediffusioncoefficientonthebasisofexperimentallyestablishedfilmparameters.
Whenepitaxyproceedsontodifferentsubstrates,thefilmthicknessdependsonthepositionofthepointofmaximumsupersaturation.From(2.5)itfollowsthat
Thevalues and aredeterminedfrom(2.9)onthebasisofexperimentallymeasuredlayerthicknesses(substituting ford/2).
Inexaminingtherelationshipbetweenthegrowthparametersandthemasstransfercharacter,ithasbeenestablishedthat,inbufferedmeltsystems,thecontributionofconvectiveflowsisinsignificantifthegapbetweensubstratesissmallandincreasessharplywithincreasingd(LitvinandMaronchuk1977;Mil'vidskyetal.1980).Thefilmgrowthrateisreadilydeterminedfrom(2.8)or(2.9).Thelineardependencev=f(d)testifiestothefactthatundertheseconditionsmasstransferislimitedtomoleculardiffusion.Asdincreases,adeviationfromlinearityinthesolutionisobservedasaresultofnaturalconvectionduetogravitationandthedifferenceinthedensitiesofthedissolvedsubstanceandthesolvent.Inthesolution,crystallizationcentresmayoccurwhicharedistributedthroughouttheentireliquid-phasevolumebyconvectiveflows.
Inadditiontothevalueofthecriticalgapd*determiningthediffusionregion,animportantfactoristhestationarity .Thetimeofappearanceofaconstantconcentrationprofileforthegap isdefinedbythecondition .
Astheprocesstime increases,theprocessapproachesthestationaryone.
Page102
Fig.2.22Filmthicknessandgrowthrateasfunctionsofgrowthsystemparameters:a,d:
1)a=0.2grad/min,2)a=0.4grad/min,3)a=0.6grad/min.b:1)calculatedvalues,2)(0001)isorientationofLiTaO3,3)(1120)isorientation
ofLiTaO3.
TocalculatethethicknessandthegrowthrateofaLiNbO3film,weshouldknowthevaluesofthediffusioncoefficientofLiNbO3intheLi2O-V2O5meltandthecharacteristicsupersaturationUdependingonthematerialandsubstrateorientation.Theexperimentaldeterminationofthesevaluesonthebasisoftheconstructedmodelrequiresrealizationofthegrowthprocessesunderconditionsverycloselyapproachingthestationaryones.LiNbO3andLiTaO3platesofdifferentorientationswereusedassubstrates.Figure2.22presentsthedependenceoftheLiNbO3filmthicknessonthesizeofthegapdbetweenthesubstrates.Intheabsenceofconvectiveflowsthisdependencemustbelinear.Thegraphimpliesthatatacoolingratea=0.2grad/min,thecontributionofconvectivemasstransferis
insignificantuptothevalued=3ram.Fora=0.4grad/min,thevalued*decreases,whichisevidentlyduetoanincreaseoftemperaturegradientsinthebufferedmeltandtheassociateddensityinhomogeneitiesoftheliquidphaseinthecapillary.Fora=0.6grad/min,thefilmthicknessdoesnotaltersubstantiallyifa>2mm,whichisduetothebeginningofcrystallizationinthebulkmelt.Ford=3mm,thefilmthicknessdecreaseslessthanexpectedwithintheproposedmodel.Thiscanbecausedbyanincompletecoveringofthesurfaceofmaximumsupersaturationbybulknuclei.Inthiscase,theeffectivelayerthickness fromwhichprecipitationcomesontothefilmmustincrease,andthemeanconcentration
Page103
inthecentreofthecapillaryissomewhathigherthanequilibrium.Thus,theanalysisoftheresultsobtainedshowsthatatthecoolingratea=0.2grad/minandthegapsized<3mmlithiumniobateprecipitatesinaccordancewiththediffusiongrowthmechanismwithoutcrystallizationinthebulk.
Precipitationoftheentireexcessivesubstanceontosubstratesisalongprocess.Butwhensubstratesareheldforalongtimeincontactwiththeliquidphaseatthefinalepitaxytemperature,themassexchangebetweentheliquidphaseandthefilmsurfaceleadstofilmroughnessandthicknessinhomogeneity.Todeterminetheoptimumsoakingtimeq,thefilmthicknesswasinvestigatedasafunctionofthesoakingtimefordifferentcoolingratesofthesystem.Fora=0.2grad/min,precipitationstops10minutesafterthecoolingisover.
Furthersoakingleadstodivergencebetweenthefilmthicknessesontheupperandlowersubstrates,whichmustbeassociatedwiththedownwardgravitationalflowofpermanentlyoccurringanddecayingquasiparticlesand,therefore,withconcentrationnonuniformity.Fora=0.4grad/min,thethicknessreachesitsmaximumvaluewithin20minutesandthendoesnotchange.Within15-20rain,thethicknessreachesitsmaximumvaluealsoatacoolingrateofa=0.6grad/min.Inthiscase,furthersoakingleadstoadecreaseoffilmthickness,whichmustbeassociatedwiththeredistributionofthesubstancebetweenthefilmandsmallcrystalsintheliquidphase.
Underquasistationaryconditionswehaveestimatedthecharacteristicsupersaturationforz-andy-planesofLiTaO3.Weinvestigatedthedependenceofthefilmthicknessonthegapsizeforidenticalsubstrates.Theinitialepitaxytemperaturewas890ºC,thefinal860ºC,thecoolingratea=0.16grad/min.Thecoolingtimewasthreehoursandthesoakingtimeaftertheprocesswasoverwas15-20min.TheresultsobtainedarepresentedinFig.2.22a.ThestraightlineI
correspondstotheonecalculatedfromformula(2.9).Sinceprecipitationisassumedtoproceedbythediffusionmechanism,theexperimentaldependencesarelinear.Thefilmthicknessonthey-planeofLiTaO3issomewhathigherthanthatonthez-plane.Thelithiumniobateconcentrationnearthey-andz-substratesinthismodelexceedsequilibriumby0.24and0.39mol%,respectively.
Characteristicsupersaturationhasastronginfluenceonthethicknessandthegrowthrateofthefilmunderprecipitationinacapillarywhichconsistsofdifferentsubstrates.Theasymmetricprofileoftheconcentrationdistributionleadstothefactthatprecipitationontosubstratesproceedsfromsolutionlayersofdifferentthicknesses.Table2.2presentsthethicknessvaluesunderprecipitationontothey-andz-substratesofLiTaO3.Foraprecipitationrateof0.16grad/min,thethicknessesmaydifferbyafactorof3.Onthebasisoftheresultsobtained,wehaveestimated,usingformula(2.10),thediffusioncoefficientD=(1.5±0.7)×10-5cm2/s.ThecoefficientDdeterminesthediffusionofconcreteatoms(ions,molecules)inthemedium.Butintheframeworkofthemodelconstructed,theestimatedvaluecharacterizesconditionallythediffusionofmolecularlithiumniobateandsimplifiesappreciablythecalculationsoffilmparameters.Thepictureremainsthesameinthecaseofhyperepitaxy.Sincetheintroductionoflithiumtantalateintothebufferedmeltheightenstheliquidustemperatureofthesystem(Kondoetal.1979),theliquid-phasesupersaturation
Page104
Table2.2ParametersofthegrowthsystemandLiNbO3filmthicknessincapillarygrowthon(0001)and(1120)LiTaO3substrate(Khachaturyanetal.1984)
dmm
hpmm adeg/min
hxmm hzmmmm mm
D×105cm2/s
DD×105cm2/s
1.5 17.19 0.16 22.1±1.5 7.3±0.5 1.13 0.37 0.87 0.1
1.5 17.19 0.2 21.0±1.5 7.5±0.5 1.11 0.39 1.02 0.15
1.5 17.19 0.4 19.5±1.010.2±1.00.98 0.52 1.35 0.3
2 22.92 0.16 29.5±1.512.3±0.31.41 0.59 1.26 0.1
2 22.92 0.2 29.0±2.011.5±0.51.43 0.57 1.65 0.18
2 22.92 0.2 27.0±1.512.5±0.51.37 0.63 2.81 0.35
D0=(1.5±0.7)×10-5cm2/s
hampersdissolvingofthesubstrate,itscompositiondoesnotchangeandalayerofpurelithiumniobateprecipitates.Thesolidsolutionisformedinthenarrowtransitionregionattheexpenseofdiffusionthroughtheinterfaceinthesolidphase.
Figure2.22demonstratesthefilmthicknessasafunctionofcoolingrate.Fora<0.4grad/minthethicknessdoesnotpracticallychange,whilefora=0.5grad/minitfallssharplyowingtothefactthatthecriticalsupersaturationisreachedandcrystallizationproceedsinthebulk.Formula(2.3)implies
Substitutingthevaluedcr=2.5mm,a=0.5grad/min,D=1.5×10-5cm2/s,m=11.6grad/mole,vz=0.39,weobtainDCm0=1.89.Fromthiswecandeterminethecriticalvaluesofthegapsforvariouscoolingrates.
InthecapillarymethodofLPEforferroelectricfilmgrowthwithallowancefortheabove-mentionedrestrictions,crystallizationoutsidethesubstrateisabsentandallthedissolvedsubstanceinthegapprecipitatesontothesubstrateasafilm.Knowingthethicknessofthesolutionlayerandthegrowthtemperaturerange,wecancalculatetheexpectedfilmthicknessusingthestatediagram.
ForacomputercalculationofthefilmthicknessasafunctionofgrowthparametersintheframeworkofthecapillaryLPEmethod,thereexistsanalgorithm,andthefollowingmethodsofcalculationarerealizedasauniversalprogram(onanexampleofepitaxialfilmsoflithiumniobate(Madoyanetal.1982)).
ThecalculationsarebasedontheliquidustemperatureofthephasediagramofthepseudobinarysystemLiVO3-LiNbO3(Madoyanetal.1979).Theanalyticalexpression(2.9)describingthedependenceofthefilmthicknessthegrowthparametersisobtainedonthebasisofcalculatingtheamountoftheprecipitatingcrystallizingsubstanceforagivensystemsupercooling.
Page105
Forconvenienceofprogramming,thephasediagramoftheLiVO3-LiNbO3systeminthetemperaturerange800-870ºCwasapproximatedbytheexponentialfunction
whereaandbareconstants;cisthemolarconcentrationofLiNbO3.WehaveusedthestandardapproximationprogramfromthesoftwareofaNairi-2computer.
ThealgorithmsforcalculatingthefilmthicknessasafunctionofgrowthparameterswerepublishedindetailbyMadoyanetal.(1982).
Thus,weobtainthecompletesetofvaluesofLiNbO3filmthicknessasafunctionofvariableparameters.Figure2.23givesthegraphsofthedependenceofthefilmthicknessontheparametersoftheepitaxyprocess.
Fig.2.23LiNbO3filmthicknessversusgrowthconditions:a)startingtemperature,b)overcoolingofthesystem,c)weightofthe
solutionmelt.Pointsareexperimentalvalues.
Thesedependencespermitsaratheraccuratepredictionoffilmthicknessunderconcretegrowthconditions.PointsinFig.2.23indicatethefilmthicknessvaluesobtainedunderexperimentally
chosenoptimumepitaxyconditions.Thedifferenceof5-10%canbeexplainedbyadditionalprecipitationfromthemeltofthesubstanceremainingonthefilmsurfaceaftertheepitaxyisover.
Thesatisfactoryagreementbetweentheexperimentalandtheoreticaldatasuggestsawiderangeofapplicabilityofprogrammingcalculationoftheepitaxialfilmwidth.
2.5.4Epitaxyunderisothermalconditions
Asdistinguishedfromthenonisothermalcaseforwhichthediffusionprocessesdeterminedbythesystemcoolingratearelimiting,inisothermalepitaxytherateofthediffusionprocessesvarieswithfilmgrowth,andthequestionofarelativecontributionofdiffusionandsurfaceprocessestothegrowthkineticsremainsopen.Inviewofthis,wehaveconsideredthegeneralcasewithallowance
Page106
forthekineticcoefficient.Isothermalepitaxyisinvestigatedunderconditionsofaquasistationaryprocesswhichtakesplaceintheindicatedsystems( ).
Asinthenonisothermalcase,crystallizationproceedsfromalimitedvolumeconsistingoftwoidenticalparallelsubstratesmountedatadistanced(Fig.2.24a).Thequantitativedeterminationofthetimedependenceoffilmthicknessatagiveninitialsupersaturationconsistsofsolvingthedifferentialequationdescribingthediffusionofadissolvedcrystallizingmaterialinsideacapillarywithcorrespondinginitialandboundaryconditions
whereyisadimensionlessdistance(intheunitsd/2)countedfromthegrowthfront.Therangeofyvariationisduetothesymmetryaboutthecapillarycentre.Theinitialandboundaryconditionsoftheproblemhavetheform
1.Fort=0C(y,0)=C0;
2.Inthecapillarycentre ;
3.Atthegrowthfrontsthereholdsthemassconservationconditionofthecrystallizingmaterial:
where
Hereqisthekineticcoefficient.TheboundaryconditionsdisregardUsinceinrealsystems .
UnderLPEconditions,theinitialsupersaturationDC0=C0-C1issosmallthatthemaximum(final)filmthicknessisnoticeablylessthanthecapillaryhalfwidth.
Solvingequation(2.12)bythemethodofseparationofvariables,weobtainthetimedependenceofthefilmthicknessh:
Page107
wheret=d2/4Disthediffusiontime,v0=v(t=0)
vnaretherootsoftheequationandjv=tanv.
Thefirstsummandin(2.13)isfinalfilmthicknessh0whichisindependentoft.
For and wecanretainonetermintheseries(2.13)
admittingherearelativeerror
Itshouldbenotedthatfort=ttheconcentrationprofilevariationduetodiffusionreachesthepointd/2(Fig.2.24a).For thefilmincreasesinthesamemannerasinaninfinitecapillary,andthedependence isdeterminedbythesolutionofequation(2.12)withtheboundaryconditions
leadingtothefollowingtimedependenceofsupersaturationatthegrowthfront
whereFistheprobabilityintegral.Itshouldbenotedthatforthereholdsakineticgrowthregime,thatis,thefilmgrowthrateisonlydeterminedbythekineticcoefficientandinitialsupersaturation
Theexpression(2.14)obtainedabove,whichholdsforj>1, ,describesthediffusionregimeinwhichthegrowthrateisdeterminedbythediffusion
Page108
Fig.2.24Concentrationdistribution(a)andfilmthicknesshasafunctionoftime(b).
coefficientandthecapillarywidthanddependsweaklyonq.
ToestablishthecharacterofLiNbO3crystallizationfromthebufferedLiVO3-LiNbO3melt,thetimedependencesofthefilmthicknessweremeasuredforvariousDC1anddvalues.
TheresultsofthesemeasurementsarepresentedinFig.2.24b.Thefinalthicknessh0isequaltothemaximumfilmthicknessvalueobtainedunderanincreasedsoakingtime.Measurementswerecarriedoutforh>4mmsinceforlowerhtheerroriscomparablewiththefilmthickness.Thelinearcharacterofthedependenceh(t)inlogarithmiccoordinatesisanevidenceofpredominanceofthediffusiongrowthregimeforh>4mm,thatis,practicallythewholeofthefilmisgrowinginthediffusionregime.Theresultsofexperimentssuggestestimatesofthequantitiesentering(2.14)andshowtheerrortowhichthisformulaholds.So,forcurve1(Fig.2.24b)
whichcorrespondstothekineticcoefficient
Thebestcoincidenceof(2.14)withexperimentalresultstakesplace
forD=0.5×10cm/s,whichagreesintheorderofmagnitudewithwhatwehaveobtained.Toevaluatetheerroroccurringintheuseofformula(2.18),weshallemploy(2.15),assuming
Page109
Fort/t>p-1,weobtainDh/h0<10-1,whichiswithintheexperimentalerrorforh.Thus,inthegrowthsystemunderconsiderationwedealwiththekineticregimeat sandwiththediffusionregimeat
s.
Theseestimatesconfirmtheconclusionthatthediffusionregimeisprevailingforfilmgrowth.
2.6CrystallizationoffilmsfromLiNbl-yTayO3solidsolutions
Obtainingepitaxialfilmswithagivencompositionisoneoftheimportantproblemsofappliedphysicssinceinsignificantcompositionvariationsmayhaveaconsiderableeffectuponthephysicalpropertiesofgrownstructures.Itisverydifficulttomaintainaconstantcompositionwhenlayersofmulticomponentdielectricmaterialsareprecipitatedfromabufferedmelt,whenintroductionofeachcomponentisspecifiedbyanindividualsegregationcoefficient,dependsonthegrowthconditionsandvarieswithlocalfluctuationsofgrowthparameters(Timofeeva1978).
Toobtainfilmswithaprescribedcomposition,itisnecessarytoestablisharelationshipbetweenthecompositionandacomplexoffactorswhichdeterminetheenteringofcomponentsinthegrowinglayer.InLPE,thesefactorsareindividualcoefficientsofsegregationandthegrowthparameters,namely,thecompositionandthicknessoftheliquidphase,theinitialtemperature,thecoolingrateofthesystem,etc.
LithiumniobateandtantalateformLiNb1-yTayO3solidsolutionsintheentirerangeofthecompositions0<y<1(seeFig.2.4)(MadoyanandKhachaturyan1985).
Aspecificfeatureofcrystallizationoffilmsofsolidsolutionsisthenecessitytotakeintoaccounttheinfluenceoftheamountof
precipitatingcomponentsontheepitaxytemperature,composition,uniformityofcomponentdistributionandfilmthickness(Madoyanetal.1985).
Inprecipitationfromahigh-temperaturemeltofmulticomponentsystems,thecompositionoftheprecipitatinglayerdifferstypicallyfromthecompositionofthedissolvedmaterialsinceenteringofeachcomponentintothelayerisdeterminedbyanindividualsegregationcoefficient.Inepitaxyoflithiumniobate-tantalatefromthesolutionintheLi2O-V2O5melt,thecompositionoftheLiNb1-yTayO3filmisshiftedrelativetothecompositionofthedissolvedmaterialLiNb1-xTaxO3towardsincreasingtantalum,thatis,y>x.AnalysisoffilmcompositionsrevealedashiftofthecompositionoftheLiNb1-yTayO3layerrelativetotheliquidphasetowardsanincreasingmolarfractionoftantalate(y>x).Numericalestimatesgiveavariationoftherelationbetweenniobiumandtantalumbynomorethan3%duringprecipitationofalayerabout10mmthick.Thecorrespondingliquidustemperaturedisplacementdoesnotexceed±5ºwhenthegrowthcelliscooledbyabout40º.Thus,theequilibriumtemperaturevariationsduringgrowthcanbedisregarded,buttheerrorinpredictingthefilmthicknessincreasesupto20%.
Intheliterature,thevariationoftheeffectivecoefficientofsegregationiscustomarilyassociatedwithmasstransferprocessesintheliquidphase,thatis,withdiffusion,convection,electromigration,etc.(Madoyanetal.1985;Milvidsky1986).
Page110
Fig.2.25Theeffectivesegregationcoefficientoftantalumversusthegrowthrateofa
Li(Nb,Ta)O3film.
Figure2.25illustratesthedependencesoftheeffectivesegregationcoefficient,definedastherelationk=y/x,onthegrowthratewhenthemolarfractionoftantalumintheliquidphaseisx=0.2and0.4.Thesegregationcoefficientassumesthevaluesfrom1.4to2.35(x=0.4)andfrom1.5to2.75(x=0.2)asthegrowthratevariesfrom0.4to0.1mm/min.Makinguseofthisdependence,wecancontrolthefilmcompositionduringgrowthandobtainLiNb1-yTayO3filmswithyrangingfrom0.2to1.
WhenaLi(Nb,Ta)O3filmgrowsfromasaturatedsolutioninthediffusionepitaxyregime,thegrowthrateisv~ad,whereaisthecoolingratesincethefilmthickness (Avakyanetal.1986).Thus,thechangeinthecoolingrateofthesystemduringgrowthleadstoavariationofthegrowthrateandmodulationincompositionoftheprecipitatinglayerinlinewiththedependencek(v)(Khachaturyanetal.1986).IftheinitialepitaxytemperatureisbelowthephaseequilibriumtemperatureT1,theprecipitationrate,whichismaximumattheinitialmoment,willdecreasetillanequilibriumconcentrationisestablished,andthelayercompositionwillchangeinasimilarway.AtT0>T1,thefilmdoesnotprecipitateandthesubstratesurfaceisslightlydissolvedwhichcausesanuncontrolledvariationoftheliquid-phasecomposition.Consequently,foranefficientcomposition
control,itisnecessarytostarttheprecipitationprocessatatemperatureequilibriumforagivenconcentration.
Independenceofthesegregationcoefficientofmasstransferintheliquidphaseprovidesanefficientlayercompositioncontrolduringgrowth.Figure2.26presentsthegraphsofaprogrammedtemperaturedecrease(1)andthecorrespondingthicknessdistributionofstructurecomponentsobtainedbymicro-X-rayspectralanalysis(2).Foraconstantcoolingrateandequilibriuminitialtemperature(a)thegrowthrateisconstantandthecompositionremainsunchangedthroughouttheentirelayerthickness.Figure2.26(b,c)presentsthegraphsofthecoolingrateatwhichfilmsgrowwithastep-likeandperiodicdistributionofcomponents,whichplaysanimportantappliedrole,forinstance,formaintainingamultiple-modecontrollingintegro-opticwaveguide.
AnimportantfactorofstructuralperfectionofLi(Nb,Ta)O3filmsisalowcontentofvanadiumimpurity.Analysishasshownthattheconcentrationofahomogeneousvanadiumimpuritydoesnotexceed0.1atom%.ApredominantamountofniobiumisexplainedbytheequalityofionicradiiofNb5+andTa5+(0.66Å)asdistinctfromtheionicradiusofV5+(0.4Å).Foranoptimumrangeofgrowthrates,inwhichthecompositionwasmodulatedrelative
Page111
toniobiumandtantalum(0.1-0.5mm/min)thevanadiumconcentrationdidnotexceed0.1mol%,andwithafurtherincreaseofthegrowthrateaninhomogeneouscaptureofthebufferedmeltwasobserved.Consequently,variationofgrowthconditionswithinthelimitssufficientforobtainingfilmsofdifferentcompositionwithrespecttoniobiumandtantaluminducesnosubstantialheighteningofthecontentofvanadiumimpurity.
2.6.1Liquid-PhaseepitaxialgrowthofLi(Nb,Ta)O3films
Inthissection,theliquid-phaseepitaxialgrowthofLi(Nb,Ta)O3solid-solutionfilmsonLiTaO3y-platesubstratesisdescribedonthebasisofthephasediagramsobtainedbyKondoetal.(1979).
Theverticaldippingtechniquewasusedfortheexperiment.Athree-zoneresistanceheatingfurnacewasused,toobtainanoptimumverticaltemperaturedistribution.Thetemperaturedifferencebetweenthemeltsurfaceandthebottomofthecruciblewaswithin1°C.Thestartingmaterialwasputinsideaplatinumcrucible.Athermocouple(Pt-Pt/Rh13%)wasattachedexternallytothecrucible.
Thesolutioncompositionwasfixedat50mol%Li2O,5mol%(Nb1-xTax)O5and45mol%V2O5,andthesolutioncompositionparameterxdefinedasTa2O5/(Ta2O5+Nb2O5)inthesolutionwasvariedfrom0.0to1.0.ThiscompositioncorrespondstothepointA,indicatedbythearrowinFig.2.18.
Approximately1mmthicky-platesubstrateswerecutfromaLiTaO3singlecrystal,andtheirsurfacesweremechano-chemicallypolished.
AtypicaltemperatureprogramforLPEgrowthisshowninFig.2.27.ThesolutioninthePt-cruciblewasheatedto1300°Candwasheldatthistem-
Fig.2.26ProgrammedtemperaturedecreaseinLPEgrownLi(Nb,Ta)O3(I)
andthecorrespondingNbandTadistributionthroughthethicknessofLi(Nb,Ta)O3/LiTaO3hyperstructure(II)
(Khachaturyanetal.1987).
Page112
Fig.2.27TypicaltemperatureprogrammeforLPEgrowth.Tsshowsthesaturationtemperatureofthesolution
(Kondoetal.1979).
Fig.2.28(right)Epilayerthicknessasafunction
ofgrowthtimeandseveralgrowthtemperatures.Thexofsolutioncompositionwas0.8
(Kondoetal.1979).
peraturefor2-4daystomakeithomogeneous.Thenthetemperaturewasloweredtoagrowthtemperatureatwhichthesolutionwassaturated.Priortodipping,thesubstratewasthermallyequilibratedjustabovethesolutiontobringittothesolutiontemperature.Thenthesubstratewasinsertedintothesolution.Afterfilmgrowth,thesubstratewaswithdrawnatarateof1cm/minfromthesolutionandslowlycooledtoroomtemperature.Thesubstrateswerenotrotatedduringthefilmgrowth.ThefluxadheredtothesamplecouldbeeasilydissolvedbydiluteHClsolution.
Aseriesofgrowthrunswerecarriedout,withgrowthtimeandthegrowthtemperaturesasparameters,todeterminetheireffectsonthegrowthrate.Figure2.28showsarelationshipbetweenfilmthicknessandgrowthtime.Thesolutioncompositionparameterxwasfixedat0.8,andthegrowthtemperatureswere1120,1125and1130°C.Itcanbeseenthatthefilmthicknessincreasesapproximatelylinearlywithtimeuptoabout30miningrowthtime.Thefilmsweregrownat1120°Candthegrowthrateofthesefilmswasestimatedtobe1mm/min.
Thefilmthicknessbelow10mmyieldedsmoothsurface.After12mmgrowth,ripplesappearedonthesurface.At50mmgrowththeripplesdevelopedintoaseriesofsharpridgesknownasfilmfacetingandthefluxwastrappedbetweentheridges.Itcanbesaidthatafilmthicknessoflessthanapproximately10mmisadequateforobtainingasmoothas-grownsurface.
Figure2.29showsthegrowthrateasafunctionofgrowthtemperaturefordifferentsolutioncompositions.Thesolutioncompositionparameterxwas0.5,0.7,0.8,0.9and1.0.Saturationtemperaturesforthesecompositionswereestimatedtobeapproximately1020,1095,1135,1165and1190°C,respectively,aswereindicatedinFig.2.29.Thegrowthtimewasfixedat15minineachcase.Thegrowthratesweredirectlyproportionaltothesupercoolingrangingfrom0toabout30°C,overwhichthegrowthratedepartedfromlinearrelationship.Thiscanbeexplainedintermsofboththecurvatureoftheliquidusslopeinthe
Page113
Fig.2.29Growthrateasafunctionofgrowthtemperatureandsolutioncomposition.
Growthtimewasfixedat15min(Kondoetal.1979).
LiVO3-Li(Nb1-xTax)O3systemandthespontaneousnucleationofLi(Nb,Ta)O3whichoccurredpriortoorduringthegrowthatlargesupercooling(Daviesetal.1974).Therefore,themagnitudeofsupercoolingwaschosentobelessthan30°C.
ElectronprobemicroanalysiswasusedtomonitorNb,TaandVconcentrationsinthefilmandthesubstrate.Thesolutioncompositionparameterxofthisfilmwas0.8andthefilmthicknesswasabout30mm.TheTaconcentrationisconstantnotonlyinthesubstratebutalsointhefilmanditvariesdiscontinuouslyattheboundarybetweenthefilmandthesubstrate.TheratioofTaconcentrationinthefilmtothatinthesubstrateisabout0.96.TheNbwasdetectedonlyinthefilmanditsconcentrationisconstantinthefilm.TheconcentrationofVions,whichisafluxelement,islessthan0.2mol%inthefilm.
TherealfilmcompositionwasdefinedasLi(Nb1-yTay)O3,whereyisthemoleratioofTa/(Ta+Nb)inthefilm,andtheresultsaregiveninTable2.3.ItisnotedthatthefilmcontainsahigherTaconcentrationthanthestartingsolution.
2.7ThinfilmsofLinbO3dopedwithdifferentelements
Neurgaonkaretal.(1979)reportedtheLPEgrowthofNa+andCo2++Zr4+dopedLiNbO3filmsfromLi2O-V2O5flux.
Table2.3Thecompositionalrelationshipthesolutionandthegrowthfilm;thesolutioncompositionwasgivenasLi2O:(Nb1-xTax)O5:V2O5=50:5:45inmol%,andthefilmcompositionLi(Nb1-yTay)O3(Kendon,Sugii,Miyasawa,Uehara,1979)
Solutionx Filmy
0.5 0.78
0.7 0.93
0.8 0.96
0.9 0.98
1 1
Page114
BeforegrowinganyepilayersofLi1-xNaxNbO3andLi1-xCoxNb1-xZrxO3components,thecrystallinesolubilityoftheseionswasfirstestimatedintheLiNbO3phase.Thesubstitutionsweremadeasfollows:
Alltheceramicphaseswerepreparedbysolid-statereactions(1000-1200°C)andwerecheckedbyX-raypowderdiffractiontechniquesinordertoestablishthesolidsolubilityrangeofLiNbO3structure.NaNbO3hasapseudo-monoclinicunitcell(Wood1951)atroomtemperatureandbelongstotheperovskitestructuralfamily.AccordingtoLeComteetal.(1974),amaximumof7mol%Na+canbesubstitutedforLi+intheLiNbO3phase.AlthoughCoZrO3doesnotformacompound,itdissolvestoagreaterextentintheLiNbO3structure.About22mol%CoZrO3canbeaccommodatedintheLiNbO3phasewithoutalteringitscrystalsymmetry.ThesubstitutionofNa+forLi+,andCo2+andZr4+forLiandNb,respectively,intheLiNbO3phaseloweredtheferroelectrictransitiontemperature.
TheLi2O-V2O5fluxwasusedforLPEgrowthwork,andmixturescontaining80mol%LiVO3and20mol%Li1-xNaxNbO3andLi1-xCOxNb1-xZrxO3,where0.04<x<0.15,wereprepared.Here,x=0.15(i.e.NaorCo=Zr)inbothoftheabovecompositionscorrespondstoabout3mol%ofthetotalofthemixtures.SincethephasediagramforthepseudobinaryLiVO3-LiNbO3systemisknown(seeFig.2.17),itwasrelativelyeasytoestablishtheliquidustemperaturefortheNa+andCo2++Zr4+containingphasesbytheDTAtechnique.Themeasurementsshowednosignificantchangesinthemeltingtemperaturesforeitherofthesystems.TheappropriateamountsofLi2CO3,V2O5,Nb2O5andNa2CO3orCoCO3+ZrO2werethoroughlymixed,heatedto600°Candthenmeltedina100ccplatinumcrucible.Averticalplatinum-woundresistancefurnacewas
used,andthegrowthtemperaturewascontrolledwithinanaccuracyof±1°C.Themixturewasheatedto1150-1200°Covernight,afterachievingcompletemelthomogeneity,themoltensolutionwascooledtoabout860°Cattherateof30°C/h.
Any-orz-cutLiNbO3substrate,positionedslightlyabovethemelttoequilibratewiththesolutiontemperature,wasdippedintothemelt.Anappropriatedippingtemperaturewas860-890°Cforboththesystems.Aftertherequiredtimeforgrowthhadelapsed,thesamplewaswithdrawnandcooledveryslowlytoroomtemperature.Thegrowthrateoftheepifilms,whichwasexaminedbychangingthedippingtime,wasestimatedtobeapproximately1.0mm/min.Theresidueofthefluxadheringtothefilmswaswashedawaywitheitherwaterordiluteacids.
ThesurfaceforboththeNa+andCo2++Zr4+-containingfilmswassmoothandclear.Microscopicobservationsathighmagnificationsshowedaslightlyrougheraspectinthecaseofthickerfilms.Co2++Zr4+-dopedfilmswerebluishtintincolour,indicatingtheinclusionoftheseionsinthefilms.Epitaxialfilmsasthickas30-35mmcouldbegrownbythistechnique.
Thecrystallinityandthelatticeconstantawerestudiedforthesubstrateand
Page115
Fig.2.30X-raydiffractionpeak(300)takenforthefilm/substrate(Neurgaonkaretal.1979).
thefilmsbytheX-raydiffractiontechnique.They-cutLiNbO3substrateshowedareflectioncorrespondingto(300).Figures2.30(a)-(d)showtherelativeintensityof(300)asafunctionoffilmthickness.ThepeakscorrespondingtoCuKa1andCuKa2representtheLiNbO3substrate,whilethefilmpeakpositionshavebeendenotedby
and .Ascanbeseenfromthisfigure,therelativeintensityofCuKa1andCuKa2graduallydecreasedwithincreasingfilmthicknessandfinallydisappearedcompletelywhenthefilmthicknesswasmorethan10mm.Thepeaksfromthesubstrateandfilmsarewellseparatedandreproducibleundersimilarexperimentalconditions.Thischaracteristicfeatureindicatedthatfilmshaveahighsinglecrystallinitywithgoodepitaxy.
Thelatticeconstantawasestablishedforthesubstrateandfilms.Althoughthelatticeconstantdifferenceforthesubstrateandfilmswaslessthan0.1%,itwaspossibletoidentifythesedifferencesbytheX-raydiffractiontechnique.ThedatashowedthatthefilmsgrownfromtheLi2O-V2O5fluxhavethelatticeconstantasmallerthanthatusuallyobservedinthebulkcrystalsofLiNbO3.Thecrystallinesolid
solubilityofNa+andCo2++Zr4+inthephasehasbeenshowntobeapproximately7and22mol%,respectively.However,itwasfounddifficulttoraisetheirconcentrationinthefilmsusingtheLi2O-V2O5flux.BasedontheseobservationsandtheresultsreportedbyBaudrantetal.(1975)onthesubstitutionofAg+,Cu+,Fe3+,andCr3+intheLiNbO3films,itwouldappearthattheconcentrationoftheseionsisverylow,~1mol%orless.
Table2.4summarizesthecompositionofameltforAgsubstitutedfilms,andtheresultscorrespondingtodifferentgrowthconditionsonthec-axisLiNbO3substrates.Theopticalmeasurementswereperformedbyusinga1.15-mmlaserbeam.IndexvariationsinfilmscontainingCu,CrandFe,weretoosmalltobemeasuredwithaccuracy.InAgsubstitutedfilmsarefractiveindexof2.2361wasfound;withanaccountofthefactthatthesubstrateindexwas2.2300,thisvariation,Dn=6×10-3,allowedthelightpropagation,forinstance,tohave
Page116
Table2.4ThecompositionofmeltforAgsubstitutedfilmsandresultscorrespondingtodifferentgrowthconditionsoncaxisLiNbO3substrates(Baudrant,Vial,Daval,1975)
Meltcomposition(molespercent)Nb2O5.9.8,Ag2O:2,Li2CO3:49,V2O5:39.2
Epitaxialgrowth
Temperature(°C)
Time(min)
Thickness(mm)
Growthrate
(m/min)
Observations
952 - 0 0 Tsaturation
950 10 2 0.2 Goodqualityfilmswithflatandsmoothsurfaces
945 10 6.5 0.65
945 30 22 0.7 Goodqualityfilmbuthillysurfaceaspect
942 10 14 1.4 Smallroughparts
935 10 - - Idem,withsmallcrystalsonthesubstrateedges
asinglemodeina5mmthickfilm.
Neurgaonkaretal.(1987)reportedthelimitofstabilityoftheLiM5+O3structurewithrespecttodopantsandtheLPEgrowthofmodifiedLiNbO3andLiTaO3forSAWdeviceapplications.
Toestablishsuchasituation,thestabilitylimitoftheLiNbO3structurewasdeterminedbyintroducingvariousionsfortheLi+,Nb5+orTa5+sites.Thesubstitutionsweremadeasfollows:
1)
2)
3)
Allphasesweresynthesizedbythesolidstatereactiontechnique,andwerecharacterizedbyX-raydiffraction.Table2.5summarizesthesitepreference,solidsolubilityrangeandbehaviourofTcforthevarioussolid-solutionsystems.Basedonthiswork,theresultsmaybegeneralizedasfollows:
(1)ThesizeofsubstitutionalionsshouldbeclosetoLi+orM5+forcompletesolidsolutionintheLiNbO3orLiTaO3phase.
(2)ThesubstitutionsshouldbemadeonboththeLi+andNb5+sitessimultaneouslytoobtainhighersolidsolubilityinLiM5+O3-M2+M4+O3.
(3)Thevalencestatesofsubstitutionalionsshouldbeclosetothehostionstoachieveasubstantialsolubility,e.g.thesolubilityofA13+,Fe3+,ory3+isminimuminLiNbO3andLiTaO3.
TheresultsofthepresentstudyshowthattheunitcellaincreasesandcdecreasesforlargecationsinLiM5+O3.LargerionssuchasNa+wereusedin
Page117
Table2.5CrystalchemicaldataonLiM5+O3phase,M=NborTa(Neurgaokaretal.1987)
Dopant Sitepreference Solidsolubility(mol%) Tc(°C)
Latticeconstants(Å)
Lisite M5+site LiNbO3 LiTaO3 a c
Na+ Na+ - 7 9 Decreased Increased Decreased
Ag+ Ag+ - 4 6 Decreased Increased Decreased
Cd2+orCa2++Ti4+
Ca2+ Ti4+ 20 20 Decreased Increased Decreased
Cd2+,Ca2++Zr4+
a)Ca2+ Zr4+ 20 - Decreased Increased Decreased
Mg2++Ti4+ Mg2+ Ti4+ 30 35 Increased Decreased Increased
Co2++Ti4+ Co2+ Ti4+ 30 35 Increased Decreased Increased
Co2++Zr4+ Co2+ Zr4+ 30 35 Decreased Increased Decreased
Fe3+,A13+ Fe3+,Al3+
Al3+,Fe3+1
1 1 - - -
Nd3+,Y3+ Y3+,Nd3+
Nd3+,Y3+
1 1 - - -
In3+ In3+ In3+ 1 1 - - -
a)Structuralchangewasobservedatx=0.21.
thepresentLPEgrowthworktoreducetheSAWvelocitytemperaturecoefficient.
Figure2.31showstheternaryphasediagramfortheLiVO3-NaVO3-LiTaO3system.TheLil-xNaxTaO3phasecrystallizesoveralargecompositionalrangeandisfoundtobeusefulforLPEwork.Asshownin
Fig.2.31,twobinarycompositions,Li0.4Na0.6VO3-LiTaOandLi0.5Na0.5VO3-LiTaO3,werestudiedforLPEgrowth.Usingtheseformulations,about2mol%ofNa+inLiTaO3phasecouldbeincorporated.Theactualsolidsolubilityaccordingtothecrystalchemistryworkisapproximately9mol%and7mol%inLiTaO3andLiNbO3,respectively.AsimilarphasediagramhasalsobeenconstructedfortheLiVO3-NaVO3-LiNbO3systembyNeurgaonkaretal.(1980)anditexhibitsasimilarbehaviour.ThedippingtemperatureoftheLi0.4Na0.6VO3-LiTaO3systemismuchhighercomparedtotheLiNbOsystemasaresultofahighermeltingtemperatureofLiTaO3.
Fig.2.31LiVO3-NaVO3-LiTaO3systeminair,
at1250°C(NeurgaonkarandOliver1987).
Page118
Table2.6GrowthconditionsandphysicalcharacteristicsofLiM5+O3films(Neurogaonkaretal.1987)
Flux Substrate/film* Growthtemperature
(°C)
Latticeconstant(Å)
TemperaturecoefficientSAWvelocity(ppm/°C)
a c
LiVO3 LiNbO3-S 700 5.148 - -
LiNbO3-F 5.142 - 86
Li1-xNaxVO3
LiNbO3-S 720 5.148 - -
Li1-xNaxNbO3-F
5.156 - 56
Li1-xNaxVO3
LiTaO3-Sb) 720 5.15213.785 -
Li1-xNaxNbO3-F
5.156 13.87 -
LiVO3 LiTaO3-S 1050 5.152 - 35
LiTaO3-F 5.146 - -
Li1-xNaxVO3
LiTaO3-S 1050 5.152 - -
Li1-xNaxTaO3-F
5.161 - 28
Li1-xNaxVOa)
LiNbO3-S 1050 - -
Li1-xNaxTaO3-F
- -
*)S=substrate,F=film;a)Polingwasproblem,b)Unsuccessfulgrowth
ThegrowthofNa+-dopedLiTaO3andLiNbO3filmsbytheLPEtechniquewassuccessfulandfilms5to60mmthickweregrown.Table2.6summarizesthegrowthconditionsandlatticeparametersfortheseNa-modifiedLiNbO3andLiTaO3films.TheresultsofX-raydiffractionstudiesshowedthatthelatticeconstantaincreasedfortheNa+-dopedLiNbO3andLiTaO3films,andbasedontheunitcellvalues,approximately1.2mol%and1.8mol%Na+isincorporatedintheLiNbO3andLiTaO3films,respectively.TheadditionofmoreNainthesefilmswasunsuccessfulduetolatticemismatchandresultantcracking.
2.8Epitaxialferroelectricfilmswithperovskitestructure
2.8.1Liquid-phaseepitaxyofpotassiumniobate
Theoreticalandexperimentalinvestigationsontheapplicationofferroelectricthinfilmsintheintegratedoptics(OstrowskyandVanneste1978)andpeculiaritiesofnonlinearopticalpropertiesofpotassiumniobate(Uematsu1974;IngleandMisshra1977)makeitoneofthemostinterestingmaterialsofoptoelectronics.Potassiumniobatecrystalwithmeltingtemperature(T=1039°C)entersthenoncentrosymmetricspacegroupmm2,withtemperaturedecreasethecubicphaseturnsintoatetragonal(T=435°C)thenintoarhombic(T=225°C)and,finally,intoarhombohedralone(T=10°C)(ReismanandHoltzberg1955).
Thepossibilityofobtainingpotassiumniobatefilmsbytheliquidphasewasinvestigatedbytheauthorsusingtheepitaxynon-stationarytechnique.TheyalsodiscussedtheresultsofK2O-V2O5-Nb2O5triplesystemphasediagramstudyandtheconditionsforepitaxialfilmgrowth.
Thephaseequilibriumwasstudiedbydifferentialthermalanalysis(DTA),
Page119
byvisuallypolythermalanalysis(VTA)andbyX-phaseanalysis(XPA)(KhachaturyanandMadoyan1984).InvestigatedcompositionswerechosensothatthemoleratioNb/Nb+Vcouldvaryfrom0to1withanintervalof0.1.
Thephasediagramofthethree-componentsystemK2O-V2O5-Nb2O5wasinvestigatedalongthestraightlinefrom46mol%ofNb2O5-54mol%ofK2Oto50mol%ofK2-50mol%ofV2O5.
SuchachoiceofinvestigatedcompositionsisexplainedbyKVO3synthesisundersolidificationofthemeltofstoichiometriccompositionK2O:V2O5=1:1(Holtzbergetal.1956)whilepotassiumniobateprecipitationispossiblewiththemoleratioK2OtoNb2O5=54:46(ReismanandHoltzberg1955).Samplesaccordingtotheindicatedratiowerecarefullymixed,heatedinthefurnaceupto1300°C,keptthereforthreehoursandthencooledtoroomtemperature.
XPAoftransientcompositionsshowedKNbO3toprecipitatewhenthemoleratioofNb/Nb+Vinthechargevariesfrom0.1to1.IftheNbconcentrationisdecreasedfrom0.3to0,otherphasesappear.TheliquidusoftheKVO3-KNbO3pseudo-systemisbuilt(Fig.2.32),varyingfrom30to100mol%.
TheLPEofpotassiumniobatewasrealizedinanindustrialset'Svet-3'byanon-stationarytechniqueinathree-zoneresistancefurnace.
Thetemperatureinthereactorwaschangedatarateof10-300deg/h.
TheK2O-V2O5-Nb2O5fluxwaspreliminarilymeltedforthreehoursat1300°Cinaplatinumcrucibleandthenmountedonaholderintheoperatingzone.Substratesweremountedonaquartzrodplacedalongthecentre.Epitaxywascarriedoutbythecapillarytechniquefromthemeltenclosedbetweentwoparallelsubstrates,duetogoodwetting.Theslotwasadjustedwithin1-5mm.Thesubstrateswerepreparedof
and{0001}platesofleucosapphireandoflithiumniobatewithdimensionsl×10×15mm.
Thesystemwasheatedupto1100°CandafterholdingforalongperiodoftimewascooleddowntotheinitialtemperatureTOofepitaxy(Fig.2.20a);thesubstrateswerethenwettedbythesolutioninmeltandwereslowlycooleddowntoT1=(850-875°C),theliquidzonetemperaturebeing1-3°higherthanthatintheexternalsideoftheplates(Fig.2.20b).Thesystembeingcooledwiththesubstratedippedintothecrucible,thelayerprecipitationwasnotobserved(KhachaturyanandMadoyan1980).
Coolingdowntoroomtemperatureproceededatarateofnotmorethan80deg/h.Thesolidchargebetweentheplateswaseasilyremovedbyboilingthesubstratesindistilledwater.
Theprincipalcharacteristicsofpotassiumniobateliquid-phaseepitaxyarepresentedinTable2.7.
HomogeneouslythickKNbO3filmswereobtainedduringepitaxyof54mol%ofK2O-23mol%ofV2O5-23mol%ofNb2O5fromthebufferedmelt.Theepitaxyinitialtemperatureof920°Ccorrespondstotheliquiduspointofthepresentsystem.TheinitialtemperatureTObeingheightenedto930°C,thesubstratesurfaceisobservedtodissolve.
KNbO3filmsobtainedbyLPEfromaK2O-V2O5-Nb2O5bufferedmeltarecolourlessandtransparent,theirboundarywiththesubstrateissharpandtheirsurfaceroughnessisabout0.1mm(Fig.2.33(a)).Thetransientregionthickness
Page120
Table2.7Principalcharacteristicsofpotassiumniobateliquidphaseepitaxy
Substratematerial
Solutionmelt,mol.%
Initialepitaxytemperature°C
Coolingrate,Idgmin-
Layerthicknessmm
Growthratemmmin-1
Remarks
54K2O 950 0.8 to2 - precipitationinseparateareas
46Nb2O5
950 0.8 - - surfacedissolution
54K2O23V2O5
920 0.5 5 - singlecrystalinsmallvolumes
{0001}Al2O3 23Nb2O5
920 0.5 to10 - noprecipitation
920 0.5 6 0.1 singlecrystallayer
925 0.5 - 0.05-0.1 singlecrystallayer
52K2O24V25
930 0.5 - - surfacedissolution
24Nb2O5
930 0.2 - - surfacedissolution
{0001}A12O3 920 0.5 - - noprecipitation
920 0.5 - - surfaceintensivedissolution
Fig.2.32LiquiduscurveofKVO3-KNbO3pseudobinarysystem(KhachaturyanandMadoyan1984).
isabout0.5mm(Fig.2.33(b)).AnX-rayweakdiffractionwithanangleof20-44.5°wasobservedfromthesamplesurface,whichcorrespondstotheKNbO3facet{200}.
Theeffectofthesystemcoolingrateontheepitaxyprocesswasfound.WithhighratesKNbO3wascrystallizedonlyintheformofplatecrystals.Atacoolingrateof0.2degmin-1thesubstratesurfacewasobservedtodissolve.ThelayerwasprecipitatedatdT/dt~0.5degmin-1.
Inallexperiments,platecrystalswereseparatedinthesolutioninmeltsimultaneouslywiththefilmgrowth.KNbO3filmswereobtainedonleucosapphiresubstratesof orientation.OnAl2O3{0001}substratesthelayerprecipi-
Page121
Fig.2.33ChippingoftheKNbO3/AI2O3epitaxialstructure
(a)andthedistributionofAIandNbalongthethicknessoftheKNbO3/AI2O3heterostructure(b)(Khachaturyan
andMadoyan1984).
tationwasnotobserved.WhenanepitaxiallayergrewonLiNbO3substrates,theplatesurfacedissolvedinthebufferedmeltandbecamedulled.
2.8.2Growthofpotassiumlithiuniobatefilmsonpotassiumbismuthniobatesinglecrystals
Potassiumlithiumniobate(hereafterabbreviatedasKLNcrystal)isoneofthemostinterestingmaterialsforvariousapplicationsbecauseofitsexcellentelectro-optic,nonlinearopticandpiezoelectricproperties(ProkhorovandKuz'minov1990).Accordingly,thinfilmsofKLNsinglecrystalshaveprovedtobeexcellentactivemediaforintegratedoptics.ThetypicalcrystallographicpropertiesandrefractiveindicesofKLNatroomtemperatureareshowncomparedwiththoseofpotassiumbismuthniobate(KBN)K1.5Bi1.0Nb5.1O15crystalinTable2.8.Asingle-crystalthinfilmofKLNcanalsobegrownonaKBNsubstratebythesametechniqueasdescribedabove,becausethecrystallinestructuresofKLNandKBNarethesametungsten-bronzetypestructure,andbecausethemeltingpointofKBN
ishigherbyabout250°CthanthatofKLN,asshowninTable2.8.ThelatticemismatchbetweentheKLNfilmandtheKBNsubstrateisabout0.32%and2.3%atroomtemperatureforthea-andc-axesintheKLNcoordinatesystembecausetheKBNcrystalisorthorhombic,asopposedtotheKLNcrystal,whichistetragonal.Thus,itisexpectedthatasingle-crystalthinfilmofKLNgrownonaKBNsubstratewillactasanopticalwaveguide,anditcanbeusedasanopticalwaveguidemodulatorbycoupledwaveinteractionbetweentheguidedandradiationmodes(Adachietal.1979).Intheirpreviouspaper,Adachietal.(1978)describedtheepitaxialgrowthofKLNsingle-crystalfilmsbytherfsputteringtechnique.Intheir1979papertheyreportedtheepitaxialgrowthofKLNsingle-crystalfilmsonKBNsubstratesbytheEGMtechnique.
Single-crystalsofKBNweregrownbytherfheatingCzochralskimethod.
Page122
Table2.8CrystallographicpropertiesandrefractiveindicesofKLNandKBNatroomtemperature(Adachi,Shiasaki,Kawabata,1979)
KLN KBN
Symmetry Tetragonal Orthorhombic
Latticeconstant,Å,a~b 12.58 17.85
c 4.01 7.84
Meltingpoint,°C 1050 1312
Refractiveindex,no 2.294 2.237
nc 2.156 2.253
Wavelength,l.,nm 632.8 450
(001)or(100)KBNsubstrateswerecutfromas-growncrystals,andtheirtopsurfaceswerelappedandopticallypolished.Ontheotherhand,reagentgradecarbonatesoflithiumandpotassium,and99.9%pureniobiumpentoxidewereusedasstartingmaterialsforthefabricationofKLNsingle-crystalfilms.Amaterialwithcomposition35mol%K2CO3,7.3mol%Li2CO3and47.7mol%Nb2O5wasmixedwellwithacetoneinaballmill,dried,pressedintoadisc,andcalcinedat800°CforthreehoursThecalcinedmaterialofKLNwasthengroundthoroughly.ThispowderofKLNwasuniformlylaidonthepolishedsurfaceoftheKBNsubstratewithasprayer.Thesubstrate,withthepowderonitstopsurface,washeatedtoabout1120°CinaresistancefurnaceinordertomelttheKLNcrushedpowderalone,andwasthencooledslowlyatarateof10°C/hthroughthemeltingpoint(1050°c)ofKLN.Inthisway,theKLNfilmcrystallizedepitaxiallyontotheKBNsubstrate.
Thetopsurfaceoftheas-grownfilmwasrelativelyrough,andtheKLNfilmobtainedwas~15mmthick.IntheX-raydiffraction
patterns,thepeakscorrespondingtodiffractionsfromtheKLNfilmsandKBNsubstratesareclearlyseparated.Further,thevalueobtainedforthestandarddeviationangleooftheX-rayrockingcurveofKLNfilmisverysmallat0.2.ThelatticeconstantsaandcoftheKLNfilmobtainedbyX-raydiffractionmeasurementare12.53Åand3.98Å,respectively.ThesevaluesagreefairlywellwiththoseoftheKLNsinglecrystal,asshowninTable2.8.TheelectrondiffractionpatternsforKLNfilmsepitaxiallygrownonKBNsubstratesandalsotheKikuchistructureindicatethatthefilmsareofasinglecrystaloffairlygoodquality.Theseresultsshowthatasingle-crystalfilmof(001)KLNisepitaxiallygrownonan(001)KBNsubstrate,andalsothatasingle-crystalfilmof(110)KLNisepitaxiallygrownona(100)KBNsubstratebytheEGMtechnique.
2.9Diffusionliquid-phasemethodofgrowingimmersedwaveguidechannels
ChannelorstriplinewaveguidesonthebasisofLiNbO3arenecessaryelementsforcreationofelectro-opticmodulators,switches,directionalcouplersandotheractivedevicesofintegratedoptics(PhotonicseditedbyBalkanski1975;Tamir
Page123
1979;Hunsperger1984;Yariv1983;House1988)suitableforjoiningwithopticalfibres.
Thephysico-chemicalpropertiesofbuffered-meltsystems,hightemperaturesoftheprocesses,alimitedchoiceofmaterialsforsolventandcontainerrestrictstronglythepossibilitiesofLPEinthecreationofvariousdevicestructuresascomparedwithmoretechnologicallyeffectivemethodsofdiffusion,exchangereactions,ionimplantation,etc.Inspiteoftheobviousadvantagesinstructuralperfectionofepitaxiallayers,thismethodonlyservesforobtainingplanarwaveguidelithiumniobatelayersonLiTaO3substrates(FukudaandHirano1980;MadoyanandKhachaturyan1983;BallmanandTien1976).
Tocreateeffectiveintegro-opticdevices,wehaveproposedacombinedmethodofliquid-phaseepitaxyofLiNbO3filmswhichusestheadvantagesofthermaldiffusionandLPEandpermitsobtainingpracticallyanyprescribedwaveguideconfigurationsandrefractiveindexprofiles(KhachaturyanandMadoyan1986).
2.9.1Striplinestructures
Toobtainastriplinestructure,itisnecessarytoprovideavariationofwaveguideparametersalongaLiTaO3substratesurfacebyagivenscheme.
Amaskwithagivenconfigurationisphotographedontoa20×30×2mmsubstratesurface(Fig.2.34),afterwhichametalliclayerisdepositedontothissurfacebysprayinginvacuum(Avakyanetal.1986).Ofparticularinterestarewaveguidelayersobtainedbytitaniumdiffusionintoalithiumtantalatesubstrate,sinceintheselayersmodesofbothpolarizationsarepossible(Zilingetal.1980;Atuginetal.1984;Sugiietal.1980;Shashkin1983).
Films,whichareiondiffusionsources,aretypicallydepositedonto
thesubstratesurfacebythermalevaporationinvacuumorbyion-plasmasprayingoftargets.Accordingtorequirementsonthelightguideparameters,diffusant-filmthicknessisvariedfrom50to80nm.Thediffusiontemperatureis1150°Candthediffusiontime10-16h.
Thedepositedmetaldiffusesintothegrowinglayerthusincreasingitsrefractiveindexalongthephotographedpicture.Theaveragedmetalconcentrationintheline isdeterminedbythesputteredlinethickness
wherehmisthewaveguidelinethickness,Am,rmandMfrfareatomicweightsanddensitiesofthemetalandfilmmaterial,respectively.
Thediffusiondepth(theheightofthewaveguideline)isdeterminedbythediffusioncoefficientofagivenmetalintoasingle-crystalfilmandbytheepitaxytemperature.Therefractiveindexvariationalongthedirection perpendiculartothelayersurfacehastheform(Zilingetal.1980):
HereAe=Dno/c,m=rm×hmisthediffusantspecificmass,q=Dt,where
Page124
tisannealingtime,D=D0exp(-U/kT),U=1.5eVistheconstantactivationenergy,D0=4×10-7cm2/s(fortitaniumdiffusion).
Theexpressionspresentedaboveallowustocalculatethenecessaryepitaxytemperatureforobtaininganyarbitraryrefractiveindexprofile.
FortherefractiveindexvariationDnetobeabout0.01whenthechannelheighthreachesapproximately2-4mm,theannealingtimeshouldbeoftheorderof5-10hours,whichexceedsgreatlythecharacteristicepitaxytimes(1-3hours).Consequently,thetimetcanberepresentedast=tpr+tan,wheretpristhelayerprecipitationtimeandtantheadditionalannealingtime.
2.9.2Symmetricwaveguides
Usingthecombineddiffusion-filmmethod,KhachaturyanandMadoyan(1986)obtainedsymmetricwaveguidechannels.Thesequenceofoperationswasthefollowing.Afterremovingtheresist(Fig.2.34),anepitaxialLiNb0.1Ta0.9O3layerwasbuiltupontheTi:LiTaO3substratebythecapillaryLPEmethod.Thefilmcompositionwasdeterminedbytherequiredrefractiveindexdistributionoverthestructurethickness.ThegrowthratevariationinawiderangeprovidedanopticalepitaxyregimeforobtainingperfectLi(Nb,Ta)O3/Ti:LiTaO3.
Thefilm-diffusionwaveguidewastheoreticallyconsideredbySpikhal'sky(1984).Hederivedthedispersionequationforcalculatingthecharacteristicsofmultilayerwaveguidestructures.Healsoestablishedtheparametercharacterizingthedegreeofthelight-fluxmodelocalizationinthevicinityofadefinedinterfacebetweenmediaconstitutingthewaveguide.
Thestudyoftheepitaxialgrowthoflithiumniobate-tantalatefilmswithtitaniumstripsdepositedontoaLiTaO3substratehasshownthat
forveg<0.2mm/minthefilmsurfaceissmoothwithseparatelinescorrespondingtodislocations.Atsuchgrowthratesthelayergrowthislaminar.
Figure2.34showsthesurface ofaLiTaO3substratewithadepositedtitaniumstrips(a)andthemorphologyoftheepitaxialLi(Nb,Ta)O3filmgrownonthissubstrate.TheepitaxialstructuresLiNbO3/Ti:LiNbO3canbereadilygrowninasimilarmanner(KhachaturyanandMadoyan1988(a),(b)).
Distler(1975)reportedthepossibilityofepitaxialgrowthonsubstrateswithpreliminarilydepositedthin(nearly50nm)metalliclayers.ThethicknessofthestripsinvestigatedbyKhachaturyanandMadoyan(1988(a),(b))lieswithintherangeofapproximately100-500nm.Structuralinformationisnottransmittedthroughtitaniumstrips,andinthenormalmechanismthefilmmustsurelybedefectiveonthesestrips.Inlaminargrowththesituationwasdifferent.Thedensityofgrowthstructuresreflectingthedefectivelayerstructureisminimumjustoverthetitaniumstrips.Themetalliclayerobviously'screens'thestructuraldefectsofthesubstratewhichontheremainingsitesgrowintothefilm.Alowdensityofthenucleiguaranteesaninsignificantamountofsmall-angleboundarieswhichaffectneitherthestructuralperfectionofthefilmnortheabsenceofdisorientedsitescausedbynucleationontitaniumstripsthemselves.
Assoonastheepitaxialgrowthprocessisover,theremainingsolventisremovedfromthesurfaceoftheepitaxialfilmusingkaolincottonplugsormicro-channelslabsasliquid-phaseabsorbent(DudkinandKhachaturyan1988).
Page125
Fig.2.34Schematicofobtainingadippedwaveguidechannel(a),thesurface
ofaLiTaO3substratewithdepositedtitaniumstrips(b)andthemorphologyofepitaxialLi(Nb,Ta)O3filmgrownonthissubstrate(c).
Amicrochannelslabisasetofregularlypositionedmicroslits-channelswithdiameterfrom7to25mmeachandthelengthchosenwithintherangeof0.3to1.2mm.Thecrosssectionofmicrochannelslabstypicallyvariesfrom30to40mm,whichexceedsthestandarddimensionsoftheworkingfieldofproductsfabricatedusingepitaxialtechnique.Whenmicrochannelslabsareusedforalongtimeattemperaturesexceeding600-1200°C,theslabsarepreliminarilywettedinliquidkaolin('kaolinmilk')andthendried.Themicrochannelslabsprocessedthiswaycanbeusedtoremovetheremainingliquid-phasefluxfromthesamplesurface.Tothisendthemicrochannelslabisbroughtclosetothegapbetweenthesubstratessothatitssurfacetouchessimultaneouslytheentirelayersurface,asshowninFig.2.35.Underequivalentcapillaryforcestheliquidresiduesaredrawnoffalongallthechannels,thatis,uniformlyalongtheentiresurface.
Thus,themethodsdiscussedabovemakeitpossibletoobtainlayerswithvariouswaveguideconfigurationsinthefilm.Varyingthegrowthrateandtheannealingtime,wecanobtainsurfaceandimmersedwaveguides,striplinestructuresandlayerswithmetallicbufferedlayersonthesubstrate-filmboundary.
2.10GrowthofepitaxialfilmsintheKTiOPO4familyofcrystals
Asanalternativetodirectlyaddressingtheionicconductivityproblem,andasameanstomoreeffectivelyconfinetheopticalwavetoyieldhigherpowerdensity,filmswithwell-definedstep-likerefractiveindexprofilecanbegrown
Page126
Fig.2.35Schematicoftheuseofmicrochannelslabsto
absorbtheliquid-phasefluxfromthefilmsurface:1)microchannelslab,2)singlechannel,3)substrate,
4)liquidphase5)epitaxialfilm,6,7)contactsofthemeltwithamicrochannelslab.
directlybyliquid-phaseepitaxy.TheKTPcrystalfamilyishighlyversatileandreadilyformssolidsolutionsamongitsmembers(BierleinandGier1976;JarmanandGrubb1988).Themonovalentcations(i.e.K,Rb,CsandT1)arefoundtobemobileduetotheirdirectcovalentlinkagetothebridgingoxygeninthelattice,thepentavalentPandAsions,andthetetravalentTiionsareexpectedtohavenegligiblemobilityevenatelevatedtemperatures.Thus,athinfilmconsistingofsolidsolutionoftheseions(e.g.KTiOAsxP1-xO4orKTixSn1-xOPO4)grownonapureKTPsubstrateisexpectedtohaveawell-definedabruptrefractiveindexprofilealongcdirection.
Effectivewaveguidingisobtainedbysatisfyingtheconditionthatthefilm'srefractiveindicesbehigherthanthatofthesubstrate.Deepchannelwaveguidescanbefabricatedontheseheteroepitaxialfilmsbysubsequention-exchange.Astheevanescentwavebarelypenetratesintothesubstrate,fluctuationinthediffusiveprofileofthesechannelguideswillnotsignificantlyaffecttheirwaveguidingproperties,therebyavoidingtheproblemofionicconductivity.
ThelatticeconstantsforseveralendmembersoftheKTPfamilyare
summarizedinTable2.9.Amongthemanypossiblefilm-substratecombinations,theKTA-KTPsystemwaschosenintheexperimentscarriedoutbyChengetal.(1991).Therearetworeasonsforthis.Asthetitanylgroupisprimarilyresponsiblefortheopticalnonlinearity,replacementoftitaniumwithothertetravalentionsisexpectedtoleadtoasignificantlossinthenonlinearity,whichinturnreducestheusefulnessofthesefilmsinnonlinearfrequencyconversion.Thearsenicforphosphorussubstitutionprovidesthedesiredrefractiveindexincreasewithoutcompromisingonthenonlinearity.TheopticalandthecrystalgrowthpropertiesofKTPandKTAarebettercharacterizedthanthoseofallothermembersoftheKTPfamily(Bierleinetal.1989).Thisallowsforbettercorrelationbetweenexperimentalresultsandtheoreticalpredictions.
Boththetungstatefluxandthepurephosphate-arsenateself-fluxwereusedintheexperimentsbyChengetal.(1991).Theself-fluxusedconsistsofthephosphate-arsenatealongwiththeK6P4O13flux(abbreviatedasK6below)usedforbulkKTPgrowth(Gier1980;Borduietal.1987).Therelativecrystal-fluxcompositionswerechosensuchthatthegrowthtemperatureswere850°C.Althoughsignificantlylowergrowthtemperaturesarepossibleusingthetungstate,theK6fluxbecomesfartooviscousforgrowthbelow750°C.
Page127
Table2.9LatticeconstantsforseveralKTPisomorphs(Chengetal1991)
Crystal Latticeconstants Cellvolume(A)
a(Å) bÅ) c(Å)
KTiOPO4 (KTP) 12.822 6.4054 10.589 869.67
RbTiOPO4 (RTP) 12.964 6.4985 10.563 889.89
TlTiOPO4 (TIP) 12.983 6.49 10.578 891.3
KTiOAsO4 (KTA) 13.125 6.5716 10.786 930.31
RbTiOAsO4 (RTA) 13.258 6.6781 10.766 953.2
CsTiOAsO4 (CTA) 13.486 6.8616 10.688 989.02
TlTiOAsO4 (TTA) 13.208 6.6865 10.724 947.09
KGeOPO4 (KGP) 12.602 6.302 10.006 794.65
KSnOPO4 (KSP) 13.146 6.528 10.727 920.56
Variouslyorientedsubstrates,namely{011},{110},{100},{111}and{201}plates,havebeensuccessfullyusedtogiveas-grownfilmswithhighlyspecularsurfaces.KTPandKTiOAsxP1-xO4substrateswereprimarilycutfromflux-growncrystals.
Theuseofhydrothermallygrownmaterialstypicallyleadstoopticaldegradationwiththeformationoffinewhitefilamentsinthesubstrate.Chengetal.(1991)speculatethatthisdegradationisduetotheprecipitationoffinewater-basedinclusionsinthesematerials.
Thesubstratesare~l×lcm2×mmthickplates,cutparalleltothenaturalgrowthfacets.Allplateswerepolishedwithsequentiallyfiner(3-0.25mm)diamondbasedpolishingpowder,andfinishedwitha30schemical-mechanicalpolishincolloidalsilica.Asmall(0.75mm)
hole,drilledatonecornerofthesubstrate,allowsittobetiedontoacrystalrotation-pullingheadwithathinplatinumwire.Thesubstratewasheldverticallytoassistfluxdrainageafterdipping.Aslightetchingofthesubstrateinwarmdilutehydrochloricacidpriortothedippingwasfoundtoimprovetheequalityoftheepitaxialfilm.
Thedippingsetupisidenticaltothebulkgrowthfurnace.Itconsistsofa250mlcrucibleplacedatthebottomofashortzonetop-loadingcruciblefurnacelinedbya4.5-inchquartztube.
Themelt(~200ml)ishomogenizedatabout50°Caboveitsliquidustemperature.AsomewhatlongersoaktimeisoftenneededwhenusingtheK6flux.Thesubstrateisintroducedintothegrowthfurnaceslowly(~5-25mm/min).Themeltisthencooledtoabout1.5-3°Cbelowthesaturationpointandallowedtoequilibratefor30min.Thesubstrateisthendippedintothemeltandspununidirectionallyat10rpm.Thedippingtimeisvarieddependingonthedesiredfilmthickness,thedegreeofsupersaturationused,thechoiceoffluxandthegrowthtemperature.Experimentally,Chengetal.(1991)foundthataslightback-etchingofthesubstratepriortogrowthresultsinsignificantlybetterqualityfilms.Thisisaccomplishedsimplybytakingadvantageofthethermalinertiaofthesystemandsubmergingthesubstratebeforethemeltreachesthegrowthtemperature.
Page128
Fig.2.36ProfileofKTiOP0.76AS0.24O4filmonaKTPsubstrate.Thetitaniumprofileisnotshownforclarity.Thespatialresolutionofthescanis~0.5mm(Chengetal.1991).
Uponcompletionofthedipping,theplateiswithdrawnfromthemeltandthefurnaceatapproximately5-25mm/min.Anyresidualfluxpresentiswashedoffwithwarmdilutehydrochloricacid.Thethicknessofthefilmisnearly±5mm.
Usingthedippingprocedureoutlinedabove,Chengetal.(1991)havegrownKTiOAsyP1-yO4filmsbetween4and20mmonsuitablychosensubstratesofKTPorKTiOAsxP1-xO4(wherex<y).Asanindependentconfirmationofthestep-likeofthestep-likerefractiveindexprofileofthesefilms,electronmicroprobetechniquewasusedtomapoutthecompositionofa50mm-thickKTiOP0.76AS0.24O4filmonaKTPsubstrate(Fig.2.36).The'abrupt'increaseinthearseniccontentfromthesubstratetothefilmconvincinglydemonstratesthatphosphorus-arsenicexchangeisnegligibleunderthegrowthconditions(~850°C).Sincetheas-grownfilmhasthesamemorphologyasthatofKTPandthesolidsolutionKTiOAsyP1-yO4istheonlystablephaseinthemelt,Chengetal.(1991)concludethatthefilmisepitaxialandisstructurallyanalogoustoKTP.Therefractiveindexofthefilmcanbeestimatedfromtheknownrefractiveindicesoftheendmembers,andisinexcellentagreementwiththem-lines
spectrometryresults.Chengetal.(1991)havealsogrownthinfilmsofRb0.2Ko.8TiOPO4onKTP.ThesignificantpenetrationoftheRb+intothesubstrateverifiedthattheK+ionsarehighlymobile,andstep-indexfilmscannotbereadilyobtainedfromthecationicsolidsolutions.
Table2.10summarizesthepartitioncoefficientsforarsenicusingthetungstateflux.Thepartitioncoefficient,k,isdefinedas:
where[As]isthemolefractionofAsinthecrystalorthemelt.ThegreaterthanunitypartitioncoefficientsuggeststhatAsisfavouredintheKTiOAsxP1-xO4lattice.Figure2.37plotsthelatticeconstantsoftheKTiOAsxP1-xO4system.Theresultsindicatethat,unliketheRbxK1-xTiOPO4
Page129
Table2.10Partitioncoefficient,k,ofarsenicfromatungstenmelt;(As)isdeterminedbyICPanalysisofAsandPinbulkcrystalsgrownatthesametemperature(Chengatal1991)
[As]crystal [AS]melt k
24 20 1.2
39.1 35 1.12
56.1 50 1.12
82.6 75 1.1
87.4 80 1.1
Fig.2.37LatticeconstantsoftheKTiOPxAS1-xO4system.
SolidlinesarepredictionsusingVegard'slaw(Chengetal.1991).
system,thelatticeconstantsa,bandc,increasemonotonicallywitharseniccontent.ThefollowingVegardlawsfittheKTiOAsxP1-xO4resultsverywell:
wherexisthemolefractionofAsinthecrystals.Itwasexperimentallyfoundthatthemaximumlatticemismatchforhighqualityfilmgrowthisabout1%,whichcorrespondstoa35%increaseinarseniccontentintheKTiOASxP1-xO4filmandtoanestimatedrefractiveindexincreaseofDnb~0.0177at1.064mm.Filmcrackingand'scaling'wereobservedforfilmswithlargerlatticemismatch.
SignificantlydifferentgrowthpropertieswereobservedfortungstatefluxandtheK6flux.Atabout850°Candwithcomparablesupercooling(about2°C),thegrowthratewassubstantiallyslowerintheK6fluxthanintungstate.ToachieveacomparablegrowthrateusingtheK6flux,asupercoolingroughlytwicethatusedintungstateisneeded.FilmsgrownfromtheK6fluxtendtohavefilm-substrateinterfacesofpoorerquality.Itislikelythatthisisdue
Page130
totheslowdissolutionkineticsoftheK6flux(Chengetal.1991),whichmakestheimplementationofpre-growthetchingdifficult.Thetimelinearityoffilmgrowthforagivensupercoolingwasestablished.
TheKTAprocesseswerereportedtohaveappreciablyhigheropticalnon-linearityandloweropticalscatteringthanKTP(Bierleinetal.1989).Theidealfilm-substratecombinationisthereforeapureKTAfilmonsuitablychosenKTiOAslP1-xO4substrate.Thiscombinationalsoeliminatesanypossiblemicroscopiccompositionalfluctuationinthefilmduetothenon-unitypartitioncoefficientkofarsenic.AlthoughcompositionalvariationsinKTiOAsxP1-xO4substratescaninprincipleoccur,theireffectonthewaveguidingpropertieswillbenegligible.Thefilmwasshowntowaveguideeffectivelyat0.632mm,withnomorethantwoopticalmodes.
Chengetal.(1991)alsoexploredthefilmgrowthofsolidsolutionsinvolvingthetitanylgroup.ThegrowthofKTi1-xSnxOPO4films,thoughpreferredoverKTi1-xGexOPO4,provesdifficultduetotheanomalouslyslowdissolutionofKSP.Incontrast,usingtheprocedureoutlinedabove,Chengetal.(1991)readilygrew10mmKTi0.96Ge0.04OPO4filmson{011}KTPsubstratesusinga20%{Ge}solution.Discouragingly,evenwithalow4.3%Geincorporation,numerouscracksperpendiculartocwereobservedinthicker(30mm)films.Chengetal.(1991)attributethisincreasedfilm-crackingtendencytothefactthat,unliketheKTiOAsxP1-xO4films,theKTi0.96Ge0.04OPO4filmsareundertensilestress.Thisinterpretationisentirelyconsistentwiththeprediction,usingVegard'slawandTable2.9,thatthecracksshouldbenormaltocasobserved.Theseexperimentssuggestthatsolid-solutionfilmsofeitherKTi1-xSnxOPO4orKTi1-xGexOPO4areoflimitedpracticalutility.Thesituationcanhoweverbeimprovedsignificantlybyreversingthefilm-substrateconfiguration,i.e.KTPfilmonKTi1-xGexOPO4substrate-providedthattherefractiveindicesconditionforwaveguidingcanbe
satisfied.
Page131
3InfluenceofElectricCurrentuponLiquid-PhaseEpitaxyofFerroelectricsProgressofmicro-andoptoelectronicsdependsmuchonhowsuccessfullytheexistingmethodsforobtainingthin-filmstructuressolvetheproblemofreproducibleformationofperfectmultilayerheteroepitaxialcompositionsbasedonmulticomponentsemiconductorsolidsolutionsofA3B5andferroelectricsmanufacturedfromniobatesandtantalatesofalkalineandalkaliearthmetals.Requirementsonthetechnologyandcrystallographicperfectionofstructuresandonthepropertiesoffilmshaveincreasedsubstantially.Amongtheknownliquid-phasemethodsforobtainingepitaxialstructureswithpredeterminedproperties,liquid-phaseepitaxypossessesthewidestpotentialitiesforfilmcomposition,thicknessandstructurecontrol.Inthischapter,wepresenttheoreticalandexperimentalresultsofstudiesoftheinfluenceofdirectelectriccurrentupontheprocessesofliquid-phaseepitaxy.Wealsopresenttheresultsoforiginalpapersongrowthandinvestigationofthin-filmstructuresofferroelectricsonanexampleoflithiumniobateandsolidsolutionsoflithiumniobate-tantalate.Weaccountforthefactthatanelectricfieldand,inparticular,adirectelectriccurrentflowingthroughacrystalisoneoftheeffectivemeansforchangingcrystallizationconditionsthataffectcrystallographicperfectionandsomephysicalpropertiesofgrownstructures(Khachaturyanetal1987).
3.1.Electricfieldandcrystallization
Anelectricfieldisafairlystrongenergeticfactoraffectingthenucleationandgrowthofanewphaseunderfirst-orderphasetransitions.Butthenumerousreportsontheinfluenceofanelectric
fielduponthecrystallizationprocessdonotprovidefinalunambiguousconclusionsconcerningaunifiedphysicalmechanismoffieldeffect.Inviewofthisweconsiderpossiblemechanismsoftheinfluenceofadirectelectricfielduponcrystallizationprocesses.
3.1.1Bulkcrystallization
In1956,A.F.Ioffegaveatheoreticaldescriptionofmotionofameltedzoneundertheactionofelectriccurrentingermaniumbars(Ioffe1956).This
Page132
motionwasexplainedbythepresenceoftemperaturegradientintheliquidzoneduetoPeltierheatrelease(orabsorption)attheliquid-solidinterfaces.In1957,W.Pfann(Pfannetal1957)gaveanexperimentalconfirmationofthetheorysuggestedbyA.F.Ioffe.Awholenumberofnewexperimentalresults(Pfann1970)onthedirectionofmotioninameltedzonedependingonitscompositionrequiredspecificationofthetheory.
TheinfluenceofanelectricfieldontheformationofcrystallizationcentresinsupersaturatedsaltsolutionswasfirstdiscoveredbyShubnikov(1956)whoshowedthatasuperpositionofanexternalelectricfieldcausesasharpincreaseinthenumberofcrystallizationcentres.
Investigationoftheactionofelectriccurrentinacrystal-meltchainingermaniumcrystalgrowthusingCzochralskiandStepanovmethodshasrevealedvariationintheintensityandstriationperiodincrystals(Levinzonetal1969;Dudniketal1973).Germaniumsinglecrystalsweregrowninthe{111}directionanddopedwithantimonytoobtainaresistivityof5-10ohm.cm.
Thedensityofcurrentincreasedfrom0to50A/cm2inthecourseofgrowthofonecrystal.Stepanovgrowningotsexhibitedadecreaseoftheamplitudeandpitchofstriation,whichdoesnotdependonthedirectionofcurrentandisonlyduetoJouleheatrelease(i.e.theJouleheatexceedsthePeltierheat).
ItshouldbenotedthattheparametersofinhomogeneityofcontrolingotsgrowninasimilarmannerbytheCzochralskimethodremainedpracticallyunalteredwhenelectriccurrentwasapplied.
WhengermaniumstripsaregrownbytheStepanovmethod,thetransmittedelectriccurrenthasaneffectnotonlyuponthenatureofstriationinsinglecrystals.Itwasshown(Egorovetal1971)thatan
applicationofadirectelectriccurrentthroughaninterfaceprovidescontroloverthecrystallizationfrontshapeduringzonecrystalgrowth.Tochoosethecurrentdensitynecessaryforcrystallizationfrontshapecontrol,oneshouldtakeintoaccounttherelationbetweenthePeltierandJouleheatswhicharerespectivelyequalto
PisthePeltiercoefficient,RistheresultantresistanceoftheportionsofliquidandcrystaladjoiningthecrystallizationfrontandJiscurrentdensity.
Theseeffectscanbesummeduporsubtracteddependingonthedirectionofcurrent.
InaregionwherethecurrentdensityissuchthatQJ>Qp,thecrystallizationfrontrises,whilefor itfalls.WhentheJouleandPeltierheatsareequaltoeachother, theappliedcurrentinducesnovariationsofthecrystallizationfrontshape.Thecorrespondingequilibriumdensityofcurrentwillbeequalto
Thedeviationoftheimpurityconcentrationfromtheequilibriumvalue(DC)atthesolid-liquidinterfacecanberepresentedinthegeneralformasan
Page133
algebraicsumofthedeviationsoftheconcentrationsfromtheirequilibriumvalues,causedbyelectrothermaleffects(DC1standsfortheJouleeffect,Peltiereffectandothers)andelectrictransfer(DC2)
In1963-1964twomodelswereproposed(Tiller1963;Hurleetal1964)attemptingallowanceformigrationofmeltcomponentsundertheactionofanelectriccurrentinstationaryconditions.Althoughtheorderofmagnitudeofdifferentialmobilityofameltedzonecomponentwasdeterminedwithinthesemodels,theywereunabletoexplaintheresultsofsubsequentworksonepitaxialgrowth.
ThePeltiereffectwasappliedtodeterminethecrystallizationrateofInSbinCzochralskitypecrystalgrowth(Singhetal1968;Lichtensteigeretal1971;WargoandWitt1984).Applicationofapulsedcurrenttoacrystal-meltboundaryresultedintheappearanceofstriationinthecrystalstructure,andvariationofthefrequencyandpulseintensitycausedvariationsinthewidthandintensityofthesestriae.ThestriaeresultedfromvariationofimpurityconcentrationduetoachangeofinstantaneousgrowthratecausedbyPeltierheating(orcooling).Theauthorsnoticedthattheimpurityconcentrationinastriaremainsconstantduringallthetimeofapplicationofacurrent,changesinstantaneouslyattheendofapulseandremainsunchangedtillasubsequentpulse.Changingthemagnitudeofelectriccurrentpulseandthuschangingtheimpurityconcentrationinastria,theyestablishedadirectdependenceofimpuritysegregationonthedensityofthecurrentflowingthroughthesystem.TheelectrictransferwhichaccompaniesthePeltiereffectisobservedtorestrictitsactioninmulticomponentsystems.
SimilarresultswereobtainedforGe(Vojdanietal1975).ThetemperaturedistributioninasystemtowhichanelectriccurrentisappliedwasshowntobeafunctionofthePeltiereffect.
Theprocessesproceedingduringthegrowthofpotassium-tungstenbronze(NaxWO3)andlanthanumhexaboride(LaB6)bythemethodcombiningelectrochemicalcrystallizationandCzochralskitechniquewereinvestigatedbyMatteietal(1976),HugginsandElwell1977)andDeMatteiandFeigelson(1978).Ifintheusualcrystalgrowththemotiveforceissupersaturationorthermalgradient,inelectrochemicalcrystallizationthekineticanddiffusionprocessesareactivatedbyanexternalelectricfieldwhosepotentialexceedstheequilibriumpotentialvalue.ElectrochemicalcrystallizationisaFaradayeffect,andtheprecipitationrateattheinterfaceisreadilycontrolledbythestrengthofcurrent.
ProblemsconnectedwiththeinfluenceofelectrictransferandPeltiereffectupontheimpuritydistributioncoefficientwerediscussedonanexampleofgrowthofBi-SbcrystalsdopedwithTe,Se,SnandPb(KrylovandIvanov1980).
Whengrowingchromium-dopedlithiumniobatecrystalsbyCzochralskitechnique,Räber(1976)andFeisstandRäber(1983)examinedtheinfluenceofthestrengthanddirectionoftheelectriccurrentflowingthroughacrystal-
Page134
meltsystemuponthevalueofthechromiumdistributioncoefficient.
Applicationof50mApulsesofagainstthebackground5mAcurrentresultedinstriationcausedbyadecreaseofchromiumconcentrationbyaboutafactoroftwo,thecurrentontheseedcrystalhavingpolarity'+'.Thedistributioncoefficient(Kcff)asafunctionofthestrengthanddirectionofcurrentwasestimated.Astheelectriccurrentdensityvariedwithintherange15<j<18mA/cm2,thedistributioncoefficientdecreasedlinearlywithanincreaseofthecurrentdensity.Outsidetheindicatedcurrentdensityrangethecrystalgrowthbecameunstable.Highvaluesofthedensityofcurrentsappliedinducedtheappearanceofgasbubblesinthecrystal.Thecolourofthecrystalchangedwithreversalofpolarity,andthesurfacebecamerough.
Voskresenskayaetal(1985)reportedtheresultsoftheirinvestigationoftheelectricfieldeffectupontheprocessesproceedingatthecrystallizationfrontofbismuthgermanategrownbyCzochralskimethod.Crystalsweregrownfromacruciblewithcathodeandanodepolarizations,thedensityofcurrentswasvariedwithintherangeof(0÷20)mA.Anelectriccurrentwasshowntohaveagreateffectontheimpuritydistributioncoefficientandonthemagnitudeofremanentstressesinthecrystal.Inthecaseofcathodepolarization,thegrowthprocesswasstable,theresistanceoftheelectriccircuitincreasedmonotonicallywithcrystalgrowth.Achangeofpolarizationforananodeoneledtoadecreaseintheelectricresistanceattheboundarybyafactorof25andinducednonstationaryprocessesatthecrystallizationfront,whichareconnectedwithanunstablevalueofresistanceinthecrystal-melt-cruciblechain.Ananalysisofthevalueofremanentstressesindifferentpartsofcrystalsgrownfromacruciblewithcathodepolarizationshowedthatthestressesfalldownto70%ascomparedwithregionsgrowingwithoutanycurrentbeingapplied.
Thus,ananalysisofthepapersinvestigatingtheinfluenceofadirectelectriccurrentuponcrystallizationofabulkmaterialrevealedthepossibilityofcontrollingtheimpuritycompositionandstructuralperfectionofgrownsinglecrystals.
3.1.2Thinfilms
Thewideapplicationofthinfilmsinmicro-andoptoelectronicsisexplainedbymanyfactors.Themostimportanthereisobviouslythefactthatitisonlythinfilmsthatpermitobtainingcompactschemesatalowconsumedpowerandahighdensityofschemeelements.Furthermore,themethodsofobtainingthinfilmsprovidehighlypuresubstancesormaterialswithacompositioncontrolledwithprecision.
Researchersengagedingrowingsinglecrystalsandfilmsareinterestedinfindingnewwaysofaffectingagrowingcrystal,whichwouldallowamoreeffectivecontroloverthegrowthrate,surfacemorphology,thedistributionofalloyingimpuritiesinacrystallizationmediumandtheconcentrationofstructuraldefects.
Alargeamountofexperimentalmaterialisavailableontheinfluenceofanelectricfielduponepitaxialgrowthfromthegasphase.Thegeneralchemicofphysicalconsiderationsimplythatsuperpositionofthedifferenceofelectricpotentialsonthesourceandsubstratemaygivethefollowingprincipaleffects:
Page135
1.Changeofconditionsofchemicalequilibriumofheterogeneousreactionsonthesourceandsubstratesurfaces.Indeed,theGibbsexpressionforthefreeenergyofaphysico-chemicalsysteminanelectricfieldcontainsanadditionaltermshowingthattheworkofelectricforcesisproportionaltothestrengthanddependsonthedirectionoftheelectricfieldstrengthvector(Sychev1970):
where istheelectricfieldstrength, theelectricinductionandthedielectricpolarization.
2.Changeofdiffusionactivationenergyanddiffusionrateinthegasphaseonthesourceandsubstratesurfaces.Themaineffectisthatthediffusivemotionofparticlesissuperposedbyadirecteddriftofionsintheelectricfield(Boltaks1972;KolobovandSamokhvalov1975):j=mEC,wherejisachargedparticleflow,mismobilityandCisconcentration.
Electrodiffusionofchargedvacanciescanproceedsimultaneously.ThechangeinthediffusionactivationenergyundertheactionofelectricfieldwasreportedbyGorsky(1969).
3.ChangeinthepositionoftheFermilevelonthesurfaceofasemiconductorcausedbyatransverseelectricfield.Thisresultsindisplacementofequilibriumbetweenachargedandunchargedformsofchemisorptiononthesurface,whichleadstoanadditionaladsorptionordesorptionofmoleculesdependingonthesignofthefield.Thisphenomenonwascalledelectrosorption(Wolkenstein1973).Therelativechangeofadsorbtiveabilityisdescribedbytheformula
whereN0isadsorbtiveabilityintheabsenceofanelectricfield,DN=
N-N0isthechangeofadsorbtiveability,DVs,isthesurfacezonebend, isarelativecontentofadsorbedparticlesonanunchargedsemiconductor(theminusreferstoacceptormolecules,theplustodonormolecules).
Thenear-surfacezonebendDVs,dependsontheelectricchargedensityonthesuperconductorsurfacecausedbothbythepresenceofelectricallychargedadsorbedparticlesandbysuperpositionofanexternalfieldofstrengthE.ForthisreasonDN/N=f(E),theexternalelectricfieldaffectingnotonlytherelationbetweentheevenlyadsorbeddonorandacceptormolecules,butalsothesorptionkinetics(Wolkenstein1973).Ifthecrystallatticeofasemiconductorischaracterizedbyasubstantialcontributionoftheioncomponentofchemicalbond,anelectricfieldcanalsoproduceadefiniteeffectuponthestoichiometryofcrystalcomposition
4.Changeofcriticalsupersaturationnecessaryfortheappearanceandstabilizationofcrystallizationnucleiinthecourseoflaminarcrystalgrowth.AsshownbySirota(1971),inthesimplestcase,whenthephasetransitionheatDH=0,thecriticalsupersaturationscritforcrystallizationnucleationisdescribed,accordingtothegeneralizedThomsontheory,bytheThomsonformula
Page136
whereVandrarethevolumeandtheradiusofthecrystallizationnucleus,qistheelectricchargeofthecrystallizationnucleus,gisthesurfacefreeenergyandkistheconstantdependentonthenatureofthesubstance.
AccordingtoChernovandTrusov(1969),thesurfacechargeslowerthenucleationactivationenergybyabout10%.
Itisanexperimentallyestablishedfactthatanelectricfieldhasaneffectuponthegrowthrateandalloydistributionbetweenthegasphaseandthegrowingfilmsofgermanium,silicon(Lyutovichetal1971)andgalliumarsenide(Palienkoetal1971).ItwasnoticedthatthethresholdtemperatureofsiliconepitaxialgrowthlowersunderhydrogenreductionofSiCl4,andtheactivationenergyofprecipitationandthemorphologyofthefilmsurfacealsochange(Chopra1969).
Thestudiesoftheinfluenceofanelectricfieldunderthechemicaltransportofsubstancefromthenearsourceontothesubstrate,i.e.bythesandwichmethod(IkonnikovaandIvleva1974;Korobovetal1977)revealthepossibilityofcontrollingthegalliumarsenidelayergrowthandofsuppressinguncontrolledinhomogeneitiesinthebulkfilm(Korobovetal1977).
Thus,theuseofelectricfieldsofdifferentpolaritiesandstrengthinthecourseofepitaxialgrowthfromthegasphaseisconsideredtobepromisingforanincreaseofintegrationandcontrolledlocalintensificationoftechnologicalprocessesinmicroelectronics.
3.1.3Liquid-phaseelectroepitaxy
Themethodofliquidphaseepitaxyinanelectricfield,calledalsoliquid-phaseelectroepitaxy,wasfirstproposedforobtainingepitaxial
filmsofsemiconductorsonanexampleofthecompoundGaSb(Golubevetal1974a,b).Thismethodisbasedoncrystallizationundertheactionofadirectelectriccurrentrunningthroughasource-bufferedmelt-substratesystem.Asopposedtoelectrocrystallization,wherethecrystallizedsubstanceisaproductoftheelectrodereaction,crystallizationinliquid-phaseelectroepitaxyisasecondaryphenomenon,aresultofthecurrent-inducedvariationinthetemperatureandconcentrationofthesubstance.
Theconcentrationandtemperaturegradientsarisingattheboundaryareaconsequenceofanumberofphysicalphenomenaduetoelectriccurrentindifferentpartsofthegrowthcell,namely,itmaybePeltierheatreleaseorabsorptionatboundaries,electromigrationofcomponentsintheliquidphase,Jouleheatandsomeothereffects.
Twotypesofliquid-phaseelectroepitaxywereinvestigated(Fig.3.1).Thefirsttypeisanequilibriumprocess,wheninthecourseoffilmgrowththeliquidphaseispermanentlyfedbyprecipitatedcomponentsfromthesource(Fig.3.1a),andthesecondtypewhentheliquidphaseisnotfed(Fig.3.1b).
Letusconsidertheessenceofliquid-phaseelectroepitaxy(Gevorkyanetal1977;Khachaturyanetal1977).Priortoepitaxy,thetemperatureofthecrystallizationcellwasT0.Intheinitialstatethesystemconsistsofasourceandasubstratewhichareincontactwiththebufferedmeltandwithcurrent-
Page137
Fig.3.1Basictypesofliquidphaseelectroepitaxywithindicationof
temperatureandconcentrationdistributionatthecrystallizationfront:a)withliquidphasefeeding;b)withoutliquidphasefeeding.
conductingelectrodes.AnexternalheatermaintainstheconstanttemperatureT0.Atthistemperature,theliquidphaseissaturatedwiththematerialsofthesourceandthesubstratewhicharedissolvedinthesystem,andtheentiresystemisinthestateofthermodynamicequilibriumyieldingnomaterialtransport.
Ifadirectelectriccurrentofappropriatepolarityrunsthroughthecrystallizationcell,Peltierheatisreleasedatthesource-liquidphaseboundaryandisabsorbedattheliquidphase-substrateboundary.Asaresult,thetemperatureattheboundarieschanges,atemperaturegradientoccursintheliquidphaseleadingtotheappearanceofaconcentrationgradient,thesourceispermanentlydissolvedanditsmaterialistransportedtothesubstrate.Thus,liquid-phaseelectroepitaxyinfactcombineselementsofordinaryliquidphaseepitaxyandelementsofzonemeltingwithatemperaturegradient.Achangeinthecurrentpolarityisresponsiblefordissolutionofthesubstrate,whilethelayerisprecipitatedontothesource.Reversibilityandlowinertiaofheatrelease(Peltierheatreleaseswithinacharacteristictimeofexcessiveenergytransfertoelectronsbyatomsofthemainsubstance)provideaquickandconvenientcontroloverliquid-phaseelectroepitaxy.
Itisalsonoteworthythataflowofcurrentthroughacrystallization
cellisresponsibleforthesubstancetransportontosubstrateduetoelectromigrationofliquid-phasecomponents.
Assoonastheelectriccurrentisoff,thetransportofsubstanceparticlesstopspracticallyinstantaneously,auniformdistributionofcomponentsisestablishedintheliquidzone,andthermodynamicequilibriumsetsupinthesystem.Thefilmgrownonthesubstrateisnotdissolved,andtheliquid-phasecompositionremainsexactlythesameasbeforethecurrentwasswitchedon.
Ifasourceisabsentinthecrystallizationsystemthensubstanceprecipitationontothesubstrateundertheactionofanelectriccurrent(underanymasstransfermechanism)maybeonlyduetoliquid-phasedepletion,whichleadstoanonequilibriumstateofthecrystallizationsystemaftertheprocessisover.
Applicationofoneortheothermethodshouldbecoordinatedwiththepurposesandtasksofaparticulartechnologicalprocess.
Page138
Fig.3.2Schematicofgrowthcellforliquidphaseelectroepitaxy,1,5)electrodes,2)substrate,3)liquidphase,4)source.
3.2Physicalbasisofliquid-phaseelectroepitaxy(Thetheoryofthemethod)
WeshallconsidertheproblempresentedinFig.3.2.Thematerialoftheliquidzoneisnotsupposedtoformchemicalcompoundsorsolidsolutionswithmaterialsofthesourceandsubstrate.Thetheoryofzonemeltingwithatemperaturegradient(ZMTG)*(Lozovsky1972)predictstwopossiblezoneregimes:kineticanddiffusion.
Weshallconsideronlythediffusionregimewhichisattainedforafairlysmalltemperaturegradient.Inthiscase,thethermalequilibriuminthesystemwillsetinmuchquickerthanthediffusiononesincetheliquid-phasediffusioncoefficientofatoms,D,ismuchlessthanthethermalconductivityK.ThetimesofestablishingthediffusiontDandthermaltTequilibriaaregivenbytherelations
Since ,from(3.1)and(3.2)itfollowsthat .InasmuchasthestationaryregimeofzonemeltingwithPeltier-inducedmotionwasearlierconsideredbyTiller(1963)andHurleetal(1964),thesolutionoftheformulatedproblemfallsintothreepartsanalysedbyLozovsky(1972)andKhachaturyan(1974):
a.temperaturedistributioninasystemtowhichacurrentisapplied;
b.filmgrowthrateasafunctionofcurrentdensity;
c.time-dependentvariationoffilmcomposition(compositiondistributionoverthickness).
3.2.1Temperaturedistributioninasystemundertheactionofanelectriccurrent
Weshallconsiderthesimplestcasewhenthematerialsofthesourceandsubstratearethesame.Intheproblemoftemperaturedistributionsuchaconsiderationisalmostalwaysadmissible.
Inthegeneralcase,thefollowingheatsourcesshouldbetakenintoaccountinthesolutionoftheproblem:
1.Peltierheat-asurfaceheatsource;
2.Jouleheat-abulkheatsource;
3.crystallizationanddissolutionheat-asurfaceheatsource;
*ItisobviousthattheprobleminindicatedgeometryissimilartoZTMG
Page139
4.Thomsoneffect-abulkheatsource;
5.Dufoureffect-abulkheatsource.
Whenanelectriccurrentisappliedtoasource-solution-substratesystem(Fig.3.2),Peltierheatisinstantaneouslyreleasedorabsorbedattheboundaries(pointsz=0andz=L),withasurfacepower
where isthePeltiercoefficientfortheinterfaces,Jisthedensityofcurrentthroughthesystem(mA/cm2),a=(a1-a2isthedifferencebetweenthethermoelectromotiveforcesofthesolventandsource(substrate)material(inV/grad).
Allcalculationsarecarriedoutforthelow-densityregionsofcurrent,andthereforetheJouleheatquadraticinJcanbeneglected.
ThedissolutionandcrystallizationheatshavereversesignsofthePeltierheat.IntheregionswherePeltierheatisreleasedthedissolutionheatisabsorbed,whileintheregionwherePeltierheatisabsorbedthecrystallizationheatisreleased.So,inthegeneralcase,thiscausesadecreaseofabsorbedandreleasedPeltierheat,thatis,adecreaseofthetemperaturegradient.Undercertaingrowthconditionsthecrystallization(dissolution)heatcancompletelycompensatethePeltierheatandsetinisothermalconditionsofcrystalgrowth.Forthesurfacepowerofcrystallizationheatwecanwrite
whereHisspecificheatofcrystallization(dissolution)(kcal/g),disthedensityofsubstanceundercrystallization(dissolution)(g/cm3),visthecrystallization(dissolution)rate(cm/s).
TheThomsoneffectisduetothetemperaturedependenceofcurrentcarrierconcentration,andinoursystemitcanbeneglected(thezonematerialisaliquidmetal).Moreover,itisalsoquadraticinJ.
TheDufoureffectinliquidsystemsisinsignificant(DeGrootandMazur1962).Thus,wecanneglectbulkheatsourcesandonlymakeallowanceforsurfacesources,thatis,Peltieranddissolution(orcrystallization)heat.Underthisassumption,theequationforthermalconductivityhastheform
whereKisthethermalconductivityoftheliquid-zonematerial,visthevelocityofzonemotion.
Weassumeherethezonethicknesstoremainunalteredandtheoriginofcoordinatestocoincidewiththeinterface(Petrosyanetal1974).Sinceinarealtechnologicalregimethecurrentdoesnotchangeatallorchangesveryslowly,inthesolutionoftheproblemitcanbethoughtofasconstant.
Thesecondtermintheright-handsideofequation(3.5)describestheinfluence
Page140
oftheinterfacemotionupontemperaturedistribution.Sincethegrowthrateinthesystemisveryslow,itseffectcanbedisregarded.Indeed,forthispurposeitisnecessarythatthefollowingshouldholdtrue
IfliquidBiorGaisusedassolvent,then ,,andfortheliquidzonethicknessL=100mmandthe
crystallizationrate thisinequalityissatisfied.
Giventhis,astationarytemperaturedistributionsetsinwithinthecharacteristictimetTwhichisoftheorderofonemillisecond.Thus,settinginofequilibriumtemperaturedistributionactuallyappearstobehigh-speedandadmitscurrentpulsesthroughthesystemoffrequencyuptotensofHertz.
ThediffusionprocessesinthesystemarecharacterizedbyatimeconstanttD.Assumingthediffusioncoefficienttobeequalto5×10-5cm2/s,wefindthatitisoftheorderofasecondandgreatlyexceedstr.Inallfurthercalculations,thetemperaturedistributioncanthereforeberegardedasstationaryandthetimederivativein(3.5)canbeneglected.Theequationforthermalconductivityhastheform
Thisequationcanbesolvedforeachpartofthesystemseparately.
Kuznetsovetal(1983)solvedtheproblemoftemperaturedistributionforthesystemdepictedinFig.3.2withthefollowingboundaryconditions.Atthesource-liquidzoneandsubstrate-electrodeinterfaces,constanttemperatures,TIIandTI,aremaintained.Attheliquidzone-substrateboundary,thecrystallizationheatreleaseistakenintoaccountalongwithPeltiereffect.Undertheseconditions,thetemperaturedifferenceATattheliquidzoneboundariesisequalto
wherels,lL,Ll,Larethetemperatureconductivitiesandthicknessesofthesubstrate(source)andliquidzone,respectively,and .Itisreadilyseenthatat ,disregardingthecrystallizationheatandtakingintoaccount ,weobtainfrom(3.7)
Wecanseethatthetemperaturegradientisindependentofthezonethicknessandisdeterminedbythemagnitudeofthedensityofcurrentflowingthroughthesystem.
Page141
WecanestimatethetemperaturejumpinthezoneandthetemperaturegradientinthesystemGaSb-Bi(Ga).Takingthefollowingvaluesoftheparameters(KhachaturyanaGdSb=150mV/grad,mBl=-20mV/grad.aGa=3mV/grad,L=10-2cm,J=25A/cm2,)lGa27W/mgrad,lBl=14W/mgradandT=723K,wefindthetemperaturedifferenceinthezone
thatis,thetemperaturegradientinthezoneisgradgrad/cm.ItmaybeseenthatthisvaluevarieswithintherangetypicalofZMTG(Lozovsky1972).
ForthesystempresentedinFig.3.2,Gevorkyanetal(1983)foundatemperaturedistributionwithsomewhatdifferentboundaryconditions:attheendsoftheelectrodesaconstanttemperatureismaintainedandattheelectrode-substrate,substrate-liquidzone,liquidzone-sourceandsource-electrodeboundariesthePeltiereffectistakenintoaccount.
3.2.2Filmgrowthrate
Inthesource-solution-substratesystemconsideredabove,alineartemperaturedistributionpracticallysetsinafteradirectelectriccurrentisswitchedon.Atthisstagethesystemisalreadynotinthestateofthermodynamicequilibrium.Ourtaskistodeterminethecomponentconcentrationdistributioninthezoneandthefilmgrowthrateinagiventemperaturefield.
Thecomponentconcentrationdistributionintheliquidzonewithallowancebothfordiffusionandelectromigrationisdeterminedfromthesolutionoftheequation
whereDisthediffusioncoefficient, istheparticledrift
velocityintheelectricfieldE,zcffisaneffectiveparticlecharge,eistheelectroncharge,risresistivityoftheliquidphase.
Inexperimentsonliquid-phaseelectroepitaxy,thecondition istypicallyfulfilled.Forthisreason,thelasttermin(3.10)canbeomitted.Equation(3.10)withoutthelasttermwassolvedbyGevorkyanetal(1983).Solvingequation(3.10),wecometothefinalexpressionforv(t):
whereCsistheconcentrationinthesolidphase.As ,from(3.11)weobtainthestationaryvelocityofgrowth,vst,
Page142
Asmightbeexpected,forE=0weobtainfrom(3.12)
From(3.12)wecanseethatvst,dependsnotonlyonthevalue,butalsoonthesignofE,thatis,thetypeofsubstrateandsourceconductivities.
3.2.3Chemicalcompositioncontrolofthefilm
Theliquid-phaseelectroepitaxymethodpermitsobtainingfilmswithcompositioncontrolledthroughoutthethicknessbymeansofcurrentdensityvariation.Birulinetal(1984),ZhovnirandZakhlenuk(1985),ZakhlenukandZhovnir(1985),Jastrebskietal(1978)andBryskiewiecz(1985)showedthepossibilityoffilmcompositioncontrolinliquid-phaseelectroepitaxyforathree-componentsystemwithaccountofPeltierandelectrictransfer.Itisassumedthatduringthewholeprocesstheliquidzoneattheboundarybetweenphasesisinlocaldynamicequilibriumwiththesourceandsubstrateatagiventemperature(thediffusionapproximation),andthefilmcompositionisdeterminedateachinstantoftimebytheliquidphasecompositionattheboundarywiththesubstrate.Ateachtimemoment,thefilmcompositionmustbeinproportionalrelationwithdiffusionfluxesatthesurface,andtheliquidphasecompositionisgivenbytheliquiduscurve.
Assoonasthecurrentthroughthecrystallizationcellisonandthetransitionprocessatthegrowthboundaryisover,acertainvalueoftheconcentrationofoneofthecomponents,Cx,setsin,whichisdeterminedontheonehandbythePeltier-inducedtemperaturevariationatthesolidphase-bufferedmeltboundaryandontheotherhandbyequilibriumoffluxesofparticlesofagivencomponent
comingtoandfromtheboundary.Attheothermeltboundary(intheabsenceofconvection)oratadistanceofthed-layer(inthepresenceofconvection)theinitialconcentrationremainsunchangedandequalsC0.Thenecessaryconditionisheretheequalitybetweentheparticlefluxescomingthroughtheboundaryofthed-layerandgoingawayintothesolidphase(Birulinetal1984):
wherek0istheequilibriumsegregationcoefficient,visthegrowthrateoftheepitaxiallayer.
DependingontherelationbetweenthevaluesofthebufferedmeltcomponentsmandD,twocomponentconcentrationvaluesnearthesubstratearepossible,namely, and .Intheapproximationthatinthetransition(d)layeroftheliquidphasetheconcentrationvarieslinearly,Birulinatal(1984)derivedtheexpressionforparticleconcentrationofthecomponent
Page143
intheepitaxiallayerasafunctionofelectriccurrentdensity
wherepisthemeltresistivity, thed-layerthickness,Jthecurrentdensity.
Theanalysisof(3.14)showsthatthedependenceofcrystallizedlayercompositiononthecurrentdensitymayonlybeabsentprovidedthattherelation
remainsunaffectedbycurrentdensityvariation,whichispossibleundertheconditionsthat
1)thetransitionlayerthicknessisverysmall,i.e.
2)thequantity isverylargeandthegrowthratedependslinearlyonthedensityofelectriccurrent;
3)vand dependlinearlyonthecurrentdensity.
Theoretically,whenthedependencev=f(J)isnonlinear,thelayercompositionmustalwaysdependonthecurrentdensity.TheformofthisdependenceisdeterminedforeachparticularcasebythevalueoftherelationbetweenmEandk0v.IfthemEvalueincreasesfasterthank0vwithincreasingcurrent(forexample, ),thecontentofthecomponentwillincrease,whereasifthemEvalueincreasesslowerthan orifthedependencev=f(J)islinear,thecomponentconcentrationwilldecrease.
Onthebasisofgeneralizedequationsofmasstransferandphaseequilibrium,ZhovnirandZakhlenuk(1985)gaveaqualitativeanalysisofsomesituationsoccurringunderliquid-phaseelectroepitaxyinthree-componentsystems,makingallowancefor
electromigrationandPeltiereffect.
3.2.4Initialstagesofnucleation
Thepresenceofchargesandelectricfieldsareknowntospeedupnucleationofanewphase(ChernovandTrusov1969;AleksandrovandEntin1971).ChernovandTrusov(1969)estimatedtheprobabilityofnucleationinapoint-chargefieldonthesurfaceofadielectric.Theycalculatedthecontributionoftheelectrostaticfieldtothecriticalnucleationenergyandsolvedthefollowingelectrostaticproblem:apointchargeqislocatedunderthecrystalsurfaceatadepthH.Thedielectricpermittivitiesofthecrystalandmediumareequaltoecrandemcd,respectively.ThesupersaturationofthemediumrelativetothecrystalisDm.Thenucleusofthenewphasehastheshapeofafiatdiscofheighta(aisequaltothelatticeconstant),Fig.3.3(ChernovandTrusov1969).
Theworkofcriticalnucleationisequalto
Page144
Fig.3.3Schematicofnucleationonthecrystal-mediuminterfaceinthepresenceofanelectriccharge.
wheree0isthedielectricpermittivityofthevacuum,thecriticalradiusr.determinedfromtheequation
whereaistheenergyoftheformationofaunitsidesurface,Vcisthevolumeofasingleparticleinthecrystal.
AleksandrovandEntin(1971)considerednucleationasadisplacementofaninfiniteplanecrystal-mediumboundarytowardsthemediumforadistanceequaltothecrystallatticeperioda.Withinsuchanapproach,theworkofcriticalnucleationDG*doesnotdependonthecriticalradiusr*
So,accordingtoChernovandTrusov(1969)andAleksandrovandEntin(1971),thepresenceofachargeonthesubstrateleadstoadecreaseofnucleationenergy,whichinturnspeedsuptheformationofcrystallizationcentres.
DhanasekaranandRamasamy(1986)investigatedtheinfluenceofanelectricfielduponatwo-dimensionalnucleation.Heconsideredcaseswheretheelectricfieldisperpendicularandparalleltothenucleation
andshowedthatsubjecttotherelationbetweenthedielectricpermittivitiesofthenucleusandthemedium,thenucleationcanbeeitheracceleratedordecelerated.
Weshallpresenttheestimatesoftheinfluenceofanelectrostaticfielduponthenucleationrate.Weshallconsiderthecasewhenanewphaseisformedonanelectrode.Inthegeneralcase,betweentheelectrodestherearetwosubstances,AandB,inthesame(say,liquid)phase.Anew(solid)phaseCcannucleateontheelectrodeeitherfromthesubstanceAorfromB(seeFig.3.4).
Tofindouttheeffectoftheelectrostaticfieldonthenucleationrate,oneshouldcalculatethecontributionoftheelectrostaticfielduponthecriticalnucleationenergy.Weshallcarryoutthiscalculationfortwocases:1)whennewnucleiontheelectrodeformametaland2)whentheyformadielectric.
Weproceedtothefirstcase.Supposethenewnucleimakeuphalfofthe
Page145
metalsphereontheelectrode.Tocalculatetheelectrostaticcontributiontothenucleationenergy,weshoulddeterminetheenergyvariationofthecondenserfilledwithdielectricA+B(withthedielectricconstante)whenaprotuberance,ahemisphereofradiusaappearsontheelectrode.Sincetheprotrusionandtheelectrodearemetals,theelectrodesurfacesareequipotentials.ThisisschematicallypresentedinFig.3.5.
Thechangeoftheelectrostaticenergyupontheappearanceontheelectrodeofahemisphericalnucleus,when ,isequalto
From(3.15)itisseenthat ,and,therefore,theappearanceofametallicnucleusontheelectrodeisenergeticallyadvantageous,thatis,thepresenceofthefieldE0mustpromotenucleation.
Thenon-electricpartoftheenergychangeuponnucleationintheformofahemisphereisgivenby(Aleksandrov1978)
whereoisthesurfacetensionattheinterface,Dmisthechemicalpotentialvariationunderphasechange,VtheparticlevolumeinthephaseC,lspecificheatofcrystallization,T-T0thesupercooling,T0theequilibriumtemperatureofphasetransition.
Summingup(3.16)and(3.15),weobtainthetotalenergyvariationundernucleation
From(3.17)wecaneasilydeterminethecriticalradiusofthenucleus,a*,andtheheightoftheenergybarrierundernucleation,DG*
Fig.3.4Schematicofnucleationontheelectrode:1)metallicelectrodes;
2)energysource;A,Bareinitialsubstances;Cisnucleusofthenewphase.
Page146
Fig.3.5Distributionofelectricpotentialincrystallisation.Horizontallinesareequipotentialsurfaces,verticallinesareelectricfieldstrengths,E0isthefield
strengthinadielectric,distheinter-electrodegap.
From(3.17)and(3.18)itisreadilyseenthata*andDG*decreaserapidlywithincreasingE0.ThisisdemonstratedinFig.3.6.
Thenucleationrateisgivenbytheexpression(Aleksandrov1978)
whereAisapre-exponentialmultiplier.Forthisreason,weassumethepre-exponentialfunctiontobeindependentofE0.Now,substituting(3.19)into(3.20),wecometothefinalexpressionforthenucleationrateasafunctionofthefieldstrength
Thenucleationrateisthusseentoincreasesharplywithincreasingfieldstrength.
Nowweturntothecasewhenthenucleusofthenewphaseisadielectric.Forsimplicityofcalculationsassumethenucleustohavetheshapeofacylindricalprotrusionofareasandheighthontheelectrode.Figure3.7presentstheschemeofnucleationinthesystemA+B.
Weexaminedacaseinwhichtherewasnoexternalfield,i.e.E0=0.SurfacetensionofthesurfaceboundarybetweenthephasesA+BandCiss,attheboundarybetweenthesidesurfaceofthenucleusandthephaseA+Bissh,attheboundarybetweentheelectrodeandthephaseA+Bitisosandatthenucleus-electrodeboundarys0(seeFig.3.7).Thentheenergyvariationuponnucleationhastheform
Itisofinteresttodeterminetheoptimumsizeofthenucleusforagivenvolume,thatis,forV=pr2h=const.Itisequalto .Inviewofthisfactwerewrite(3.22)as
Page147
Fig.3.6Energyvariationuponnucleationasafunctionofparametera.
Differentiating(3.23)withrespecttohandequating tozero,weobtaintheequationfromwhichwecanfindtheoptimumvalueoftheheighth*ofthecylindricalnucleus
Thedependence(3.24)hasasimplephysicalmeaning.Asshouldbeexpected,h*increaseswithincreasingss.Forthegivenvolume,thenucleusacquirestheformwhichcorrespondstotheminimumofsurfaceenergy.
Substituting(3.24)into(3.23),weobtainthefollowingexpressionforDG*
From(3.25)wecanseethatDG*asafunctionofVhasamaximum,thatis,theappearanceofsmall-volumenucleileavesthesystemstable,butitbecomesunstableassoonaslarge-volumenucleioccur.Thecriticalnucleationenergycanbereadilyobtainedfrom(3.25)
Thecriticalheighth**andthecriticalvolumeV**havetheform
Thecoefficientoftheformofthecentreofthenewphaseh**/V**canbeeasilyobtainedfrom(3.27)and(3.28)
Page148
Fig.3.7Schematicofformationofacylinder-shaped
crystalnucleusonanelectrode.
Theresults(3.26)and(3.29)wereobtainedbyBolkhovityanovandYudaev(1986).
IfanucleusisformedinanexternalfieldE0,thecontributionoftheelectricenergyintothenucleationenergyfor hastheform
whence ,and,therefore,theexternalfieldmustpromotenucleation.Thisfacthasaclearphysicalmeaningsince,asiswellknown,adielectricwithahighdielectricpermittivityvalueisalwaysdrawnintoacondenserconnectedwiththeexternalvoltage.
Withallowanceforthecontributionoftheelectrostaticfield,theenergyvariationis
From(3.31)and(3.23)onecanseethatasubstitutionoffor( )informulae(3.26),(3.27)and(3.28)
givesthedependenceofDGonj.
Thenucleationratewillbedeterminedfromtheformula
whichshowsthatfor thenucleationrateincreases.
3.3Theroleofthermoelectriceffectsinthecourseofliquid-phaseelectroepitaxyofferroelectrics
Theapplicationofadirectelectriccurrentinthecontrolovercrystallization
Page149
ofepitaxialstructuresgrownfromaliquidphasearecloselyconnectedwiththermoelectriceffectsobservedduringthisprocess.WeshallagainturntothecrystallizationcellshowedschematicallyinFig.3.2.Thephenomenaoccurringinacrystallizationcellunderliquid-phaseelectroepitaxyarethefollowing(digitsrefertozonesorinterfaceswherecorrespondingphenomenatakeplace):
-(1-5)heattransfer,
-(1-5)Jouleheat,
-(1-5)Thomsonheat,
-(3)diffusion,
-(3)electrictransfer.
Thesewereheatexchangeeffects.Nextcomesurfaceeffects:
-(3-4)heterogeneouscrystallization,
-(4-3),(3-2)crystallization(dissolution)heat,
-(4-3),(3-2),(5-4),(2-1)Peltierheat.
So,inthegeneralcasesystemsofliquid-phaseelectroepitaxyinvolveseveralmechanismsofheatabsorptionmechanisms.Electrictransfer,crystallizationanddissolutionofsolidphasesleadstotheappearanceofconcentrationgradientsofacrystallizingsubstanceintheliquidzoneanddiffusionleadstolevellingupthesegradients.
Thefirstquestiontobeansweredintheanalysisofcrystallizationprocessesishowthemotiveforcesofcrystallizationdependuponcrystallizationconditions.Thesemotiveforcesaredeterminedbythevariationsoftemperatureandconcentrationofacrystallizingsubstanceatthecrystallizationfrontascomparedtoequilibriumvaluesoftheseparameters.
Whenadirectcurrentrunsthroughinterfaces,PeltierheatproportionaltotheproductofcurrentdensitybythePeltiercoefficientisinstantaneouslyreleasedandabsorbed.
Owingtothiseffectthetemperatureattheinterfacefalls,thisfallbeingequalto(Jastrzebskietal1978):
where isthedifferenceofthermoelectromotiveforcesbetweenthesubstrateandsolvent,L1isthesubstratethickness,lsthethermalconductivityofsubstratematerial,T0thetemperatureinthesystempriortoapplicationofcurrent.
Aconsequenceoftemperaturedifferenceinthesystemisconcentrationvariationintheliquidzone
wheremistheslopeoftheliquiduscurve.
Attheinterface,Peltierheatisabsorbedandcrystallizationheatreleased(sincetheyhaveoppositesigns).
Consequently,thisleadsintheendtoadecreaseofabsorbedandreleasedPeltierheat,i.e.toadecreaseofthetemperaturegradient.
Page150
TheresultsofcomparisonoftheoreticalandexperimentaldatasuggestthatthecrystallizationheatcanbeneglectedascomparedtothePeltierheat.Then
wherelListhethermalconductivityofthemelt.
Thus,thetemperaturegradientoccurringattheinterfaceisindependentofthezonethicknessandisdeterminedbythevalueofthecurrentdensity.
Sincethetimewithinwhichthetemperaturegradientissetinthesystem, ,iscomparativelysmall,thecurrentrunsthroughanonuniformlyheatedsystem,thatis,fromtheverystartoftheprocessanadditionalThomsonheatisreleased
wheretTisThomson'scoefficient.
OwingtotheThomsonheat,thesystemcanbeadditionallyheated,thetemperatureincreasebeing
whereMandcarerespectivelymassandthermalcapacityofthesubstrate.
Whenadirectelectriccurrentisapplied,Jouleheatissimultaneouslyreleasedinthesystem:
whereRistotalsystemresistanceandRLisliquidphaseresistance.
Since ,theJouleheatmainlyaffectsthesubstrate.
Beginningfromsomeinstantoftime(tcr),theJouleeffectmaybecomegreaterthanthePeltiereffectsinceaconstanttemperature
gradientattheinterfaceismaintainedbythePeltierheat,whiletheJouleandThomsonheatsareaccumulatedinthesystem.Consequently,theresultanttemperatureofthesystemstartsexceedingtheequilibriumtemperatureTOandthesystemmayappeartobeundersaturated,whichwillresultindissolutionofthecrystallizedlayer.
Ascanbeseenfromtheaboveformulae,theJouleheatisquadraticandthePeltierheatislinearinJ.ThismeansthatthereexistsacertainoptimumvalueJoptwhentheJouleheatbecomespredominantoverthePeltierheat.TheJouleheatcanthereforebeneglectediftheappliedcurrent
TheThomsoneffectishereduetotemperaturedependenceofcarrierconcentration,andinsuchasystemitcanbeneglected,providedthezonematerialisaliquidmetal.Moreover,thiseffectisalsoquadraticinthecurrent.
GabrielyanandKhachaturyan(1984)investigatedferroelectricfilmgrowthusingliquid-phaseelectroepitaxyandestimatedthecontributionofthermoelectriceffectstothisprocessonanexampleoflithiumniobate.
Page151
Figure3.8presentstemperatureversuscurrentdensityunderliquid-phaseelectroepitaxyofLiNbO3withallowanceforPeltier,JouleandThomsoneffects.ThefigureshowsthatattheinitialinstantsoftimetemperaturevariationsduetoheatexchangeeffectsaresmallerbyseveralordersofmagnitudethantemperaturevariationsduetothesurfacePeltiereffectandcan,therefore,beneglectedatearlystagesofgrowth.Whenthegrowthtimeislong,theresultanttemperatureofthesystemexceedstheequilibriumtemperatureToandthesystemmayappeartobeincompletelysaturated,whichleadstolayerdissolution.
3.4Electro-LPEgrowthoflithiumniobate-tantalatefilms
Thestandardmethodsworkedoutforsemiconductormaterialscannotbeusedforcurrent-inducedliquid-phaseelectroepitaxyofferroelectricsbecauseofthephysico-chemicalspecificitiesofoxidesystems.Weproposetwowaysofcurrent-inducedliquid-phaseelectroepitaxyofferroelectrics:
-current-inducedliquid-phasecapillaryepitaxy
-liquid-phaseelectroepitaxyfromanunlimitedvolumeofthesolutioninmelt.
Filmgrowthinanelectricfieldopensnewhorizonsforgrowthofthin-filmferroelectricswithacurrent-controlledcomposition,thicknessandstructuralperfection.Ofparticularinterestisobtainingasingle-domain(polarized)stateoflayersinthecourseofgrowth.
Inthissectionweconsidertheuseofcurrent-inducedliquid-phaseepitaxialgrowthoffilmsoflithiumniobate-tantalate,electrochemicalprocessesproceedingintheliquidphaseandmodulationinthecompositionofferroelectricfilmsundertheindicatedgrowthconditions.WealsooptimizeconditionsofepitaxialgrowthofLi(Nb,Ta)O3filmswithaccountofJouleheat.
3.4.1Epitaxialgrowth
Theuseofcurrent-inducedliquid-phaseepitaxyforgrowingLiNbO3andLi(Nb,Ta)O3filmsfromalimitedliquid-phasevolumecontainedbetweentwosubstrateslocatedclosetoeachotherwasproposedbyKhachaturyanetal(1986).Figure
Fig.3.8Melttemperaturevariationsduetothermaleffectsasafunctionofcurrentdensityinthecourseof
LEPoflithiumniobate.
Page152
3.9presentstheschemeofafilmgrowthdevice.Thecompositionof90%LiVO3+10%Li(Nb,Ta)O3waschosenassolventforliquid-phaseelectroepitaxy.(0001),(1120)platesofLiTaO3servedassubstratesandcrystallineplatesofLi(Nb,Ta)O3servedasasource.Thesubstrateandsourcesizewas20×15×l.5mmandtheliquid-phasethicknesswas1.5÷2mm.Theelectrodesweremanufacturedusingplatinumblackeningandaconductinghigh-temperatureglue.
Apreliminarilypreparedplatinumnielloisdepositedoninoperativesubstrateandsourcesurfaces,thentheplatesareannealedforonehourat400°C.Afterthisashiningmetallizedsurfaceiscoveredwithahigh-temperatureconductingglue.Thesubstrateandsourceplateswithafixedgap(intermediateplane-parallelplatesofagiventhicknessareusedforfixation)aregluedtoaquartzholderwithelectrodes.Thegapbetweenplatesissochosenthatundertheactionofcapillaryforcesthebufferedmeltisuniformlydrawnfromthecrucibleintothespacebetweenthesourceandsubstrate.Foroxidesystems,thegapbetweenthesourceandsubstrateischosenwithintherangeof1-2mm,whichpermitsavoidingconvectivemixing.Thenthesystemismountedinafurnaceoveracruciblefilledwithbufferedmelt.
Thefurnacetemperatureisgraduallyincreasedtillitbecomes50-100°Chigherthantheinitialepitaxytemperature,whichismaintainedfor0.5-1huntilacompletehomogeneityisattained,andthenthetemperatureequaltotheinitialepitaxytemperatureisestablished.Aftersomeholding,theplatesareimmersed1-2mmintothecruciblecontainingthebufferedmelt,asaresultofwhichtheliquidphaseaffectedbycapillaryforcesisdrawnintothegapbetweentheplates.Themomentofcontactbetweentheplatesandthemeltisfixedbyanindicatorlamp.Thentheplateswithliquidphaseareseparatedfromthecrucibleandreturntotheinitialstate.Constant(orpulsed)voltageisappliedtotheplates.Thelayergrowthproceedswhenthepotential
onthesubstrateispositive.Assoonasthecurrentisoff,thelayergrowthceases,andaliquid-phaseabsorberistakentothegapbetweentheplates(DudkinandKhachaturyan1986),afterwhichthesystemisslowlycooleddowntoroomtemperature.
Theessenceofliquid-phaseelectroepitaxyfromanunlimitedbufferedmeltvolume(GabrielyanandKhachaturyan1985)isillustratedinFig.3.9b.Thismethoddiffersfromtheoneindicatedaboveinthattheliquidphaseisnotfedfromthesource,andtheliquid-phasethickness
.
3.4.2Electrochemicalprocessesintheliquidphase
Inthestudyoftheprocessofliquid-phaseelectroepitaxyanimportantroleisplayedbyacorrectestimateoftherelativecontributionofdifferentstagesofthisprocess.Thedifferenceinthenatureofchargecarriersinoxidecompoundsleadstovariationofthephysicalprocessesproceedinghereascomparedwithliquid-phaseelectroepitaxyofsemiconductorsystems.Asaconsequencethereoccuranumberofspecificeffectstypicalofliquid-phaseelectroepitaxyofcomplexoxideswhicharetobeexaminedonanexampleoflithiumniobate.
Tospecifythecharacterofmasstransferunderliquid-phaseelectroepitaxyofoxidesystems,electrochemicalprocessesattheinterfacebetweencontactingphaseswereinvestigatedandthelayergrowthratewasdeterminedasafunctionofstrengthandtimeofthecurrentappliedtothecrystallizationcell(Khach-
Page153
aturyan1988;Gabrielyanetal1989).
Figure3.10showsthetemperaturedependenceofthenumberoflithiumionstransferredinlithiumniobatesinglecrystalofcongruentcomposition.Wecanseethatinthetemperaturerangeof800-900°Csinglecrystalsaremixedconductorswithcomparablecontributionsoftheionandelectroncomponentsofconductivity.AsconcernsmeltsofthesystemLiVO3-LiNbO3,wecanassume,accordingtoPastukhovetal(1984)andShumov(1984),thattheconductionmechanisminthemiscompletelyionandisduetolithiumionmigration( ).Thisimpliesthatinthechain(Fig.3.2)thenatureofthemainchargecarriersdoeschange.AsaconsequenceofionconductivityofthemeltLiVO3-LiNbO3andamixedion-electronconductivityofthecrystalLiNbO3,electrochemicalprocessesproceedinthechainwhenadirectelectriccurrentisappliedtothecrystallizationcell.
Inregion2-3themostprobableistheprocess
withdissolutionofreleasedoxygeninthemeltandaccumulationofLiNb3O8attheboundarywiththeplatinumelectrode.
Throughtheboundary2-3thecurrentcanonlybetransferredbylithiumions,butthroughtheboundary1-2comesonlyhalf( )theamountoflithiumionsrequiredforcurrenttransferinthechain,whiletherestoftheionsareformed,accordingto(3.39),onthesurfaceofalithiumniobatefilm.Finally,attheboundary3-4thereproceedsoxidationofoxygendissolved
Fig.3.9DeviceforLPEfilmgrowth:1)platinumcrucible;2)quartzholder;
3)alayerofcurrent-conductinghigh-temperatureglue;4)substrate;5)Li(Nb,Ta)O3source;6)platinumconductors;7)thermocouple;8)liquidphaseabsorber;9)quartztube;
10)ceramicstand.
Fig.3.10(right)Temperaturedependenceofthenumberoflithiumionstransferredinalithiumniobatesinglecrystalofcongruent
composition.
Page154
inthemelt
whichobviouslyleadstoLi2O-enrichmentofthemeltnear(4),bythereaction
Thus,thekineticsofliquid-phaseelectroepitaxywillbedeterminedbytheratioofcrystallizationratesduetoPeltierheatabsorptionandtoelectrochemicalfilm(orsubstrate)dissolutionbythereaction(1)orthelike.
Theroleofdifferenteffectsunderliquid-phaseelectroepitaxyofoxidesystemscanbeconvenientlyillustratedusingafragmentofthesystemstatediagram(Fig.3.11).Supposethatthebufferedmelthasacompositioncorrespondingtopoint1.Peltierheatabsorptioncorrespondstoashiftofafigurativepointofthesystemtowardspoint2.ThesolutionappearstobesupersaturatedwithLiNbO3,andthelatteriscrystallizedonthesubstrate.
Alongapplicationofcurrentmayberesponsibleforheatingoftheentiresystem(GabrielyanandKhachaturyan1984),whichleadstogrowthdecelerationandthentofilmdissolution(thefigurativepointshiftstowardspoint3).Itshouldbenotedthatinthecourseofcrystallizationthemeltcompositionshiftsinthedirection'4'(liquid-phaseelectroepitaxywithoutfeedmaintenance),andinthepresenceofasourceitcanremainunalteredattheexpenseofequivalentfeeding(ZhovnirandZakhlenyuk1985).Accordingtotheanalysiscarriedoutabove,theiontransfer,causingvariationsinthemeltcomposition,inducesdisplacementofpoint1inthedirectionperpendiculartotheplaneofthepicture,thatis,achangeoftheLi2O/Nb2O5ratio.
Theprobablemechanismsconsideredaboveallowustoanalyzethe
dataonlithiumniobatefilmgrowthbytheliquid-phaseelectroepitaxymethod.
WhenaLi(Nb,Ta)O3sourceisabsentfromthecrystallizationcellandcurrentisappliedforatimeexceeding50min,theobserveddecreaseofthegrowthrateorevendissolutionoflithiumniobatefilmiscausedbothbyadecreaseofsupersaturationduetoJouleheatreleaseandbyfilmelectrolysisgoingbyreaction(3.39)(GabrielyanandKhachaturyan1984).Filmdissolutioncanalsobestimulatedbythefactthatasaresultofalimitedamountofoxygendissolvedinthemelt,itsconcentrationfallswhenthecurrentisapplied,thatis,thespeedofthecathodereaction(3.40)necessaryforchargetransferfromthemelttotheelectrodedecreases.Then,tomaintainaconstantcurrentstrengthinthecircuit,thespeedofthereaction(3.39)whichistheonlymolecularoxygensupplierofthemelt,mustobviouslyincrease.Aconsequenceofcathodereactiondecelerationisanincreasedresistanceofthecircuit,whichleadstothenecessityofahighervoltagetobeappliedtothecellinordertomaintainJ=const.
Thus,theanalysisoftheavailableexperimentaldatashowsthatthebuffered-meltsystemLiVO3-LiNbO3isanion-conductingmediumwithaclearlypronouncedelectricproperty.Thedegreeofdissociationdecreaseswithincreasingcontentoflithiumniobateinthebufferedmelt.Themainchargecarriersin
Page155
Fig.3.11FragmentofthephasediagramofthepseudobinarysystemLiVO3-LiNbO3.
theliquidphaseattheepitaxytemperaturearelithiumions.Electrochemicalandnear-electrodeprocessesintheliquidphaseleadtotheoccurrenceofLi2Omoleculesand , ionswhosecontributiontoepitaxialprecipitationofLiNbO3layersisinsignificant.
3.4.3Growthkineticsofelectro-LPEgrownlithiumniobate-tantalatefilms
Todeterminethecharacterofmasstransferinelectro-LPEofLi(Nb,Ta)O3,wehaveanalyzedthedependenceoffilmthicknessandgrowthrateonthetimeofapplicationofcurrentinanequilibriumelectro-LPEconsistingofsubstrate-bufferedmelt-source.Fromthethermodynamicpointofview,itwouldbemoreprecisetothinkofthisprocessasaliquid-phaseelectroepitaxywithfeedmaintenanceorwithasource.
Figure3.12presentsthedependenceoffilmthicknessonthetimeofapplicationofcurrenttothecrystallizationcellfordifferentvaluesofcurrentdensity.Therateoflayerformationalterswithintherangeof0.6-0.1mm/minandthefilmsurfaceappearstobemirror-smooth(Khachaturyan1987).MicroX-rayspectralanalysisshowedanevendistributionofthemaincomponentsoftantalumandniobiumovertheheterostructure.Theamountofvanadiumcomingtotheepitaxialfilm
fromtheliquidphaseisminimum(0.005÷0.01at%).
Acharacteristicfeatureofelectro-LPEofferroelectricfilmsand,inparticular,oflithiumniobate,isthatsimultaneouslywithlayergrowththefilmismadesingle-domain(polarized).ThemethodofpolarizationofLi(Nb,Ta)O3filmswas
Fig.3.12ThicknessofaLiNbO3filmversusthetimeofapplicationofcurrenttothecrystallizationcell.
Page156
workedout.Forheterostructures,thisprocessischaracterizedbyadifferenceintheCurietemperaturesofthesubstrateandthefilmandbythepresenceoftransitionregionswithasmoothlyvaryingcomposition.10×15and40×60mmcontainerswithplatinumcontactsforsixstructuresweremade.Regimeswereestablishedthatprovideminimumpotentialandtemperaturedifferences,whichisnecessaryfordecreasinginterdiffusionoffilmcomponents,forpalladiumdiffusionintothestructurealongthesidecontactsandforpreventingsamplecrackingundertheactionofcurrent.
Figure3.13presentsthecurvesofthedegreeofpolarizationasafunctionofcurrentdensityforvariousepitaxytimes.Whenthetimeofapplicationofcurrentisincreasedfrom10to35min,single-domainfilmsoflithiumniobateareformedwithinthecurrentdensityrangeof10-15mA/cm2.
TogrowfilmsofsolidsolutionsLi(Nb,Ta)O3,Khachaturyanetal(1987)appliedopposite-polaritypulsestothecrystallizationcell.Thecontrolparameterswerechosenfromthefollowingrelations:currentdensityinpulsesJdirect=3Jrev;therelationbetweenpulsedurationandpausesbetweenthem ,whereJdirectiscurrentdensityinadirectpulse(mA/cm2);Jreviscurrentdensityinareversepulse(mA/cm2);tdirectisdurationofadirectpulse(s);trevisdurationofareversepulse(s);tpauseispauseduration(s);tdifisthecharacteristicdiffusiontime(s).
Thegapbetweenthesourceandthesubstrateisdiminishedto0.5mmforthereasonthatinprecipitationoflayersofsolidsolutionsLi(Nb,Ta)O3.Thisreducesthetimeofdiffusion,fromthesourcetothesubstrate,ofcomponentsdissolvedintheliquidphase,whichimprovescompositioncontrolinsolidsolutions.
Theliquidphasecompositioncorrespondedto90mol.%LiVO3+5mol.%LiNbO3+5mol.%LiTaO3.InitialepitaxytemperatureTcpit=
980°C.Jdirect=10mA/cm2,tdirect=30min,trev=3mA/cm2,trev=6min,tpause=1min.
Whenadirectpulseisapplied,anepitaxiallayerprecipitatesonthesubstratesurface.Then,toneutralizetheelectricallyinducedstateintheliquidphaseandtopreventelectrictransfer,a1minpauseismade,afterwhichareversepulseisappliedtomixionsintheliquidphase.Thenagaina1minpauseandthentheprocessisrepeated.ThelayercompositiondeterminedbymicroX-rayspectralanalysiscorrespondedtoLiNb0.5Ta0.5O3andhadathicknessh=10mm(seeFig.3.14a).
IfweapplyaunipolarpulsedcurrentwithamplitudesJ1andJ2,thecompositionofthegrowingfilmofthesolidsolutionLi(Nb,Ta)O3changesaccordingtoappliedpulses(Fig.3.14b).
ComponentdistributioninafilmwasdeterminedbyamicroX-rayspectralanalysis.ThecharacteristicdistributionspectraofthecomponentsNbandTaoverthestructurethicknessarepresentedinFig.3.15.Asdistinctfromdiffusionwaveguides,epitaxiallayersexhibitasharptransitionfromthesubstratetothefilm.Compositionconstancyofsolidsolutionsoflithiumniobate-tantalateoverfilmthicknessshowsthattheepitaxyprocessisstationary,thatis,theconcentrationprofileintheliquidphaseandtheeffectivecoefficientoftantalumsegregationremainunchanged.Thecalculationofthecompositionscorrespondingtothemicroprobecurveshasshownthatthecontentofniobiumandtantalumina
Page157
Fig.3.13DegreeofLiNbO3filmpolarizationasafunction
ofcurrentdensity.Thetimeofapplicationofcurrent:1-10min;2-20min;3-25min;4-35min.
filmofsolidsolutionisconstantandisdeterminedbythelayergrowthrate.Asthecurrentdensityand,therefore,thegrowthratedecrease,theeffectivecoefficientincreasesfrom1.4to2.35(Fig.3.15).Thegrowthrateofthelayer,v,changeswithcurrentdensitybyalinearlawwithintheindicatedrangeofJvalues.
Inprecipitationofmulticomponentsystemsfromasolutioninmeltatahightemperature,thecompositionoftheprecipitatedlayerdifferstypicallyfromthecompositionofthedissolvedmaterialsincethepresenceinthelayerofeachcomponentisspecifiedbyanindividualsegregationcoefficient.InlithiumniobatetantalateepitaxyfromthesolutionintheLi2O-V2O5melt,thecompositionoftheLiNbl-yTayO3shiftsrelativetothecompositionofthedissolvedmaterialLiNbl-xTaxO3towardsanincreaseoftantalum,thatis, .
Thecompositionalshiftisdifferentunderdifferentgrowthconditions.Variationsoftheeffectivesegregationcoefficientarecustomarilyassociatedwithmasstransferintheliquidphase.Alimiteddiffusionofdissolvedcomponentsleadstotheappearanceofconcentrationprofilesintheliquidphaseandmakesitpracticallyimpossibletocontrolefficientlythecompositionofmulticomponent
Fig.3.14TopogramoffilmsofLiNb05Ta05O3solidsolutionsof(1120)and(0001)orientations(a)anddistribution
ofcomponentsalongtheLi(Nb,Ta)O3/LiTaO3heterostructure(b).
Page158
Fig.3.15Layergrowthrate(1)andeffectivesegregationcoefficient(2)ofTaversuscurrentdensityinLPEofLi(Nb,Ta)O3.
films.Masstransitioninliquid-phaseelectroepitaxyisduetodiffusionandelectrictransferofcomponentstothecrystallizationfront.Theniobium-to-tantalumratioinafilmisdeterminedbythekineticprocessesofcrystallization.
3.5Optimizationofconditionsofepitaxialgrowthoflithiumniobatefilmswithallowanceforjouleheat
Oneofthebasicnegativeeffectsuponliquid-phaseelectroepitaxyisJouleheat.Topreventthiseffectinliquid-phaseelectroepitaxyofferroelectrics,itisnecessarytospecifyitsroleandcontributiontothecrystallizationprocess(Avakyanetal1988).WecanconditionallydistinguishbetweentwomainsourcesoftemperaturenonuniformityatthecrystallizationfrontassociatedwiththeJouleeffectandleadingbothtopreventingPeltiercoolingandobtainingnon-planarstructures.Thefirstofthesesourcesisduetoconstructiveimperfectionofgrowthdevice,unsatisfactoryqualityofelectriccontactsbetweenconductingelements(Jastrzebskietal1978;Nikishin1984a)andtoinappropriategeometryoftheelements(BarchukandIvaschenko1982).ThesecondsourceisofamorefundamentalnatureandisconnectedwiththefactthatthegrowthdeviceisessentiallyinhomogeneousfromtheviewpointofreleaseanddispersionofJouleheat.Byvirtueofconstructivevarietyofrealgrowthdevicesfor
liquid-phaseelectroepitaxyofsemiconductorsandferroelectrics,theroleofoneoranotherfactorandtheirinterrelationsarenotobvious(Milvidskyetal1982).
Themainunitofadeviceforequilibriumandnonequilibriumregimesofelectro-LPEofferroelectricsconsistsofgrowthcellsdepictedinFig.3.16a,b.Conductingelectrodesweremadeofplatinum.Applyingthemethodofequivalenceofthermalandelectricschemes(Stefanakosetal1976)withallowanceforJouleheatingofthegrowthcell,thetemperaturevariationofthecrystallizationfront,T,isdescribedbytheexpression
Page159
where ,isthethermalconductivityoftheithelement, ,isthelineardimensionoftheithelement,R2andR4areresistancesofthesubstrateandsource,respectively.PlkisthedifferenceofPeltiercoefficientsbetweentheelementsiandk,Jisd.c.density,T0isthetemperatureofexternalsurfacesoftheelectrodescorrespondingtothesaturationtemperature,T1isthecrystallizationfronttemperature.
Whenderiving(3.42),thecontactresistanceswereassumedtoplayaninsignificantroleunderJouleheatrelease,whichisconfirmedbyexperimentalmeasurements.Thevaluesofcontactelectrode-substrateandsubstrate-liquidphaseresistanceswererespectivelyequalto5×10-3ohm/cm2and8×10-3ohm/cm2,whichismuchlessthanthesubstrateandsourceresistances,102ohm/cm2,
Withaccountofexperimentalconditions×12=×14=×1,×23=×34=×3,G2=G4G2,R2=R4=R,formula(3.42)acquiresthefollowingsimpleform
From(3.43)wecanwritethecriterionforcoolingthesubstrate-solution-meltboundary
andtherefore
Thequantity
willcorrespondtothecriticalcurrentofelectro-LPE.Withaccountof
and ,formula(2.37)acquirestheform
Page160
and
Itisofinteresttoexaminethephysicalnatureofcriticalcurrentunderelectro-LPEasafunctionofsystemtemperature.Thegraphofthedependenceforbothregimesisconstructedanalytically(Fig.3.17).
Aswecanseefromthegraph,thecriticalcurrentofelectro-LPEdependsonsubstratematerial.Thelimitofad.c.JcpitpreventingtheJouleeffectincreaseswithincreasingtemperatureT0.
Sincethecriticalcurrentofelectro-LPEisafunctionofgeometricaldimensionsofthesubstrate,itfollowsthat
wherer0isresistivity,sandlarerespectivelytheareaandthethickness;therefore,increasingthesubstrateareaanddecreasingitsthickness,wecanincreasetheboundaryvalueofJ0.
Anincreaseoftheareaandadecreaseofthethicknessofthesubstrateandthesourceprovideextensionoftherangeofoperatingcurrentdensitiesforelectro-LPEofferroelectrics.
ThethicknessofepitaxiallayersofLiNbO3grownonLiTaO3substratesis
Fig.3.16Schematicofacellshowingtemperaturedistribution
a)equilibriumregimeofLPE;b)nonequilibriumregimeofLPE.1)platinumelectrode;2)LiTaO3orLiNbO3substrate;3)solutionin
melt[N%LiNbO3-(100-N)%LiVO3];4)LiNbO3source;5)thermalinsulation.
Page161
Fig.3.17TemperaturedependenceofthecriticalLPEcurrent(J0).1)nonequilibriumregime,
2)equilibriumregime(dashedlinesareforLiNbO3,solidlinesforLiTaO3
Fig.3.18(right)ThicknessesofepitaxiallayersofLiNbO3onLiTaO3substratesasfunctionsofcurrentdensity
inequilibrium(+)andnonequilibrium()LPEregimes.
plottedagainstthecurrentdensityvariationinequilibriumandnonequilibriumregimesofliquid-phaseelectroepitaxy(Fig.3.18).Thegraphisdividedintothreeregions.Inregion(1),layergrowthproceedsandthefilmthicknessincreaseslinearlywithincreasing
currentdensity.ThisdependencedeviatesfromlinearwhencurrentdensityisclosetoJ0=10mA/cm2inequilibriumregimeandJ0=17mA/cm2innonequilibriumregimeofliquid-phaseelectroepitaxy.Region(II)ischaracterizedbyadecreaseofgrowinglayerthicknessduetotheJouleeffect,whichresultsinasurfacedissolutionofthegrownlayerresponsiblefortheappearanceofetchingpatternsonthesurface.
Accordingtotheexpressions(3.19a,b),theJouleeffectmustexceedthePeltiereffectwithrespecttothechosenparametersforJ0=9mA/cm2inequilibriumregimeandJ0=17mA/cm2innonequilibriumregimeofliquid-phaseelectroepitaxy,andtheformationofLiNbO3layersundersuchcurrentsisexplainedbytheabove-saidapproximations.ForcurrentdensitiesJ0>9mA/cm2inequilibriumregimeandJ0>20mA/cm2innonequilibriumregimetherearenoLiNbO3layersonthesubstrates,thatis,theJouleheatcompletelyoverlapsthePeltiercooling(region(III).
Figure3.19presentsthegraphoftheexperimentaldependenceofepitaxiallayerthicknessonthesubstrateandsourcethicknessbothinequilibriumandnonequilibriumregimes.Asthesubstrateandsourcethicknessesincrease,thecriticalcurrentofelectro-LPEdecreasesand,therefore,theJouleheatincreases,andforthicknessesd>3mminequilibriumregimeandd>4mminnonequilibriumregimethegrowthprocessceases.Consequently,proceedingfromthesolutionofthesystemofequationsofequivalentthermalandelectricschemes
Page162
Fig.3.19ThicknessesofepitaxiallayersofLiNbO3on
LiTaO3substratesasfunctionsofsubstrateandsourcethicknessesinequilibrium(x)and
nonequilibrium()LPEregimes.
forequilibriumandnonequilibriumregimesandfromcomparisonwithexperimentalresults,anoptimumrangeoftheprocessparametersischosenwhichprovidesanepitaxialgrowthofLiNbO3layersofaLiTaO3substrate:
Nonequilibriumregime Equilibriumregime
TosimplifytheanalysisoftemperaturedistributionatthecrystallizationfrontwithallowanceforJouleeffect,weneglectthecontactthermaleffectsassumingthatthephysicalpropertiesofcellelementsareisotropicandthattheisotropyofthepropertiesandthegeometryoftheelementsaretemperatureindependent.Fromthesolutionofthermalconductivityequationincylindricalcoordinatesweobtain,accordingtoBarchukandIvaschenko(1982),theanalyticexpressionforastationarytemperaturedistributionatthecrystallizationfront
whereA.andBµarecoefficientsdefinedbytheboundaryconditionsoftheproblem,r1isresistivityofthei-thelement,Ri=j2r/4ki;kiarethecoefficientsoftemperatureconductivityoftheithelement,µaretherootsoftheequationj0(µa)=0,j0(µr)isthezero-orderfirst-classBesselfunction.TheexplicitexpressionsforAµandBµaretoocumbersometoberepresentedhere,andwereferthereaderto(Carslaw1945)wherethealgorithmfortheirdeterminationisgiven.Fromtheexpressionpresentedaboveitisseenthatinthegeneralcasethetemperaturefieldatthesubstrate-liquidphaseinterfaceisnonuniform.BecauseofcomplicacyoftheexplicitanalyticexpressionsforDT(h,r),theanalysisoftemperaturedistributionatthecrystallizationfronthasbeenper-
Page163
Fig.3.20Temperaturevariationatthecrystallizationfrontfordifferentcurrentdensities:1)4mA/cm2;
2)17mA/cm2;3)10mA/cm2
Table3.1GrowthcellparametersofLPE-grownlithiumniobate
Cellelement
r,ohm.cm Wcm-1K,grad-1k,cm2/s-1
l,cm a,cm J,mA/cm2
Platinum 1.05×10-4 0.71 1.4×107 10-2 5×10-14÷17
electrode 4×10-4 2×103
Substrate 6×105 3×10-2 10-1 5×10-14÷17
(T=400°C)
2×10-1
Liquidphase
148 1.5×10-2
(T=1200°C)
5×102
(T=890°C)
Source 5×105 4.2×l0- 10-1 5×10-14÷17
3
(T=400°C)
2×10-1
140 2×10-3
(T=1200°C
formed,inlinewithBarchukandIvashchenko(1982),onthebasisofthenumericalvaluesofgrowthcellparameterslistedinTable3.1.
Figure3.20illustratesthecalculationofAT(h,r)atthecrystallizationfrontinthegrowthcellbothinequilibriumandnonequilibriumregimesofliquid-phaseelectroepitaxyfordifferentcurrentdensities.
ThetemperaturegradientalongtheradialaxisforacurrentdensityofJ=10mA/cm2isaboutsixtimestheoneforJ=4mA/cm2,andforthecurrentdensityJ=17mA/cm2thesamegradientincreasesbyafactorof17.Accordingto(3.49),thegradientbecomesthreetimessmallerasthesubstratediameterdecreasesbyhalf.The'boundary'effectisnotobservedexperimentallyforcurrentdensitiesJ=(4÷6)mA/cm2andforthesubstrateradiusof0.5cm.Theepitaxialstructuresobtainedarecharacterizedbymorphologicaluniformityandplanarity.
Page164
Thus,usingthemethodofequivalenceofthermalandelectricschemesforexperimentalcellsinequilibriumandnonequilibriumelectro-LPEregimesofferroelectrics,wehaveintroducedtheconceptofacriticalcurrentofelectro-LPEanddeterminedtheoptimumgrowthparametersforLiNbO3onLiTaO3andLiNbO3substrates,whichpermitplanarstructurestobeproducedunderliquid-phaseelectroepitaxy.
Page165
4StructureandCompositionofLightGuidingFilmsForanefficientuseofepitaxialfilmsoflithiumniobatetantalateinoptoelectronics,itisnecessarytoobtainlayershomogeneousinthickness,possessingahighstructuralperfection,alowdefectdensityandalowcontentofuncontrolledimpurities,whichsubstantiallydecreasesattenuationinthecourseofwavepropagationoflightinthefilm.Thishasstimulatedinvestigationsofthecrystallinestructure,composition,orientation,surfacemorphology,substratefilminterface,domainanddislocationstructuresofthefilms.Theinfluenceofgrowthconditionsupontheseparametershasbeenestablished.
4.1Structureandphysico-chemicalpropertiesoflithiumniobateandtantalatecrystals
Lithiumniobate(LiNbO3)isoneofthemostinterestingandwidelyusedferroelectrics.FirstcrystalswereobtainedbyLapitsky(1952)andSue(1937).ThestudyofthestatediagramofthesystemLi2O-Nb2O5hasshownthepossibilityofformationoffourcompounds:Li2O-14N2O5,Li2O-3Nb2O5,LiNbO3andLi3NbO4(RusmanandHolzberg1958).
CrystallizationofLiNbO3ispossibleintheregionof40-60mol.%Nb2O5attemperaturesbetween1160and1253°C.Detailedstudiesofthephasediagraminthisregionhaverevealeddistinctionbetweencongruentandstoichiometriccompositions.TocongruentcompositiontherecorrespondstheratioLi2O/Nb2O5=0.946andthemeltingtemperatureTmelt=1170°C.Upontheliquidphasecompositionvariationwithintherangeof45-58mol.%Li2O,thecrystalcompositionvariesfrom47to50mol.%(Carruthersetal1971).Thus,crystalsofstoichiometriccompositioncanbegrownfromamelt
containingupto58mol.%Nb2O5,butbecauseofthelargedifferenceinliquidandsolidphasecompositionsthisleadstothegrowthofinhomogeneouscrystals.
X-rayandneutrondiffractionanalyseshaverevealedthatlithiumniobatehasthestructurerelatedtoilmenite(Abrahamsetal1966).Boththestructuresare
Page166
constructedfollowingthepatternofhigh-densityhexagonalpackagingbutdifferinalternationofoccupiedandunoccupiedoctahedra.InroomtemperatureLiNbO3crystals,octahedralintersticesformedbyoxygenionsinanalmosthigh-densityhexagonalpackagingarefilledwithniobiumions(1/3)andlithiumions(1/3),theremaining1/3beingvacant.Thesuccessionobservedwasasfollows:
Figure4.1showspositionofelementarycellsinlithiumniobate.TheoctahedronwithNbionsformsacommonfacetwiththevacantoctahedronwhichinturnformsafacetoftheoctahedronoccupiedwithlithiumion.Afteradistanceofc/2(cisthelatticeconstant)thepositioningofmetallicionsisrepeated:Nboccupiesthefourthoctahedron,thefifthremainsvacant,Lioccupiesthesixthoctahedron.Thenthecellisrepeated.
ThesymmetryofLiNbO3andLiTaO3crystalsistetragonal(class3m).IntheferroelectricphasethespacegroupisC3v-R3C,inparaphaseD3d-R3C.Therhombohedralcellcontainstwoformulaunitsandthehexagonalcellcontainssix.Thelatticeconstantsintherhombohedralcella=5.4944Å,a=55°52;inthehexagonalcella=5.14829±2×10-5Å,c=13.8631+4×10-4c/a=2.693.Interplanarspacesinthelatticeareequalto1.286Å(x-cut),1.489Å(y-cut)and1.15A(z-cut).Theprincipalcrystallographicdirections(planes)oflithiumniobatearepresentedinthestereographicprojectionofFig.4.2.The[0001]axiscorrespondstothespecialcrystallographicdirection(theopticalaxis)andcoincideswithspontaneouspolarizationdirection.
TheparametersofthecrystallographiccellsandionpositionsintheminLiNbO3aretabulatedinTable4.1.
Ionpositionsinthecrystallatticeareofinterestfromthepointofviewof
Fig.4.1CrystallinestructureofLiNbO3;a)seriesofdistortedoctahedralsalongthepolarc-axis;b)reallocation
ofoxygenatomsrelativetolithiumandniobiumatoms(Abrahamsetal1966).
Page167
Table4.1Physico-chemicalconstantsofLiNbO3crystals(Prokhorov,Kuz'minov,1990)
Characteristic Experimentaldata
Densityofsinglecrystals(g.cm-3) 4.612
Mohs'shardness 5
Meltingpoint(°C) 1260
Curiepoint(°C) 1210
Parametersofaunitcell:
Rhombohedral
a(Å) 5.4920
Angle 55°531
Hexagonal
a(Å) 5.14829±0.0002
c(Å) 13.86310±0.00004
Numberofformulaunitsincell
Rhombohedral 2
Hexagonal 6
Thermalexpansioncoefficient
aaxis 16.7±10-6
caxis 2.0±10-6
Dielectricconstant
Refractiveindices(l=0.623µm) no=2.286ne=2.220
Loss-angletangent(v=1kHz) lessthan0.02
Specificresistance(Wcm)
200°C over1014
400°C 5×108
1200°C 140
Watersolubility(mol1-1)
25°C 2.8±10-4
50°C 4.3±10-4
100°C 7.4±10-4
Dissolutionheat(kcalmol-1) 6.2
DiffusionactivationenergyQD(kcalmol-1)
68.21±0.48
68.17±1.24
( tocaxis)
EvaporationactivationenergyQv(kcalmol-1)
70.6
59.0
( tocaxis)
Evaporationcoefficient,a 10-4
3
Thermoelectriccoefficientofmelta1(mV.K-1) -0.4
Thermoelectriccoefficientofcrystalas(mV.K-1) 0.76±0.02
Coefficientofcrystallizationemfav(mVs.m-1) 1.25±0.2
Page168
theferroelectricpropertiesoflithiumniobate.Asdistinctfromotherferroelectriccrystals,lithiumandniobiumexhibitaconsiderableionshiftfromthesymmetricpositionintheparaphase.Theniobiumionisatadistanceof0.897Åfromthenearestplaneofoxygenatomsandat1.413Åfromthenextplane.TheLiionshiftmakesuprespectively0.714Åand1.597Å.So,appreciableshiftsoflithiumniobateionsarerequiredforreachingaparaelectricstateorpolarizationreversal.AtatemperatureexceedingtheCuriepoint,lithiumandniobiumionsshiftinthesamedirectionsothatNb5+occupiesthecentreoftheoxygenoctahedronandLi+liesintheplaneofoxygenlayers(Fig.4.1(b)).InLiNbO3crystals,theshiftonionsfrompositionstheyoccupyintheparaelectricphaseasthetemperaturelowersthroughtheCuriepointisresponsiblefortheappearanceofspontaneouspolarization.Spontaneouspolarizationmaybealignedeitheralongpositiveoralongnegativedirectionofthethird-orderaxis,boththesestatesbeingenergeticallyequivalent.
ThelargestandmostperfectwereCzochralskigrownlithiumniobatecrystals(Fedulovetal1965;Nassauetal1966).Crystalsobtainedinotherwayshadsmallersizeandsomestructuralimperfections.
Thegrowthconditionsoflithiumniobatecrystalsareconnectedwiththepresenceofcontrolledanduncontrolledimpuritiesinthemelt.Whenstoichiometryisviolated,lithiumandniobiumionsmayenterasimpurities.SolvabilityoftheNb2O5componentintheliquidphaseis45-58mol.%andinthesolidphaseitnarrowsto48-50mol.%.ThisleadstostoichiometryviolationandaffectstheCurietemperature,birefringenceandphasematchingtemperature.ThehighestperfectionofcrystalsisobtainedfortheratioLi/Nb=0.946whichcorrespondstocongruentcomposition.
Theexperimentaldataonthephysico-chemicalpropertiesoflithiumniobate(Kuz'minov1975)arepresentedinTable4.1whichshowsthat
ifimperfectcrystalsaredisregarded,theirdensityrangesbetween4.6and4.7g/cm3.ThemeltingtemperatureofstoichiometricLiNbO3crystalsis1253°C.Thephasetransitiontemperatureis1210±5°C.Atatemperatureof1200°C,lithiumniobatemeltinvacuumandinairisnonvolatile,whichisveryimportantforthetechnologyofthismaterial.ThesurfacetensionofLiNbO3measuredbythemoltendropmethodatthevacuum-meltboundaryatthemeltingtemperaturemakesup50-150dyn/cm.
Refractiveindicesoflithiumniobatearesensitivetostoichiometryviolation,whichleadstoopticalinhomogeneityinbulkcrystal.CrystalsgrownfromameltwithadditionofLi2OandMgOhasalowerrefractiveindex,thedecreaseofnebeingsubstantial,whichleadstoanincreaseofbirefringence.AnexcessNb2O5hasnoeffectuponnoandaverylittleeffectuponne.
AnimportantroleforliquidphaseepitaxyisplayedbythephasediagramofsolidsolutionLiNbO3-LiTaO3andthedependenceoftheCurietemperatureonthecomposition.
Thesolidusandliquidustemperaturesweredeterminedupto1575°Conthermoanalyser.TheresultsofdifferentialthermalanalysisareillustratedinFig.2.4.BothliquidusandsoliduscurvesshowasmoothvariationfromLiNbO3toLiTaO3.Asexpected,thesecurvesdonotmeetateitherendofthispseudobinarysectionsincethestoichiometricandcongruentmeltingcompositiondonotcoincide.
Page169
Fig.4.2StereographicprojectionofLiNbO3
Awiderspacingwasfoundbetweenthesolidusandliquiduscurvesbecauseofthelowerhomogeneityofthesamples.
Curietemperaturesweremeasuredonpowderspecimenshydrostaticallypressedatroomtemperatureandsinteredat1100°Cfor12h.ThestraightlineshowninFig.4.3wasfittedtothedatabyleast-squareanalysis.Thestandarddeviationis13°C,andthecorrelationcoefficientof0.9966indicatesthatthestraight-lineapproximationisvalid.
Abrahamsetal(1966)havedeterminedthecrystallinestructureoflithiumniobateoverthetemperaturerangeof24-1200°CbymeansofapolycrystalX-raydiffractionanalysis.Theerrorsinvolvedinhigh-temperatureX-raypowderdiffractionarefrequentlylarge,thusthereisconsiderablescatterinthedatafortheoxygenpositionalparametersasfunctionsoftemperature.
Fig.4.3VariationinferroelectricCurietemperaturewithsolidcompositioninLiNbO3-LiTaO3solid-solutionsystem(Petersonetal1970).
Page170
Petersonetal(1970)havethereforedonealinearleast-squaresfittothedatawiththeconstraintthatthehighlyaccuratesingle-crystal(Abrahamsetal1966;1967)parametersshouldbereproducedatroomtemperature.Thepositionalparameterssocalculatedwere(Petersonetal1970)
x=0.005027(T/1000)+0.04908,
y=0.3451-0.0207(T/1000),
z=0.00401(T/1000)+0.06460
andthetemperatureTwasindegreesCentigrade.
LithiumniobatecrystalsgrownbyCzochralskimethodfromacongruentmeltpossessthemosthomogeneouscompositionbutarenonstoichiometricandlithiumdepleted(~1.4mol.%Li2O)(ScottandBurns1972;PetersonandCarnevale1972).Awideenoughhomogeneityregion,fluctuationsofgrowthparametersinthecourseofcrystalgrowthandotherfactorsareresponsiblefortheappearanceofregionswithlocalcompositiondeviationsinlithiumniobatecrystals(Holman1978).Inhomogeneityofcompositionisobservedbothalongtheboulelengthandinradialdirection.Asshownbygravimetricmeasurements(Holman1978),adeviationoflithiumniobatecompositionfromthemeanvalueforspecimenscutoutofonecrystalbouleisinmostcasesequalto0.2andcanevenreach0.66mol.%Li2O.Inhomogeneityofcompositionwasidenticalfordifferentregionsofoneandthesamecrystalcut.Congruentcompositionoflithiumniobatemakesup48.6±0.2mol.%Li2O(Holman1978;Chowetal1974).
Thelargewidthofhomogeneityregionoflithiumniobateisduetothepresenceofintrinsicpointdefectssuchasintersticeatomsandvacanciesincationandanionsublattices(Carruthersetal1971).Thenatureofpointdefectsofthecrystallatticeoflithiumniobate,which
stemfromcrystalcompositiondeviationfromstoichiometry,isnotexactlyknown.Thereexistmodelsofthedefectstructureoflithiumniobate,oneofwhichisconstructedonanidealcationlatticeofniobiumwithlithiumvacancychargecompensationbytheformationofoxygenvacancies(Fayetal1968).Butthedependenceoflatticeconstantsanddensityoflithiumniobateonthecompositioncastdoubtonthemodeloflithiumvacancies.Lerneretal(1968)assumetheexcessniobiuminthelatticeofLiNbO3tooccupythevacantpositionsoflithiumandthustoformantistructureNbL1defects.TheNb+5ionchargeintheplaceofLi+iscompensatedbytheformationoffourVL1vacancies.NassauandLines(1970)proposedamodelofextendedcationpackagingdefectinthedirectionofzaxiswithalternationoflithiumandniobiumatoms.Inextensionofsuchdefectcomplexesthereoccursacomplicatedstructuraldisorder.AmoredetailedreviewandanalysisofthemodelsofdefectstructureoflithiumniobateisgivenbyBallman(1983)andJarzebski(1974).
X-raydiffractionmethodsareinconvenientfortheproofoftheexistenceofniobiumatomsoccupyingthepositionoflithiumatomsinthecrystallatticebecauseoftheirlowconcentration(~1%).PetersonandCarnevale(1972)discoveredtwotypesofsignalsfrom93NbinthespectraofnuclearmagneticresonancefromnonstoichiometricLiNbO3crystals.Theauthorsascribedthe
Page171
firstandmostintenselinetotheniobiumthatoccupiescrystallographicallyregularpositioninlithiumniobatelatticeandthesecondtypeofsignaltoexcessniobium,NbL1.Buttheintensityofthesecondlinemadeup6%oftheintensityofthefirstone,thatis,NbL1concentrationexceededtheexpectedone.ThepresenceofanadditionallineintheNMRspectrumtestifiestotheexistenceofthesecondtypeofniobiumatompositioninthelatticeoflithiumniobatebutprovesneitherofthedefectstructuremodelsdescribedabove.Theabsorptionspectraof7LiNMRalsoexhibitedweakadditionallineswhosepresencewasassociated(YatsenkoandSergeev1985)withdynamicdisorderoflithiuminthecrystallinestructureoflithiumniobate.
So,lithiumniobatecrystalsshowappreciablecompositionvariations,aswellasacomplicatedpointdefectspectrum.
Peculiaritiesofconstructingthephasediagramoflithiumniobateandtheobserveddeviationsofcrystalcompositionfromstoichiometrymayleadtoprecipitationoflithiumtriniobateasasecondphaseinthesecrystalsundercertainconditionsofthermaltreatmentorundercoolingofgrowncrystals.Fewdataintheliteraturetestifytothefactthatphaseformationoccursbothinthebulk(ScottandBurns1972)andonthesurface(Armeniseetal1983)oflithiumniobatecrystals.
ThebasicresultsontheformationofLiNb3O8inbulklithiumniobatecrystalswereobtainedbySwaasandetal(1974).TheX-rayphaseanalysisandmeasurementsofopticaltransmissioncoefficientswereusedtoexaminethepropertiesoflithiumniobatecrystalsafteralong-termannealingintheairwithinthetemperaturerangeof600-1000°Cfor100-1000h.Afterthelithiumniobatespecimensofdifferentcompositionwerecooleddowntoroomtemperature,theiropticaltransmissiondecreasedconsiderablyduetotheappearanceofmilk-whiteopalescentregions.Transparencyofthecrystalsdecreasedwith
increasingannealingtimeanddecreasingLi2Ocontentintheoriginalspecimens.So,lithiumniobatecrystalsgrownfromameltwithlessthan48mol.%Li2Oshowedopalescencealreadyaftera10hourannealingat800°C,whereascrystalsgrownfrommeltswithahigherLi2Ocontentrequireda500-hourannealingatthesametemperature.Theauthorsbelievethatachangeinthebulkcrystaltransparencyunderannealingisduetoprecipitationofasecondphase-lithiumtriniobateLiNb3O8whichbordersuponLiNbO3onthesideofniobium-enrichedcompositions.ThisassumptionwasfullyconfirmedinanX-rayphaseanalysisofannealedcrystals.
Uponasecondannealingatatemperatureexceeding1000°Candarapidcoolingtoroomtemperature,inspecimensoflithiumniobatecrystalscontainingthesecondphasethescatteringcentresdisappearedandthecrystalsbecameclearagain.TheX-raydiffractionpatternsofsuchspecimenscontainedreflectionsonlyfromlithiumniobate.Thetemperatureabovethatofbacktransformationdependedonthespecimencomposition,andhadavalueofabout910°Cforcrystalsgrownfromacongruentmelt.Onthebasisofmeasurementsofbacktransformationtemperatureforlithiumniobatespecimensofdifferentcomposition,theauthorstracedoutthelineofLiNb3O8-LiNbO3phaseequilibrium,foundthewidthofthesolidsolutionregionandbuiltthephasediagramfortemperaturesT<100°C(Fig.4.25).
Page172
Thus,lithiumniobatecrystalsaremetastableatroomtemperature,unstableunderalong-termthermaltreatmentandwithinacertaintemperaturerangecancontainthesecondphaseLiNb3O8.
TherearecomparativelyfewdataontheconcentrationandlocalizationofLiNb3O8phase.Examinationbyopticalmicroscopyandlightscatteringmethodsshowsthatuponannealinginthetwo-phaseregion,thesubmicroscopicparticles(r<10-5cm)ofthephasearenucleatedheterogeneouslyatblockboundaries,ondislocationsand,alongwithinclusionsofplatinumparticlesandotherimpurities,arelightscatteringcentresinlithiumniobatecrystals.
IncoolingannealedorgrowncrystalsitisalsonecessarytotakeintoaccountthetemperaturefallratesincethisrateisresponsibleforthetimeduringwhichthecrystalwillremainwithinthetemperaturerangetypicalofprecipitationofLiNb3O8.Whenthecoolingrateincreasesto3-5°C/min,thelithiumniobatewaslesspronetocrackingthancrystalscooledataratelowerthanl°C/min.Withoutdenyingthecontributionofothermechanisms,ScottandBurns(1972)supposethattheprecipitatesofthesecondphasecanserveasnucleifortheappearanceanddevelopmentofcracksinlithiumniobatecrystals.Topreventlithiumtriniobatefromprecipitatinginbulkcrystaloflithiumniobate,thecoolingrateshouldbe>20°C/min(Holmanetal1978).
Pioneeringreportsonvariationofthephasecompositionoflithiumniobatecrystalsurfacecausedbytheformationoflithiumtriniobateappearedon1983asaresultofanalysisoftitaniumdiffusionintolithiumniobatecrystalsinthecourseofmanufacturingopticalwaveguides(Armeniseetal1983;DeSarioetal1985).ThecompoundLiNb3O8occurredonthesurfaceoflithiumniobateslabscoveredwithatitaniumlayerinthecourseofannealingwithinthetemperaturerangeof550-900°Cinoxygenatmosphere.Underascanningelectronmicroscopelithiumniobateshowedupasshapelessspotsofmorethan
100µmlocatedinaTiO2layer.Analysisofatomiccompositionhasshownthatthecontentoftitaniumisdecreasedandthatofniobiumincreasedinsuchregionsascomparedtophase-freeregions.AstheannealingtemperatureheightenedtoT>900°C,LiNb3O8wasdisintegratedandspotsdisappearedfromlithiumniobateslabsurface.
InvestigationsofLiNbO3substrates(Armeniseetal1983)haveshownthatLiNb3O8isalsoformedintheabsenceoftitaniumlayer,thatis,phaseformationonthecrystalsurfaceisaspecificbehaviouroflithiumniobateitselfinthecourseofannealingwithintheindicatedtemperaturerange.ThepresenceofLiNb3O8phaseorientationrelativeto(0110)and(0110)LiNbO3substrateswasdiscoveredfromLauediffractionpatternstakeninvariablegeometryandfromthespectraofbackwardRutherfordheliumionscattering.PrecipitationofLiNb3O8phaseoncrystalsurfaceproceedsnotonlyunderannealinginoxygenatmosphere,butalsointheairaswellasinaN2orArflux.AdditionofwatervaporsintotheatmosphereofannealingpreventstheformationofLiNb3O8andinducesdisintegrationofthesecondphaseifithasalreadybeenpresentonthespecimensurface(DeSarioetal1985).DisintegrationofLiNb3O8underannealinginmoistatmospherewashypotheticallyexplainedbytheformationofthehydroxylgroupOH-and(Li1-yHy)NbO3moleculesduetoprotondiffusionintothecrystal.
Page173
Phaseformationonthesurfaceoflithiumniobatecrystalswasalsoobservedunderradiationdamagesoflithiumniobate(JetschkeandHehl1985).
AchangeinthephasecompositionofLiNbO3surfaceirradiatedbyN*andP*ionswasdiscoveredbybackwardRutherfordscatteringatatemperatureof279°C.Niobiumconcentrationinthenear-surfacelayerwasfoundtobeincreased.ConnectionbetweenphaseprecipitationandstructuraldamageinthesurfacelayeroflithiumniobatesubstrateswasreportedbyGan'shinetal(1985,1986)whoobservedtheoccurrenceofthecompoundLiNb3O8afterannealingatT=450°Cfor3hofproton-exchangedwaveguidesmanufacturedon(0001),(0110),(2110)and(0114)facetsoflithiumniobate.
Theoperationareaofmanyacousto-andoptoelectronicdevicesisthenear-surfacelayer,aswellasthesurfaceoflithiumniobatesubstrates,andthereforeofparticularimportanceforthecreationofeffectivedevicesiscontroloverthestateoflithiumniobatecrystalsurface,itsstructureandphasecomposition.ThestudyofphaseformationinlithiumniobatecrystalsplaysapracticalrolesinceheattreatmentofLiNbO3isawide-spreadtechnologicaloperationinmanufacturingvariousdevicesonthebasisoflithiumniobatecrystals.
4.2X-raydiffractionanalysisoffilms
InvestigationsoffilmstructurewerecarriedoutusingtheX-raydiffractionmethod.Theanalysisofpatternsthusobtainedallowsustojudgeofpolarization,orientationandlatticeconstants.PolarizationandlatticeconstantswerealsodeterminedbytheelectrondiffractometryandthecompositionbytheX-raydiffractionmethodandlasermicroanalysis.
4.2.1Layercomposition
Thedistributionofcomponentsoverthethicknessofthelightguidinglayerwasexaminedbymicroroentgendiffractionanalysis(MRDA).Figure4.4presents
Fig.4.4Distributionofcomponentsalongthethicknessof(a)LiNbO3/LiTaO3,
(b)Li(Nb,Ta)O3/LiTaO3and(c)LiNbO3/Al2O3heterostructure.
Page174
graphsofcomponentdistributioninfilmsonLiTaO3(Fig.4.4(a,b))andA12O3(Fig.4.4(c)).Theconcentrationofthemaincomponentofthesubstrate(TaorA1)attheinterfacedecreasestozerowhileniobiumconcentrationbecomesmaximum(Fig.4.4(a,b,c)).IngrowingfilmsofsolidsolutionLiNb1-yTayO3onaLiTaO3substratetheTaconcentrationattheinterfacedecreasesfrom100%toequaltheTaconcentrationinthefilmFig.4.4(b).Analysisofconcentratedprofileshasshownthatthecompositiondoesnotchangethroughoutthefilmthickness.TherelativecontentofNbandTainafilmofsolidsolutionisdeterminedbytheircontentintheliquidphasewhentheeffectivecoefficientoftantalumconcentrationKcff~1.5.
Asdistinctfromdiffusedwaveguides,epitaxiallayersarecharacterizedbyasharpsubstrate-filminterface.Epitaxialfilmsoflithiumniobate-tantalatearecolourless.
Theresultsobtainedsuggestsomeconclusionsconcerningthegrowthprocess.Sincetantalumconcentrationinagrowinglithiumniobatefilmiszero,thesolution-meltattheinitialepitaxytemperatureisinthemetastableregion,andthesubstratesurfaceisnotadditionallydissolved.ThecompositionconstancyoffilmsofLiNb1-yTayO3solidsolutionsimpliesthattheconcentrationprofileremainsunalteredinthecourseofgrowth,whichcorrespondstothediffusionmodel.
Besidesthedistributionofmacrocomponents,theuncontrolledimpurityofvanadiumatomsinthefilmandthecontentofironions,introducedinconcentrationsof1and2mol.%intothesolution-meltintheformofFeCO3,weredetermined.MRDAdoesnotpermitqualitativeestimationofthecontentoflow-concentrationcomponents.Thepresenceofvanadiumandironimpuritiesinthefilmswasdeterminedbylaseremissionmicroanalysis.
Analysisofthespectraoftheexaminedpatternshasshownthatthefilmscontainvanadiuminconcentrationrangingundergrowth
conditionsbetween0.005and0.1atm.%.ThespectraofLiNbO3filmsandLiTaO3substrateweremeasuredforthesecondtimeusingafour-stepGortmandiaphragmunderthesameconditions.Inthiscase,filmspectrawereinvestigatedbycomparisonwiththespectraofvanadiumandironoxides.Theresultsconfirmedtheabsenceofvanadiumspectrallinesinthelithiumtantalatesubstrate,whereasinthefilmstheywereclearlypronouncedinthesamewavelengthregion.Underoptimumcrystallizationconditions(thegrowthratev<0.2µm/min),aLiNbO3filmonaLiTaO3substrateof(0001)orientationcontains0.005-0.01atm.%ofvanadium.Themaximumconcentration(0.01atm.%)ofhomogeneousvanadiumimpuritywasobtainedataprecipitationrateof0.6-0.8µm/min.Ahomogeneoushighlyconcentratedvanadiumimpuritywasnotobservedwithafurtherincreaseofprecipitationrate.TheupperlimitofhomogeneousvanadiumimpurityconcentrationisobviouslyduetothedifferenceinV5+andNb5+ionradii(Rv=0.4Å,RNb=0.66Å),whichleadstostronglatticedistortionsunderthe substitution.
Asdistinctfromvanadium,theradiiofFe3+ions(0.67Å)areclosetothoseofNb5+andLi5+(0.68Å),whichmakesitpossibletoobtainlithiumniobatecrystalswithironimpurityreaching3weight%(Gabrielyan1978).Investigationofdopedsampleshasshownthatironconcentrationinthesampledepends
Page175
Table4.2LatticeparametersandinterplanedistancesofLi(Nb,Ta)O3filmsandLiTaO3substrate(Madoyanetal1985)
No Filmmaterial Latticeparameters(Å)
Orientation Interplanedistances(Å)
a c
LiNbO3 5.137 13.828 (0001) 1.1523
1 ( ) 1.3884
( ) 1.2030
LiNb07Ta03O35.1385 13.808 (0001) 1.1507
2 ( ) 1.3888
( ) 1.2034
LiNb05Ta05O35.1395 13.798 ( ) 1.1498
3 ( ) 1.3891
( ) 1.2036
LiNb02Ta08O35.1408 13.78 ( ) 1.1483
4 ( ) 1.3894
( ) 1.2040
LiTaO3 5.1421 13.772 (0001) 1.1477
5 ( ) 1.3898
( ) 1.2042
onironcontentintheliquidphaseandremainsessentiallyunchangedastherateincreases.Theestimatesoftheeffectiveironsegregationcoefficientobtainedbylaseremissionmicroanalysisliewithinthe
rangeof0.2-0.5.
4.2.2Monocrystallinityandinterplanardistances
X-raysincidentonthecrystallinestructuresurfacediffractinthenear-surfacelayerwhosethicknessisdeterminedbythesamplematerialandlightbeamintensity.X-raysincidentonthesurfaceofepitaxialstructurecanpenetrateintothesampledepthlargerthanthefilmthickness.Inthiscase,X-raysdiffractattwoanglesoneofwhichcorrespondstodiffractiononthefilmandtheotheronthesubstrate.Therelativeintensitiesofthesebeamsdependonfilmthicknessandonthedepthofthelayersonwhichdiffractiontakesplace.Superpositionofbeamsispossibleinthecaseofclosediffractionangles,andthepositionofthediffractionlinescannotthereforebepreciselydetermined.Figure4.5presentsdiffractioncurvesforLiNbO3andLi(Nb,Ta)O3filmsonLiTaO3substratesof(0001)and(1120)orientations.Thedifferenceinthediffractionanglesoflithiumniobateandlithiumtantalateequalto10'forthe(0001)planeand6'forthe(1120)planegivesdifferentpeaksfromtheLiNbO3filmandLiTaO3substrate.ForaLiNbl-yTayO3filmthediffractionmaximumisdisplacedfromthesubstratewithincreasingytowardsthemaximum(Madoyanetal1985;Madoyan1984).Thedifferencebetweenthemaximafromthefilmandsubstratereachesy=0.8.Furtheron,thepresenceofthefilmaffectstheasymmetryofthediffractionpeakprofilebroadened,dependingonthelayerthickness,towardsthefilmorsubstrate(Fig.4.5(c,d)).Theattempttoobtainseparatepeaksfromfilmson(1010)-orientedsubstratesfailed(Dq~3').Forclosevaluesofdiffractionangles,investigationswerecarriedoutonverythickfilms(Fig.4.5(e,f)).Sincethediffractiondepthmakesupabout60µm,forfilmsthickerthan
Page176
Fig.4.5X-raydiffractionpatterns:LiNbO3filmsonLiTaO3substratesof(a)(0001)and(b)( )orientations,LiNb0.5Ta05O3onasubstrateof(c)(0001)and(d)( )orientations,LiNb02Ta08O3
onasubstrateof(e)(0001)and(f)( )orientations.
Fig.4.6
HexagonalcellparametersversusLiNb1-yTayO3filmcomposition.
Page177
50µmX-raysdonotpracticallyreachthesubstrate,andthediffractionangleisdeterminedbythefilmalone.Thevaluesofthediffractionanglesandlatticeconstantswereestimatedforthick(1010)-orientedLiNbO3andLiNb1-yTayO3films(y<0.8).
Table4.2presentsthevaluesofinterplanardistancesandlatticeconstantsofLi(Nb,Ta)O3filmsandLiTaO3substrate.
ThereiscontroversyintheliteratureastothecharacterofthedependenceofcrystallographicparametersandCuriepointofsolidsolutionsLiNb1-yTayO3ontheamountoftantalum,y.Shapiroetal(1965)andSugiietal(1976)pointtothenonlineardependence,whereasShimuraandFujino(1977)showthatthedivergenceisduetoalackofcorrespondencebetweentheparameteryinthesynthesizedsolidsolutionLiNb1-yTayO3andtheparameterxoftheinitialmaterialLiNb1-xTaxO3.TheconstructeddependenceofthelatticeconstantsaandConthetantalumcontentinthefilmisclosetolinear(Fig.4.6).
AnalysisofX-raydiffractionpatternsallowsustojudgeofstructuralperfectionofepitaxialfilms.Theexistenceofonlyonepeakindicatesthatthefilmissingle-crystal,andasmallhalfwidth(notlargerthanthatofthesubstrates)pointstothelackofblockstructureofthefilmandtoperfectionnotlowerthanthatofbulkcrystals.
Diffractionstudiesoffilmswerealsocarriedoutbytheelectrondiffractometrywhichprovidesahighaccuracyindeterminationoflatticeconstants.Itwasestablishedthatfilmsonsubstratesof(0001),( )and( )orientationsaresingle-crystal,whichfactaccountsforthepoint-likecharacteroftheelec-
Fig.4.7ElectrondiffractionfromtheLiNbO3filmsurfaceonaLiTaO3(1120)substrate,Kikuchilinesareobserved.
Page178
trondiffractionpattern(Fig.4.7).Furthermore,highstructuralperfectionofthenear-surfacelayerofthefilmpermitobtainingdiffractionintheformoftheKikuchi-lines.
Fig.4.8Schematicarrangementofatriple-crystalspectrometer(Sugiietal1978).
Sofaraselectrondiffractionpatternonlyprovidesinformationaboutanear-surfacelayer,itpermitsdeterminationoflatticeconstantsofafilmirrespectiveofitsclosenesstothesubstrateparameter.ThisisofparticularimportanceforthediffractionstudyofhomoepitaxiallayersandfilmsofLiNbO3ona( )-alignedLiTaO3substrate.WeshouldnotethatinallthecasestheinterplanardistancesdidnotdifferfromtheresultspresentedinTable4.1.
HomoepitaxialLiNbO3filmsareofinterestinthecasewhentheyaredopedwithtransitionmetalatoms.AdetailedanalysisofFeatomdistributionovercrystallographicpositionswasgivenbyRubinina(1976)whoshowedthatFe2+andFe3+ionssubstitutelithiumorniobiumones.Suchironimpuritymustnotleadtosubstantiallatticedistortions.VariationoflatticeconstantsofLiNbO3uponirondopingwasnotestablishedwithinexperimentalerror.ThediffractionstudiesofLiNbO3filmsonasapphiresubstrateshowedfilmpolycrystallinity.
CreationoflightguidinglayersinLiNbO3usingdiffusionofmetal(inparticulartitanium)ionsnecessitatesdeterminationofstrainsinthesurfacelayerandtheformationofmisfitdislocations.Tosolvetheseproblems,Sugiietal(1978)successfullyappliedX-rays.
4.2.3Measurementofstrainsinthediffusedlayer
TheX-rayrockingcurvemethodwasemployedbySugiietal(1978)forprecisedeterminationofstrainsinthediffusedlayer.Rockingcurvesweretakenusingatriple-crystalspectrometerasshowninFig.4.8.ItconsistsoftwonearlyperfectgermaniumsinglecrystalsC1andC2,andasimplecrystalC3arrangedinthe(+,+,-)position.ForC1andC2thesymmetric(333)reflectionwasused,theBraggangleforCuKa1radiation,q,beingabout45°.TheangularandwavelengthdistributionsoftheX-raybeamdiffractedfromthesecondcrystalC2wereco=2×10-5rad(4''arc)andDl/l0=2×10-5(l0=1.5405Å),respectively.Theyweresmallenoughtoobtainanintrinsicrockingcurveofthesmallsampleforanylatticeplane(hkl).Inaddition,thebeamthusobtainedisalmost
Page179
Table4.3StrainsintheTi-diffusedlayerofLiNbO3(Sugii,Fukuma,Iwasaki,1978)
Diffusiontime, t=10h Diffusiontemperature, T=1000°C
T(°C) ey×103 t(h) ey×103 ey×103
1000 -1.3 1.25 -2.19 1.2
1050 -0.71 2.5 -1.66 0.75
1000 -0.39 3.75 -1.28 0.62
- - 10 -0.759 0.52
o-polarized(anelectricfieldvectorEperpendiculartotheplaneofincidence)becausethescatteringangle,2q,isnear90°.AslitwasplacedbetweenC2andC3toobtainabeamofwidth0.5mmandheight2.0mm.Undiffusedsamplesproduced(030)rockingcurveswithwidthathalfmaximumintensity(WHMI)ofabout12''arc,whichisessentiallythetheoreticalWHMIforthe(030)reflectionofaperfectLiNbO3crystalundertheseexperimentalconditions.Ontheotherhand,thediffusedsamplesproduces(030)rockingcurvesaccompaniedbyadiffractionsatellite,displacedinanglewithrespecttothediffractionpeakoftheunperturbedregioninthesubstrate.Precisedeterminationofstrainsinthediffusedlayerispossiblesinceastandardoflatticeconstantisavailableinthesametraceasthediffusedlayer.Thestrainalongtheaaxis,ey(ex),isobtainedfromashiftinangleq030ofthesatelliteas
whereq030istheBraggangleforthe(030)reflection.However,strainalongthecaxis,ez,cannotbedirectlymeasuredonthediffusedlayer,sincethecaxisisparalleltothesurfaceinthey-platecrystal.IfashiftDqhklcanbeobtainedfora(hkl)reflectionwithnon-zerol,thestrain
eziscalculatedfromapairofshiftsDq030andDqhklusingthefollowingexpression
Fig.4.9(a)Relationshipbetweenthe(036)latticeplaneandtheincidentX-raybeam.(b)Inclinationinthe(036)latticeplanesbetweenthesubstrateandtheTi-diffusedlayer.Thedottedlinerepresentsalatticeplane
parallelto(036)s(Sugiietal1978).
Page180
Fig,4.10Familyof(036)rockingcurvesforthesamplesofdiffusedLiNbO3:Ti
(Sugiietal1978).
wheredisthe(hkl)latticespacingandqhklistheBraggangleforthe(hkl)reflection.A(036)reflectionwasusedforthispurpose.Thegeometricalrelationshipbetweenthe(036)latticeplaneandthesurfaceisshowninFig.4.9.Theanglebintheinterplanaranglebetweenthe(036)planeandthesurface.Inthe(036)asymmetricreflection,ashift foranincidentbeamwithaglancingangle(q036+b)isgenerallynotequaltoashift foronewithaglancingangle(0036-b),sinceaninclinationofthe(036)latticeplane,Db,isinvolvedinbothshifts(seeFig.4.9(b)).Itisreadilyshownthat( )/2givesDq036tobesubstitutedinequation(4.2),whichisashiftdueonlytothedifferenceinthe(036)latticespacingbetweenthediffusedlayerandthesubstrate.
Thelatticeconstantawasobservedinthediffusedlayersofallthesamplesinvestigatedinthisstudy.Figure4.10showsthreepairsof(036)rockingcurves andDq>036ofthesamples.Theratioofsatellitetosubstratepeakintensityincreaseswithdiffusiontimet,althoughtheabsoluteintensitybecomessmall,duetotheeffectofasymmetricreflection.Thesubstratepeakscouldhardlybedetectedsincetheywereabsorbedbythethickdiffusedlayers.
Usingequations(4.1)and(4.2),Sugiietal(1978)couldcalculate
strainseyandezAlinearrelationshipisfoundbetweenln(ey)and1/T.ThestrainseyandezforLiNbO3:TisamplesaregiveninTable4.3.Thestrainezisaboutoneorderofmagnitudesmallerthanthestraineyineachsample.Thestrainseyareplottedagainstt.Theslopeln(ey)versusIn(t)plotiscalculatedtobe-1/2.Thesetworelationshipsfoundbetweeneyand1/T,andbetweeneyandtaresimilartothosebetweenCsandI/T,andbetweenCsandt,respectively.Therefore,itcanbeconcludedthatthestraineyinthediffusedlayerisproportionaltothesurfaceconcentrationCs.
4.2.4Tidistributionindiffusedlayers
Figure4.11showstheTidistributionsofLiNbO3samples.Here,apositiononthechartwasregardedasthesurfaceatwhichanEPMAresponsedecayedtoavaluehalfwaybetweenthemaximumandbackgroundlevels.Allthediffusedlayershavebell-shapedTidistributionscharacteristicoftheGaussiandistri-
Page181
Fig.4.11TidiffusionasdeterminedbyEPMAof
slicesforthesamplesofLiNbO3:Ti(Sugiietal1978).
Table4.4TitaniumatomicfractionsatcrystalsurfaceNs,(Ti),anddiffusioncoefficientsD,diffusiontimet=10h,inLiNbO3:Ti(Sugii,Fukuma,Iwasaki,1978)
T(°C) Ns(Ti)×1021cm-3 D,10-12cm2s-1
1000 1.23 0.506
1050 0.82 1.06
1100 0.57 2.13
bution.TheGaussiandistributionC(y)isexpressedasfollows
whereyisthedepthbelowthesurface,pisthenumberofatomsperunitvolumeinthedepositedfilmofthicknesst,andDisthediffusioncoefficientgivenby
ValuesofEPMAresponseatthesurface,Rs,correspondingtoCs,and
ofthediffusioncoefficientDcouldbedeterminedinsuchawaythatthetheoreticaldistributioncalculatedbyEqs.(4.3)-(4.5)wasfittedtothemeasuredone.Then,theTiatomicfractionatthesurfaceNs(Ti)wasestimatedfromaratioofRstoR0ontheassumptionthattheEPMAresponsewasproportionaltoC(y).ThecalculatedvaluesofNs(Ti)andDaregiveninTable4.4.ItistobenotedthatTihasaremarkablyhighsolubilityinLiNbO3inthetemperaturerangefrom1000to1100°C.ThediffusiondatawerecalculatedasD0=2.19×10-4cm2sec-1andQt=2.18eV.
Page182
Fig.4.12Lidepthprofiles(a),Hdepthprofiles(b)andionchanellingresults(c)forX-cutblink,afterprotonexchangeinbenzoicacidat180°C
for1handafterthermalannealinginairat350°Cfor10h(Hsuetal.1992).
4.2.5theStructureofproton-ExchangedLiNbO3
SeveralstudieshavebeenreportedonthestructuralcharacterizationofLiNbO3.Rice(1986)reportedanapproximatephasediagramforthestoichiometricLiNbO3-HNbO3system.Dependinguponcomposition,samplesundergoone,two,orthreephasetransitionswithtemperature.Canalietal(1986)reportedresultsofstructuralanalysisofproton-exchangedlithiumniobateopticalwaveguidesfabricatedinx,y,andz-cutsubstratesimmersedinpurebenzoicacid.Theymeasuredatomiccompositionprofilesandnotedamarkedlatticedistortion.HandLiconcentrationmeasurementsindicatedanexchangeofabout70%oftheLiatoms.Thehydrogendepthprofilemeasurementsshowedasteplikeshapeinagreementwiththerefractiveindexprofilemeasuredoptically.Theyconcludedthatexchangeincludesalargecrystaldistortionstronglycorrelatedtothepresenceofprotons.Leeetal(1986)studiedstructuralphasechangesinproton-exchangedLiNbO3usingtransmissionelectronmicroscopy.Regionsofdiffuseintensitywithinthesinglecrystalelectron
diffractionpatternsofLiNbO3wereobserved.Minakataetal(1986)measuredthelatticeconstantsandelectro-opticconstantsofz-cutproton-exchangedLiNbO3crystalsbymeansofthex-rayrockingcurvemethodandthephasemodulationtechnique.Theyfoundthattthestrainalongthecaxis,Dc/c,wasextremelylarge(+0.45%)whilstthestrainperpendiculartothecaxis,Da/a,wasnegligiblysmallinproton-exchangedLiNbO3singlecrystals.Theelectro-opticcoefficientvalueinthelayerreducedtoone-tenthofthebulkcrystalvalue.Vohraetal(1989)measuredtheconcentrationprofilesofprotonandlithiumprotonexchangedLiNbO3crystalsusingsecondaryionmassspectroscopyandfoundprotonconcentrationprofilesnearlyrectangularinshape.Lonietal(1991)reported,usingsecondaryionmassspectrometry(SIMS)andanopticalmethod,adirectcomparisonof
Page183
hydrogendepthdistributionsandrefractiveindexprofilesinannealedproton-exchangedz-cutLiNbO3waveguides.Novaketal(1992)havereportedSIMSdepthprofilemeasurementsofH,Li,Nd,andErinLiNbO3andLiTaO3.Theabovediscussionindicatesthatextensivestudieshavebeencarriedoutonthecharacterizationoftheproton-exchangeprocess.Someresultshavealsobeenreportedonthedegradationoftheelectro-opticcoefficient.Toourknowledge,noresultshavebeenreportedcorrelatingthedegradationofthenonlinearcoefficienttoitsstructuralaspects.Hsuetal(1992)reportedtheresultsofx-rayrockingcurvesstudiesaswellasdepthprofilesofHandLiandionchannelingmeasurementsusingforwardrecoilspectrometry(FRES),theioninducednuclearreactionLi(p,a)He4andRutherfordbackscattering(RBS)techniques,respectively,thatprovidesomestructuralcharacterizationofproton-exchangedandannealedLiNbO3samples.Thesemeasurementsarecorrelatedwithopticalmeasurementsoftherefractiveindexandsecondharmonicgeneration.
Figure4.12ashowstheLiprofilesfrombulkLiNbO3crystal,aproton-exchangedcrystalandanannealedsample.TheseresultsindicateasignificantlossofLifromthesurfaceuponproton-exchangeandrecoveryofitafterthermalannealing(althougharegionofabout0.1µminthicknessstillremainsLideficient).Figure4.12bshowsthehydrogenprofilesofthesamesetofsamples.ThehydrogenpeakatthesurfaceoftheuntreatedLiNbO3crystalcouldbeduetothemoisturepresentatthesurface.Thesimulationresultsindicateasteplikeprofileofhydrogenafterproton-exchangeinagreementwithLonietal(1991).Afterannealing,thehydrogenconcentrationfalls,exceptforasmallpeakinthenear-surfaceregionofthesample.TheRBSchannelingresultspresentedinFig.4.12cshowthattheproton-exchangeinducesdisorderintheNbsublatticeextendingfromthesurfaceofthesampletoadepthofapproximately0.7µm.This
disorderedregioncoincideswiththeLidepletedandhydrogen-occupiedregionsshowninFig.4.12aandb,respectively.Inthermalannealing,mostofthelatticedisorderisrecoveredexceptforanarrowregion,approximately0.1µmthickclosetothesurfaceofthesample.Figures4.12aandbshowthatthisregionisalsoLi-deficientandpresumablyH-rich,respectively.Inthesecond-harmonicreflectancetechnique,thesecond-harmonicsignalisobtainedonlyfromthefrontsurfacesincetheskindepthforthewavelengthemployedisoftheorderof0.1µm.Thisimpliesthatthereflectancetechniquedoesnotprovideafullcharacterizationofthedegradationinwaveguidesthataretypically1µmdeep.Also,sincethereisamarkedrecoveryindeeperregionsofsample,efficientsecond-harmonicgenerationispossibleinLiNbO3,althoughconversionefficienciessmallerthantheoreticalvaluescanbeexpected.
TheRBSchannelingresultsofanx-cutLiNbO3samplethatwasproton-exchangedinbenzoicacidfor30minat180°Candsubsequentlyannealedinairfor2hat350°C,revealeddisorderinthecrystallatticeafterproton-exchangetoadepthofabout0.35µm.However,inthiscase(shortp-exchangetime)thereisalmostcompleterecoveryafterthermalannealing.Indeed,anSHGsignalwasobservedafterthermalannealing,butnotafterprotonexhcange.Also,theprismcouplingmethodindicatedawaveguideinthesampleafterthermalannealing,butnowaveguidewasobservedafterprotonexchange.The
Page184
RBSchannelingresultsofanx-cutLiNbO3samplethatwasproton-exchangedfor30rainat230°Cinpyrophosphoricacidandsubsequentlyannealedinairfor1hat350°C,indicateddisorderinthecrystallatticeafterprotonexchangeextendingtoadepthof1.8µm,whichpartiallyrecoversuponthermalannealing.Therefore,protonexchangewithpyrophosphoricacidproducessimilarlatticedisorderasprotonexchangewithbenzoicacid.
ThelargestrefractiveindexofLiNbO3isaresultoftheextremepolarizabilityoftheNb-Obonds.TheprotonexchangeprocessinducesadistortionofthecrystallatticeandhenceadistortionoftheNb-Obonds.Thischangeoftheniobatestructureappearstocausetheindexincrease.Thiseffectappearstobealsothesourceofthedecreaseinthenonlinearopticalcoefficient,apropertythatisalsorelatedtothepolarizabilityoftheNb-Obond.Therefore,itappearsthatitisnotthepresenceoftheprotons,butrathertheireffectontheNb-Olattice,thataffectstheopticalproperties.Afullrecoveryoftheopticalpropertiesoccursnotbyremovingtheprotons,butbyrestoringthecrystallattice.
4.2.6Orientationrelations
X-raydiffractionstudiesalsodeterminedthedirectionofthecrystallographicaxesofsubstrateandfilmsurfaces.Theresultsweremostpreciseonsamplesthediffractionfromwhosesurfacegavetwoclearlyseparatedmaxima.Inthiscase,theabsolutelossoffilmandsubstrateorientationwasmeasuredbytheirorientationlossrelativetothestandard.ItwasestablishedthatcrystallographicdirectionsofthefilmofpurelithiumniobateandsolidsolutionsLiNb1-yTayO3coincidewithidenticaldirectionsofLiTaO3substratesupto20'for(0001)and( )sampleorientationsirrespectiveoforiginalorientationlossinthesubstratesurface.
Ninomuraetal(1978)describedtheprocessofobtainingLiNbO3
filmsonaMgOsubstrate.Sputteringontothe(111)planeofthesubstrateresultedincrystallizationofa(0001)-orientedLiNbO3layer.Suchorientationrelationisexplainedbythefactthatthepositionofoxygenionsintheindicatedplanesisidenticalandtheircoordinatesintheplanedonotdifferbymorethan0.2%oftheoxygensublatticeperiod.
AsdistinctfromMgO,thestructureofLiTaO3isidenticaltothatofLiNbO3,andtheirparametersdifferby4%incand1%ina.
Becauseofsimilarityoflattices,filmorientationispreserved,asexpected,andthesubstrate-to-filmtransitionisduetoformationofthetransitionlayerofLiNb1-zTa2O3ofvariablecomposition,inthecourseofwhichthelatticeconstantchangesfromfilmtosubstrateparameter.Intheabsenceofadditionalsubstratedissolving,thewidthofthetransitionregionappearstobesmall(1µm)andisdeterminedbytheinterdiffusiondepthofsubstrateandfilmatomsafterprecipitation.
Ingrowinghomoepitaxialfilmswithironimpuritynodeviationoflayerorientationfromthatofsubstratewasobserved.
Alithiumniobatefilmgrownona( )sapphiresubstrateexhibitednoX-raydiffractionatananglecorrespondingtothesinglecrystal.ThemostintensescatteringcorrespondedtothezplaneofLiNbO3.Itismostlikelythat
Page185
Fig.4.13Mechanismsofepitaxialgrowthoflithiumniobate.
a)model,b)photographsofsurfacemorphologyofLiNbO3
aLiNbO3filmprecipitatesontoan{ }A12O3plateintheformofapolycrystallinelayeroralayerconsistingofregionswithdifferentorientationswithpredominanceofthezdirection.Suchaconclusionisalsoconfirmedbythefactthatnopointelectrondiffractionpatterncorrespondingtoasinglecrystalcouldbeobtained.
4.3Morphologyandperfectionoflayers
Attenuationofalightwaveinawaveguideistheprincipalparameterresponsibleforefficiencyoftheepitaxialstructureinintegratedoptics.Inazigzagpropagationoflight,attenuationisdeterminedbytwofactors-bylightscatteringuponrepeatedreflectionfromsubstrate-filmandair-filminterfacesandbyabsorptioninthebulk.Thescatteringlosstypicallyincreaseswithincreasingorderofthewaveguidemode,whereasthebulklossremainsalmostunchanged.Inthisconnection,perfectionofthefilmsurfaceandofthesubstrate-filminterfaceisofimportance.Thebulklossisduetoabsorptionandscatteringoflightonstructuralinhomogeneitiesofthefilms,whicharedeterminedbythefilmformationmechanisms.
Accordingtomodernconceptsofthenucleationtheory,themost
importantfactorwhichdeterminesbasicallythemechanismofsinglecrystalnucleationandthekineticsoftheirsubsequentgrowthisthestructureoftherealsurfaceofthesubstrate(Veinsteinetal1979).Oneshouldbearinmindthatthedifferenceinthelatticeperiodsofcontactingmaterialsaffectsthemagnitudeofthesurfaceenergyoftheinterfaceand,accordingly,thecharacterofelementarygrowthprocessesattheearlystageofheteroepitaxyestablishingeithertwo-orthree-dimensionalnucleationmechanism.Thecharacterofelementarygrowthprocessesessentiallydeterminesthestructureperfectionandthemorphologyofthinepitaxiallayersnearheteroboundary.
Figure4.13presentsmodelsofthelayergrowthmechanismfordifferentsupersaturationsintheliquidphaseandthecorrespondingsurfacemicromorphologies
Page186
ofheteroepitaxialstructuresLiNbO3/LiTaO3(Khachaturyan1987;Khachaturyanetal1987).
Ananalysisofrecentpublicationsonthemechanismoforientedgrowthofvarioussubstancesshowsthattheircommontendencyisrevisionofconventionalandgenerallyacceptedviewpoints.Theseworksrejectthedimensionalgeometricapproachandmakeuseofphaseequilibriumasoneofthecriteriaofthepossibilityofepitaxy(Chernovetal1980;BolkhovityanovandYudayev1986).
4.3.1Micromorphologyoffilmsurfacefordifferentcrystallographicorientationsofthesubstrate
MorphologicalstudiesoflithiumniobateandsolidsolutionsLiNb1-yTayO3haveshownthatsurfacemorphologydependsonthefollowingfactors:materialandpreparationofsubstratesurface,orientation,compositionofprecipitatedlayer,growthrateandtemperatureregimeofepitaxy.
Platesofpreferentiallyzandycutsofsingle-domainsinglecrystalsaretypicallyexploitedtomanufactureintegro-opticelements.Thestateoftheirsurfacelayer,whichisofprincipalimportancefortechnologyoflightguideformation,dependsessentiallyonfinishpolishing.
Thedamagedsurfacelayerisadevelopedsystemofstructuraldefectsandviolationofchemicalcomposition.Directstructuralstudiesofreflectionusingelectrondiffractometryshowthataftermechanicalpolishingthesurfacelayeroflithiumniobateplatesiscompletelydisorderedandamorphous(Sugiietal1980;Rakovaetal1986).Itsstructuralperfectioncanbeimprovedbysubstrateannealinginoxygenatmosphere.Optimumannealingconditionsare1000°Cand1h.Aftersuchheattreatment,electrondiffractionpatternsofsamplesshowKikuchilines,whichisindicativeofhighperfectionofcrystal
surfacestructure.
Figure4.14presentsthephotographsofsurfacemorphologyofLiNbO3filmsonLiTaO3substratesofz,yandxorientations.Perfectlysmooth,mirrorsurfacesaretypicalwhoseroughnessheightonthezplaneisnotlargerthan0.1µm(Fig.4.14(Ia,IIa)).Introductionofironimpurityintosolutionleadstotheformationofroundfiguresofgrowthonthefilmsurface.HeterolayersonLiTaO3substratehavemorphologyanalogoustohomolayersbutthefiguresofgrowthhavepronouncedcontours,theroughnessheightreaches0.5µm(Fig.4.14(IIb,c)).
Thepicturesshowthatthesurfacemorphologyoffilmsisdeterminedfirstofallbythesubstrateorientation.OnthexplaneofepitaxialLiTaO3,thefiguresofgrowthhavetheshapeofatriangleandsometimesofatruncatedpyramid1µmhigh.Longnarrowhillocksdirectedalongthex-axisareobservedony-orientedhomo-andheterolayers(Fig.4.14(lb,IIb,IIIb)).Themorphologyofepitaxiallayersissubstantiallyaffectedbyinterfaceinstability.Athighgrowthrates,thesurfaceonwhichcrystallizationtakesplacebecomesunstableanditsroughnessincreases.Atlowcoolingrates,theeffectofgradientsalongsubstratesincreases,whichleadstotheformationoflayerswithsignificantlydifferentthickness.InvestigationoftheeffectofgrowthrateuponsurfacemorphologyofLiNbO3filmshasshownthatthesmoothestlayerscorrespondtothegrowthrateofnotmorethan0.6µm/min.Anincreaseinthegrowthratehasaspecialeffectuponthemorphologyofz-orientedlayers,atratesnear
Page187
Fig.4.14TypicalmorphologyofLiNbO3filmsurfacesofa)(0001);b)( )'c)( )substrateorientations.I)y=0.3,v~0.2µm/min;LiNbO3substrate;II)y=0.8,v~0.6µm/min;LiTaO3substrateIII)y=0.3,v~0.1µm/min;
LiTaO3substrate(Khachaturyanetal1984).
1µm/minthereappearsmosaicstructureofthesurface,andabovethisvaluethefilmiscompletelycoveredwithhillocks.Anincreaseofprecipitationrateonyandxplanesentailsanincreaseinthedensityofthefiguresofgrowthwhichsomewhatincreaseinsizeandhaveatriangularshape(Fig.4.14(IIIb,c)).
Thus,thesurfacemorphologyofLiNbO3filmsisbasicallydeterminedbysubstrateorientationandgrowthconditions.Theappearanceofthree-dimensionalpatternsisduetocrystallographicspecificitiesoflithiumniobatestructure:theyaredeterminedbytheshapeofcross-sectionofelementaryrhombohedronwith(0001),( )and( )planes.
ConnectionbetweenthelatticeparametermismatchandthesurfacemorphologyalsomanifestsitselfinepitaxyofsolidsolutionsLiNb1-yTayO3onaLiTaO3substrate.Figure4.14showsadecreaseinsurfaceroughnesswithincreasingTacontentinthefilmanda
decreaseinthedensityandsizeofthegrowthpatterns.Thesurfaceroughnessdoesnotexceed0.2µm.Theresultobtainedtestifiesclearlytothefactthatsurfacemorphologyisdeterminedbythestructuredefectsoccurringattheinterfaceduetomismatchoflatticeconstants.Thefilmsurfaceroughnessisconsiderablyinfluencedbythemannerinwhichthesubstratesurfaceisprepared.Mechanicalpolishingleadstotheappearanceofadamagednear-surfacelayer.High-temperatureannealingorchemicaletchinginducetheappearanceonthesamplesurfaceofsomesignsofpolishinghiddenbythenear-surfacelayer.Scratchesonthesubstrateoccuronthesurfaceofthinlayersintheformofshallowgroovesupto3µmwide.Toobtainaperfectsurface,thesubstratewaspreliminarilytreatedinKOHatatemperatureof280-340°Cfor2-3min.
Examinationofsurfacemorphologyhasshownthattoobtainsmoothlayersitisofimportancetocompletelyremovetheresiduesofsolution-meltfromthefilmsurfacewhenthegrowthprocessisover.Arapidcoolingtoroom
Page188
temperaturetypicallycausesanuncontrolledadditionalcrystallizationfromtheremainingdropsofliquid.
4.3.2Diffusion-induceddefectsinfilms
Thediffusedlayerandsubstratecanbediffractedseparatelybyutilizingthediffractionanglecorrespondingtoeachlatticeconstant.Thusseparatetopographiescanberecordedforthediffusedlayerandsubstrate.Thistechniqueisveryusefulfortheinvestigationofdefectsgeneratedbydiffusion.Sugiietal(1978)tooktopographiesoftheTi-diffusedlayerusingtheLangcameraappliedtothereflectioncasewithCuKa1radiation.
Figure4.15ashowstopographyofthediffusedlayersofthesamplesofgroupI.Theexcessdiffractionconstantobservedinallthesamplesisduetoahighdensityofdefects.Itisfoundthatthehigherthediffusiontemperature,thelessseriousthedegradationincrystallinityinthediffusedlayer.Thiscorrespondstotheresult,obtainedbytherockingcurvemeasurement,thatthemismatchdecreasedwithincreasingdiffusiontemperaturefrom1000to1100°C.
Figure4.15bshowstopographyofthediffusedlayersofsomesamplesofgroupII.Threetypesofdefectsareclearlyobserved:mismatchdislocations,cracksoftypeIrunninginthedirectionperpendiculartothexaxis,andcracksoftypeIIrunninginthedirectionperpendiculartothez-axis.AllofthedefectswereinducedbytheTidiffusion.Mismatchdislocationsshouldbegeneratedsoastorelievestressesinthediffusedlayer.ThedirectionsofthecrackssuggestthatthetypeIcracksmustbegeneratedbyastressalongthea-axisandthetypeIIcracksbyastressalongthec-axis.DensitiesofthemismatchdislocationsandofthetypeIcracksincreasewithdiffusiontimet,however,thedensityoftypeIIcracksisalmostindependentoft.
WhentheTi-diffusedlayerisutilizedasanopticalwaveguide,thedefects
Fig.4.15Diffusion-induceddefectsinTi-diffusedlayersofsamples
ofLiNbO3:TigroupI(g=030)(a)1000°C,10h,(b)1000°C,2.5h,groupI[(Sugiietal1978).
Page189
mayincreasethescatteringlossofopticalguidedwavesasobservedintheNb-diffusedLiTaO3waveguides(RamaswamyandStandley1975).
Applyingthecombineddiffusion-filmmethod,onecanobtainchannelsofan'immersed'orsymmetricwaveguide.Figure4.16ashowsaLiTaO3substrateof(1120)orientationwithan'Y'-shapedcouplerpreliminarilydeposedbytitaniumthermodiffusion.Thechannelwidthwasequalto6µmandthegapbetweenthechannelsfordepositingcontrolelectrodesto10µm.Onthissurface,anepitaxialLiNb0.1Ta0.9O3layerwasgrown.Figure4.16bshowsthesurfacemorphologyofepitaxialstructureLiNb0.1Ta0.9O3/Ti:LiTaO3.Thechannelsandthe'Y'-shapedcouplerareclearlyseen.
Varyingthelayercomposition,thesubstratematerial,thethicknessoftitaniumsputteredontosubstrateandthetimeoftheprocessweformdifferentprofilesoftherefractiveindexwithamaximumvalueonthesubstrate-filminterface.Thelighttransmittedthroughthewaveguidehasminimumscatteringlossontheinterface.Therefractiveindexvariationonthewaveguideboundary,whichdeterminesscatteringundercompleteinternalreflection,isbyanorderofmagnitudesmallerthanthatonthefilm-airinterface.
4.4Substrate-filminterfaceandtransitionregion
Thestateandpropertiesoftheinterfacebetweenthewaveguidinglayerandsubstratehaveaneffectuponthepropertiesofthefilmasawholeanduponitsstructure.Theinfluenceofthesubstrateupontheinterfacestructuredependsonthelayergrowthconditionsanddeterminethedensityanddistributionofdefects(inclusions,dislocations,impurityatomsandvacancies)andelasticstressinthetransitionlayer.
Fig.4.16ThesurfaceofaLiNbO3substratewithaTi-diffused'Y'
coupler(a)andthesurfaceofanepitaxialfilmgrownonthissubstrate(b).
Page190
Epitaxiallayersarecharacterizedbyaclearlypronouncedsubstrate-filminterface.Thethicknessofthetransitionregionisdeterminedbythegrowthconditionsandmaterials,aswellasbytheinitialepitaxytemperatureatwhichthesubstrateismoistenedbythesolution-melt.Thesubstratesurfacedissolutionincreaseswithincreasinginitialtemperatureforthesamesolutioncomposition.Thisleadstothefactthatunderepitaxy,beforethebeginningofprecipitationattheLiTaO3crystallizationfront,thiscausestheformationofathinliquid-phaselayerenrichedwithTaascomparedtotherestoftheliquidphase,andunderasubsequentcoolingalayerofvariablecompositionisprecipitated.Uponprecipitationofapurelithiumniobatefilm,onthesubstrate-filminterfacethereformsasolidsolutionLiNb1-yTayO3.ThisobviouslyoccursduetosubstratedissolutionsinceintheindicatedpapertheconcentrationofNb2O5inthesolution-meltisby5%smallerthaninstoichiometriccompositions.
Transitionregionswereexaminedonchipsandpolishedcutsofthegrownstructures.Underidealhomoepitaxythefilm-substrateinterfaceisnotpronounced.Figure4.17presentsphotographsofchipsofLiNbO3andLi(Nb,Ta)O3filmsonLiNbO3andLiTaO3showingaclearandstraightinterfaceandaflattransition.IdentityofcrystallinestructuresoffilmandsubstrateandequalNb5+andTa5+radiileadtointerdiffusionofniobiumandtantalumatomsthroughtheinterfaceandtotheformationofthetransitionregionLiNb1-7TazO3wherezvariesfrom0toy.
Theformationofthe'transition'regionisanundesirableprocesswhichmakesepitaxiallayerscloserinthepropertiesandstructuretothediffusionlayers.
Filmswithaconcentrationprofileclosetorectangularcanbeobtainedin
Fig.4.17Boundariesbetweenepitaxialstructures:a)LiNbO3/LiNbO3;
b)Li(Nb,Ta)O3/LiTaO3;c)LiNbO3/LiTaO3(Khachaturyanetal1984).
Page191
differentways.Precipitationontoz-LiTaO3throughabufferlayersubstantiallydecreasesinterdiffusion,andthethicknessofthetransitionregionappearstobelowerthanthemicroproberesolution(~0.2µm).Theconcentrationprofiledependsonthegrowthconditions.Theinterdiffusiondepthisdeterminedbytheheattimeanddecreaseswithdecreasingholdtimeafterprecipitation.Forstructuresobtainedatagrowthrateoflessthan0.2µm/minandannealingfor3hthetransitionregionistypicallywide(upto3-5µm)andtheinterfaceisonlypronouncedunderselectiveetchingasshowninFig.4.17a.Precipitationataratev~(0.2-0.3)µm/minandholdingfor1.5hleadstotheformationofstructureswithatransitionregionnotwiderthan0.5µm,whichisobservedatchipswithoutadditionaletchingoftheinterface(Fig.4.17c).
4.5Dislocationstructure
Tocreateeffectivewaveguideswithinsignificantattenuation,filmswithlowdefectdensity,sharpsubstrate-filminterface,mirror-smoothsurfaceoftheepitaxiallayerandhomogeneityoffilmpropertiesthroughoutthethicknessarenecessary.Investigationofstructuralinhomogeneitiesandsurfacemorphologyplaysanimportantroleforgrowingfilmswithprescribedparametersandlowdefectdensity(MadoyanandKhachaturyan1987).
Morphologicalstudieswerecarriedoutusingscanningelectronandlightpolarizingmicroscopes.Structuralinhomogeneitieswererevealedbyselectiveetchinginaboiling1:2mixtureofconcentratedacidsHFandHNO3andinKOH.Etchingtimewasvariedfrom1to40mindependingonthepolarizationvectordirection.
Themosttypicalinhomogeneitiesofepitaxiallayersaredislocations.Analysisofexperimentalpapersonexaminationofthedislocationstructureofferroelectricsshowsthatthemostlikelymechanismofthe
occurrenceofdislocationsisthefollowing:
-penetrationofdislocationsfromthesubstratetothefilminwhichtheydegenerate;
-nucleationofdislocationsunderstresscausedbynonuniformimpuritycaptureunderlaminargrowth;
-occurrenceofdefectsduetothenonuniformimpuritydistributioninagrowinglayer.
Onthesubstrate-filmboundary,defectsmayoccurduetomismatchinlatticeconstantsbetweenthefilmandsubstrate.Tominimizethemismatchbetweenthetwolattices,elasticdeformationoffilmsisenergeticallyadvantageous.Ifthemismatchisnotcompensatedcompletelybytheelasticstress,mismatchdislocationsalsooccur(MilvidskyandOsvensky1977).Arelativecontributionofelasticstressesandmismatchdislocationstotheaccommodationofcrystallatticesdependsonthedifferenceinlatticeconstants,filmthickness,geometryofdislocations,characterofbondsontheinterfaceandelasticconstantsoftwointergrowingmaterials.Mismatchdislocationsslidefromthefreesurfaceintotheinterfaceregion.
PlaceswheredislocationsappearonthefilmsurfaceasconicaletchpitswithaclearlypronouncedvortexshowninFig.4.18e,f.Butamixtureofhydrofluoricandnitricacidsdoesnotpermitanexactlocationofdislocationetchpitson
Page192
Fig.4.18Dislocationstructureanddomainconfigurationsinepitaxialfilms,successiveetchingoffilmsurfacewithataperedoutpositive
domain(a,b);domainconfigurationsinsubstrate(c)andinafilmgrownonthissubstrate(d);microdomainson(0001)(e)and( )
(f)surfacesofLiNbO3structureinhomogeneitiesonthesurface( )ofaLiNbO3film(g)andetching-revealeddislocationsandmicrodomainsina(0001)film(h)(Khachaturyanetal1984).
thepositivez-planeand,asanalysisshows,doesnotatallpossesspropertiesofselectiveetchingforthex-plane.ThedislocationstructurewasunambiguouslydeterminedbyetchingintheKOHmeltatatemperatureof400°C.Figure4.18eandfshowszandysurfacesofLiNbO3afteretchinginKOHfor2min.
Sincesubstratedislocationsemergingonthesurfaceunderpseudomorphousfilmgrowthcontinueinthegrownlayer,thestructuralperfectionofthelayerdependsondislocationdensityinthe
substrate.Adirectcountofetchingpitshasshownthatthedensityofdislocationsemergingonthesubstratesurfaceisdeterminedbythepositionofthissurfacerelativetothegrowthaxisoftheoriginalcrystal.Thenumberofdislocationsonthey-planeofLiTaO3andz-planeofLiNbO3(thatis,ontheplaneperpendiculartothecrystalgrowthaxis)makesupN~104cm-2,fortheotherplanesitisbyanorderofmagnitudesmaller.
SelectiveetchingoflithiumniobatefilmsinKOHhasshownthatgrowthhillocksonthefilmsurfaceareofdislocationnature.Intheplaceofhillocks
Page193
removedbypolishingtheretypicallyappeardislocationetchingpits(Fig.4.18c).Twomechanismsofthisphenomenonarepossible.
Inmatingtwosingle-typelatticeswithinterplanardistancesa1anda2thereoccurmismatchdislocationswiththelineardensity
where
Forapseudomorphouslygrownlayerthereexistsacriticalthickness
Onreachingthisthickness,thelayerstopsbeingpseudomorphous,andnetsofmismatchdislocationsappearontheboundary.
Dislocationsofthesubstrate,thatemergeonitssurfaceuponpseudoamorphousfilmgrowth,stretchtothegrownlayeruptothecriticalthickness.Afterthat,dislocationswiththeBurgersvectorparalleltothesubstratebend,becomemismatchdislocationsandthengotothegrownlayer.Inthiscasethereappearonlyseparateregions,insteadofawholenet,ofmismatchdislocations.Asubstitutionofthevaluesofinterplanardistancesoflithiumniobate,dx=1.284Å,dy=1.486Å,dz=1.152Å,andlithiumtantalate,dx=1.286Å,dy=1.487Ådz1.147ÅobtainedbytheX-raydiffractionmethodyieldsthevaluesoflineardislocationdensitiesNy=6.79×104cm-1,Nx=8.48×104cm-1,Nz=34.84×104cm-1andcorrespondinglythevaluesofpseudomorphouslayerthicknesshy.cr=0.074µm,hx.cr=0.059µm,hz.cr=0.014µm.
Thus,duringcrystallizationonthez-planeofLiTaO3themismatchdislocationdensityisminimum,andthesurfacemorphologymustbenearlyisotropic.Fory-andx-orientedlayersthenumberof
dislocationscausedbymismatchbetweentheinterplanardistancealongthezaxisandalignedperpendiculartoitishigherbyanorderofmagnitude.Therefore,thesegmentsofmismatchdislocationsoccurringonthegrowthdislocationsthatstretchtothefilmareexpectedtobeperpendiculartothez-axis.
Suchamodelagreeswithsomeoftheexperimentalresults.Inparticular,thesurfacemorphologyonthezplaneisclosetoisotropic,andthedirectionofgrowthhillocksony-andx-orientedfilmsareperpendiculartothez-axis.Introductionoftantalumpentoxidetoalithiumniobatefilm(i.e.matingthelatticeconstantsofthefilmandsubstrate)decreasesthenumberandsizeofthegrowthhillocks.Butthereexistessentialcontradictions.Becauseofsmallthicknessofthepseudomorphouslayers,themismatchdislocationsegmentsmustoccurattheinitialinstantofepitaxy(0.1µm)andmustnothaveanyeffectuponthemorphologyfurtheron.Thefiguresofgrowthincreasewithincreasingfilmthickness,whereastheeffectoflatticemismatchdecreases.
Page194
UnderhomoepitaxyontoaLiNbO3substratethelatticemismatchisabsent,butelongatedhillocksoccuronthefilmsurface.Growthpatternsondislocationsareobviouslyduetoalieninclusions.
Analysisofcrystallizationfromsolutionhasshownthatsheaf-shapedgrowthdislocationsoccuroninclusionsconcentratedforthemostpartalongplaneswhicharetracesofterminationoraccelerationofagrowingfacet.
Inepitaxialgrowth,suchaplaneisthesubstratesurface.Thedifferenceinionradiiofvanadiumandniobiumcausessegregationofsolventintheformofinhomogeneousmicroinclusions.Thedirectionofdislocationsinasheafisconnectedwithfreeenergyanisotropyofunitdislocationlengthwhichisdeterminedbytheelasticmoduliofthecrystal.Forlithiumniobateandtantalate,anisotropyony-andx-orientedplanesissingle-typerelativetothez-axis.Divergenceofthesheavesmustleadtoincreaseinthegrowthpatternsize.Captureofthesolventmayoccurbothunderhomo-andheteroepitaxy.Theshape,sizeandconcentrationofinclusionsaredeterminedbysurfaceprocesses.Introductionoftantalumoxideintheliquidphase,whichstimulatesanincreaseinthegrowthtemperatureandadecreaseinthegrowthratemustresultinadecreaseinthesolventcaptureprobability.Thepresenceofsheavesofdislocationsduetoinclusionsinalithiumniobatefilmisinagreementwiththesurfacemorphology.Thestructureoftheinterfaceisworsenedbyinclusionsleadingtoascatteringofthewaveguidemode.
Thedislocationdensityinthefilmisthusofthesameorderasinthesubstrateorevenhigher.Inadditiontodislocationsgrowthfromthesubstrate,newdislocationsoccurinthefilmduetolatticemismatchandsolventinclusions.Onthelayersurface,dislocationsappearascharacteristicgrowthpatternswhoseshapeisdeterminedbyorientationofthesubstrateandthesizebythethicknessandgrowth
rate.Mismatchdislocationsoccurinpseudomorphouslayersnotthickerthan0.1µm.Theirdensityisminimumonthe(0001)plane.Onthe( )and( )planestheyappearashillocksstretchingperpendiculartothe(0001)axis(Fig.4.18g).Introductionoftantalumpentoxidetothemeltfromwhichalithiumniobatefilmisgrown(i.e.matingthelatticeconstantsofthefilmandsubstrate)decreasesmismatchdislocationdensityandthesizeofthegrowthhillocksintheplacesofdislocationoccurrence.
Duringcrystallizationfromsolution,growthdislocationsintheformofdivergentsheavesoccuroninclusions(Golubevetal1982).Inclusionsarelargelyconcentratedalongtheplaneswhicharetracesofterminationoraccelerationofagrowingfacet(inparticular,thesubstratesurface).Thedifferenceinionradiiofvanadiumandniobium(0.4Åand0.66Å)restrictssolventcapture,andforhighconcentrationsleadstosegregationintheformofinhomogeneousmicroinclusions.Forlowvanadiumconcentrations,strongdeformationsandlocalstressesappearinthelatticethatinitiatetheformationofdislocationsandmicrodomains.Figure4.18h)illustratesetchingofa(0001)filmofLiNbO3withadislocationstretchingthroughtheentirelength.Thefigureshowsthatdislocationsoccuralongwithmicrodomainsalignedperpendiculartothesurface.Dislocationsalignedalongthe( )axisaregeneratedatdifferentdepthsofthefilmandaremostlyconcentratedneartheinterface.
Figure4.19presentsagraphofthedistributionofdislocationdensityover
Page195
Fig.4.19Distributionofdislocationdensityalongthethickness
oftheepitaxialstructureLiNbO3/LiTaO3.
thethicknessoftheepitaxialstructure.Dislocationsarebasicallygeneratedinthetransitionregionwhichisthickerbyanorderofmagnitudethanthecalculatedvalueofthepseudomorphouslayer(0.1µm).Therefore,besidesmismatchdislocations,othertypesofdislocationsmustdevelopinthefilm,whichoriginateontheimpuritycentresthatinducelatticedeformationandmicrostrains.Thelatterlead,inturn,totheformationofmicrodomainscoupledwithdislocations.
Structuralinhomogeneitiesoffilmsaffectessentiallytheiropticalproperties.Inparticular,theycausescatteringofchannelledlightonmicroinclusionsanddomainwalls.Thepresenceofdomainswithdifferentpolarizationlowerstheefficiencyofelectro-opticmodulation.
Wepresenttheresultsofmorphologicalstudiesofthefilmsurfaceandsubstrate-filminterfaceoflithiumniobatestructuresgrownbyLPEandliquid-phaseandelectroepitaxy.Figure4.20presentstypicalpicturesofsurfacemorphologyandtransversechipsofthesefilmsgrownbythetwomethodsmentionedabove.
Inthefigureonecanseeimperfectionsclosedonthesubstrate-filmtransitionregionunderliquid-phaseelectroepitaxyoflithiumniobate
(lb,IIb),thicknessandplanarityofepitaxialfilms,aswellasregionsofgrowthdislocationclustersandandoccurrenceofmicrodomains(III).
Figure4.21presentsthedependenceoftheratioofdislocationdensitiesinlithiumniobateunderliquidphaseelectroepitaxyandliquidphaseepitaxy(1)andfilmthickness(2)onthecurrentdensity.Asisseenfromthefigure,anincreaseinthecurrentdensity(J>15mA/cm2)inducesasharpincreaseinthegrowthdislocationdensityascomparedwithliquidphaseepitaxyoflithiumniobate.ThisisapparentlyconnectedwithagrowinginfluenceofJouleeffectuponcrystallizationabovetheindicatedcurrentdensityrange.
4.6Domainstructure
Themosttypicalinhomogeneitiesinferroelectricsaredomainboundaries,growthdislocationsandmicroinclusionsofalienphases.Inplanarintegro-opticwaveguidesonthebasisoflithiumniobate,theseinhomogeneitiesleadtoanadditionalscatteringofchannelledlightandtoloweringofthedeviceefficiency.
Polydomainlithiumniobateandtantalatecrystalsconsistof180°domainswithpolarizationalongthe(0001)axis.Lithiumtantalateusedassubstrateisaperfectstructuralanalogueoflithiumniobate,butthedomainsizeissmallerbytwoordersofmagnitude(10µm).Thedislocationdensitymakesup~104
Page196
Fig.4.20Photographsoftransverselayers(I)andmorphology
ofthesurface(II)oflithiumniobatefilmsgrownbyliquidphaseepitaxy(a)andliquidphaseelectroepitaxy
(b)(Khachaturyanetal1987).
Fig.4.21Dislocationdensityratiosinlithiumniobate
filmsgrowthbyliquidphaseepitaxyandliquidphaseelectroepitaxy(1)andthicknessofelectro-LPEfilm
asfunctionsofcurrentdensity(Khachaturyanetal1989).
cm-2,mostofthedislocationsoccurringduringgrowth.Thinrods(upto300µmlong)ofneedle-shapedmicrodomainswereobservedinlithiumniobatealongthe(0001)axiswithpolarizationreversetothatoftheprincipaldomain(Fig.4.22)(ProkhorovandKuz'minov1990).Thepresenceofvacantoxygenoctahedrainthestructurepromotesentrapmentofimpurityandfirstofallmetalions.
Defectstypicaloflithiumniobateareoxygenvacancieswhichcanbereadilywithdrawnbyhigh-temperatureannealinginoxygenatmosphere.
Lithiumniobatecrystalsarehighlysensitivetoheattreatmentwhichaffects,besidesoxygenvacancies,alsodislocationmigration,impuritydistributionandthecontentofmicrodomains.(Rakovaetal1986;Bocharovaetal1985)pointedouttheappearanceofalienphasesonthesurfaceofLiNbO3underannealingatT=900°C,(OhnishiandYizuka1974)reportedrepolarizationofnear-surfacelayersundermechanicaltreatment.
Page197
Fig.4.22Needle-shapeddomainstructureofLiNbO3crystal(ProkhorovandKuz'minov1990).
Fig.4.23(right)Growthrateofalithiumniobatefilmversus
coolingtemperature.Thecoolingrates1)0.3deg/min;2)0.16deg/min, )onanegativedomain;)
onapositivedomain.
4.6.1Epitaxialfilmonadomainboundaryofthesubstrate
Nonsymmetricpositionofionsintheferroelectricphaseisresponsibleforthedifferenceinchemicalactivitiesofsurfaceswith
differentpolarizations,whichisobservedinparticularinselectiveetching.
Underepitaxy,whenthegrowthrateisdeterminedbysurfaceprocesses(kineticregime),thesurfaceactivitymusttelluponthekineticsofcrystallizationprocesses.TheCuriepointoflithiumtantalate(660°C)islowerthantheepitaxytemperature,andprecipitationunderheteroepitaxyproceedsonsubstratesintheparaphase.Thesurfacepropertiesareidenticalthroughout,andspontaneouspolarizationhasnodirecteffectupongrowthkinetics.Underepitaxyon(0001),aLiNbO3crystalisintheferroelectricphase(Tc=1210°C),andprecipitationmaytakeplaceontosingle-andpolydomainsubstrates.
Crystallizationfromsolutionassumesthatprecipitatedatomscomefromthedepthofsolutiontothecrystallizationfront,areadsorbedontothegrowingsurfaceandbuiltinthecrystallattice.Forsmallsupersaturations,thegrowthrateislimitedbydiffusionmasstransferandsurfaceprocessesdonotaffecttheprecipitationrate.Filmthicknessesonpositivelyandnegativelychargedsingle-domainsubstratesareequal.Indiffusionregime,theinfluenceofdomainstructureisobservedwhenprecipitationtakesplaceontoapolydomainsubstrate.Ondomainswithdifferentpolarizationsthefilmthicknessisnotatalluniform,butitbecomesuniformfarfromdomainboundaries.Suchapicturecanbeeasilyexplainedifwetakeintoaccountthefactthatfarfromtheboundariesthegrowthrateisonlylimitedbymasstransferandnearthedomainboundariesadifferenceinsurfaceactivitiesleadstoafasterconcentrationloweringon
Page198
thenegativedomainand,accordingly,toredistributionofthefluxofprecipitatingatoms.Thus,themasssupplyonthesidesoftheboundaryisdifferent,thegrowthrateonthenegativez-surfaceishigherbyafactorof1.5thanthatonthepositivesurface(Fig.4.23).
Asthesystemcoolingrateincreases,crystallizationislimitedbybuilding-inofatomsintothelattice(kineticregime).Butthereisnoessentialdifferenceinthegrowthratesonpositivelyandnegativelychargedsurfacesofsingle-domainsubstratessincethebreakingeffectofthelessactivepositivesurfaceleadstoanincreaseofsupersaturationandgrowthrate.So,thegrowthratesonsingle-domainsubstratesaredeterminedbythecoolingrateofthesolution-melt(Fig.4.23)(MadoyanandKhachaturyan1987;Madoyanetal1985).
Underepitaxyonapolydomainsubstrate,ahighactivityofthenegativesurfaceleadstotaperingoutofthepositivedomain.Whenthefilmthicknessexceeds30µm,thegrowingfilmsaretypicallysingle-domainandnegativelypolarized.
Figure4.18bdemonstratessuccessiveetchingoffilmsabout25µmthick.Thedashedlineindicatestheregionsofnegativelypolarizedsurface,onwhichpositivedomainsappearafteretching.
4.6.2Domainconfigurationsinfilms
Analysisofdomainstructureofepitaxialfilmshasshownthattheconfigurationandsizeofdomainsdependonsubstratematerialandorientationandonthethicknessoftheprecipitatedlayer.
Ithasbeenestablishedabovethattheboundaryofadomaingrowsthroughthesubstrate-filminterface.Investigationsshowedthatwhenfilmthicknessdoesnotexceed20µm,thedomainconfigurationsofthesubstratearefullyinheritedbythefilmbothunderhomo-andheteroepitaxy.UnderheteroepitaxyonLiTaO3,thesubstrateisin
paraphaseandthelithiumniobatefilmiscrystallizedintheferroelectricphase.ThefinalformationofdomainconfigurationsproceedswhenthesampleiscooledthroughtheCuriepointofthesubstrate(Tc=660°C).Thepolydomainstructuresoffilmandsubstratewerefoundtobeperfectlyidentical.Experiencingnoactionoftheelectricfieldofthesubstrate,aprecipitatedfilmobviouslyacquiresthedomainconfigurationwhichisenergeticallymoreadvantageous.Takingintoaccounttheconnectionbetweenpolarizationdirectionandgrowthkinetics,wemayassumethatthefilmmustbenegativelypolarizedorpolydomainwithpredominanceofnegativedomains.Whenthesampleiscooledbelow660°C,thepolarizationoccurringinthesubstrateleadstofilmrepolarization.Thisprocessispromotedbyalargenumberofintergrainboundariesresultedfromgrowthofnucleiatthecrystallizationfront.Theseintergrainboundariesareplacesofpointdefectanddislocationpile-upalongwhichnewlyformeddomainboundariescanrun.Moreover,thepolarizationeffectofthesubstrateisstrengthenedduetothepresenceinepitaxialstructuresoftransitionregionswithsmoothlyvarying2µm-thickcompositionLiNb1-xTaxO3.Toobtainsingle-domainLiNbO3/LiTaO3films,itsufficestocarryoutcoolinginanelectricfieldthatprovidessubstratepolarization.
Figure4.18canddpresentsthedomainstructureofhomoepitaxialfilmandsubstrateoflithiumniobate.Thefilmnaturallyrepeatsthedomainstructure
Page199
ofthesubstrate.Taperingoutofthepositivedomainisobserved,asmentionedabove,forthicknessesof30µm.Onsingle-domainsubstratesthefilmisalsosingle-domainandthepolarizationdirectionofthefilmisidenticaltothatofthesubstrate.
4.6.3Microdomainsinsubstratesandinepitaxiallayers
Atypicalfeatureofthedomainstructureoflithiumniobateisthepresenceofthinneedle-shapedmicrodomainswithapolarizationreversetothatoftheprincipaldomain(Bocharovaetal1985;OhnishiandYizuka1975).Uponselectiveetchingofanegative(0001)plane,needle-shapedmicrodomainsappearastrianglepyramidswithside-faceorientation( ).Theverticesofthesepyramidsareplaceswheremicrodomainsemergeonthefilmsurface(Fig.4.18d).Onthepositivezplane,insuchplacesthereformsmallirregular-shaped(upto1µm)etchingpitscorrespondingtoneedle-shapedmicrodomains.Thesizeofthepitsremainsunchangedastheetchingtimeincreases.Onthe( )planetheyappearasthin300µmstripsrunningalongthez-axis(Fig.4.18f).
Theinfluenceofalienfactorsuponthedomainstructurewasinvestigated.Mechanicalpressingwithadiamondneedle(P=5,10,15g,thediamondneedlepointcurvature~10µm)onthe(0001)planeofLiNbO3leadstotheappearanceofmicrodomainclusterswiththedensityinthecentreupto106cm-2andareasincreasingwithincreasingpressure.
LaserradiationproducesthesameeffectuponLiNbO3crystals.Thedensitiesofmicrodomainsformedundernear-thresholdradiationintensity(l=1.06µm,Jthrcsh=6.5GW/cm2)reached109cm-2inthecentreand105-106cm-2attheclusterboundaries.Thesizeoftheclusterareasdecreasesslightlywithdecreasingintensity,andonthewholetheclusterdiameterisdeterminedbythediameterofthefocalspot.Underselectiveetchingatypicalpatternisobservedinthe
irradiatedarea.
Thisphenomenoncanbeinterpretedindifferentways.LevanyukandOsipov(1975)showedthepossibilityofaphotoinducedreversalofspontaneouspolarizationinferroelectricswithoccurrenceofa'frozen'bulkcharge.Butthismechanismdoesnotaccountfortheindicatedphenomenonsincetheresultantchargeofirradiatedregioniszero.Moreover,thepolarizationreversalregionisstrictlylimitedtotheirradiatedarea,whereasirradiation-inducedmicrodomainsareobservedoutsidetheirradiatedareaaswell.Themechanismofmicrodomainnucleationduetoelasticstrains,whichwasproposedby(Abul-FadlandStefenakos1977)andconfirmedbyexperimentswithmechanicaltreatment,seemstobemostrealistic.Becauseofashortirradiationtimeandalowheattransfercoefficient,irradiationwithahigh-intensitylaserbeaminducedathermalshockwhichisresponsibleforhighlocalstrainsandmicrodomainnucleation.
InepitaxialLiNbO3filmsmicrodomainsareonlyobservedin(0001)-alignedlayers.Themicrodomaindensityvariesfromsampletosample(from10to105cm-2),butasaruleexceedsthemicrodomaindensityonthesubstrate.Thus,microdomainsgrowfromthesubstratetothefilmandemergeinthelayeronlocalinhomogeneitiesandstrains.
Page200
4.6.4PeriodicallyinverteddomainstructuresinLiTaO3andLiNbO3usingprotonexchange
SHGbyquasi-phasematching(QPM)ofthefundamentalandharmonicmodescanreleasehighconversionefficiencyandisversatileforgenerationofshorterwavelength,QPMisbasedonthemoodulationofnonlinearpolarizationbyperiodicallydomain-invertedstructure,andthusitispossibletophasematchanarbitarywavelengthbyanappropriatechoiceofperiodofmodulation.Byusingthistechnique,bluelightgenerationinLiNbO3waveguidehasbeenrealized(Liraetal1989;Webjornetal1989).Thisdeviceofferstheadvantageofefficientconversionoflaserradiation,becausethewaveguidealllowslonginteractionlengthwithstrongmodalconfinement.However,asphotorefractivedamageisknowntooccurinLiNbO3itspotentialathigherpowersmaybelimited.
LiTaO3wasreportedtobehighlyresistiveagainstphotorefractivedamageanditalsohastheadvantagesoflargenonlinearsusceptibilities,andshortwavelengthtransparencyfrom280nm.
SeveralmethodshavebeenusedtofabricateperiodicdomaininversioninLiNbO3andLiTaO3.Tiin-diffusion(Miyazawa1979)orLiout-diffusion(Webjornetal1989)neartheCurietemperaturearewell-knowntechniquestoreversethepolarizationinLiNbO3,buttheshapeoftheinverteddomainisnotrectangular.Electronbeambombardment(Keysetal1991;YomadaandKishima1991;Itoetal1991)hasalsobeenemployedtomake'well'-shapedinverteddomains.butitisdifficulttofabricateshortperiodpatterns.PeriodicallypoledstructuresinLiNbO3canberealizedthroughselectiveprotonexchange(PE)followedbyheattreatmentneartheCurietemperature(Mizuuchietal1991).Afewmicrondeepsemicircular-shapeddomainswithafirst-orderperiodhasbeenfabricatedusingprotonexchangeandaquickheattreatmentnearthe
Curietemperature,generating15mWofbluelight(MizuuchiandYamamoto1991).
Makioetal(1992)reportedontheformationoflong(>40µm),'spikelike'inverteddomainstriggeredbyprotonexchangewithone-directionalheating.Thesedomainshavestraightwallsandthesameperiodastheprotonexchangedgrid,whicharefavourableconditionstoachievefirst-orderQPMdevices.
Authorsdescribedtheirfabricationprocessasfollows;a30nmthickTamaskwasdepositedonthec+orc-faceof0.5mmthickLiTaO3orLiNbO3substratesusinganelectronbeamdepositionmethod.Thefirst-orderperiodicpatternwitha3.2µmperiodwasfabricatedontheTamaskbyconventionalphotolithographyandCF4dryetching,formingwindowstoallowprotonexchange.AsmallamountofpyrophosphoricacidwasdroppedontheTamasksideofthesubstrate,whichwasthenplacedonanalreadyheated(230-260°C)hotplateforseveralminutes,namely,one-directionalheatingfromtherearsurfaceofthesubstrate.AfterremovaloftheTamask,somespecimenswerecutintostrips,polished,andetchedwithHFandHNO3toexaminetheprotonexchangeandthedomaininversion.
Theyfoundthatthepolarizationflippedduringtheprotonexchangeprocess,farbelowtheCurietemperature.Figure4.24showsacross-sectionalviewofaLiNbO3sample,protonexchangedat260°Cfor30minandwithoutanypost-PEannealing.Althoughtheproton-exchangedlayerislessthan1µmthick,inverteddomainsstemmedandstretchedfromtheproton-exchangedregiondeep
Page201
Fig.4.24Crosssectionalmicrographoftheperiodically
invertedspikelinedomainsfabricatedonLiNbO3(Makioetal,1992).
insidethesubstratefrommorethan40µm.Thedomainslooklikespikes,withthinandsharpends.
Thespikelikedomainscanbeformedonbothc+andc-facesofLiNbO3,unlikeothertypesofdomains.SpikelikedomainscouldbesuccessfullyfabricatedonLiNbO3aswell,inspiteofitshighCurietemperature.
Thesespikelikedomainsseentobesimilartotheso-called'needle-shaped'microdomains(OhnishiandIizuka,1975)whicharecommoninpoledcrystalsasresidualantidomains,usuallybeingisolatedandrandomlydistributed.Theinversionmechanismisnotclear,buttheperiodicstressduetoprotonexchangeislikelytotriggerthegrowthoftheantidomains,whichisacceleratedbythethermalgradientcausedbyone-directionalheating.
Thethermalstabilityofthespikelikedomainswasexaminedduringpost-PEannealing.Heattreatmentwascarriedoutat525°Cforupto2min.Thoughthedataarespreadoutoverawiderange,theyindicatethetendencyforthedomainstobecomeshorterandfinallyvanishastheheattreatmenttimeincreases.Atlowertemperature,though,theysurvivelongertreatmenttime.Fromthepracticalpointofview,itis
essentialforthedomainstosurvivethe350-
Fig.4.25Measureddepthofinvertedregionswitha20µmperiodagainsttheheattreatment
temperatureforvariousproton-exchange(PE)conditions(Mizuuchietal1991).
Page202
380°Cheatcycleinordertofabricatewaveguidesonthesubstratebytheannealedprotonexchangemethod.
Thedependenceoftheinverteddepthontheconditionofprotonexchangeandheattreatmenttemperaturewasexaminedforthe-cfacesubstratewithaTamaskof20µmperiod.Onlythe-cfacedoesproduceinversion.Thereasonwhyinversioncannotbeobservedin+cfaceisnotclear,andinvestigationoftheformationprocessofdomaininversionisbeingconductedtoresolvetheinversionmechanism.Figure4.25showstheinversiondepthasafunctionofheattreatmenttemperatureforaheattreatmenttimeof10min.Theinvertedregionbecamedeeperwithincreasingtemperature,butabove610°Caperiodicstructurecannotbeobserved,becauseitisabovetheTcofpureLiNbO3.Thefigurealsoshowsthatthethresholdtemperaturetocausedomaininversionbecomeslowerwithincreasingproton-exchangetimeandsaturatesatalowerlimitof450°C.ThissaturationperhapsindicatestheTcofproton-exchangedLiNbO3.Furthermore,thelargedifferencebetweenthislowerlimitandtheTcofpureLiNbO3showsthelargeextenttowhichtheLiionsareexchangedbyprotonsforthecaseofpyrophosphoricacid.Byknowingthisthresholdtemperaturefordomainreversal,Mizuuchietal(1991)wereabletocarryoutotherprocesses,suchasannealing,atanylowertemperaturewithoutdisturbingthedomain-invertedregions.
4.6.5Waveguideperiodicallypoledbyapplyinganexternalfield
Yamada,etal,(1993)reportedthefabricationofaperiodicallyinverteddomainstructureinaLiNbO3substratebyapplyinganexternalelectricfield,whichyieldsanefficientfirst-orderQPM-SHGdevice.
ItwassaidthatthedomaininversionofLiNbO3isdifficultatroomtemperature.LiNbO3isusuallybrokenwithoutdomaininversion
whenanexternalfieldisappliedatroomtemperature.TheexternalfieldfordomaininversionofLiNbO3isclosetothatoftheelectronavalanche,sotheLiNbO3substrateisbrokenwithoutitsspontaneouspolarizationbeinginvertedwiththeapplicationofanexternalfield.
Yamadaetal,(1993)fabricatedtheperiodicdomainstructureforfirst-orderQPM-SHGdevicesinLiNbO3asfollows.Figure4.26showshowexternalfieldisapplied.Theyalsousedaz-cutLiNbO3crystalasthesubstrate.AnAlthinfilm200nmthickwasdepositedonthepositiveandnegativec-faceofthe
Fig.4.26Schematicofapplyingvoltageforperiodically
domaininversion(Yamadaetal1993).
Page203
LiNbO3substrate.TheAlthinfilmonthepositivec-facewasperiodicallypatternedwitha2.8µmperiodbywetetching.Electrodeswerethenfabricatedonbothc-faces.
Next,atroomtemperature,anegativepulsewithawidthof100µsandavoltageof24kV/mm(theelectriccoerciveforceofLiNbO3isabout20kV/mm)wasappliedonaplaneelectrodeonthenegativec-faceandaperiodicelectrodeonthepositivec-facewasgrounded.Afterapplyingthevoltage,theAlelectrodewasremovedinanaqueoussolutionofNaOH.
Thereasontheperiodicelectrodesshouldbefabricatedonthepositivec-faceisthattheinverteddomainnucleiappearonthepositivec-face.Thereasonwhypulsedexternalfieldshouldbeappliedcanbeunderstoodiftheprocessofdomaingrowthisobserved.Whenthereexistsadependenceofthedomaingrowthonthetimetheexternalfieldisapplied,firstthedomainsgrowalongthec-axis,thengrowundertheelectrodes.Iftheexternalfieldisappliedtoolong,thedomainsspreadoutfromundertheelectrodesandcomeintocontactwitheachother.Theexternalfieldmustbeshutoffbeforethedomainsgrowoutformundertheelectrodes.
Usingtheaboveprocedure,az-cutLiNbO3substratewitha2.8µmperiodlaminardomainstructurewasobtained,whichissimilartothatillustratedinFig.4.24.Fromthefigureitisseenthatthedomainsboundariesareparalleltothec-axis.Thisperiodicallyinverteddomainstructureisidealforfirst-orderQPM-SHGdevices.
4.6.6DomaininversioninLiNbO3usingdirectelectron-beamwriting
Directelectron-beamwritingwasachievedusingascanningelectronmicroscope(SEM)convertedforthispurpose(Nuttetal,1992).Beamcurrentsusedwereintherangeof3-7nAandthebeamvoltagerangedbetween20and30kV.Theelectron-beamspotsizewas0.5
µm.Patternswerewrittenwithsaturatedfilamentcurrentatbeamvoltagesof20,25,and30kV.Thebestgratingresolutionwasobtainedat30kV.Althoughsurfacecrackingwasobservedathighvoltages(30kV)andatlowerscanvelocities(235µm/s)withabeamcurrentof7nA,surfacecrackingwasavoidedbyreducingthebeamcurrentwhilstkeepingthebeamvoltagehigh.Samplesusedinthisstudywere500µmthickz-cutLiNbO3.Thedomaininversionprocessiscontrolledbytheelectricfieldcreatedbyelectronbombardment.Hence,a30nmfilmofTametalwassputteredonthec+face,whichactedasagroundelectrode.Sampleswerescannedonthec-facewheretheelectronbeamdepositedavxechargeonthesurface.Thescanvelocitieswerebetween200and800µm/s.Typicalsheetresisitanceofthemetalfilmwas200W/cm2.DomaininversionwasrevealedbyetchingtheLiNbO3sampleinasolutionoftwopartsHNO3andonepartHFat90°Cfor5minsincetheetchrateforthec-faceismuchhigherthanthatofthec+face.
Tounderstandthedomaininversionmechanismunderdirectelectron-beamwriting,metallinesweredepositedonthec+facethatwere200µmwideandspaced280µmapart.Thisgaveaperiodicgroundplane.Singlelinesusingdifferentbeamscanspeeds(500,250,166.7,71.4,and33.3µm/swith30kWbeamvoltageand7nAbeamcurrent)werewrittenperpendiculartothemetallinesonthec-face.Theseresultsshowthatdomaininversioncanbeachieved
Page204
betweenmetallineswherethereisnodirectgroundand,secondly,domainspreadingoccursatthemetaledges.Theseresultsimplythatdomaininversionisrelatedtotheelectricfielddensity,whichishigheratthemetaledges.Nosignificantdomainspreadingwasobservedonthec+face.
Thewidthofthedomain-invertedregiononthec+facewasabouttwicethedomainwidthonthec-face.Thisspreadinglimitsthefabricationofhigh-resolutiongratingsonthec+face.
Surprisingly,domaininversionthroughthethicknessofthesamplewasobservedonLiNbO3,whichhadnometalfilmgroundingwhatsoeveronthec+face.However,high-resolutiongratingsonthec+faceshoweddistortion.Thisispossiblyduetocharginganddischargingeffectsobservedduringthewritingprocess.Thisimpliesthatmetalgroundingisneccessaryforhigh-resolutiongratingsalthoughlarge-periodgratingscanstillbewrittenwithoutdirectgrounding.Moresurfacecrackingwasobservedwithsampleswithoutmetalgrounding.
Electronbombardmentwithfocusedbeams(0.5µmindiameter)onthec-faceofLiNbO3withthec+faceasgroundedcanproducehighelectricfieldsnearthesurface.Thedistributionofthenormalcomponentofelectricfield,E(x),duetoapointchargeinauniformdielectricmediumnearaconductingplaneisgivenby(Becker,1982)
where
wherexandyaretheperpendiculardistancesofapointchargefromtheconductingplaneasshowninFig.4.27.Thechargeisqandeis
thedielectricconstantofthemedium.Asexpected,ahighelectricfieldisproducednear
Fig.4.27Normalizedelectricfieldlog(4pea2E(x)/q)contours
duetothepointchargeqneartheconductingsurface(Nuttetal1992).
Page205
thepointcharge.Beamcurrentsusedinthisstudywereoftheorderofafewnanoamperesandthetypicalscanvelocityusedwas300µm/s.Thebeamdiameterwas0.5µm.Thiscorrespondstoadwelltimeofabout1.5msper0.5µmtravel.Hence,thechargedepositedisabout10-10Cin0.5µm.Ifwetakethisasapointchargeq,thenthefieldintensityatadepthof5µmisabout108V/m.Thisisinthevicinityofthebreakdownvoltagefordielectrics.Hence,veryhigh-fieldintensitiesareproducednearthepointcharge.Thefieldintensitynearthepointchargeissimilarinmagnitudetothatofthepolarizationfieldsintheferroelectricmaterial.Thisfieldcanproducereverseddomainsnearthesurface.
Theroleofelectronenergyinthedomain-inversionprocessrequiresfurtherinvestigation.HaycockandTownsend(1986)proposedamechanismfordomaininversioninLiNbO3andLiTaO3whereexcitationofthecrystallatticebyanenergeticbeamofelectronsisrequiredwhileanexternalfieldisapplied.IntheexperimentscarriedoutbyNuttetal(1992),energeticelectronscanprovideexcitationofthecrystallatticeandatthesametimeanelectricfieldiscreatedduetoagroundelectrodeonthec+face.Itisalsopossiblethatlow-energyelectrons(<10keV)maynotproducedomaininversionduetosurfaceconduction,whilehigher-energyelectronspenetratedeeperinthecrystal.
Thedomain-inversionprocessstartswithnucleationofdomains,withtheirpolarizationPorientationantiparalleltotheoriginalpolarizationfieldPsatthesurface.Thereisrapidgrowthofthesenucleiintolongdomainsthroughthethicknessofthecrystal.Finally,thereissidewisegrowthorexpansionofdomains.Theinitialshapeofthedomainmayfollowthefieldprofileduetothepointcharge.Therewillbeacriticalfieldfornucleation.Theinverteddomainsinduceadepolarizingfieldthataidstheexternalfieldinthefurthergrowthofinvertedregionsalongthec+axisofthecrystal.So,theinverteddomainshapewillbe
essentiallyparalleltothecaxisofthecrystalasitgrowsfurther.Thedomainwidthonthec+andc-facesoftheLiNbO3crystalincreasedasthescanspeeddecreased;thissuggeststhatthereisafieldlimit,which,whenexceeded,allowsdomainreversaltooccurspontaneously.Whensmaller-periodmetallines(10µm)wereused,nolateraldomainspreadingwasobservedonthec+faceoftheLiNbO3crystal.The10µmperiodgratingobviouslyactedexactlylikeacontinuousground.Therefore,thesamplethicknessplaysapartinthereversalmechanismbecauseofthedropinfieldintensityacrossthesample.
4.7Annealing-inducedvariationofthephasecompositionandcrystallinestructureofthelithiumniobatecrystalsurface
4.7.1Annealing-inducedvariationofthecrystallinestructureofthelithiumniobatecrystalsurface
Electrondiffractionstudieshaveshownthatthesurfaceofmechanicallypolishedx-,y-andz-cutsoflithiumniobatesubstratesiscoveredwithalayerwithadamagedcrystallinestructure,whichisformedduetobrittlefailureofthematerialinthecourseofmechanicaltreatment.Theelectrondiffractionpatternscontainingonlythediffusionbackgroundwithoutanyreflexessuggestamorphityofthethinnear-surfacelayerofthecrystal(Bocharova1986).
Todeterminethedamagedepthinmechanicallypolishedsamples,thedam-
Page206
agedlayerswereetchedonebyoneinamixtureofacidsHF+HNO3atroomtemperaturewithsimultaneouscontrolofthesurfacestructure.Aportionofthesurfacewascoveredwithpiceinwhichpreservedthesurfacefromtheetchingagent,andtheheightofthestepwasindicativeoftheetchedlayerthickness.Thedegreeofstructureperfectionoftheetchedsurfacewascontrolledbyelectrondiffractometryandtheheightofthestepwasdeterminedusinganopticalinterferencemicroscope.Thethicknessoftheamorphouslayervariedwithintherange5nm<d<30nm,wasdependentonthequalityofpolishingandremainedunalteredfromsampletosample.
Betweentheamorphouslayerandtheperfectcrystalthereliesadamagedarea.Thedepthofthedamagedlayerinlithiumniobatecanbeestimatedbyellipsometryandrepeatedtotalinternalreflection.Theellipsometricmeasurementscarriedoutonthey-cutlithiumniobatehaveshownthattheeffectivethicknessofadamagedsurfacelayerdependsstronglyonpolishingqualityandrangesbetween35and160nm(Yakovlev1985).Themethodofrepeatedtotalinternalreflectionwasappliedtorevealanincreaseoflightabsorptionina200nmsurfacelayeroflithiumniobate,whichisexplainedbyahigherdefectdensityinthislayer(Zverevetal1977).
Electrondiffractometricandopticaldatasuggestthatnearthelithiumniobatesurfacethereexistsathinstronglydamagedamorphouslayer(~30nm)andadeeper-lyinglayer(~200nm)ofstrainedmaterial.Therealstructureoflithiumniobatecrystalscontainsdislocations,blockboundaries,microdomainsandothertypesofdefects.Accordingtotheresultsofselectivechemicaletching,thedislocationdensitywas104-105cm-2andthelineardislocationdensitywas~3×104cm-2.
Duringannealingofmechanicallypolishedcrystalsthefollowingtwoprocessesproceed:
-damagedlayerrecrystallization,
-phasecompositionvariation,
thatcanberecordedbyhigh-energyelectrondiffractionbyreflection.Theseprocessesaresimultaneousanddependessentiallyontheannealingtemperature.
Recrystallizationinsolidbodiesconsistsofachangeintheircrystallinestructureandremovalofstructuraldefectscausedbypreliminarymechanicaltreatment.Thestructureofmatterisorderedbythenucleationandgrowthofgrainsaswellasbyenlargementofsomegrainsattheexpenseofothergrains.Thisprocedureresultsinreliefofinternalmicro-andmacrostrains.Theassembled(theassembledrecrystallization)recrystallizationmayequallyoccurinstrainedandunstrainedmaterialsandtypicallyfollowsthedamagedlayerrecrystallization.
Asshownbyelectrondiffractionanalysis,beginningwithT=300°Crecrystallizationofthedamagedlayerinducedbyannealingproceedsataratherhighspeed.Figure4.28a-dpresentsaseriesofelectrondiffractionpatternsoflithiumniobatesamplesalignedparalleltothecrystallographic(0001)planeandannealedatdifferenttemperaturesduringequaltimeintervals(t=4h).Reflectionsfromthesamples,annealedatT=300°C,intheformofarcsandringsarrangedconcentricallyneartheprimarybeam(Fig.4.28a)characterizethechangeinthestructureoftheuppersubstratelayers.Moreover,theelectrondiffractionpatterns
Page207
Fig.4.28Electrondiffractionpatternsofthebasefacet(0001)oflithiumniobateversusannealing
temperature(annealingtimet=4h):a)300°C,b)650°C,c)750°C,d)950°C(Bocharova1986).
exhibitweakKikuchilines,farfromtheprimarybeam,formeddeepinsidethecrystal.Thepresenceofarc-andring-shapedreflectionsisindicativeoforderingofthesurface-layerstructureandofformationofsmallcrystallineaggregatesinthislayer.TheestimateofthesizelofthesecrystallitesobtainedfromthehalfwidthofreflexesBgivestherangeof10-50nm.ThecrystallitesformedatT=300°Chavebasicallyrandomposition,butshowatendencyfortextureformation.
Anincreaseofannealingtemperaturefrom300°Cto700°Ccausesadecreaseofazimuthaldisorientationandsegregationofcrystalliteswithpreferentialorientationparalleltoalithiumniobatesubstratesurface.
TheelectrondiffractionpatternsofsamplesannealedatT>650°C(Fig.4.28bandc)show,togetherwitharcsfromthetexture,alsoasystemofpointreflexesformedbyamosaicsinglecrystal.Withafurtherincreaseoftemperaturefrom700°Cto900°Cthereflectionsfromthetexturedisappear,andtheelectrondiffractionpatternsonlycontainanetofpointreflexes,whichtestifiestothepresenceofsimilarlyalignedgrains.AnnealingoflithiumniobatesamplesatT=950°Cfor4hsufficesforacompleterestorationofcrystallinityofthenear-surfacelayer.Theelectrondiffractionpatternsofsuchsamplesexhibit
Page208
Kikuchilines(Fig.4.28d).Thevariationofthecrystallinestructureoflithiumniobatefacets( )and( )dependingontheannealingtemperatureproceedsinasimilarmanner.
Thus,recrystallizationofthedamagednear-surfacelayerofcrystalsproceedsgraduallyintheentiretemperaturerangebeginningwith300°C.Thesurfacestructurechangesfromamorphousthroughtexture(T=300-650°C)andmosaic(T=650-900°C)uptosingle-crystal.Thefinalrestorationofasingle-crystalstateofthenear-surfacelayerisachievedatatemperatureT>900°C.
Aspecificfeatureoflithiumniobaterecrystallizationisthatwithinacertaintemperaturerangeitproceedsintheexistenceregionofatwo-phasesystem.
4.7.2Annealing-inducedvariationofthephasecompositionofthelithiumniobatecrystalsurface
Diffractionanalysisofspecimensannealedbetween300and900°Crevealsphasetransformationproceedingonthesurfaceoflithiumniobatecrystalssimultaneouslywithrecrystallization.ThisisalsoconfirmedbytheelectrondiffractionpatternsshowingasimultaneousdiffractionfromLiNbO3andLiNb3O8,bywhichonecantraceoutannealing-inducedvariationofthecrystallinestructureandofthephasecompositionofsubstratesurfacesofdifferentorientations.
VariationsofthephasecompositionandcrystallinestructureofthelithiumniobatesurfaceareobservedalreadyatT=300°C.Thesystemofring-andarc-shapedreflectionsobservedinelectrondiffractionpatterns(Fig.4.28a)isinducedinamonocliniccellwithparametersa=15.26Å,b=5.033Å,c=7.46Å,b=107.33gradcorrespondingtolithiumtriniobatewhichbelongstothespacegroupP21/a(Lundberg1971).DuetoclosenessoftheinterplanardistancesofLiNb3O8andLiNbO3andreflexsmearing,partofreflectionsfromthematrixand
phasearenotseparates,butapermanentstrengtheningofindividualreflexestestifiestothepresenceofatwo-phasesystemonthesamplesurface.
Reflexesfromthemonoclinicphaseoflithiumtriniobateandfromtrigonallithiumniobateareseenmoreclearlyinelectrondiffractionpatternsastheannealingtemperatureincreases.WithinthetemperaturerangeT=300-700°Cthenewlyformedcrystalsofthesecondphasegetlargerandacquireepitaxialorientationrelativetothesubstrate.Pointreflexesappear(Fig.4.28b),andatT=700-900°Ctwophasesareformedconnectedwitheachotherbycertainorientationrelations(Fig.4.28c).Thissuggestssolid-phaseepitaxialgrowthofamonoclinicphaseonthelithiumniobatesurface.
Theoccurrenceofthesecondphaseisvisualizedasatypicalthindullcoatingonthesubstratesurfaceandcanalsobeidentifiedbylightscatteringinplacesofphasenucleation.Thephasechange
proceedsbasicallyinthenear-surfacelayerofalithiumniobatecrystaldamagedinthecourseofmechanicaltreatment.AfterthesurfacelayerhadbeenremovedbyetchinginthemixtureHF+HNO3,theelectrondiffractionpatternsshowedreflectionsonlyfromlithiumniobate,whichisindicativeofspatiallimitationofnucleationandgrowthoftheLiNb3O8phase.Therateoflithiumtriniobatenucleationonthecrystalsurfaceisratherhigh:themonoclinicphaseappearsonelectrondiffractionpatternsaftera10minstayofthesubstrateinthehotregionatT=750°C.
Page209
Fig.4.29PhasediagramoftheLi2O-Nb2O5system(Holman1978).
Opticalinhomogeneityofthebulkcrystalbeforeandafterannealinginthetwo-phasetemperatureregionwasdeterminedbycomparingtheRayleighIRandstimulatedBrillouinISBcomponentsofscatteredlight.
UnderannealingatatemperatureT=750°Cfor5-20h,thenumberofscatteringcentresinthebulkcrystalremainsunchanged,whereasalayeroflithiumtriniobatephaseformsonthecrystalsurface.Aconsiderableincreaseinthenumberofscatteringcentresinthebulkcrystalwasonlyobservedafterannealingatthesametemperaturefor40h.
Anincreaseofthenucleationrateonastronglydamagedsurfaceascomparedwiththecrystalbulkisduetotheloweringofthenucleationbarrierandthehigherdiffusionrateofcomponentsintheamorphouslayer.Thisconclusionisconfirmedbythefactthatthelithiumdiffusionactivationenergyinasinglecrystal,equalto68±1.2kcal/molfallsdownto14.28±1.6kcal/mol(Carruthersetal1974;JetschkeandHehl1985).
Electrondiffractionanalysisshowsthatthevariationofthephase
compositionofthelithiumniobatesurfaceduetomonoclinicphasenucleationisareversibleprocess,andatT>900°Cthephasechange
isobserved.TheboundaryoftheexistenceregionoftwophasesforcrystalsofcongruentcompositionliesnearT=900°C,whichagreeswiththephasediagram.Abovethistemperature,onlyLiNbO3ispresentonthesamplesurface,andreflectionsfromLiNb3O8disappearfromelectrondiffractionpatterns(Fig.4.28d).Thephasechange onthesurfaceoftitanium-dopedlithiumniobatecrystalsproceedsinasimilarmanner.
WenotethatatT<900°Cnomonoclinicphasewasobservedonthesubstratesurfaceifannealingwascarriedoutinalithium-enrichedatmosphere,thatis,thepresenceofLivapoursinannealingandtheirabsorptiononthesurfaceinhibitsphasenucleation.Initsnature,theindicatedtransition referstosolid-phaseorder-disordertypetransitionsoccurringinsolidsolutions.ThenucleationofthemonoclinicphaseLiNbO3correspondstodissolvingofexcesssolid-stateniobium.
Page210
Lithiumniobatecrystalsofcongruentcompositionaremetastableatroomtemperatureandcontainpointdefects,duetolithiumdeficiency,inaconcentrationexceedingtheequilibriumone.Accordingtothephasediagram(Fig.4.29),atatemperaturebelow900°C,LiNbO3andLiNb3O8canexistsimultaneously.ThenarrowingofthehomogeneityregionwithloweringtemperatureleadstoLiNb3O8phasesegregationaccompanyingannealingofmetastablenonstoichiometriclithiumniobatecrystalswithinthetemperaturerange300-900°C,whichbringsthesystemtoastateenergeticallymoreadvantageousandlowerstheconcentrationofpointdefectsinthecrystals.ThetemperaturerangeT>900°Ccorrespondstotheone-phaselithiumniobatesystemandhasawidehomogeneityregion(upto6mol/%Li2O)withinwhichtheexistenceoflithiumniobatewithwidelydifferentcompositionisenergeticallyadmissible.Atannealingtemperaturesexceeding900°C,thechange isobserved,themonoclinicphasedisappearsandthesamplesurfacebecomessingle-phase.
ThephysicalandchemicalpropertiesoflightguidingferroelectricfilmsaretabulatedinTable4.5.
Temperaturevariationsaffectnotonlythestructureandphasecomposition,butalsothesurfacemorphologywhichisdeterminedbycrystallographicorientationofthesamplesurface.
Theshapesofgrowinglithiumtriniobatecrystalsandthespecificitiesofmicrocrystalpositionsonthesubstratesurfaceinthemonoclinicphasearebestofallpronouncedinthetemperaturerangeof700-900°CthatcorrespondstoanorientedgrowthofLiNb3O8.Thesizesanddensityofislandsofthesecondphasedependontheannealingtimeandonthedegreeofdamageofthenear-surfacesamplestructure.ThethicknessoftheLiNb3O8layerwasestimatedbytheheightofthegrowthpatternsonelectron-microscopicpicturesand
ellipsometrically.AfterannealingatT=750°Cfor4h,thegrowthpatternsofLiNb3O8rangedontheaveragewithin150-500nm,andtheellipsometricallymeasuredthicknessoftheislandlayerofthephasemadeup15-40nm.TheislanddensityNofthephasevariedfromsampletosamplewithinarangeof107to1010cm-2,thedistributionofislandsoverthesurfaceofoneandthesameislandbeingnonuniform.Phasesegregationareconcentrated,inparticular,inthevicinityofscratchesresultingfromsamplepolishing.Theislanddensityinsuchplacesmakesup1010-1011cm-2.
Accordingtoelectrondiffractiondata,lithiumtriniobateisorientedrelativetothe(0001)substrateasfollows:( )
TheshapesofgrowingLiNb3O8crystalsonthebasefacetoflithiumniobatearebasicallyrepresentedbypinacoidal and{h00}typeplaneselongatedalongthe[010]direction(Fig.4.30a).Itshouldbenotedthatthepinacoid( )paralleltothesubstratesurfaceisnotalwayspresentinthehabitusofmicrocrystalsofthenewphase,andisoccasionallytaperedoutwithitsotherfacetspositionedatanangletothesurface.InFig.4.30aphaseislandswithsuchfacetsareshownbythearrows2;thearrow1indicatesaLiNb3O8microcrystalwhosehabituscontainsthe( )facet.Thisisindicativeofthedifferenceingrowthconditionsofislandsononeandthesamesubstrate,which
Page211Table4.5Physico-chemicalparametersofcrystalsandfilmsofoxideFerroelectrics(Ivleva,Kuzminov,1985)
Crystal Solvent Meltingpoint
Latticeparameters Refractiveindex
Electro-opticcoefficient
Films-substrate T,°C a,Å c,Åno ne r33 r13l=0.63µm 10-12 m/V
1LiNbO3 1253 5.14813.8622.289 2.201 30.8 8.6
2LiNbO3-LiNbO3 LiVO3 5.142
3LiTaO3 1650 5.15213.7852.177 2.183 35.8 7.9
4LiNbO3-LiTaO3 LiVO3 13.851
5LiNbO3-LiTaO3 LiVO3 13.85 2.288(4)2.191(4)
6LiNbO3-LiTaO3 2.200 2.184 12 2.3
7LiNbO3-LiTaO3 2.29 2.20 28.5
8LiNbO3:Li+-LiTaO3 Li2WO4 5.143
9LiNbO3:Nb5+-LiTaO3 K2WO4 5.153
10Li1-xNaxNbO3-LiNbO3 LiVO3 5.154
11Li1-xCOxNb1-xZrxO3--LiVO3 LiNbO3 5.144
12LiNbO3:Ag+-LiNbO3 LiVO3 2.2361
13LiTaxNb1-xO3-LiTaO3 LiVO3 13.80
14KNbO3 1039
15Sapphyre(Al2O3) 2030 4.75812.9911.766 1.758
16KNbO3-Al2O3 KVO3
17LiNbO3:Cr3+(Fe3+,Cu2+)-LiNbO3 LiVO3
18K289Li1.55Nb5.11O15 1050 12.584.01 2.294(8)2.156(8)
19K1.5Bi10Nb5.1O15 1312 17.857.84 2.237 2.253
K1.5Bi10Nb5.1O1520K239Li155Nb5.11O15--K1.5Bi1.0Nb5.1O15
12.533.98
Comments:1.Prokhorov,Kuz'minov,1990;2.Baudrantetal,1975;3.Kuz'minov,1975;4.Miyasawa,1973;5.Miyasawaetal,1975;6.Fukunishietal,1974;7.Tienetal,1974;8.Baudrantetal,1975,Ballmanetal,1975;9.Baudrantetal,1975,Ballmanetal,1975;10.Neurgaonkar1981;11.Neurgaonkaretal,1979;12.Baudrantetal,1975;13.Kosminaetal,1983,Tienetal,1974;14.Prokorov,Kuz'minov,1990;15.Schaskolskaya1982;16.Khachaturyanetal,1984;17.Baudrantetal,1975;18,19,20.Adachietal,1979.
isevidentlyduetoinhomogeneityoflithiumniobatecompositionandinhomogeneityofstrainsinthesurfacelayerofthecrystal.
Accordingtothesymmetryofthebasefacetoflithiumniobate,LiNb3Omicro-crystalsoccupythreeequivalentpositionsonthesubstrate,makinganangleof120°(Fig.4.30b),whichformdendrite-typeadhesions(joints)showninFig.4.30a.
Page212
Fig.4.30(a)Surfacemorphologyofthe(0001)facetoflithium
niobateafterannealingatT=750°Cfor4h.(b)Positionsoflithiumtriniobateisletsonthe(0001)
facetoflithiumniobate,(Bocharova1986).
Page213
5PhysicalPropertiesofWaveguideLayersPracticaluseofvarioustypesofthin-filmferroelectricstructuresneedsadetailedstudyofthephysico-chemicalpropertiesofthesubstancesinvolved,aswellastechnologicalperfectionofobtainingthesesubstances.Thiswillpermitcreationofmaterialswiththerequiredphysicalpropertiesoptimumforaparticularapplication.
Inthischapterwedescribetheinvestigationsofwaveguiding,nonlinearopticandferroelectricpropertiesofepitaxialfilmsoflithiumniobateandlithiumtantalateandtheirsolidsolutions.Thedielectricandpyroelectricproperties,andthetemperaturedependenceofthermoelectriccoefficientsarepresented.Wealsoconsidertheopticalpropertiesofthethin-filmstructures:surfaceresistanceandtheeffectoflaserradiation,therefractiveindicesandthemodestructureoffilms,lightextinctionuponwaveguidepropagation.
5.1Opticalpropertiesoflithiumniobateandtantalatesinglecrystals
Lithiummeta-niobatesinglecrystalsareuniaxialnegative(no-ne),transparentfromabout0.4to5mm(Fig.5.1)(Boydetal1964).Thenatureoftheirtransmissionspectradependsontheconditionsofheattreatmentandpolarizationofcrystals.Crystalspreparedwithnodirectcurrentmaintainedthroughthemduringthegrowthareclearandcolourless.
ThedispersiondependencesofnoandneoverawidefrequencyrangeforlithiumniobatecrystalsgrownfromcongruentmeltcompositionsarecollectedinTable5.1.
Thetemperaturedependenceofrefractiveindiceswasmeasuredusingalithiumniobateprismwiththeopticalaxisparalleltothetwomajor
facets.Theprismwasarrangedinasmallfurnaceonaspectrometerstage.Therefractiveindicesweretakenateighttemperaturesbetween19and374°Cforeightlinesoftheheliummetalvapourlampat447.1,471.3,492.2,501.6,587.6,667.8,and707.6nm.
Page214
Table 5.1 Refractive indices of lithium niobate crystals (Weiss andGaylord1985)
l,nm Laser Stoichiometric(T=25°C)
Congruentlymelting(T=24.5°C)
no ne no ne
441.6 He-Cd2.3906 2.2841 2.3875 2.2887
457.9 Ar2.3756 2.2715 2.3725 2.2760
465.8 Ar2.3697 2.2664 2.3653 2.2699
472.7 Ar2.3646 2.2620 3.3597 2.2652
476.5 Ar2.3618 2.2596 2.3568 2.2627
488.0 Ar2.3533 2.2523 2.3480 2.2561
496.5 Ar2.3470 2.2468 2.3434 2.2514
501.7 Ar2.3535 2.2439 2.3401 2.2486
514.5 Ar2.3370 2.2387 2.3326 2.2422
530.0 Nd2.3290 2.2323 2.3247 2.2355
632.8 He-Ne2.2910 2.2005 2.2866 2.2028
693.4 Ruby2.2770 2.1886 2.2726 2.1909
840.0 GaAs2.2554 2.1703 2.2507 2.1719
1060.0Nd2.2372 2.1550 2.2323 2.1561
1150.0He-Ne2.2320 2.1506 2.2225 2.1519
Fig.5.1Thedispersionspectrumoflithiumniobate.
Ananalysisoftheexperimentaldatahasyieldedtwoequationsforthetemperaturedependencegivingtherefractiveindicesbetween400and4000nm:
whereTisthetemperature,K,listhewavelength,nm.
Page215
Table5.2Refractiveindices,noandne,formixedLiNb1-yTayO3crystalsat (accordingtoShimura1977)
lÅ y=0.81 y=0.92 y=0.97 y=1.00
no ne no ne no ne no ne
58932.2057 2.1986 2.1984 2.1946 2.1902 2.1933 2.1862 2.1910
63282.1954 2.1888 2.1888 2.1853 2.1800 2.1829 2.1766 2.1815
80002.1702 2.1638 2.1643 2.1604 2.1561 2.1589 2.1531 2.1579
85002.1666 2.1606 2.1598 2.1559 2.1516 2.1545 2.1484 2.1529
90002.1615 2.1553 2.1557 2.1519 2.1478 2.1507 2.1446 2.1491
106002.1517 2.1457 2.1460 2.1422 2.1385 2.1413 2.1351 2.1396
Thestandarddeviationof112experimentallydeterminedvaluesoftherefractiveindicesfromthosecalculatedaccordingtoformulae(5.1)and(5.2)is2.2×10-4.
Thevalueofthenegativebirefringencedecreaseswitharisingtemperatureanddropsofftozeroat882°Cforl=632.8nmandat
888°Cforl=1152.3nm.
Thechangein(no-ne)withtemperature,aspredictedbyequations(5.1)and(5.2)differsby±0.0010fromtheexperimentaldataforabout600°C.Abovethistemperaturehigher-ordertermscomeintoplay.Inthelithiumniobatecrystal,itistheextraordinaryrefractiveindex,ne,thatdependssignificantlyonthemeltcompositionratio,whiletheordinaryrefractiveindex,no,remainsvirtuallyataconstantlevel(Fig.5.2)(Bergmanetal1968).Thecompositionofthemeltand,hence,thecompositionofcrystalsgrowntherefrommayvarythroughoutthegrowthprocess.Anisomorphicdopantofniobiumistantalum.Thestartingmaterialmaycontainacertainamountoftantalumoxide.Sometimes,toreducetheCurietemperatureandnaturalbirefringence,mixedLiNb1-yTayO3crystalsaregrown.Suchcrystalshavedifferentrefractiveindicesandtheirdispersions.Table5.2isacompilationofthedispersionsoftherefractiveindices,noandne,forvariouscontentsoftantaluminmixedlithiumniobatetantalatecrystals.ForpracticalapplicationsrefractiveindicesforvariouswavelengthsarecalculatedaccordingtotheSellmeierrelation(DiDomenicoandWemple1969):
where istheaverageoscillatorpositionandS0istheaverageoscillatorstrength.The andS0-valuesforvarioustantalumcontentsarelistedinTable5.3.TherefractiveindicesnoandneandthebirefringencecalculatedusingtherelationaregiveninFigs.5.3and5.4,respectively.
5.2Opticalwaveguidemodesinsingle-crystalfilms
Theopticalpropertiesofplanarwaveguidescanbearbitrarilydividedinto
Page216
Fig.5.2Refractiveindicesno(uppercurve)
andne(lowercurve)oflithiumniobateversusmolarratioLi2O/Nb2O5inthe
melt(Bergmaneta11968).
Fig.5.3(right)Refractiveindicesno(fullcircles)andne(opencircles)versusTacontentinmixedLiNb1-yTayO3crystalsfor
variouslightwavelengths(Shimura1977).
Table5.3Sellmeierconstants andS0forcalculationofrefractiveindicesofLiNb1-yTayO3crystals(accordingtoShimura1977)
y ,mm>
no ne nb ne
1.00 1.2195 1.2123 0.1687 0.1696
0.97 1.2121 1.2121 0.1695 0.1698
0.92 1.2036 1.2121 0.1709 0.1699
0.81 1.1905 1.2121 0.1724 0.1703
twogroups,thefirstresponsibleforwaveguidepropagationandthesecondforlightcontrolefficiency.Thefirstgroupincludesrefractiveindices,theirprofiles,themodecompositionandopticallosses.Thesecondinvolveselectro-,acousto-andnonlinearopticalfilmparameterswhosevaluesdependonthewayinwhichthewaveguidewasmanufactured.
5.2.1Waveguideandradiationmodes
Tien(1971)gaveavisualinterpretationoftheoccurrenceofmodesincoplanarwaveguides,whichwerepresentbelow.
Thefilmconsideredherehasathicknessoftheorderof1mmorless;itissothinthatithastobesupportedbyasubstrate.Wethusconsiderthreemedia:afilm,anairspaceabove,andasubstratebelow.AsshowninFig.5.5,thethicknessofthefilmisintheX-Yplane.Forathinfilmtosupportpropagatingmodesandtoactasadielectricwaveguideforthelightwaves,therefractiveindexofthefilmn1mustbelargerthanthatofthesubstratenoandnaturallythanthatoftheairspaceaboven2.Mathematically,theprobleminvolvesasolutionoftheMaxwellequationsthatmatchestheboundaryconditionsatthefilm-substrateandfilm-airinterfaces.Thesolutionsindicate
Page217
Fig.5.4Birefringence(ne-no)inmixedLiNb1-yTayO3
crystalsversus forvariousTacontentsinthecrystal(Shimura1977).
Fig.5.5(Right)Thelightwavepropagatesinthefilmto
thex-axis.Thesurfaceofthefilmisinthexy-planeanditsthicknessinthezdirection(Tien1971).
threepossiblemodesofpropagation.Thelightwavecanbeboundandguidedbythefilmasthewaveguidemodes.Itcanberadiatefromthefilmintoboththeairandsubstratespacesastheairmodes,oritcanradiateintothesubstrateonlyasthesubstratemodes.TheairandsubstratemodesaretheradiationmodesdiscussedbyMarcuse(1969,1970).ThemodesdescribedabovecanbeexplainedsimplyandelegantlybytheSnelllawofrefractionandtherelatedtotalinternalreflectionphenomenoninoptics.
Let(Fig.5.6a)n0,n1,andn2berefractiveindicesand , ,and betheanglesmeasuredbetweenthelightpathsandthenormalsoftheinterfacesinthesubstrate,film,andair,respectively.Here We
havethenfromtheSnelllaw
and
Letusincrease graduallyfrom0.When issmall,alightwave,forexample,startsfromtheairspaceabovethefilm,canberefractedintothefilm,andisthenrefractedagainintothesubstrate(Fig.5.6a).Inthiscase,thewavespropagatefreelyinallthethreemedia-air,film,andsubstrate-andtheyaretheradiationfieldsthatfillallthethreespaces(airmodes).Next,as isincreasedtoavaluelargerthanthecriticalangle ofthefilm-airinterfaceasshowninFig.5.6b,theimpossibleconditionincurredinequation(5.4), ,indicatesthatthelightwaveistotallyreflectedatthefilm-airboundary.Nowthewavecannolongerpropagatefreelyintheairspace.Wethusdescribeasolutionthatthelightenergyinthefilmradiatesintothesubstrateonly(substratemodes).Finally,whenq1islargerthanthecriticalangle ofthefilm-substrateinterface,thelightwave,asshowninFig.5.6c,
Page218
Fig.5.6(a)When ,thelightwaveshown
representstheairmode.Thelightwaveoriginatedinthefilmisrefractedintoboththesubstrateand
airspace(b).As increasessothat ,thelightwaveshownnowrepresentsthesubstratemode.Itisrefractedintothesubstratebutistotallyreflectedatthefilm-airinterface(c).When increasesfurthersothat ,thelightwaveshownistotally
reflectedatboththefilm-airandfilm-substrateinterfaces.Itisconfinedinthefilmasistobeexpectedinthewave
guidemode(Tien1971).
Fig.5.7(right)(a)Lightwaveinthewaveguidemodecanbeconsideredasaplanewavewhich
propagatesalongazigzagpathinthefilm.ThewavecanberepresentedbytwowavevectorsA1andB1.(b)ThewavevectorsA1andB1canbedecomposed
intoverticalandhorizontalcomponents.Thehorizontalcomponents determinethewave
velocityparalleltothefilm.Theverticalcomponents determinethefielddistributionacrossthethicknessof
thefilm(Tien1971).
istotallyreflectedatboththeupperandlowersurfacesofthefilm.Theenergyflowisthenconfinedwithinthefilm;thatistobeexpectedinthewaveguidemodes.
Itisinterestingtonotethatinthewaveguidemodesthelightwaveinthefilmfollowsazigzagpath(Fig.5.6c).Thelightenergyistrappedinthefilmasthewaveistotallyreflectedbackandforthbetweenthetwofilmsurfaces.ThiszigzagwavemotioncanberepresentedbytwowavevectorsA1andB1,asshowninFig.5.7a.Thenthewavevectorsaredividedintotheverticalandhorizontalcomponents,asinFig.5.7(b).ThehorizontalcomponentsofwavevectorsA1andB1areequal,indicatingthatthewavespropagatewithaconstantspeedinadirectionparalleltothefilm.TheverticalcomponentofthewavevectorAtrepresentsanupwardtravelingwave;thatofthewavevectorB1,adownwardtravellingwave.Whentheupward-anddownwardtravelingwavesaresuperposed,theyformastandingwavefieldpatternacrossthethicknessofthefilm.Bychanging ,wechangethedirectionofthewavevectorsA1andB1andthustheirhorizontalandverticalcomponents.Consequently,wechangethewavevelocityparalleltothefilmaswellasthestandingwavefieldpatternacrossthefilm.
Sincewediscusshereaplanargeometry,thewavesdescribedaboveareplanewaves.TheyareTEwavesiftheycontainthefieldcomponentsEy,Hz,andHx;theyareTMwavesiftheycontainthefieldcomponentsHyEzandEz.Herexisthedirectionofthewavepropagationparalleltothefilm.ThewavevectorsA1andB1discussedabovehavethusamagnitudekn1,where ,wandcare,respectively,theangularfrequencyofthelightwaveandthespeedof
Page219
Fig.5.8(a)Alightwaveinthewaveguidemodeisaninfinitelywidesheet
ofplanewavewhichfoldsbackandforthinazigzagmannerbetweenthetopandthebottomsurfaceofthefilm.(b)Alightwavepropagatinginsidethefilmistotallyreflectedatthetwofilmsurfaces.Thefigure
showsthatinorderthatthewaveanditsreflectionscouldaddinphase,thetotalphasechangeforthelightwavetotravelacrossthethicknessofthefilm,upanddowninoneroundtrip,must
beequalto2mp.Thefigurealsoshowsthatthelightwavesuffersaphasechangeof and attheupperandlowerfilm
surfaces,respectively.Thesephasechangesdeterminethefielddistributionacrossthethicknessofthefilm,whichisshownattherightofthefigure
forthem=3waveguidemode(Tien1971).
Fig.5.9(right)Anyradiusofthequarter-circleattheright
sideofthefigurerepresentsapossibledirectionforthewavevectorB1.Intheblackregionofthecircle,thewavevectorrepresentsthesubstrateorairmode.Inthewhite
regionofthecircle,thewavevectorrepresentsthewaveguidemode,butonlyadiscretesetofthedirectionsinthisregionsatisfiestheequationofthewaveguidemodes.
Eachdirectionofthisdiscretesetrepresentsonewaveguidemodeandeachwaveguidemodehasitsownfielddistributionasshownintheleftsideofthefigure
(Tien1971).
lightinvacuum.Inthepictureofwaveoptics,thewavevectorsA1andB1arethenormalsofthewavefronts,whenaninfinitelywidesheetofplanewavefoldsbackandforthinazigzagmannerbetweenthetwofilmsurfaces(Fig.5.8a).Nowconsideranobserverwhomoveswiththewaveinthedirectionparalleltothefilm.Hedoesnotseethehorizontalcomponentsofthewavevectors.Whatheobservesisaplanewavethatfoldsupwardanddownward,onedirectlyontopoftheotherasshowninFig.5.8b.Thecondition,then,forallthosemultiplereflectedwavestoaddinphase,asseenbythisobserver,isthatthetotalphasechangeexperiencedbytheplanewaveforittotraveloneroundtrip,upanddownacrossthefilm,shouldbeequalto2mp,wheremisaninteger.Otherwise,ifafterthefirstreflectionsfromtheupperandlowerfilmsurfaces,thephaseofthereflectedwavediffersfromtheoriginalwavebyasmallphased,thephasedifferencesafterthesecond,third,...,reflectionswouldbe2d,3d,...,andthenthewavesofprogressivelylargerphasedifferenceswouldaddfinallytozero.AsshowninFig.5.8b,theverticalcomponentsofthewavevectorsA1andB1haveamagnitude ThephasechangefortheplanewavetocrossthethicknessWofthefilmtwice(upanddown)isthen .Inaddition,thewavesuffersaphasechangeof duetothetotalreflectionattheupperfilmboundaryand,similarly,aphasechangeof atthelowerfilmboundary.Herethephase and represent,infact,theGoos-
Page220
Haenchenshifts(Lotsche1968).Consequently,inorderthewavesinthefilmcouldinterfereconstructively,thecondition
musthold,whichistheconditionforthewaveguidemodes.Herem=0,1,2,3,...,istheorderofthemode.AccordingtoBornandWolf(1970)onthetheoryoftotalreflection,
fortheTEwaves,and
fortheTMwaves.
Itisclearthatinspiteofthezigzagwavemotiondescribedabove,thewaveinthewaveguidemodeappearstopropagateinthehorizontaldirectiononly;theverticalpartofthewavemotionsimplyformsastandingwavebetweenthetwofilmsurfaces.Toavoidconfusion,itisdesirabletousebandvexclusivelyforthephaseconstantandthewavevelocityparalleltothefilm.Thus,
Anotherquantitywhichwillalsobeusedfrequentlyistheratiob/k.Asshowninequation(5.9),itistheratioofthespeedoflightinvacuumtothespeedofwavepropagationinthewaveguide.
Aftersubstitutingequations(5.7)and(5.8)intoequation(5.6),Tien(1971)foundthatboth(5.6)and(5.9)aretranscendentalequations.Fortunately,thetranscendentalfunctionsinvolve only.Foragivenn0,n1,n2,andmonecanreadilycomputebothb/kandWforacommon ,andthentabulateb/kandWbyassigningdifferentvalues
for .ThecurvesshowingWversusb/kusingmastheparameterarethemodecharacteristicsofthewaveguide(seeFig.5.15below).
Tosummarize,anyradiusofthequarter-circleshowninFig.5.9representsapossibledirectionforthewavevectorB1describedabove,and istheincidentanglemeasuredbetweenthewavevectorandtheverticalaxis.Thewaveguidemodesoccurintherange
.Withinthisrangeof thereisadiscretesetofthedirectionswhichsatisfiestheequationofthemodes(5.6).Eachdirectioncorrespondstoonewaveguidemodeofthefilm.Thehorizontalcomponentofthewavevector, ,determinesthewave
Page221
motionparalleltothefilm,whileitsverticalcomponent, ,determinesthestandingwavefieldpatternacrossthefilm.AsshownintheleftsideofFig.5.9,whenm=0thestandingwavepatternhasaformsimilartoahalf-sinewave.Whenm=1,ithasaformsimilartoafullsinewave,andsoon.Theairandsubstratemodesoccurintherange ;theyoccupytheblackregionofthequartercircle.As isvariedcontinuouslyfrom0to fortheairmodesand
to forthesubstratemodes,thecorresponding andsweepthroughtheentirespaceofthesubstrateandtheairspace.Itisthuspossibletoexpressanyradiationfieldbysuperposingwavesoftheairandsubstratemodes.WhathasbeendiscussedhereisthereforesimplyanexpansionofthesolutionoftheMaxwellequationintoplanewavesofallpossibledirections.
5.2.2Waveequationandfielddistribution
Havingbeendescribedpurelyonanintuitivebasis,themodesoflightwavepropagationcannowbederivedmathematically.Forsimplicity,assumethelightwaveinthefilmtobeinfinitelywideintheYdirectionsothat (Fig.5.5).LetXbethedirectionofthewavepropagationparalleltothefilm.TheMaxwellequationsinEyforTEwaves(orHyforTMwaves)canbereducedtothewaveequationbelow
wherenJistherefractiveindexofthemediumj.Thesubscriptsj=0,1,and2denotethesubstrate,thefilm,andtheairspace,respectively.Atimedependenceexp(-iwt)isusedinequation(5.10),where .Thesolutionofthewaveequationisintheformofexp
,whichmaybesubstitutedintoequation(5.10)toobtain
Theboundaryconditionsatthefilm-airinterfacesdemandthesamewavemotionparalleltothefilminallthethreemediaconsidered;thiscanbewrittenas
Allthefieldsthusvaryintimeandxaccordingtothefactor.Thiscommonfactorwillbeomittedinallthelater
expressionsforsimplification.Combiningequations(5.11)and(5.12)givesanimportantrelation
Inthefilm, and arethehorizontalandverticalcomponentsofthewavevectorA1orB1discussedbefore.Theyarerespectively
Page222
and .Inthewaveguidemodes,onecanfindfromequation(5.13)andfromthecondition that , isreal,and and areimaginary.ThefielddistributioninFig.5.10aisthusastandingwaveinthefilmandexponentialinthesubstrateandintheairspace.Next,forthesubstratemodes,thereholdsequation(5.13)andfromthecondition that and arereal,butisimaginary.Thefieldsinthiscasearestandingwavesinthefilmandinthesubstrate,butexponentialintheairspace(Fig.5.10b).Finally,fortheairmodes, ,and , ,and arereal.Thefieldsinallthethreemediaarenowstandingwaves(Fig.5.10c).Itisconvenienttodenote by whenitisrealandby whenitisimaginary.For thewaveguideisasymmetric.Theupperandtheupperandlowerfilmsurfacesarechosentobe and .Thethicknessofthefilmisthen .
Thefielddistributionsarederivedbychoosingz=0atthepositionwhereEyismaximumforanywaveguidesubstrate,orevenairmode,andEy=0foranyoddairmode.Itisimportanttonotethatthesepositionsofz=0aredifferentfordifferentmodesinanasymmetricwaveguide.Thesechoicesarenecessarytosimplifymathematicssothatthefielddistributionsofvariousmodescouldbeeasilywecanvisualized.Toavoidconfusion,EyofaTEwaveonlyisconsideredbelow.
Forthewaveguidemodes,asmentionedearlier,thewavesuffersaphasechangeof attheupperfilmsurface,andaphasechangeof
atthelowerfilmsurfacebecauseoftheinertialtotalreflections.Thefieldsatthetwofilmsurfacesmustthereforebe and
,respectively,whereAisaconstant.Letthefieldatz=0beamaximumvalue,A.Thenonecanchoose sothatthefieldattheupperfilmsurface, ,canbeA .Similarlyonecanchoose sothatthefieldatthelowerfilmsurface, ,canbeA ifm=evenand-A ifm=oddsshownin
Fig.5.10a.Thesechoicesgive ,whichsatisfiesequation(5.6).TheboundaryconditionsrequireEyandtobecontinuousatthetwointerfaces.Therefore,
Fig.5.10Theelectricfielddistributionof(a)aTEwaveguidemode;(b)aTEsubstratemode;(c)aTE(even)airmode(Tien1971).
Page223
intheairspaceand
inthesubstrate.
Forthesubstratemodes,oneagainassumesamaximumfieldAatz=0andchooses (Fig.5.10b).Thefieldat isstillAandthatintheairspaceisstillA .ThefieldatthelowerfieldsurfaceisthenA andthatinthesubstrateis
Fortheairmodes,theevenandoddmodesmustbetreatedseparately.Foranasymmetricwaveguide,thez=0planecanbechosenanywherebetween and .However,onceitischosen,thesamez=0planeshouldbeusedforalltheairmodes.Fortheevenmodes,thefieldisamaximumatz=0andthefieldsatthetwofilmsurfacesareA andAcos ,respectively(Fig.5.10c).Theboundaryconditionsrequirethefieldsinthesubstrateandintheairspaceintheform
wherej=0and2.Fortheoddmodesthefieldiszeroatz=0andisAand-A atthefilmsurfaces.Thefilmsinthesubstrate
andairspacearethen
wheretheplussignisforj=2andtheminussignisforj=0.TheresultsdiscussedabovearesummarizedinTable5.4.
Mathematically,thefielddistributionsdescribedaboveareidenticaltothoseoftheproblemofasquarepotentialwellinquantummechanics.Heretheairspaceandthesubstratearethepotentialbarriers.Thewaveenergyisdividedhereintothehorizontalandverticalcomponents,keepingthetotalenergyconstant.Itistheverticalcomponentofthewaveenergythatnegotiates
Page224
Table5.4Electricfielddistributionin(a)awaveguidemode,(b)asubstratemode,and(c)theevenandoddairmodes(Tien1972)
Waveguidemode
Medium Ey(TEwave)
Film =b =b1 A
Substrate =b = A
Air-space =b = A
Substratemode
Medium = Ey(TEwave)
Film =b =b1
Substrate =b =b0
Air-space =b = A
Evenandoddairmodes
aInderivingtheseexpressions,wehavechosenz=0atthepositionwhereEyiseitherzeroormaximum.Thesepositionsofz=0arethereforedifferentfordifferentmodes.
thepotentialbarriersmentionedabove.Thewavevectorrepresentsthe
momentumanditssquare,thewaveenergy.Withintheinterval and,becauseofthelargehorizontalcomponentofthewavevectorb,
theverticalcomponentoftheenergyissmallenoughsothatthewave,ortheparticle,istrappedinthepotentialwell.Themodespectrumortheenergylevelisthusdiscrete(waveguidemodes).Asthehorizontalcomponentofthemomentumisreducedtoavalue ,theverticalcomponentofthewaveenergyislargeenoughtoovercomethelowerpotentialbarrier.Thewavefunctionspillsovertheentiresubstratespaceandoneentersintotheregionofthesubstratemodes.Themodespectrumortheenergylevelisnowcontinuous.Astheverticalcomponentofthewaveenergyisincreasedfurtherbyreducingbbelow thewavecanspillovertheupperandthelowerbarriers.Themodespectrumremainscontinuousanditbelongstotheairmodes.
5.2.3OpticalmodesinepitaxialLi(NbTa)O3waveguides
Solid-solutiongrowthof single-crystalfilmsonLiTaO3substrateshasbeendiscussedabove.ThesefilmsaregrownbyEGM(epitaxial
Page225
growthbymelting)method.However,thespecialprocessusedbyTienetal(1974)permittedobtainingverythinfilmswithagradedcomposition.Thecompositionofeachfilmismaximumattheair-filminterface,anditdecreasesgraduallytozerotowardsthesubstrate,asillustratesbycurveAinFig.5.11b.Becauseofthisgradedcomposition,anyeffectduetomismatchinlatticeconstantbetweenthefilmandthesubstrateisminimized,andconsequentlyfilmsasgrownareuniformandsmooth.InFig.5.11a,thezaxisisnormaltothesurfaceofthefilm,andz=0andz=daretheair-filmandfilm-substrateinterfaces,respectively.Alltheopticalmeasurementswereperformedbyusinga0.6328-mmhelium-neonlaser,andthexaxiswaschosenasthedirectionoflightwavepropagation.Becauseofthedifferencesintherefractiveindicesandthegradedcompositionofthefilm,therefractiveindexvariesinsidethefilmasshownbycurveAinFig.5.11c.Thesolid-solutionfilmhas andathicknessof3.87mm.Thefilmsformedexcellentopticalwaveguides;allthewaveguidemodesobservedarewellseparated,andtheycanbeindividuallyexcitedbyaprismcoupler.Moreover,severalfilmshadoneTEandoneTMwaveguidemodeonly.Tienetal(1974)reportedsomeinterestingobservationsofthewaveguidemodesanddiscussedasimplemethodofcalculationforthegradedwaveguides.Thissimplemethodcanbeusedforcalculationoftheeffectiveindicesofthewaveguidemodesaswellasfortheevaluationoftheindexdistributioninthefilm.Theprismcoupler(Tien1971;Tienetal1972)isanimportanttoolforthestudyofthefilmproperties.
Tostudythewaveguidemodes,afilmwithnineTEmodeswaschosen.ThefilmwasgrownparalleltooneofthecleavageplanesofLiTaO3.Thecaxisthusformsanangleof33°fromthesurfaceofthefilm(Fig.5.11(a)).Letabeaprojectionofthecaxisonthefilmandletbbenormaltoa.TheTEwaveisanordinarywavewhenthelightpropagatesalonga,and
Fig.5.11(a)Positionofthec-axiswithrespecttothegeometrical
axesinasolid-solutionLiNbO3-LiTaO3film.(b)CurveAshowsthegradedcompositioninthefilm.(c)CurvesAandBshow,respectively,theindexvariationinasolid-solutionfilmandthatinadiffusedfilm.(d)Photographofthemlinesofasolid-solutionfilm.(e)Photograph
ofthemlinesofauniformwaveguidemadeofaTa205filmonaglasssubstrate(Tienetal1974).
Page226
Fig.5.12(a)Modeindicescalculatedonthebasisofanexponentialdistributionofrefractiveindex.
(b)Modeindicesmeasuredfromoneofthesolid-solutionfilms.(c)Modeindicescalculatedonthebasisofanindexdistributionintheformofa
Fermifunction(Tien1974).
itisanextraordinarywavewhenthelightpropagatesalongb.Themlines(Tien1971;Tienetal1969)observedforthecaseoftheordinarywaveareshowninFig.5.11(d).TheTMwaveisalwaysanextraordinarywave.Consequently,asthedirectionofthelightpropagationvariesfromatob,theeffectiveindices(Tienetal1972)b/koftheTEmodesvarycontinuously,whereasthoseoftheTMmodesdonotvary.Toavoidconfusion,onecanuse'uniformwaveguides'forthosehavingaconstantrefractiveindexnFthroughoutthefilmand'gradedwaveguides'forthoseinwhichnFvariesinz.Forcomparison,themlinesobservedinauniformwaveguidemadeofaTa2O5filmonglassareshowninFig.5.11e.Thedifferencebetweenthemodepatternsofauniformandagradedwaveguideisthatthemodespacingincreaseswiththemodenumbermintheformer,whereastheoppositeistrueinthelatter.
Modesinthegradedwaveguideshavebeencalculatedbymanyauthors(Tayloretal1972).Inparticular,aneleganttheoryhasbeen
developedbyConwell(1973).Sheusedanindexdistributionforthefilminthefollowingform:
where istherefractiveindexofthesubstrate.SuchadistributionisillustratedbycurveBinFig.5.11c.ThistheorywasusedtocalculatetheeffectiveindicesofthemodesforthecaseofaTEwavepropagatingalonga.Forhavingninemodes,theargument(Conwell1973)oftheBesselfunctionX=29,d=2.23mm, ,and
werechosen.TheresultsofthecalculationsareplottedinFig.5.12aandtheyshouldbecomparedwiththemeasuredvaluesofFig.5.12b.Obviously,theexponentialdistributiongivenbyequation(5.14)doesnotapplytothesolid-solutionfilms,sincethemodespacingshowninFig.5.12adecreasesmuchmorerapidlywiththemodenumbermthanthoseobservedinFig.5.12b.
Searchforatheorywhichappliestoanydistributionofthefilmhasled
Page227
totheWKBmethod(DickeandWittke1960).Recallthatforauniformwaveguidethemodeequations(Tien1971)are
and
Hereweareconsideringazigzagplanewavepropagatinginthefilmas ,wherebandbarerespectivelytheaandxcomponentsofthewavevector,manddarerespectivelythemodenumberandthefilmthickness, ,wherewistheangularfrequencyandcisthevelocityofthelightwaveinvacuumand,finally, and arerespectivelythephasesadvancedbythezigzagwaveduetothetotalreflectionsofthewaveatthefilm-substrateandfilm-airinterfaces.OnthebasisoftheWKBmethod,foragradedwaveguideofanyindexdistribution
and
Here istheturningpointoftheWKBmethodand,at , and.Consequently,a,canbeconsideredasafunctionofb.For
Fig.5.13ValuesoftheintegralAversusthemodeindices,b/kforthetwocasesdescribedin
thetext(Tieneta11974).
Page228
Table5.5Modeindices,b/k's(Tienetal1974)
Case1:9modes
m Conwell'stheory Tien'smethod
0 2.2400 2.2399
1 2.2196 2.2192
2 2.2059 2.2057
3 2.1961 2.1959
4 2.1889 2.1888
5 2.1838 2.1835
6 2.1802 2.1800
7 2.1781 2.1778
8 2.1771 2.1771
Case2:2modes
m Conwell'stheory Tien'smethod
0 2.1897 2.1898
1 2.1789 2.1790
allthefilms, issmallandtheindexofthefilmissubstantiallylargerthanthatoftheair;onecantake .AccordingtothestandardlinearapproximationoftheWKBmethod(DickeandWittke1960)attheturningpoint, isobviouslyp/4.Lettheintegralin(5.17)beA.Withagivenindexdistribution ,Tienetal(1974)couldcomputeb(z)from(5.18)and from(5.19),andthenevaluatetheintegralAforanyvalueofb.Infact,wecanplotAversusb/k,andthevaluesofb/kcorrespondingtoA=(m+0.75)pform=0,1,2,...,aretheeffectiveindicesofthewaveguidemodes.Tosubstantiatethis
method,thedistributiongivenbyequation(5.14)wasusedandthecalculationswereperformedfortwocases.Onecasehasninemodesand ,ns=2.177,andd=2.23mm;theothercasehastwomodesonlyandDn=0.043,ns=2.177,andd=0.931mm.TheA-versus-b/kcurvesforthesetwocasesareshowninFig.5.13.TheresultsobtainedbythismethodarethencomparedinTable5.5withthosecalculatedfromtheexacttheoryofConwell(1973).Theagreementbetweenthetwomethodsiswithin .
Itisalsopossibletouseequations(5.17)-(5.19)toevaluatetheindexdistributionofthefilmfromthemeasuredb/k'softhewaveguidemodes.Asnoticedearlier,themodeindexb/kistherefractiveindexofthefilmattheturningpoint.Thelocationsoftheturningpointsforthewaveguidemodescanbesolvedintermsofthemeasuredb/k'sbyforming,basedon(5.17),asetofsimultaneousequations,oneequationforeachmode.Extensivecalculations
Page229
ofthisnaturehaveshownthattheindexdistributionofthesolid-solutionfilmscanbecloselyrepresentedbyaFermifunction
SuchadistributionisshownbycurveAinFig.5.11b.Thereisaregionnearz=0,inwhichtherefractiveindexisrelativelyconstant,indicatingthebeginningoftheformationofahomogeneousepitaxiallayer.Thishomogeneousregionisfollowedbyabroadtransitionregionwheretherefractiveindexvariesmorerapidly.Theparametersdandadetermine,respectively,thethicknessofthefilmandthesharpnessofthetransitionregion.Currently,theseparametersarecorrelatedwiththegrowthprocess.Fortheparticularfilmdescribedabove,Dn=0.0710,a=0.286mm,andd=3.87mm.Basedontheseconstants,thecalculatedmodeindicesareshowninFig.5.12c,whichagreeswiththemeasurementshowninFig.5.12bwithintheexperimentalerroroftheorderof .
5.2.4Characteristicsofout-diffusedwaveguides
Theasymmetricplanarslabwaveguide,producedbydepositingauniformguidinglayeronasubstrate,andtheplanargradedindexguidearesimilarintheirwaveguidingpropertiesbutdiffersomewhatindetail.Carruthersetal(1974)comparedtwocharacteristicsoftheslabandgradedguides,namely,thenumberofthemodesNsupportedbytheguideandtheeffectivepenetrationdepthwlforenergyinthei-thmode.
TherefractiveindexprofilesfortheslabandgradedguidesareillustratedschematicallyinFig.5.14.Forbothguides,n=1forx<0,and for .Fortheslab,
andforthegradeguide,
Thewavefunctionsfortheslabaresinusoidalintherange andexponentiallydecayingoutsidethisrange.Formodessufficientlyfarfromcutoff,mostoftheenergyisconfinedwithin .Thus,neglectingtheevanescenttail,onecandefineaneffectivepenetrationdepthforallTEslabmodesas
Page230
Fig.5.14Refractiveindexprofilesfor(a)anasymmetricplanar
slabwaveguideand(b)aplanargradedindexwaveguide.TE0andTE1wavefunctionsareindicatedschematicallyalongwithturningpointsx1(Carrutherseta11974).
Thevariousmodeshavepropagationconstantsbithatareplottedasindexlevels inFig.5.14(a),with andltheopticalwavelength.ThenumberofTEmodesthatcanbesupportedistheintegerlessthan
withasimilarexpressionforTMmodes(NelsonandKenna1967).Theanalogywiththequantummechanicalproblemofaparticleinaboxhavingturningpointsatx=0andx=Bisapparent.Intheopticalproblem,theturningpointsrepresentreflectingsurfacesforraystrappedintheguide.
Thegradedindexproblem,likemostquantummechanicalpotential-wellproblems,cannotbesolvedanalyticallywithoutapproximationexceptinspecialcases.Marcuse(1978)givesWKBsolutionstoathree-segmentpiecewiselinearapproximationtoanarbitraryindexprofile.Ifequation(5.22)isapproximatedbylinearsegmentsthat
passthroughthepoints , , and ,thenitisfoundthat
Thefactor1.38isofcoursedependentonthechoiceof ,butitcanbeseenthatNsandNgaresimilarforcomparableA,Banda,bparameters.Forexample,ifA=a,then whenB=0.69bforlargeN.
ThewavefunctionsandindexlevelsfortheTE0andTE1modesareshownschematicallyinFig.5.14b.Theintersectionoftheindexlevelwiththecurven(x)definestheturningpoint ,atwhichanequivalentopticalrayoraquantum-mechanicalparticleinasimilarpotentialwellwouldreverseits
Page231
direction.Mostoftheenergyinamodefarfromcut-offisconfinedtotheregion ,sothepenetrationdepthcanbedefinedas
where increaseswithincreasingmodenumberi.Thewavefunctionsareoscillatoryintherange ,andincreaseinamplitudenear ;theydecayexponentiallyoutsidethisrange(Marcuse1978;Smithgalletal1977;Conwell1973).
Toobtainanestimatefor ,thequantityn(x)maybeapproximatedcrudelybyastraightlinetangentton(x)atx=0asshowninFig.5.14b.Itcanbeseenthatthevalueof obtainedfromsuchanapproximationwillbesmallerthanthetruevalueandwillgivealowerboundon .Forthisapproximation,Marcuse(1978)found
with86%oftheTE0modeenergywithin .Combiningequations(5.25)and(5.27)yields
Solutionsforthewavefunctionsofthe erfc(x/b')profile(seeFig.l.9),whichshouldbesimilartothosefor ierfc(x/b),havebeencomputednumericallyandcomparedgraphicallywiththosefortheslabguide(Smithgalletal1977).Theseresultsshowclearlythatthemodeenergyisburiedmoredeeplyforhigherordermodes.Herea'=a,b''=0.73bforcoincidenceatDn=a,a/2,and0.
Theexponentialfunction
alsogivesareasonablygoodfittothedata,asshowninFig.l.9.ForcoincidenceatDn=a,a/2,and0,Carruthersetal(1973)requirea''=a,b"=0.506b.AsshownbyConwell(1973),theexponentialprofile
isoneofthefewthatgivesexactanalyticalsolutionstothewaveequation.Thesesolutionsalsoshowanincreaseinthestrengthofthewavefunctionsasxapproachestheturningpoint,withdeeperpenetrationforhigher-ordermodes.Althoughthenumberofmodes,wavefunctionsandpropagationconstantscanbecalculatedwhena"andb"areknown,simpleexpressionsforNandwintermsofa"andb"arenotgiven.However,usefulexpressionscanbeobtainedincertainlimitsasfollows.
Definethefunctions
Page232
then,for
where and ,arerelatedsothattheBesselfunction
Nearcut-off, ,andinthislimitthezero'sinequation(5.33)aregivenapproximatelyby
Themaximum isgivenbyequation(5.30);andthenumberofmodesisthelargestintegeri+1obtainedfromequation(5.34)atcut-off
whichmaybecomparedwithequation(5.25)forb=1.97b".Becauseofitsextensivetail,theexponentialprofileoverestimatesbothNand.
Theturningpoint maybeobtainedbyequatingtheright-handsideofequation(5.32)to ;then
Intheotherlimit,farfromcut-off,miand ,arelarge;fori=0,equation(5.33)issatisfiedfor
Equation(5.37)maybeinsertedintoequation(5.32)toobtainthedispersioncurvefarfromcut-off.Theturningpointmaybeestimated
byequatingtheright-handsideofequation(5.32)to for ;then
Page233
Fig.5.15Normalisedguideindex
versusnormalisedfrequency (Carruthersetal1974).
whichisnearlyidenticalwithequation(5.27)forb"=0.506b.
UniversaldispersioncurvessuitableforbothTEandTMmodesoftheexponentialprofileinequation(5.29)calculatedfromcomputersolutionsofequations(5.32)and(5.33)for areplottedinFig.5.15.TheexponentialTE0modeshowsmuchlessdispersionthantheTE0modeforaslabhavingthesamecut-off,thatis,A=a",B=4b"/3.
ItisclearfromtheprecedingdiscussionthatNandwforthegradedguidecanbeadjustedjustasfortheslabguideprovidedaandbcanbecontrolledindependently.Toassuresinglemodeoperation,itisnecessarytorestrictNtotherange: .SuchguideshavebeenmadeinLiNbO3for mmbyrestrictingttoafewminutes.Anexampleofasinglemodeguideisasampleforwhicht=5minandT=1100°C,yieldinga=1.65x10-4andb=20mm.Fromequations(5.25)and(5.27),respectively,itiscalculatedthat and .Ontheotherhand,usingConwell'sexponentialapproximation(Conwell
1973),itisfoundthatNe=1.95and mm.
From(5.27)and(5.38),thepenetrationdepthw0islimitedbytherangeofsurfacegradient a/bavailablebyvaryingT.ForLiNbO3,
mm-1ispracticallytemperatureindependentbecause,so mmfortheavailablerangeT<Tc.Therefore,itmaybe
preferabletoout-diffuseatlowertemperatureswheretherequireddiffusiontimesarelongertomaintainbettercontrolovertheprocess,i.e.theheatingandcoolingtransientswillhaveasmallereffectontheprofile.ForLiTaO3,ontheotherhand, a/bcoverstherange
,so coverstherange6-16mmasTvariesfrom1400°Cto930°C.Therefore,smallerpenetrationdepthsareachievedathighertemperatures;however,theshorttimesrequiredmakecontroloftheprocessdifficult.Anevengreaterchangeofpenetrationdepth,w0withTwouldbefoundinmaterialsforwhichQvandQDdiffermorewidely.
Page234
Thus,verylow-lossout-diffusedlayerscanbefabricatedwithcharacteristicssimilartothoseofasinglemodeslabguidethickness
,where mmforLiNbO3and forLiTaO3.Theseratherlargeeffectivewidthsmaylimittheoperationofdevicesbasedoninteractionswithsurfacefieldsofshortwavelength.Ontheotherhand,thelargewidthmayproveadvantageousinapplicationswheretheplanarguideisconvertedtoaridgeorstripguidebyetching.Inthesecases,fieldscanbeappliedalongedgesoftheridge;andcouplingcantakeplaceattherelativelylargefacets.
5.2.5Propertiesofdiffusedwaveguides
Toestablishtheparametersoftherefractiveindexprofileindiffusedwaveguides,thefollowingmethodsareused:
1)interferentionalmicroscopy,2)directmeasurementofTiconcentrationdistributioninthewaveguidecross-section(X-raymicroanalysis,Augerspectroscopy),definitionofthefunctionn(y)fromtheobservedspectrumoftheeffective values(Naitohetal1977;Zolotovetal1976).
Inviewofthefactthatinterferentionalmicroscopyisonlysuitableforastudyofthickenough(>10mm)diffusedlayersandthesecondgroupofmethodsrequiressophisticateddevicesandasubsequentcalibration,Zolotovetal(1980)usedidentificationofdiffusedwaveguideprofilesfromthespec-tramofeffective values.Theparametersofn(y)distributionoveradiffusedwaveguidewereidentifiedfromthespectrumof valuesusingthecombinationoftheparabolicandexponentialfunctions(Zolotovetal1976)forwhichthereexistsananalyticalsolutionofdifferentialequationsofthetype
thatdescribetheelectricfielddistributioninweak diffused
waveguides.
ThedependenceofthewaveguideparametersonthetimeofdiffusionwasdeterminedusingmeasurementsforE-andH-waves(ifthecrystalorientationisfixed,theordinaryrefractiveindexn0(y)correspondstoE-waveswhiletheextraordinaryrefractiveindexne(y)correspondstoH-waves).InthewaveguidesinvestigatedbySugiietal(1978),two-threeE-modesandfive-sixH-modescouldbeexcitedatawavelengthof0.63pro,whileatawavelengthof0.44mmfour-fiveE-modesandsix-nineH-modeswereobserved.Thespectrumofvalueschangedwithdiffusiontime.Theanalysisofthespectra
obtainedhasshownthatthewaveguideprofilesforordinaryandextraordinarypolarizationsareapproximatedfairlywellbythecombinationoftheparabolicandexponentialfunctions
Page235
Hereaandbareparabolaparameters,histheexponentparameter,cisthedistancefromtheparabolavertextoitsconjugatepointwiththeexponent.
Thedistributionsof obtainedforawaveguidewithdifferentdiffusiontimesarerepresentedinFig.5.16andTable5.6givesthenumericalvaluesoftheirparameters.ThedistributionsoftherefractiveindicesofTi-diffusedLiNbO3waveguidesforwaveswithdifferentpolarizationsdifferpracticallyonlyintheincrementoftherefractiveindexonthewaveguidesurface,Dn,andintheexponentialfunctionparameterh.ThedifferenceAncanbeexplainedbydifferentproportionalitycoefficientsbetweenthetitaniumconcentrationCT1,andtheincrementsoftheordinaryandextraordinaryrefractiveindices.Theassumptionofdirectproportionalitybetween and isconfirmedbythelackofdependenceoftheratio onthediffusiontime(seeTable5.6).
Thedifferenceintheexponentparameterhinthedistributionsofn0(y)andne(y)isduetothefactthattheincrementoftheextraordinaryrefractiveindexiscaused,besidestitaniumdiffusion,alsobythereversediffusionofLi2Owhichincreasessubstantiallythewaveguidelength.
Themodefieldsintheabove-mentionedwaveguidesareobtainedfromthesolutionofthewaveequation(5.39)forordinarywaves(E-polarization)and
Table5.6Numericalvaluesofdiffusedwaveguideparameters( )(Zolotoval.1980)
,h E-waves H-waves
b/a c/a h,m b/a c/a h,mm
5 0.0161 2.99 -0.6 0.89 0.88 0.0374 2.99 -0.6 0.98 3.32 2.32
10 0.0127 4.27 -0.6 0.89 1.23 0.0296 4.00 -0.6 0.97 4.10 2.33
12 0.0115 4.56 -0.56 0.9 1.09 0.0259 4.56 -0.56 0.97 4.73 2.25
15 0.0112 5.20 -0.45 0.85 1.63 0.0231 4.95 -0.45 0.97 4.83 2.26
19 0.0088 6.27 -0.45 0.85 1.86 0.0192 6.17 -0.45 0.95 4.60 2.18
Fig.5.16Distributionofordinary(a)andextraordinary(b)refractiveindicesforTi-diffusedwaveguides(dashedlinesindicatecalculatedvalues).1)diffusiontime h;
2)10h;3)15h(Zolotovetal1980).
Page236
havetheform
here isadegenerategeometricalfunction, istheBesselfunction
Forextraordinarywaves(H-polarization)
Fig.5.17DispersionofordinaryandextraordinaryrefractiveindexincrementforwaveguideswithdiffusiontimetD=12h(dashedlinesindicatecalculatedvalues-seethetext)(Zolotoveta11980).
Fig,5.18(right)Opticalwaveguidingapparatus(KaminowandCarruthers1973).
Page237
TheconstantsC1,C2andC3aredeterminedfromtheconditionofequalitytozeroofthewavefunctionattheboundarywithairandcontinuityofthefuctionatthesewingpoint
Animportantcharacteristicofopticalwaveguidesisthedispersionoftherefractiveindexincrement.Thedataonthewaveguidedispersionarenecessaryforcreationofsomeintegro-opticaldevices,inparticular,nonlineartransducers.Zolotovetal(1980)investigatedthedispersionofwaveguidecharacteristicsinawidewavelengthrange:0.44,0.53,0.63,0.89,1.06,1.15mm.Itisanexperimentallyestablishedfactthataslvariestheshapeoftheprofilesofno(y)andne(y)remainsunaltered,anditisonlytherefractiveindexincrementsDnoandDnethatexhibitdispersion(Fig.5.17).
Guidingcanbedemonstrated(Tien1971;TienandUlrich1970)withtheprismcouplerarrangementshowninFig.5.18,wherecrystalsareorientedwitha,b,andcalongz,x,andy,respectively,andanincidentbeamispolarizedasanextraordinary(TE)wave.Abrightstreakappearsalongthesurfacewhenqisadjustednearanangleq0slightlylessthanthecriticalangle.Thereisnoobservabledecayinthestrengthofthescatteredlightoveracentimetrelengthofthestreak,whichsuggeststhatthelossis<1dB/cm.Themodesradiatesfromtheendoftheguide,producingafar-fieldpatternnarrowintheydirectionbutelongatedinthexdirection.Measurementofbeamangleaprovidesanestimatefortheextenthofthefieldinthexdirectionintheguide: .ForsampleI-3, (KaminowandCarruthers1973),whichindicatesthat,beingcoupled,theopticalenergyforthe
modesisconfinedtotheneighbourhoodofmaximumDnenears=0,wheresisthedepth.
Anoutputprismcouplerproducesawell-definedspotatq'=q0whenq=q0.Afaint'm-line'passesthroughthespot,indicatingonlyminorscatteringintodegeneratemodespropagatinginotherdirectionsintheplane.Waveguiding,asdemonstratedbythecoupled-outspot,existsoverarangeofanglesDq0.CalculationsshowthatDq0foreachsamplecorrespondstoarangeofwaveguidepropagationconstantsDbgivenapproximatelyby2pA/l.Thus,thewaveguidesupportsalargenumberofunresolvedmodes.Toproduceguidesthatsupportonlyafewlow-ordermodes,theproductA1/2BmustbereducedbyadjustmentoftandT.
5.3Secondharmonicgenerationinwaveguides
Integratedopticsisawidefieldforheighteningtheefficiencyofnonlinear
Page238
interactions.Theuseofopticalwaveguidespermitsobtaininghighintensitiesoflight,inafilmwiththicknessoftheorderofthelightwavelength,fromcomparativelylow-powersources,e.g.gaslasers.Asdistinctfromthecasewhennarrowingthelightbeamtosmalldimensionscausesitslargediffractiondivergence,asmallcross-sectionofthebeam(andthereforeitshighdensity)inawaveguideremainsunchangedthroughout.Anotheradvantageofthin-filmwaveguidesisthepossibilitytoattainphasematchingofinteractingwavesduetomodedispersion.Thisallowstheuseofisotropicmediapossessinghighnonlinearcoefficients.Anisotropicwaveguidesdonotrequiretemperaturetuningforattaininga90-degreematchingthatcanbereachedthroughthechoiceoftherefractiveindexprofile.
Butinspiteoftheobviousadvantagesofopticalwaveguidesfornonlinearconversion,thesuccessinthisfieldremainsrathermoderate.Inparticular,theefficiencyofsecondharmonicgenerationreachedexperimentallyinvariousmaterialswastwoorthreeordersofmagnitudelowerthanthetheoreticallypredictedone(Itoetal1974;VanderZieletal1975),whichisobviouslyexplainedbyalowqualityoftheguides.Toobtainaneffectivenonlinearconversion,thefilmnonuniformitythroughthethicknessmustnotexceed0.01mmper1min.Non-observanceofthisconditionleadstophasemismatchand,therefore,toaloweringofthesecondharmonicpower(Boyd1972).
Planarwaveguidesonthebasisoflithiumniobatearenowpromisingforthestudyandpracticaluseofnonlinearsecond-ordereffects.Thisisconnectedwithalargevalueofthenonlinearsusceptibilitytensorofthecrystalaswellaswiththepossibilityofangularandtemperaturetuningofmatchedinteraction.
Weshallmentionsomemosttypicalpapersoutofacomparativelysmallnumberofpublicationsconcerningnonlinearprocessesinplanar
waveguides.
Fejeretal(1986)obtainedsecondharmonicgeneration(SHG)inalaseronagarnetwithneodymiuminaTi:MgO:LiNbO3waveguide,inwhichatemperature-inducedphasematchinggeneratedradiationatawavelengthof532nmwithanefficiencyof1.5×10-2.SHradiationof22mWwasobtainedinanon-stopregime;inapulsedoperationtheconversionefficiencywasoftheorderof25%.Phasematchingwasreachedbothforthecase (thezerothmodeoffundamentalradiationisconvertedintothezerothmodeofsecondharmonic)andfor .
ThecorrespondingmatchingtemperaturesareequaltoT=102ºCand21.7ºC.
SHGinTi:LiNbO3waveguideswasobtainedbyArvidssonandLaurell(1986)andRegeneretal(1981)whoreached,usinganadditionalresonatorforproducingthefundamentalfrequency,asubstantialincreaseofthefieldstrengthinthewaveguide,whichresultsinasharpheighteningoftheefficiencyofnonlinearopticconversion.InasimilarwayRegeneretal(1981)reachedanefficiencyoftheconversionintoasecondharmonicoftheorderof10-2forameaninputradiationpowerof1.5mW.
Othernonlinearprocessessuchasdifferencefrequencygeneration(Uesugi1980;Suche1984),parametricamplificationandgeneration(Sucheetal1985)werealsoattainedinplanarwaveguides.
Page239
5.3.1Phasematchinginanopticalwaveguide
Asiswellknown,aneffectivesecondharmonicgenerationrequiresphasematchingofinteractingwaves.Inanisotropiccrystals,dispersionatfrequenciesoffirstandsecondharmonicsiscompensatedbyexploitingdifferentpolarizationsofinteractingwaves.Thephasematchingdirectionwillcoincidewiththedirectionofintersectionofindicatricesoftheirrefractiveindicesn(j0,w)=n(j0,2w),whichinthethree-dimensionalcaseisdeterminedbybirefringenceanddispersionofthecrystal.Ifthematchingdirectiondoesnotcoincidewiththeopticalaxis,theinteractionlengthwillbelimitedtothedivergenceofwavesofthefirstandsecondharmonicsduetobirefringence.Therefore,toobtainaneffectivenonlinearinteractionitispreferabletousea90-degreematchingwhichgivesnobirefringenceandinthethree-dimensionalcaseisreachedbytemperaturetuning.
Inopticalwaveguides,therefractiveindiceshaveincrementsDnoandDnerelativetothesubstrate.Iftheseincrementsexceeddispersionoftherefractiveindices,nw-n2watthefrequenciesoffirstandsecondharmonics,thenthenw-n2wcanbecompensatedbymodedispersion.Isotropicmediacanwellbeusedinthiscase,too.Inthecaseof'weak'waveguidesinwhichtheincrementoftherefractiveindexofthewaveguidinglayerismuchlessthantherefractiveindexofthesubstrate ,phasematchingisonlyduetobirefringence.Theuseofmodedispersionwidenssignificantlytheregionofphasematching.ThiscanbereadilyseenfromFig.5.19whichshowspossiblepositionsofmodeindicatricesatfrequenciesofthefirstandsecondharmonicsinananisotropicwaveguideinanegativecrystal.Theregionswhichcancontainindicatricesofordinarilyandextraordinarilypolarizedmodesaredashed,andtheoverlapoftheseregionsdeterminestherangeofpossiblematching.Foreachpairofmodes,phasematchingoccursatacertainangleatwhichmode
indicatricesintersect.Varyingthedepth,shapeoftheprofileorincrementoftherefractiveindexofawaveguide,wecanvarythematchinganglesofnonlinearmodeinteraction.Itshouldbenotedthattoperformsuchvariationsoneshouldknowthedependenceofphasecharacteristicsofawaveguideonitsstructureparametersandbeabletocontrolthemduringwaveguidemanufacturing.For
Fig.5.19Indicatricesofordinaryand
extraordinarypolarisationmodesinLiNbO3(Zolotovetal1979).
Page240
Ti-diffusedwaveguidesinLiNbO3,theanglesofpossiblemodematchingliewithintherange ,thatis,a90-degreematchingcanbeattainedwithouttemperaturetuning.
5.3.2Overlapoffieldsofinteractingmodes
Phasematchinginanopticalwaveguideisnotasufficientconditionforobtaininganeffectivenonlinearconversion.Thedecisiveroleisplayedbythedegreeofoverlappingofopticalfieldsofinteractingmodeswhichischaracterizedbytheoverlapintegral
whereYw(y)andY2w(y)isthetransversedistributionofmodefieldsatafrequencyofthefirstandsecondharmonics.Theoverlapintegralentersintheexpressionfortheefficiencyofsecondharmonicgeneration(derivedforthecaseofphasematchingintheplainwaveapproximation(ZernikaandMidwinter1973;Conwell1973):
wheredisanonlinearcoefficient,Ppumthepumpingpower,P2wthesecondharmonicpower,Ltheinteractionlength,lthepumpingwavelength,ntherefractiveindexofthesubstance,Wthebeamwidthinthewaveguideplane.
Asisseenfromtheexpression(5.41),theoverlapintegraldependsonthefielddistributionofmodeofbothharmonics,whichareverydifficulttofindfordiffusedwaveguidessincetheirprofilesarenotknowninadvance,buteveniftheywereknown,itisnotalwaysthatthereexistsananalyticsolutionofthewaveequationforthem.IfLiNbO3isused,thesituationbecomesevenmorecomplicatedbecauseananisotropiccrystalandwaveguideshavedifferentprofilesforordinaryandextraordinarypolarizations.Moreover,inTi-diffused
waveguidesofLiNbO3awaveguideformsnotonlyduetoTidiffusionintoacrystal,butduetoareversediffusionofLi2Oaswell.Theseprocesseshavedifferentkinetics,andthereforethewaveguideprofileforextraordinarypolarizationiscomplex.
ThemethoddevelopedbyZolotovetal(1977)wasusedtodetermineYw(y)andY2w(y).Thismethodpermitsdeterminationofthecharacteristics(includingmodefieldsanddispersiondependences)ofdiffusedwaveguideswithanyprofileofrefractiveindexdistribution.Themethodisbasedonapproximationoftheunknownwaveguideprofilebythefunctionsthatallowobtainingsolutionsofthewaveequationinananalyticform.InTi-diffusedwaveguidesofLiNbO3(Y-cut),theprofileofthetransversedistributionn0(y)forordinarypolarizationisdefinedbythecombinationofasmoothlysewedparabolaandexponent(5.40).
Page241
Fig.5.20Overlapintegralsfordifferentinteractionsversusdimensionlessthicknessaofawaveguide(dashedlinecorrespondstothicknessofsampleunder
investigation)(Zolotovetal1979).
TheoverlapintegralsI1m(m-1,2,3,4)fortheinteractiono+o=ewerecalculatedusingtheobtainedmodefielddistributionsinaTi-diffusedLiNbO3waveguide.ThedependencesofI1monthevalueofdimensionlessthickness fortypicalparametersoftheTi-diffusedwaveguide(seeTable5.6)areshowninFig.5.20.Thecalculationsdidnotmakeallowanceforinsignificantvariationsofthestructureparameterratiosc/a,h/awithvaryingasincetheydidnotpracticallyaffectthecharacterofthedependencesoftheoverlapintegralsI1m(a).TheoverlapintegralsInmofmodesinthickerwaveguides(a>6),wheren>1,isnotconsideredsinceinthesewaveguidesphasematchingisattainedforhighermodesonly(m>3),andthereforetheoverlapintegralsaresmall.
AnanalysisshowsthatforoptimizationofsecondharmonicgenerationinT-diffusedwaveguides,fromtheviewpointoftheoverlapintegralofinteractingmodesoneshouldchoosenotverythick
waveguideswiththeuseoflowermodeinteraction.
5.3.3Angularmatching
Secondharmonicgeneratedusingawaveguideobtainedby
thermodiffusionofTiintotheY-cutofLiNbO3.Thewaveguidemodespectrum wasmeasuredonagoniometerbyradiationoutputthroughaphotoresistivegrating(l=0.3462mm)depositedonthesurface(Zolotovetal1976).TheresultsareshowninFig.5.21.ModesH1-H4,E1andE2wereexcitedinawaveguideatawavelengthl=0.53mmandmodesE1andH1atawavelengthD=1.06mm.Figure5.22presentsindicatricesofrefractiveindicesofwaveguidemodesatthefrequenciesoffirstandsecondharmonics.Phasematchingconditionsareonlymetforthefollowingo+o=etypeinteractions:
TheindicatrixofthemodeH1doesnotintersecttheindicatricesofofmodesoffirstharmonic,andthereforethephasematchingforH1isunattainable.
Page242
Fig.5.21Distributionofrefractiveindicesandopticalfieldsforordinaryandextraordinarywavesofdiffused
waveguides:a)l=1.06mm,b)l,=0.53mm(Zolotovetal1979).
Fig.5.22Indicatricesofeffectiverefractiveindicesofdiffusedwaveguidemodes(Zolotovet
al1979).
Theprofilesofrefractiveindexdistributionforordinaryandextraordinarypolarizations,whichwererespectivelycharacterizedbytheparameters ,Dno=0.0035,ao=4mm,(c/a)o=0.7,ho=1.5mm, ,Dne=0.015,ae=14mm,(c/a)e=0.97,(b/a)e=-
0.63,he=8.5mmwerefoundfortheinvestigatedwaveguideonthebasisoftheobtainedspectra .
Themodefieldsoftheinvestigatedwaveguide(Fig.5.21)wereobtainedandtheoverlapintegralsI1m(m=2,3,4)weredeterminedusingtheprofiles.TheintegralI12ismaximumandclosetotheoptimumvalue(Fig.5.20),andtherefore
Page243
Fig.5.23Theoretical(dashedline)andexperimental(solidline)dependencesofeffectiveSHGonthepumpingpower(experimental)pointscorrespondtoCWlaserpumping
(D),apulsedlaserpumpinginfreegenerationregime(o)apulsedQ-switching,()(Zolotov,etal,1979).
theconversion wasused.PumpingwasrealizedbyYAG:Nd3+-lasersoperatinginpulsedandnon-stopregimes.Alightbeamwasfedinto(andout)withthehelpofrutileprismsinthedirectionofmatching,thebeamwidthbeing .
TheefficiencyofsecondharmonicgenerationasafunctionofpumpingpowerisgiveninFig.5.23.Themaximumconversionefficiencywasobtainedthroughpumpingof andmadeup16%.
Thedependenceoftheefficiencyofnonlinearconversiononthepumpingpower(seeFig.5.23)wasnoticeablyoverestimatedincalculationsascomparedwithexperimentalvalueswhichweresaturatedalreadyfor .Suchadifferenceisexplainedbynonuniformityofthewaveguideoverthickness andbytherefractiveindexinhomogeneities,inducedbysecondharmonicradiation,whichwereobservedatapumpingpowerof .So,afurtherincreaseinthenonlinearconversionefficiencywasduetotheimprovementofthewaveguidesurfacequalityaswellastotheheighteningofthethresholdoftheoccurrenceofoptical
inhomogeneities.
Thedependenceofsecondharmonicpowerontheanglebetweenthepump-
Fig.5.24Angulardependenceoftheoutputsecondharmonicpowerinadiffusedwaveguide(Zolotoveta11979).
Page244
ingwavepropagationdirectionandtheopticalaxisofthecrystal(Fig.5.24).Thefigureshowsthatthiscurveisnonsymmetricrelativetothecentralmaximum(theinteraction )sinceitsleftsideisoverlappedbythemaximacorrespondingtotheinteractions and
.Therelativeheightofthemaximaisinsatisfactoryagreementwiththevaluesoftheoverlapintegrals.Thewidthofthecentralmaximumwasfourtimesthetheoreticalvalue,whichisexplainedbyinhomogeneityofthewaveguide.
5.3.4Temperaturematching
Figure5.25showstheexperimentalsetupusedbyUesugiandKimura(1976).Thefundamental-frequencylaserbeamatawavelengthof1.064mm,generatedbyacwNd:YAGlaser,wasfedintoasingle-modefibrewitha×20microscopeobjective.Thecoredimensionofthefibrewasequalto5.5mmandtheindexdifferenceDnbetweenthecoreandcladwas0.25%.Thefibrewasthenbutt-joinedtoaLiNbO3waveguidewithamanipulator.Single-modelaunchingwithacouplinglossaslowas1.4dBwaspreparedwiththebutt-joinedprocedure.TheLiNbO3opticalwaveguidewasmountedonacopperblockwhosetemperaturewascontrolledwithathermoelectricelement.Theopticalwaveguideandthecopperblockwerekeptinadry-nitrogengasambienttopreventwater-vapourcondensation.Thewaveguidetemperaturewasmeasuredatthecrystalsurfacebyacopper-constantanthermocouple(Uesugietal1976).
Thethree-dimensionalLiNbO3opticalwaveguidewasfabricatedbyTi-in-diffusionintoac-plateofLiNbO3crystalat1050ºCfor20h.TheindexdifferenceAnwas0.002-0.003andthecoredimensionwasabout5mm.Thewaveguidelengthwas1cm.Therefractive-indexdistributionwasassumedtobeGaussian.Itwasestimated,fromlighttransmissionexperiments,thattheextraordinaryrefractive-indexdifferencebetweenthecoreandsubstrateislargerthanthatofan
ordinarywave.ThisisattributedtoLi2Oout-diffusionduringthefabricationprocess(Nodaetal1975).TheguidecansupportonlydominantTE00andTM00modesat1.064mm,anduptothird-ordermodesat0.532mm.
Figure5.26showsthesecondharmonicpowerversusfundamentalfrequencypowerunderaphasematchedconditiondescribedinthesequel.Experimentalresultscoincidewiththoseshownbythesolidlinewithaslopeof2.The
Fig.5.25Experimentalconfigurationofthesecond
harmonicgenerationusingathree-dimensionalLiNbO3opticalwaveguide(UesugiandKimura1976).
Page245
Fig.5.26Dependenceofsecondharmonicpoweron
fundamentalfrequencypowerunderphase-matchingcondition(Uesugiand
Kimura1976).
fundamental-wavepolarizationcorrespondstotheTE(ordinary)wave,andthegeneratedsecond-harmonicwaveisfoundtobelinearlypolarizedwithTM(extraordinary)polarization,whichisinducedbythesecond-ordernonlineartensorelementd31.Opticaldamagewasnotobservedintheexperimentuptoabout3mWfundamentalinput.
ThephasematchingconditionissatisfiedbyusingthetemperaturedependenceofLiNbO3birefringence.Figure5.27showsthetemperaturedependenceoftheharmonicpower.Inthismeasurement,thecrystalwascooledatfirstto-29ºCandthetemperaturewasraisedatarateofabout1ºC/min.Photographsshowingtypicalnear-fieldpatternsofthesecondharmonicwaveguidemodesaredepictedinFig.5.27.Thepeaksat-2and15ºCcorrespondtothesecondharmonicTM00andTM20modes,respectively.Thepeakat10ºCisestimated,fromthenear-fieldpattern,tobeCherenkovradiation.TheCherenkovradiationisgeneratedwhenthenonlinearpolarizationpropagationconstantislargerthanthatoftheharmonicwaveinthebulkcrystal(Tienetal1973).For2mWfundamentalfrequencyinputpowerintheTE00mode,theconversionefficiencyat-2ºCwas1.5×10-4.A
conversionefficiencyashighas0.1isexpectedforan1.4Winput.Theconversionefficiency,calculatedonthebulk-crystaldata,is3.1×10-4fora2mWfundamentalplane-waveinput,whichisconfinedina5×5-mmcross-sectionforthelengthofacm.Thedifferencebetweentheexperimentalandcalculatedvaluesmaybeduetofractionalspatialoverlapofthenonlinearpolarizationandtheharmonicwaveguidemode,waveguideloss,andinsufficientcoherentinteractionlengthbetweenthefundamentalandharmonicwaves.Thegeneratedsecondharmoniclightwaseasilyobservedonascreenandatthewaveguideendsurfacewithanakedeye.
Theconversionefficiencyofsecondharmonicpowerintheopticalwaveguideisproportionaltothesquareoftheoverlapintegralbetweenthefielddistributionofthefundamentalandsecondharmonicwaves.TheoverlapintegralisthelargestwhenthefundamentalandsecondharmonicwavesarebothinthedominantTE00andTM00modes,respectively.TheharmonicTM10modewashardlyobserved.TheTM20modewasweakerthanthedominantmode.ThephasematchingtemperatureoftheLiNbO3opticalwaveguidedepends
Page246
Fig.5.27Harmonicpowertemperaturedependence.Insettedphotographsshowtypicalnear-fieldpatternsofsecondharmonicwaveguidemodes(Uesugiand
Kimura1976).
Fig.5.28Calculatedphase-matchingtemperaturedifference
betweenTM00andTM20ofathree-dimensionalLiNbO3opticalwaveguide.FundamentalfrequencymodeisassumedtobeTM00.
Theexperimentaltemperaturedifferenceisshownontheordinate.Thewaveguideheightbisestimatedtobeabout5mmfromaninterference
fringemeasurement(UesugiandKimura1976).
onthecompositionofLi2OandNb2O5andonwaveguidedispersion.Itisalsoaffectedbythepyroelectriceffectwhenthecrystaltemperatureisswept.However,thephasematchingtemperaturedifferenceDTbetweenthesecondharmonicdominantTM00modeandthehigherTM20modeareinsensitivetothecompositionand
pyroelectriceffect.Figure5.28showsthecalculatedtemperaturedifferenceDTasafunctionofthewaveguideheightb.Hereitisassumedthattheindexprofileisastepdistributionoverthecross-section.ThepropagationconstantiscalculatedaccordingtoMarcatili'sapproximation(Marcatili1969).Sellmeier'sequationwasusedtoexpressthetemperatureandwavelengthdependenceofrefractiveindices.Figure5.28servestoexpressseveralaspectratios(a/b).ThesolidlinecorrespondstotherefractiveindexdifferenceDn=0.0025.TheexperimentalresultshowninFig.5.27isequaltoDT=17ºC.
Page247
LiNbO3hasapyroelectriccoefficientaslargeas4×10-9C/cm2Cat25ºC.Whenthecrystaltemperatureisraisedby1ºCandthespontaneouspolarizationremainsuncompensated.theelectricfieldalongthec-axisbecomes1.67kV/cm.Thiselectricfieldinducesbirefringence,whichcorrespondstoatemperaturechangeof0.4ºC.Inthisexperiment,theobservedphasematchingtemperaturesarehigherthanrealphasematchingtemperatures,duetothepyroelectriceffect.Itwasobservedthatwhenthecrystaltemperatureissweptfromhightolow,thephasematchingtemperatureislowerthanthatintheoppositesituation.Thehysteresisseemstoresultfromthepyroelectricsurfacechargecompensation.Thepyroelectriceffectcouldbeavoidedifab-platecrystalwithshort-circuitedelectrodesonc-surfaceswereused.
5.3.5Second-harmonicgenerationinawaveguidewithperiodicallydomain-invertedregions
Second-harmonicgeneration(SHG)thatusesaquasi-phasematching(QPM)inLiNbO3opticalwaveguidewithperiodicallydomain-invertedregions(PDRwaveguide)isapromisingapproach(Limetal1989(a)).Suchwaveguidespossessahighpowerdensityandalargenonlinearcoefficient.However,sincetheQPMconditionisverydifficult,thehigh-conversionexperimentsweremadearrangingsuitableperiodsofdomain-invertedregionspreciselyorusingatunablelaserforthefundamentalwave(Limetal1989(b)).
Shinizakietal(1991)describedaself-quasi-phase-matchedSHGthatusesaPDRwaveguide.ThefundamentalwavesatisfyingtheQPMconditionwasgeneratedbyanLD(laserdiode)whichwaslasedbyafeedbackwavesfromthePDRwaveguide.Astheopticalrefractiveindexofthedomain-invertedregionsisslightlyhigherthantheundopedregion,theperiodicaldomain-invertedregionsactasadistributedBraggreflector(DBR).Astheperiodofthedomain-
invertedregionswasdesignedtosatisfytheQPMconditionsandthehigh-reflectanceconditionsofthequasi-phasematchedfundamentalwave,theLDwaslasedatthewavelengthsatisfyingtheQPMcondition.
Intheexperimentalarrangements,showninFig.5.29,thePDRwaveguideandtheLDwithantireflectioncoatingfacetsareopticallyconnectedbysingle-modefibre(SMF).Periodicaldomain-invertedregionswereformedbyTi-diffusion.TheTilayerevaporatedonac-cutLiNbO3substratewaspatternedbythelift-offtechnique.TheTilayerwas5nmthickandtheTilineswere4mmwide.Heattreatmentconsistedofa2hrampupfromroomtemperatureto1050ºCand1hsoakat1050ºC;afterthisthefurnacewasturnedoff.Thedomain-invertedperiodwasL=13mm.Theopticalwaveguidewasfabricatedtooverlapperpendicularlyontheperiodicaldomain-invertedgrating.Thewaveguide(6mmwide,2mmlong)wasfabricatedbyproton-exchangedprocess(seeChapter1).TheLDwaslasedbyfeedbackwavesfromthePDRwaveguide.Theperiodofdomain-invertedregions,actingasDBR,is13mm.Iftheeffectiveguideindexfortheradiatedwaveat1.327mmisequalto2.195,thehighreflectanceconditionissatisfied.WhenrgwLDlasedat1.327mminwavelength,thesecond-harmonic(SH)wavewasobserved.TheSHspectrumwhichwasmeasuredisshowninFig.5.30.ThewavelengthoftheSHwaveis662.4nm,whichcorrespondstothehalfwavelengthofthefundamentalwave.The
Page248
Fig.5.29Experimentalarrangementoftheself-QPMSHG.TheSHGdeviceiscomposedofPDRwaveguideonthe+cfacetofthelithiumniobatewafer.LDswithanantireflectioncoatingfacetareopticallyconnectedtotheSHGwaveguidebysingle-mode
fibre(Shinozakietal1991).
Fig.5.30SHGspectrumfromthePDRwaveguide.The
fundamentalwavewasgeneratedbytheInP/InGaAsPLDwithAR-coatedfacets
(Shinozakietal1991).
normalizedSHconversionefficiencywas4.1%/Wcm2.
TheQPMconditionsaresatisfiedifthehalf-periodofdomain-invertedregions,L/2,isequaltooddtimesofthecoherencelength.Thecoherencelength isgivenby
wherelisthewavelengthofthefundamentalwaveinvacuum,n(l)istheopticalindexforwavelengthl.TheconditionforQPMis
Page249
Fig.5.31Lengthofdomaininvertedregions(Lc)infirstorderofQPMandthehalfperiodsof43rdorderofDBR(Lw)versusthefundamentalwavelength.These
linesintersectat1.327mminfundamentalwavelength,6.5mminLcorLw(Shinozakieta11991).
wheremispositiveinteger,andk1andk2arethewavevectorsforthefundamentalandSHwaves,respectively.Thentheperiodofthedomain-invertedregions,L,isgivenby iftheLsatisfiestheQPMconditiongivenasequation(5.46).Theperiodicaldomain-invertedregionsactasDBR.IftheperiodLisdesignedtosatisfythehighreflectanceofthefundamentalwave,theQPMconditionissatisfied.Thatis,iftheLDwithanantireflection-coatedfacetislasedbythefeedbackwavesfromtheperiodicaldomain-invertedregions,theradiatedwavesatisfiestheQPMcondition.Theself-QPMconditionsareasfollows
wherepispositiveinteger.Figure5.31showstherelationshipsgivenbyequation(5.47),thelengthofthedomain-invertedregions, ,inthefirstorderofQPM(m=0)andthehalf-periodof43rdorderofDBR(p=43),Lw[=pl/4n(l)],againstthefundamentalwavelength.Thedispersionfunctionoftheproton-exchangedLiNbO3materialisgivenbyn(l)=n'(l)+0.05(DeMichelietal1983),wheren'(l)isanopticalindexdispersionofcongruentLiNbO3.Thesetwolinesintersectat1.327mminfundamentalwavelength,6.5mminLcor
Lw,asshowninFig.5.31.Intheexperiment,thewavelengthofthefundamentalwavewas1.327mm,thehalfperiodofDBR,L/2,was6.5mm.TheallowanceoftheDBRperiodDLisequalto0.039mm.Itisverydifficulttodesignandfabricateadomain-invertedregiontoachieveahighSHconversionefficiency.
5.3.6Effectofprotonexchangeonthenonlinearopticalproperties
Protonexchangeusingbenzoicacidhasbeenshowntobeaccompaniedbyasubstantialreductionintheelectro-opticcoefficient(Becker1983;Yan1983);somedecreaseinthenonlinearopticalcoefficient(d)hasalsobeenobserved(Suharaetal.1989;Caoetal.1991).Limitedrecoveryofanelectro-opticalcoefficientandanonlinearopticalcoefficientoccursunderthermalannealing(Caoetal,1991;Suchoskietal,1988).Laurelletal(1992)havereporteda30-foldreductionintheopticalnonlinearityforLiNbO3,theyfoundthattheopticalnonlinearitycannotbeeffectivelyrestoredbythermalannealing.
Page250
Bortzetal(1992)havemeasuredthed33nonlinearcoefficientinproton-exchangedLiNbO3usingangle-dependingreflectedSHGandobservedareductionto<1%ofthebulkLiNbO3value.
Recently,animprovedprotonexchangesourceusingpyrophosphoricacidhasbeenimplementedbecauseofitshigherboilingtemperature(300ºC)andlowvapourpressure.Low-loss(0.5dB/cm)waveguideshavebeenpreparedinLiNbO3andLiTaO3usingpyrophosphoricacidandefficientblue-lightgenerationhasbeenachieved(Mizuuchieta1.1991)However,theeffectoftheprotonexchangeprocessusingpyrophosphoricacidonthenonlinearopticalcoefficientisnotknown.Hsuetal.,(1992)reportedtheeffectoftheprotonexchangeprocesscarriedoutusingbenzoicacidandpyrophosphoricacidonnonlinearopticalpropertiesofLiNbO3andLiTaO3andrecoveryofthenonlinearcoefficientunderthermalannealing.Thenonlinearopticalcoefficientwasevaluatedusingareflectiontechnique.
X-cutandZ-cutLiNbO3andLiTaO3crystalswereusedinthisstudy.Waveguideswerepreparedbyprotonexchangeinbenzoicacidandinpyrophosphoricacid(H4P2O7)withaheatingrateof10ºC/minandcoolingrateof20ºC/min.
Iftheincidentbeammakesanangleqi,withthesurfacenormal,hasapolarizationanglejwithrespecttothenormaltotheplaneofincidence,andhasanintensityI,thenthenonlinearpolarizationforZ-cutLiNbO3withtheY-axisperpendiculartotheplaneofincidencecanbewrittenas(Dicketal.1985)
wheredijarenonlinearcoefficientsandfiarelinearFresnelcoefficients.Themeasuredintensityofthes-andp-polarizedSHGin
reflection(neglectingbirefringence)ispropotionaltononlinearpolarization.
Figures5.32and5.33showresultsofsuchmeasurementsat1064nmandtheoreticalcalculations.Theratioofd33/d31andd22/d31wasobtainedas6.2and-0.30byfittingthetheoreticalresultswithexperimentaldata.Thesevaluesareslightlydifferentfromthepublishedvalues(7.0and-0.53fromNishiharaetal1989),butthereappearstobequiteavariationintheliteraturedata(Yariv1984).
Resultsofd-coefficientmeasurementsatfundanmentalwavelengthsof532nmforproton-exchangedLiTaO3usingbenzoicacidandpyrophosphoricacidarepresentedinTable5.7.Theincidentbeampowersusedwerebelowthresholdforphotorefractiveeffectstobeobservedasnochangeinsignalwasobservedevenfor1hexposuretotheincidentbeam.Theshapeofthepatternisrelatedtothestructuralsymmetryofthecrystalandofthesurface.Thelargescatterintheexperimentaldataattheincidentp-polarizedlightonX-cutcrystaloccursbecauseofpossiblesmallmisalignmentsofthecrystal.
Page251
Fig.5.32VariationofSHGintensitywithincidentpolarizationangleforaZ-cutLiNbO3crystalwiththeXaxisperpendiculartotheplaneofincidence.Crossesareexperimentalpointsandthesolidlineisfromtheoreticalcalculationsfor(a)p-polarizedand(b)s-polarized
outputbeams(Hsuetal1992).
Fig.5.33(right)VariationofSHGintensity
withincidentpolarizationangleforX-cutLiNbO3crystalwiththeZaxisperpendiculartotheplaneof
incidence.Crossesareexperimentalpointsandthesolidlineisfrom
theoreticalcalculationsfor(a)p-polarizedand(b)s-polarizedoutputbeams(Hsuet
a11992).
Insitumeasurementofrecoveryofd33wasmadeunderthermalannealing.ThesaamplewaslocatedinaheatingfurnaceandtheSHsignalwascontinuouslymonitoredwhilstthesamplewasmaintainedatatemperatureof310ºC.Figure5.34showstherecoveryoftheSHsignalasafunctionoftime.Norecoveryisseenfortheinitial30minduringwhichthefurnacewasheatedupfromroomtemperaturetothefinalannealingtemperature(310ºC).Thereisquickrecoveryofd33,whichbeginsatapproximately1.25hintotheannealingprocess,whichsaturatestoavalueofapproximately50%oftheblankLiNbO3value.
Becker(1983)hasshownthataprotonexchangeprocessusingbenzoicacidgivesrisetoaconsiderablereduction,byafactorof2.7,intheelectro-opticcoefficient.Ifthenonlinearresponseispurelyaresultofelectronicpolarizations,theelectro-opticanddcoefficientsareproportional(Yariv1984),andanydecreaseintheelectro-opticcoefficientisnecessarilyaccompaniedbyacorrespondingdecreaseind.However,theelectro-opticcoefficientforLiNbO3isknowntohavecontributionsformionicpolarizations.SuchpolarizationshavenoeffectupontheSHGprocess.Hence,itispossiblefortheelectro-opticandSHGprocessestobeaffecteddifferentlybyprotonexchange.Suharaetal.(1989)reporteda50%reductioninthedcoefficientat1064cmforprotonexchangeinbenzoicacid.Similarly,Caoetal.(1991)havereporteda40%reduction,howeverannealingrestoredthedcoefficientto90%ofthebulkvalue.Intheexperimentsat532nm,Laurelletal.(1992)findthattheopticalnonlinearitycannotbeeffectivelyrestoredbythermalannealing.Bortzetal.(1992)suggestthatthedifferencebetweentheirresultsandthosereported
Page252
Table5.7Measuredvaluesofdcoefficientforx-cutp-exchangedLiNbO3andLiTaO3relativetotheblankcrystal.Measurementerroris±10%.Annealingtemperature350ºC
Annealingtime
Protonexchangetime(h)
LiNbO3,%recoveryofd33comparedtoblank
LiNbO3
LiTaO3,%recoveryofd33comparedtoblankLiTaO3
0h 1h 3h 7h 17h 0 1h
0.5 0% 52% 51% 59% 54%
1 Norecoveryobserved
1.5 Norecoveryobserved 69%* 56%*
0.5 Norecoveryobserved
1 Norecoveryobserved 39%** 0%**
*protonexchangedat200ºC
**at230ºC
Fig.5.34VariationofSHsignalwithannealingtime
foranx-cutLiNbO3samplethatwasproton-exchangedinbenzoicacidfor0.5hat180ºC.Annealingtemperaturewas310ºC(Hsu
etal1992).
byCaoetal.(1991)isduetoneglectofthereflectedsecond-harmonicfieldonboththed33discontinuityatthefilm-substrateinterfaceandangulardependenceofthenonlinearpolarization.TheresultsreportedbyHsu,etal.(1992)indicatethatLiNbO3samplesproton-exchangedfor0.5hat180ºCshowedsomerecoveryofthenonlinearcoefficient,whilstsamplesthatwereproton-exchangedfor1and1.5hdidnotshowanymeasurablerecoveryunderthethermalannealingconditionsused.
Theprotonexchangeprocessfollowedbyannealingmayproducehigherlatticedisorderatthetopsurface,whichcouldexplainwhyitispossibletoseesomewaveguideSHconversioneventhoughthenonlinearcoefficientisdegraded.
IncontrasttoLiNbO3,LiTaO3showedonlypartiallossofopticalnonlinearitymeasuredat532nmuponp-exchangeusingeitherpyrophosphoricacidorbenzoicacid.ThermalannealingproducedonlysmalllossinnonlinearityofLiTaO3p-exchangeinbenzoicacid.Completelossofnonlinearitywasobservedinthecaseofpyrophosphoricacid.TheseresultsalsodifferfromannealingresultsforLiNbO3wheresomerecoveryoftheopticalnonlinear
Page253
coefficientwasobserved.TheLiTaO3indexincreasesafterannealingwhiletheLiNbO3indexdecreases.Increaseintheindexmaycausesomedistortioninthestructure,whichcanaffecttheSHsignal.Tounderstandthedegradationmechanism,structuralcharacterizationofproton-exchangedandannealedLiNbO3andLiTaO3isongoing.
5.3.7Sum-frequencygenerationinwaveguides
Therehasbeenrecentincreasedinterestincompactshort-wavelengthlightsourceswiththeobjectiveofrealizingoutputpowersinthemWrangebasedondiodelasers.OneofthemostpromisingtechniquestodothisistousenonlinearfrequencyupconversioninQPMwaveguides(Limetal.1989;vanderPoeletal.1990;Mizuuchi,etal.1991).Byfarthemostwidelyusednonlinearprocessissecond-harmonicgeneration(SHG)sinceonlyonelightsourceisrequired.AnalternativetoSHGissum-frequencygeneration(SFG),especiallywhenfinetuningofthegeneratedwavelengthisrequiredorfundamentallightsourceforSHGisdifficulttofind.SFGcanalsobecombinedwithSHGinsuchawaythattwoIRlightsourcesgeneratethreevisiblewavelengthssimultaneously(Yamamotoetal.1991).WaveguideSFGhasbeenreportedusingbirefringencephase-matching(Useugietal.1978).Cherenkovradiation(SanfordandRobinson1989;Laurelletal.1990).Amajordrawbackwithalltheseexperimentshasbeenthelow-outputpowderobtained.
Laurell,etal.,(1992)reportedefficientSFGinsegmentedKTPwaveguides(Bierleinetal.1990)usingQPM(vanderPoeletal.1990).
Twoconditionshavetobefulfilledtoobtainquasi-phased-matchedSFG,energyconservation
andmomentumconservation,
wherel1andl2arethefundamentalwavelengths,l3theSFwavelength,N(l)istheeffectivemodeindexatthecorrespondingwavelengths,andmandLaretheorderandtheperiodoftheQPMstructure,respectively.
A4.5mm-longflux-grownz-cutKTPsamplewasmaskedwithatitaniumfilmwithrectangularopeningsforionexchangetoformthewaveguideinthex-direction.Thesamplewasthenendpolishedandimmersedfor45minina98mol%RbNO3:2mol%Ba(NO3)2moltensaltbathat330ºCforsimultaneousionexchangeanddomainreversal.Thewaveguidesinvestigatedonthesamplewere4mmwideandhasperiodsof3,4,5and6mm.Fortheseperiods,theratiobetweentheexchangedandunexchangedregionswas2/1,3/1,4/1and5/1respectively.Theseperiodswerechosentogiveup
Page254
Fig.5.35Tuningcurveforthesumfrequencygenerationvsfundamentalwavelengthsinwaveguideswith
(a)3mm,(b)4mm,(c)5mmand(d)6mmperiods(Laurelletal1992).
convertedlightfromnearUVtoblue-greenbyfirstorder(m=1)QPM.
Toanalyzethenonlinearpropertiesofthewaveguide,twoindependentlytunableTi-sapphirelaserswereused.ThelasersystemconsistedofanArionlaserwhichpumpedtwocwTi:sapphirelaserstogeneratetunableradiationbetween730and1070nm.Theradiationfromlaserswascombinedusingabirefringentbeamsplitterandusedasthefundamentalwavelengthsforthesum-frequencygenerationexperiment.ThewaveguidesonthesamplewerefirstinvestigatedinSHGexperiementswherethelaserwavelengthwastunedoverthephase-matchingpeakandtheSHintensityrecorded.ThewavelengthofthefundamentalandtheSHwavewasmeasuredwithawavemeterandamonochromator,respectively,andthepowersweremeasuredwithcalibrateddetectors.FromthewidthandshapeoftheSHcurveswereofhighhomogeneity,sothefullwaveguidelengthwasutilized
forconversion.BoththemodeatthefundamentalandattheSHwavelengthswereapproximatelycircularinalwaveguides.Atdegeneracy,thesecond-harmonicwavelengthwas394,425,454,and480nmforthe3,4,5and6mmperiodwaveguides,respectively.Agoodagreementwasobtainedbetweenthemeasuredandthecalculatedphase-matchingwavelengths.
TheSHGmeasurementswerefollowedbySFGexperiments.Here,bothlaserswerefirsttunedtoSHGandthenthewavelengthofthelaserstunedinoppositedirections,maintainingthephasemathcing.Thetuningrangewaslimitedbythewavelengthregionthelaserscouldcover.Figure5.35showsthetuningcurveforthefourperiods.Theaccuracy(0.1nm)ofthemonochromatorwasfoundtobeinsufficienttouseintheplotofthetuningcurve,andtheSFGwavelengthwasthereforecalculatedfromthefundamentalwavelengths,Eq.(5.48).ThelargesttunabilityoftheSFwavelengthwas3nmobserved
Page255
forthe5mm-periodwaveguide.Thiswaveguidealsogavethehighestoutputpowerintheblue,2.7mWofthe454nmradiation,generatedwith149mWat942nmand106mWat875nmcoupledthroughthewaveguide.Thefundamentalpowersmeasuredattheoutputofthelaserswereapproximatelythreetimeshigher.Normalizedattheoutputofthewaveguide,thiscorrespondstoaconversionefficiencyof84%W-1cm-2or17%/W.ThehighestefficiencyforSFGwas112%W-1cm-2,obtainedwiththe4mm-periodwaveguide,butlowertotal-fundamentalpowersinthiscaseresultedinlowerSGFoutput.
5.4SecondharmonicgenerationintheformofCherenkovradiation
Enhancedfluxdensityoflightandlargeinteractionlengthexplainanincreasinginterestinnonlinearopticaleffectsinopticalwaveguidestructuresforrealizingefficientfunctionaldevices(StegemanandStolen1989).Amongtheseeffects,thesecond-ordernonlineareffectpermitsobservingfrequencyconversionsuchasSHGandsum-ordifference-frequencygeneration.Inparticular,SHGinopticalconfinementstructuressuchasopticalfibreschannelwaveguideswillfindmanyapplicationsthatrequireaminiaturizedvisiblelightsourcewithlightcoherence.Anefficientguided-waveSHGdevicestructurewhichcanextractbluelighthasbeendemonstrated.ItemploysaCherenkovradiationschemetoachievephasematchingata0.84mmwavelengthfromaGaAslaserdiode(TaniuchiandYamamoto1987,SanfordandConnors1989),andbluepowerontheorderof1mWfrom50to100mWinputhasbeendemonstratedwitha6mmdevicelength(TaniuchiandYamamoto1987).Inthisscheme,thephasematchingconditionbetweenthefundamental(pumping)guidedmodeandthesecondharmonicradiationmodecanbeautomaticallysatisfiedbyadjustingthewaveguideparameters(Tienetal1970).However,thesecondharmonicpowergenerateddependsontheparametersinacriticalfashion,andthereforeitisofgreatimportance
todetermineoptimumparametersfortheguidestructure,crystallineorientation,refractiveindex,etc.(SanfordandConnors1989;HayataandKoshiba1989;Hayataetal1990).
AnotherpossibilityforperformanceofCherenkovtypeSHGdevicesbymeansoftailoringthetransverse(ydirection)nonlinearsusceptibilityprofileintheguidingregionisexamined.Moreradiationefficiencyisexpectedasaresultoftheincreasingoverlapbetweenthenonlinearpolarizationwave(dividingsource)andthegeneratedSHwave(drivenfield)inanalogywiththebeamsteeringtechniqueinaphased-arrayantenna.Linearanddomain-inverted(poled)channelsembeddedinanonlinearsubstrateareconsidered,andtheSHGefficiencyforeachcaseiscomparedwiththatforaconventionalnonlinearchannelwithoutdomaininversion(SanfordandConnors1989).NumericalresultsobtainedbyawaveopticstreatmentshowthataremarkableenhancementoftheSHGisrealizable,particularlywithadomain-invertedchannel.
TheschematicillustrationsareshowninFig.5.36,wherenisthebuilt-inrefractiveindexdependentonthewavelengthanddisthethicknessofthechannel.InFig.5.36bthevalueofthechannelwidth(W)isimplicitlyincludedthroughanapplicationofaneffectiverefractiveindexapproximation
Page256
Table5.8ParametersofLiNbO3waveguidesn1=n'1(air)
l,mm n2x n2y n2z n3x n3y n37
0.84LDpumping 2.373 2.293 2.373 2.25 2.17 2.25
1.06YAGpumping 2.352 2.276 2.352 2.232 2.156 2.232
l,mm n'2x n'2y n'27 n'3x n'3y n'32
0.84 2.601 2.491 2.601 2.411 2.301 2.411
1.06 2.514 2.425 2.514 2.324 2.235 2.324
(HayataandKoshiba1989;HayataandSugawara1990).HayataandYanagawa1990)thusconsidertheslabwaveguideasshowninFig.5.36binwhatfollows.
Here,caremustbetakentoemploythisreducedgeometry.AlgebraicmanipulationofMaxwell'sequationswithnonlinearpolarizationyieldsthefollowingequationforthey-polarized(TM)mode(HayataandKoshiba1989):
whereh'xistheslowlyvaryingenvelopeofthelateralcomponentoftheSHmagneticfield,e=[ex,ey,ez]Tisthepumpingelectricfield(Tstandsfortransposition), ,bisthepropagationconstant,k0isthefree-spacewavenumber, , ,Z0=337W,[e']isthelinearrelativepermittivitytensorwhosediagonalelementsaree'x,e'y,ande'z[d']isthesecondordernonlinearopticaltensor,andtheprimeandthehatdenoterespectivelythequantityforthesecondharmonicwaveandaunitvector.Inthederivationofequation(5.50),theslowlyvaryingenvelopeapproximationhasbeenemployedandpump
depletionhasbeenneglected,thatis, .
ConsidertheZ-cutLiNbO3(caxis/yaxis)asasubstratematerial.WaveguideparametersusedintheanalysisareasinTable5.8;theexplicitvalueof[d']hasbeenobtainedfromtheTableshownbyYarifA.Yehp(1984).TheTM0modeisconsideredasapumpingconditionontoz=0.
Asanonlinearsusceptibilityprofileinthefilm(|y|<d/2;thefilmcentreisaty=0),Hayataetal(1990)consideredthreecases:(A)linearfilm,i.e.alltheelementsin[d']vanishanywhereinthefilm;(B)nonlinearfilmwiththesamesignofnonlinearsusceptibilityinthesubstrate;and(C)domaininvertedfilmwithoppositesignofnonlinearsusceptibilityinthesubstrate,thatis,[d']film=-[d']substrate.Occurrenceofthecasesconsideredabovedependsontheactualfabricationprocess.Forinstance,case(A)maybeobservedin
Page257
Fig.5.36Schematicsofproblem(a)3Dview;(b)sideview(Hayataetal1990).
Fig.5.37TotalSHpowerversusguidethickness(w=2.0mm).Solid,dottedanddashedlinesindicatedomain-inverted[case(C)],linear[case(A)],andnonlinearchannelwithoutdomaininversion[case(B)],respectively.(a)l0=0.84mm,
(b)l0=1.06mm(Hayataetal1990).
asituationinwhichdegradation(damage)oftheidealcrystallinestructureinthechannelcannotbeignored.Ontheotherhand,case(C)canberealizedbyadequatelypolingacertainkindofferroelectriccrystalsuchasZ-cutLiNbO3(Limetal1989;ThaniyavarnandMiyazawa1979).
Figure5.37showsacomparisonbetweenthesecases,wheretheSHGefficiencyisdefinedbyP'/P2withP'asthesecondharmonicpowerandPasthepumpingpower.Theseresultsareobtainedfromastationaryanalysis inequation(5.50)],withwhichtheoptimumgeometryoftheguideispredictable.Thevalidityofthisapproachhasalreadybeenensuredintheliterature(Nodaetal1975;Tienetal1973)throughacarefulcomparisonwiththeresultsobtainedbya
moreinvolvednonstationaryanalysisandwithexperimentalresults.Thesharpminimaoccurringinthefiguresareduetointerferenceeffectsacrossthefilmforgrazinganglesofthesecondharmonicwave(Tienetal1973).Itisevidentfromtheseresultsthattheutmostsecondharmonicpowerisobtainableincase(C).Inthevicinityoftheoptimumgeometry,d=0.35mmforl0=0.84mmandd=0.53mmforl0=1.06mm,theefficiencyofcase(C)isanorderofmagnitudegreaterthanthatofcase(B)(i.e.theorderof10mWfroma50-100mWinputwithl0=0.84mmanda5-10mmdevicelength).ThissignificantenhancementoftheSHGcanmathematicallybeattributedtotheincreasingoverlapquantifiedbytheintegraloftheproductbetweenthenonlinearpolarizationtermandthedesiredsecondharmonicmodepropagatingalongtheCherenkovangle.Inordertoprovidephysicalinsightintotheresults,Fig.5.38givesschematicillustrationsfortherelationshipbetweenthenonlinearpolarizationwave(source)andthe
Page258
secondharmonicwave(radiation).Itshouldbenotedthat1)aconsiderablepartofthenonlinearpolarizationwavepenetratesthesubstrateasaresultoftheextendedevanescenttailofthepumpfieldand2)thewavefrontofthesecondharmonicwavetiltswiththeCherenkovangleagainstthatofthenonlinearpolarization(z-direction).AsisseenfromFig.5.38,secondharmonicwavesgeneratedatdifferentlocations(oneinfilmtheotherinsubstrate)alongthey-directionaddpartiallyoutofphaseandcanceleachotherintheconventionalgeometry(Fig.5.38a),whereastheyaddinphasebymakingthefilmdomaininverted(Fig.5.38b).Thelinearfilm(case(A))isintermediatebetweenthetwoextremecases.Itisinterestingtonotethatonecanfindananalogousmechanismtobeamprofilinginaphased-arrayantennasysteminwhichtherelativephasedifferencebetweenadjacentdipoleelementsistailoredsothatinterferenceisinphaseforthedesireddirection.Thisfactindicatesthattheuseofhomogeneouslydomain-invertedchannelisveryeffectiveinenhancingCherenkov-typeSHGefficiencyinLiNbO3opticalwaveguides.
5.5Electro-opticeffectsinopticalwaveguides
Electro-opticcoefficientsinwaveguidesofsolidsolutionsoflithiumniobatetantalateweremeasuredbytheinterferentionalmethod.TheschemeofmeasurementsispresentedinFig.5.39.
Acoherentlightbeamisseparatedbyaseparationprismintotwoindependentlightbeamseachofwhichisfedintoalightguidebytheprism
Fig.5.38SchematicillustrationsforexplainingtheenhancedSHG,NLPandSHareabbreviationsfornonlinearpolarizationandsecondharmonic,respectively.(a)Conventionalgeometry(caseB),
(b)domain-invertedfilm(casec)(Hayataeta11990).
Fig.5.39Schematicillustrationofadeviceformeasuringelectro-opticcoefficients:
1)radiationsource;2)l/4-plate;3)focusinglens;4,6)input-outputprismsforopticalradiation;5)investigatedsample;7)objective;8)screen;
9)microscope;10)controlelectrodes;11)mounting.
Page259
method.Oneofthebeamsisledintheinterelectrodegapofthesystemofcoplanarelectricguides(10),thesecondbeampropagatesoutsidetheelectrodesysteminthedirectionparalleltothefirstone.Theoutputofopticalradiationfromthespecimenisrealizedusingthesecondprism(6).Thecollectinglens(7)providesconvergenceofbothlightbeamsintheplane(8)inwhichinterferenceisobserved.
Whencontrolvoltageisappliedtotheelectrodes,therefractiveindexofthemodechangesbyaquantityDnproportionaltotheelectro-opticcoefficientsofthelightguidematerialandtotheappliedvoltage.Thisleadstoachangeoftheopticalpathlengthofthelightbeampropagatinginafilmneartheelectrodes.ThischangeisequaltoDL=Dnl,wherelisthelengthofthecontrolelectrodes,whichinturninducesadisplacementoftheinterferencepatternbyMfringes(DL=Ml).
Inthecaseoflinearelectro-opticeffect,thechangeoftherefractiveindexofagivenmode,Dn,isgivenbytheexpression
wherenistherefractiveindexofthefilmforagivenlightmode,rijistheelectro-opticcoefficient,Ezisthelongitudinalcomponentoftheelectrodefieldinthefilm.
Inthecase ,del>2s,wheredelistheinterelectrodedistance,histhefilmthickness,sishalfwidthofthelightbeam,thequantityEzisdeterminedbytheexpressionEz=2U/pdel(Uisthevoltageappliedtotheelectrodes).SincethequantityAncanalsobeexpressedas
,thevalueoftheelectro-opticcoefficientisdeterminedbytheexpression
Whenlightpropagatesinthex-directionalongtheY-cutofLiNb1-yTayO3,wehaverij=r33.
Thevoltageappliedtothestructureofelectricguidesischangedinthecourseofmeasurements,andthedisplacementMiscontrolledvisually.IftoameasuredMtherecorrespondstheappliedvoltageU,thenknowingthelightwavelengthl,theelectrodelength ,theinterelectrodegapdelandtheeffectiverefractiveindexofthemode,onecancalculatetheelectro-opticcoefficientusingtheexpression(5.52).
Investigationshaveshownthatinepitaxialstructuresthathavenotbeenmadesingle-domaintheelectro-opticcoefficientsaresmall,butthesensitivityofthedevicewasnothighenoughtomeasurethesecoefficients.Afterfilmsarepolarized(andthusbecomesingle-domain),theirelectro-opticcoefficientsincreasesignificantly.Measurementsofthecoefficientr33foranumberofsingle-domainspecimenshaveshownthatitsvaluevarieswithintherange(15-24)×10-12m/V,whichisclosetothevalueofthiscoefficientforlithiumtantalate.
Page260
Thedependenceofinducedbirefringenceontheelectricfield(3×102-5×105V/m)islinearandisindicativeofahighpolarizationofheteroepitaxialfilms.
Theelectro-opticconstantsofproton-exchangedLiNbO3opticalwaveguidesweremeasuredbyMinakataetal(1986)bymeansofphasemodulationtechnique(Yariv1985)633nmlaserlightwasfedintothewaveguidefromtheendfacet,andthepropagationmodewasthefundamentalTM-likemode.Therelevantelectro-opticconstantwasr33.Themodulationcharacteristicsweremeasuredbyapplyinga50MHzsinusoidalsignalviaelectrodes.ThemodulationspectraweredetectedbyusingthescanningFabry-Perotresonator.Figure5.40showstheexperimentalresults.Thepowerratio(orpeakvalueratio)ofthefirstsidebandfrequencytothecarrierfrequencywasgivenbytheBesselfunctionasaparameterofamodulationindexuasfollows:
wherel=633nmand anddarecoplanarelectrodelengthandthegap,respectively.G,determiningthemodulationefficiency,isgivenbythefollowingequation(Minakata1978):
whereE(yz),Ez(yz)areanopticalelectricfieldandanappliedelectricfieldofthezcomponent,atpointP(yz)inthecrystal;x,y,zarethecoordinates.Aguidedwavepropagatesalongthex-axis.They-andz-axesareparallelandperpendiculartothesubstratesurface,respectively.E0=V/dandEGistheaverageappliedelectricfieldviaelectrodes,whichiscalculatedbythesuccessiveoverrelaxationmethod(Minakataetal1978).ThecalculatedGvaluewas0.32forthetestsamples.InFig.5.40,opencirclesareexperimentaldata,thethreesolidlines,asaparameterofr33,aretheoreticalcurves.When
r33=3.3×10-12(m/V),thetheoreticalvaluesareingoodagreementwiththeexperimentalones.Thusitisclearthatthevalueofr33reducedtoone-tenthincomparisonwiththevirgincrystal.
Figure5.41showstherelationshipbetweentheLi%,thestrainDc/c,themeasuredr33,andtheDnequotedfromDeMichelietal(1983).ItisclearthatstrainDc/candDnearereduced,andr33isincreasedwithanincreaseinLi%.
5.6Lightresistanceoflightguides
Theopticalqualityoflightguidesisbasicallycharacterizedbytheopticallossfactorandbyradiationresistance.Theradiationresistancemustbetakenintoaccountinworkwithlasersofpowerhigherthan1mW.Atthisandhigherpower,itsdensityinthelightguidecanreachthevalueof105-106
Page261
Fig.5.40Measuredmodulationspectraandphasemodulation
characteristics;opencirclesareexperimentaldata,threesolidlines,asparameterr33,aretheoreticalcurves
(Minakataetal1986).
Fig.5.41RelationbetweenLi%,strainDc/c,
measuredr33,andDnequotedfromDeMichellietal1983(Minakataetal1986).
Wcm-2atwhichnonlinearandthermaleffectsaffecttherefractiveindicesofthematerial.
Asisknown,thedamageofthesurfaceofoxygen-containingcrystals(LiNbO3,LiTaO3,BaTiO3,etc.)possessessomespecificfeatures:thedamageisduetoaccumulationwhichlowersthelightresistanceof
thesurfaceandleadstoacharacteristictemperaturedependenceofthedamagethreshold.Zverevetal(1977)hypothesizedtheexistenceinLiNbO3ofanoxygen-depletedabsorptionsurfacelayercontainingtwotypesoftrapslinkedwithoxygenvacanciesandwithreducedNb4+.Anincreaseofabsorption,frompulsetopulse,inthesurfacelayerisduetoaccumulationofelectronsonshallowtrapswhoseabsorptioncross-sectionislargerthanthatofdeeptraps.Anincreaseoflightresistanceofthesurfacewithincreasingspecimentemperatureiscausedbytheemptyingofshallowtrapsforthetimebetweenlaserpulsesduetotheirthermoionization.
InvestigationsofradiationresistanceofLiNbO3filmsandtheirsubstrateshaveshownthatthemechanismsoftheirdamageareabsolutelyidentical.
AQ-switchedgarnet-neodymiumlaser(l=1.06mm,pulseduration10
Page262
Table5.9DamagethresholdvaluesforsurfacesofepitaxialLiNbO3filmsondifferentsurfaces
No.Material Breakdownthreshold(GW/cm2)
Accumulationthreshold(GW/cm2)
Maximumnumberofflares
1 LiNbO3 3.2 0.45 10-15
2 LiTaO3 12 4.1 8-12
3 LiNbO3/LiNbO3 6.5 0.25 50
4 LiNbO3/LiTaO3 6.1 1 30-40
5 LiNbO3(Fe)/LiTaO3 4.5 0.3 50
ns)wasusedasaradiationsource.Theradiationwasfocusedbyashort-focuslens(f=11mm)ontofilmspecimensunderinvestigation.Theneckdiameterwas15mm.Thelaseroperatedinasingle-pulseregime,pulserecurrenceratebeingequalto2Hz(Khachaturyan1980).
Table5.9presentsaveragedvaluesofthedamagethreshold,aswellasthedamagethresholdvaluesdeterminedbytheaccumulationeffectbothinfilmsthemselvesandintheirsubstrates.
Itwasestablishedthatthethresholdintensityofthedamageofalithiumniobatefilmincreasedseveraltimesascomparedwithabulkcrystal.BreakdownthresholdsofahomoepitaxialLiNbO3filmandofaheterolayeronLiTaO3donotdiffermuch,andanintroductionofironimpurity(upto0.5at.%)lowersthethresholdby .
Analysisoftheresultsobtainsshowsthatthethebreakdownthresholdoflithiumniobatefilmsisdeterminedbyperfectionofthespecimenstructureandsurface.Zverevetal(1977)reportedthepresencein
lithiumniobatecrystalsofasurfaceabsorptionlayerofabout2mmthick,buttheydidnotdescribethemethodsofsamplesurfacepreparation.Asisknown,mechanicalpolishingofthesurfaceleavesadamagedlayerofabout1mm.Mirror-smoothsurfacesofepitaxialfilmsrequirenoadditionaltreatment.Theincreaseinthedamagethresholdofthefilmisevidentlyduetothelackofadamagedsurfacelayeronit.
Investigationoftheeffectoflaserradiation(l=1.06mm)uponlithiumniobatefilmshasshownthatat'under-threshold'radiationintensityahighlydense( attheclustercentreand105-106Wcm-2ontheperiphery)clusterofmicrodomainsoccursataplaceofirradiation.Whentheirradiatedpositivez-planeundergoesselectiveetching,becauseoftheirhighdensitytheetchingholesmergetoformatypicaltracery.Clusterareasdecreasewithdecreasinglightintensity.Thesevariationsintheclusterareasarehoweverinsignificant,andthediameteroftheclusterismainlydeterminedbythediameterofthefocalspot.
Thisphenomenoncanbeinterpretedasfollows(LevanyukandOsipov1975;HolmanandGressman1982).LevanyukandOsipov(1975)haveshownthe
Page263
possibilityofaphotoinducedchangeofspontaneouspolarizationinferroelectrics.Whenaregionofacrystalisexposedtolight,polarizationreversalinthisregionleadstotheappearanceofadepolarizingfieldwhich,actingonfreecarriersthatinteractunderimpurityionization,causestheoccurrenceoffreechargeattheboundariesofthisregion.Assoonasthelightisoff,thephotoexcitedstatesofimpuritiesrelax.Thespacechargemayremainforalongtimesinceitsonlyclean-outchannelinalow-conductivitycrystalisatemperature-inducedejectionofcarrierstrappedondonorsintotheconductionband,whichishardlyprobableatalowtemperature.Thus,whenaspecimenisexposedtolight,spontaneouspolarizationisreversedandthechargedistributionoverthebulkis'frozen'afterthelightisoff.Thismechanismdoesnotobviouslycorrespondtotheobservedphenomenonsincetheoccurrenceofmicrodomainsimpliesadecreaseofthetotalpolarizationintheexposedregion,andthe'frozen'volumechargeisclosetozero.Moreover,thepolarizationreversalregionmustbestrictlylimitedbytheexposedregion,whereastheradiation-inducedmicrodomainsarealsoobservedoutsidetheexposedregion.
Themechanismofoccurrenceofmicrodomainsduetoelasticstrainisobviouslyclosertotherealprocess.Asmentionedabove,localstraininaspecimenleadstotheappearanceofatenseregionofmicrodomainclusters.Whenahighlyintenselaserbeamisused,athermalshockisobserved.Becauseofashortradiationtreatmenttimeandasmallheattransfercoefficient,thisthermalshockcausesahighlocaltensionand,asaconsequence,theappearanceofmicrodomains.Thegeometryoftheobservedpatternisdeterminedbythecrystalsymmetry.Theclusterareaisdeterminedbythediameterofthelightspot.Thislimitationisnotstrict,andathighradiationintensitiesthetensionnearthespotmayprovesufficientfortheoccurrenceofmicrodomains.
Wehavecarriedoutcomparativestudiesofopticaldamageofsingle-modelightguidesformedusingautodiffusion,metaldiffusion,ion-exchangedoping(Goncharenko1967)andliquid-phaseepitaxy.Theoutputpowerwasmeasuredasafunctionofexposuretimeandoftheinputlightintensity.Thelatterwasvariedwithintherangeof0.5÷7mW,andtheobservationtimereached200h.Allthespecimensexhibitedloweringoftheoutputsignalwithsaturation.ThedependenceofoutputlightintensityontheinputintensityisdepictedinFig.5.42whichshowsthatTi:LiNbO3lightguidespossessthelowestopticalstrengthandepitaxialonesthehighest.
Experimentsonlightresistancesuggestthattheopticalstrengthoflightguidesisfirstofalldeterminedbytheconcentrationoftrapstheroleofwhichcanbeplayedbyoxygenvacanciesinthecrystallattice(particularlyforlightguidesformedinavacuum).Importantisalsotheimpurityionizationenergyvariationsinacrystal,trapdepthandequilibriumconcentrationshiftinoxidizedandreducedformsofactiveimpurities.JudgingbytheresultsreportedbyHolmanandGressman(1982),thelowlightresistanceofTi:LiNbO3isexplainedbytheappearanceinthelightguidestructureofaspecialtypeoftrapsforphotoinducedelectron-holepairsoccurringduetoanuncompensatedchargeexchangeunderthe substitutioninthecrystallatticesitesinthecourseofdiffusion.
Page264
Fig.5.42DependenceofthepowerlossT,atthesaturationlevel,ontheinputpowerPininlightguides:1)LiNbO3:Ti;2)LiNbO3:Tl;3)out-diffused;
4)epitaxial.
5.7Photorefractivepropertiesoflightguides
Theinterferometricmethodisusedtoexaminephotorefractivepropertiesofepitaxialstructures,namely,refractiveindexchangesundertheactionofphotoactiveradiation.
Thismethodisrealizedinthesameschemeasthestudyofelectro-opticpropertiesoffilms(seeFig.5.39).Thepartofthewaveguidebetweenelectrodesisexposedtolaserradiationperpendiculartotheplaneofthewaveguidelayer.Argon(l=488,514nm;P=6W)andkrypton(l=647nm;P=8W)laserswereusedforphotorefractiverecording.
ThevaluesofinducedrefractiveindexchangeDne(t)weredeterminedfromthenumberofdisplacedfringesMintheinterferencepatterngivenbytheformulae
Theestimatesofthemaximumlight-inducedrefractiveindexchangeshowthatwithintheexperimentalerror theDnevalueispracticallyindependentofthewavelengthofrecordinglightand
(Dne)maxmakesup .Thelimitingvalue(Dne)maxdoesnotpracticallydependontheLi(Nb,Ta)O3filmcompositioneither.
Thechange(Dne)maxisaresultofelectro-opticeffectinthebulkcrystal.Fromitsvalueonecanestimatethestationaryvalueoftheinternalelectricfield:
Usingthevaluesne=2.187,r33=2×10-11m/Vand(Dne)st=2×10-3atthewavelengthl=632.8nm,weobtainthelowerestimateoftheexternalelectricfieldinthefilm,Est~191kV/cmwhichagreeswiththevaluesobtainedforbulkmaterials(188kV/cmforLiNbO3and250kV/cmforLiTaO3(Schwarz1986)).
Page265
TheobtainedEstvalueisindicativeofahighelectricresistanceoftheinvestigatedepitaxialstructuresandisnotlimitingsincethevalue(Dne)maxthatcanbereachedinexperimentsisrestrictedbyelectricbreakdownsalongthefilmsurface(whichleadstoaspontaneousloweringofDne).
Assumingthelightabsorptioncoefficientalayerintheepitaxiallayertobeclosetotheabsorptioncoefficientinthesubstrate(a<5cm-1forl=488nmanda<1cm-1forl=647nm),onecanestimatethephotorefractivesensitivitySph:
whereWistheabsorbedenergy,Iistheincidentlightintensity,tistheexposuretime.
Substitutingtypicalexperimentalvalues forl=488nm,W/cm-2andt=15min,weobtain
Theobtainedvalue(l=0.488m)isanoverestimation.Sinceforlithiumniobatetheboundaryoffundamentalabsorptionliesatl<0.4mmandforlithiumtantalateforl<0.3mm(ed.byShaskol'sky1982),onemayassumethataLi(Nb,Ta)O3filmhas,infact,alaycr(l)>lsubstr(l)for>0.3mm.
TheSvaluesobtainedforLi(Nb,Ta)O3filmsareincloseagreementwiththevaluesofphotorefractivesensitivityoflithiumniobate,S=2×10-8,andlithiumtantalate,S=6×10-11cm2/J(Kuz'minov1982),andindicatethatthewaveguidestructuresobtainedpossesshigheropticalresistancethanlithiumniobatestructures.
5.7.1Holographicformationofgratingsinopticalwaveguidelayers
Theformationofthickphase(Bragg)gratingsinopticalwaveguidesbyelectro-optic(Hammeretal1973)oracousto-optic(Kuhnetal
1970)effectsiswellknown.Suchgratingsmayfindapplicationinintegratedopticsdevicessuchasswitches(Kenanetal1974;TaylorandYariv1974),modulators(TaylorandYariv1974),mirrors,beamsplitters,etc.Gratingsthatareformedphotorefractively,thatis,throughchangesintheindexofrefractionoccurringwhenamaterialisilluminatedwithlightcapableofalteringthedistributionormagnitudeofthepolarizabilitiesofitsconstituents,appeartoofferthefollowingadvantages:(i)thegratingspacingcanbesmallenoughsothatarbitrarilylargediffractionanglescanbeachieved;(ii)therefractiveindexchangesproducedcanbequitelarge,consequentlyefficientdiffractiongratingsarepossible;and(iii)noexternalstructuresareneededandnooperatingpowerisrequired.
Woodetal(1975)haveproducedsuchgratingsbyintersectingguidedcoherentbeamsof0.488-mmwavelengthinwaveguidesformedonthesurfaceofLiNbO3crystalsbyeffusionoflithiumandinawaveguideformedonthesurfaceofaLiTaO3crystalbyin-diffusionofavapour-depositedlayerofNb,
Page266
bywhichmeansavarying-compositionlayerofLiTa1-xNbxO3wasformed.Formingthegratingthiswayismuchsuperiortousingexternalbeamsintersectingatthewaveguidelayer.Theprincipaladvantagesofusingintersectingguidesbeamsarethattheavailablewritingpowerdensitiesarehigh,thepropergratingorientationisachievedautomatically,andthegratingislocatedintheregionofmaximumenergydensityoftheguidedwave.
AschematictopviewoftheexperimentalarrangementusedtowriteanddetectthegratingsisshowninFig.5.43.TheLiNbO3orLiTaO3slabandtherutileprismcouplersarerotatableasaunitabouttheaxisAAwhichliesintheslab.Thisdegreeoffreedomisrequiredfortheadjustmentofthecouplingangle.Thegratingiswrittenbythephotorefractiveeffectutilizingthe0.488µmlineonanargon-ionlaser.Thepowerdensityinthewaveguideisestimatedtobeabout1W/cm2.Writingtimesforthegratingswereinthe1-10minrange,dependingupontheironcontentofthesample.
Afterthegratingwaswritten,mirrorsM1andM2wereusedtoindependentlyadjustthedirectionandpositionofthe0.633µmbeamtomaximizetheamountof0.633µmlightdiffractedbythegrating.Sincetheacceptanceangleofthegratingis mrad,thisadjustmentiscritical.
ThegratingsineffusedwaveguidesweredoneusingY-cutcrystalsofundopedLiNbO3heatedinoxygentoformLi-deficientsurfacelayerswithhigherextraordinaryrefractiveindicesthanthebulk.SuchlayerscanbeproducedtosupportanywherefromonetoseveralhundredTEmodes;TMmodesarenotguided.Whileitwasnotdifficulttoformgratingsinsuchlayers,andwhileadiffractionbeamcouldbeobserved,itsintensitywasverylow.Thisappearedtoresultfromthelowmaximumdiffractionefficiency(generallyunder1%)obtainableinundopedorverylightlydopedLiNbO3.
Thehighestdiffractionefficiency(definedaspowercoupledoutinthediffractedbeamdividedbysumofpowerscoupledoutinboththediffracted
Fig.5.43Schematicofapparatususedtowriteanddetectgratingsina
slabwaveguide.Thegratingvectorisparalleltothec-axisoftheLiNbO3slab.Allopticalbeampolarisationsareparallelto
thesurfaceoftheslab.PinandPoutareprismimputandoutputcouplers(Woodetal1975).
Page267
andundiffractedbeams)inaneffusedguidewasobtainedinamultimodeguideinheavilyiron-doped(1000ppminmelt)LiNbO3.Aninterferencephotographshowedthatthisguidehadanoverallextraordinaryindexchangeofabout0.004andadiffusionlengthofabout140µm;itshouldsupportaround60TEmodesatthe0.488µmhologramwritingwavelength(KaminowandCarruthers1973).Adiffractionefficiencyof52%at0.488µmwasattained.
GratingformationwasalsostudiedinashallowguideproducedbyheatingaLiNbO3platefor14minat1118°C.Suchaguideshouldsupportonlyabout5TEmodesat0.633µm;individualmodescouldnotberesolvedexperimentally.Thisplatewasfromaboulegrownfromameltdopedwithjust50ppmiron,andthemaximumdiffractionefficiencyobtainableinthebulksample(withoutthewaveguide)foragratingwrittenwith0.488-µmlightandreadat0.633µmwas2.4%.Themaximumdiffractionefficiencywasobtainedwiththeread-beampolarizationparalleltothecaxis,thesameorientationasintheguideTEmodes.Themaximumdiffractionefficiencyat0.633µmforagratingwrittenwith0.488-µmlightinthewaveguidewas3.1%greaterthanthatobtainableinthebulkcrystal.Neitherthedifferenceingratingthickness(extentinthedirectionoftheincidentbeam)northedifferenceintheanglebetweenthewritingbeamsissufficienttoaccountfortheobserveddifference.Possiblythehigherpowerdensityintheguidedbeamledtoahighermaximumrefractiveindexchange.
Shallowwaveguidelayerswithlargeindexchanges,supportingonlyafewmodes,maybeproducedbydiffusingNbintoLiTaO3(seechapter1).
TEmodespropagatingalongtheaaxiswereusedtowrite(at0.488µm)andread(at0.633µmandat0.488µmbyblockingonewritebeam)agratinginthewaveguide.Anefficientgratingwithaperiod
of1.4µmformedreadilydespitethepresumablyunpoledstateofthesample.Themaximumdiffractionefficienciesobtainedwere28%at0.633µmand65%at0.488µm.Forcomparison,nodiffractionefficiencyabove1.2%couldbeobtainedateitherwavelengthforgratingsformedthroughoutthebulkLiTaO3crystal,eitherwithorwithouttheinfusedNblayeratthesurface.
Analternativelinearphotorefractivetechniqueistheuseofshort-wave-lengthlighttoformthehologramsandlong-wavelengthlight,forwhichthephotorefractivesensitivityisnegligible,astheoperatingwavelength.Thistechniqueissatisfactoryonlyforsimpleplane-gratinghologramssincecomplexthickhologramssufferlargelossesinfidelityandefficiencyifthereadandwritewavelengthsdiffer.
Aholographicwritingtechniquewhichhastheusefuladvantagesofavoidingdestructivereadout,producingstableholograms,andretainingthelowopticallossofout-diffusedwaveguidesinundopedcrystalsisbasedupontheuseofmultiphotonabsorption(vanderLindeetal1974)forinitiatingthephotorefractiveprocess.Veberetal(1977)havedemonstratedthathologramsmayberecordedbyatwo-photonabsorptionprocessinout-diffusedLiNbO3waveguidesbyintersectingtwoguidedwaves,andthattherequiredenergyandintensityarereadilyachievedinthewaveguideusingcommerciallyavailablelasers.
Page268
TheabsorptionofabeamoflightofintensityI(W/cm2)inatwo-photonprocessisdescribedby
wherea2isthesecond-orderabsorptioncoefficientandxisdepthinthecrystalmeasuredfromthesurfaceuponwhichthebeamisincident.Theindexchangeassociatedwiththephotorefractiveeffectisproportionaltothenumberofelectronsexcitedintotheconductionband.Forthetwo-photonprocess,thisnumberwillbeproportionalto(1/2)N,whereNisthenumberofphotonsabsorbedpercm3.Theindexchangeisthen
whereSisaproportionalityconstantcharacteristicofthematerialandthegeometry.Foranopticallythinsample,Dnisnotafunctionofxand
wheretisthetimeduringwhichthesampleisirradiatedandhnisthephotonenergy.IftheirradiationoccursintheformofMequalrectangularpulsesofdurationDt,then
whereallconstantshavebeenabsorbedintok.Thetwo-photonprocessisthenindicatedbyaquadraticdependenceofDn/MuponI.
ThisquadraticdependencewasobservedusingaNd:YAGlaserwithanintercavitydoublerwhichproduced140nspulsesof0.53µradiation.Afterreflectionfromawedgebeamsplitterthelaseroutputwasprismcoupledintoanout-diffusedwaveguideinthesurfaceofanundopedLiNbO3slab.ThevalueoftheinducedAnwasmonitoredbymeasuringthediffractionefficiencyoftheholographicgratingformedinthebeamoverlapregion.Thedatashowninthelog-logplotin
Fig.5.44clearlydisplaythequadraticbehaviourindicativeofthetwo-photoneffect.Fromthemaximumpowerincidentuponthecouplingprismof2kWandestimatesofthecouplingefficiencyandeffectivewaveguidethickness,onecanestimateamaximumpowerdensityof106W/cm2inthewaveguide.Diffractionefficienciesofseveralpercentwereobservedwithnosignofsaturation.Comparisonoftheseresultswiththedata(vanderLindeetal1974)obtainedusingthesamewavelengthbutinabulkconfigurationshowsafargreatersensitivityforthewaveguidecase.Thediscrepancyislargerthancanbeaccountedforbyexperimentalerrorsorerrorsinestimatingthepowerdensityinthewaveguide.Thediscrepancymaybeduetovariations
Page269
Table5.10DiffractionefficiencyhandphotorefractivesensitivityaSofplanarTi-diffusedwaveguidesat0.458µm(Glass,Kaminow,Ballman,Olson,1980)
Inputpower(µW)
Exposuretime(s)
EnergydensityEinguide(J/cm2)
h h/E(cm2/J)
(cm2/J)
17 120 20 0.011 0.0052 1.3×10-7
120 20 24 0.1 0.013 3.0×10-7
250 10 25 0.1 0.016 3.0×10-7
Fig.5.44Log-logplotofDn/pulseversuspowerdensityforagratingwritteninanout-diffusedLiNbO3waveguidewithpulsed0.53µradiation.Thesolidlinehasaslopeof2.Thegratingspacingis0.55µ
(Vebereta11977).
inducedbytheout-diffusionprocessortoothercompositionaldifferencesinthesamplesusedforthetwosetsofmeasurements.
5.7.2PhotorefractiveeffectinplanarTi-diffusedguides
Theformationofelementaryhologramshasbeendescribedaboveforout-diffusedLiNbO3waveguides(Glassetal1980).AsimilarmethodisemployedusingaTi-diffusedplanarguide.Thetechniqueinvolved
couplingtwobeamsintotheplanarguide,asshowninFig.5.45sothattheyformathickhologrambymeansofthephotorefractiveeffect.Themagnitudeoftheindexchangecanbemeasuredfromthediffractionefficiencyofthehologram(Kogelnik1969)
where istheinteractionlengthandqistheanglebetweenthetwobeams.Thewritingbeamswerecoupledinandoutofthewaveguideusingasingleprism(Saridetal1978),andthediffractionefficiencywasprobedwithaHe-Nebeambyrotatingtheentireprism-waveguideassemblytoobtaincouplingatdifferentwavelength.
Hologramscouldnotberecordedat0.633µm,with300µWofoptical
Page270
Fig.5.45Experimentalarrangementformeasuring
photorefractivesensitivityofplanarTi-diffusedLiNbO3waveguides.Thepolaraxisisinthe
planeofthewaveguideparalleltotheprismapex(Glassetal,1980).
power.Theresultswerethesamewithinexperimentalerrorsat0.515µm.Boththeexposureandthediffractionefficiencycouldbemeasuredwithanaccuracyofbetterthan5%,thusthemajorerrorliesintheestimateoftheenergydensityintheguide.InTable5.10theenergydensityinthewaveguidewasestimatedasfollows.Thewidthofthetwobeamswas0.3mm,andtheeffectivedepthoftheguidewastakentobe3µm.(Twomodescouldbelaunchedintheguide.)At0.458µmthetotalinsertionlossoftheentireprism-waveguideassemblywas15dB(at0.633µm,loss=10dB).Thislossisconsiderablygreaterthanthatreportedforoptimizedprisms(Saridetal1978)presumablybecausenospecialprecautionsweretakentooptimizethetaperbetweentheprismsandguidesforanywavelength.Glassetal(1980)assumedthat10dBofthelossoccurredattheinputcouplergivinganenergydensityintheguideofabout104timestheincidentpower.Anerrorinestimatingthecouplingefficiencyof±5dBleadstoanerrorintheestimatedpowerdensityintheguideofafactorof3.
Theinducedhologramwasfoundtorelaxveryrapidlyafterexposure.Forthisreason,longexposureswerealwaysfoundtobelessefficientthanshortexposuresforrecordingholograms.ForshortexposuresthedatainTable5.10gives
Usingthevalueofa=0.08l=0.633and0.515µm(Glassetal,1980)theresultisaphotorefractivesensitivityof
Thisresultisevensmallerthanthatobtainedforthesubstratecrystal,andhencedespitetheexperimentalerrorstheyprovideconclusiveevidencethat
Page271
TiimpuritiesdonotcontributesignificantlytothephotorefractiveeffectinLiNbO3waveguidesdirectly.Theresultsofequation(5.63)and(5.64)areconsistentwiththeinterpretationthatthephotorefractiveeffectinTi-diffusedwaveguidesisduetoresidualFe2+impuritiespresentintheLiNbO3substratematerialbeforediffusion.
Fujiwaraetal(1989)reportedonanewnovelmethodofquantifyingthephotorefractivesensitivityofTi-indiffusedLiNbO3waveguides.TheproposedmethodissimilartotheonebyBeckerandWilliamson(1985)inusingawaveguideMach-Zehnderinterferometer.Byseparatingtheirradiationlight(includingtheindexchange)andprobelight,theintensityandthewavelengthoftheirradiationlightcouldbereadilyvariedemployingthesamewaveguidepattern.Frommeasurementsofthephotorefractivesensitivityatvariousirradiationwavelengths,Fujiwaraetal(1989)estimatedthelevelofcrosstalkdegradationasafunctionofirradiationintensityandwavelength.
ThewaveguidepatternwasdesignedandfabricatedbyFujiwaraetal(1989)asshowninFig.5.46.ItisbasicallyaMach-Zehnder(MZ)interferometerforthe1.3µmwavelengthinwhichtheirradiationbeamofwavelengthlirisfedintotheupperarm.LightinputfromportAbroughtaboutaphotoinducedindexchangeandconsequentlyanasymmetryoftheopticalpathbetweenthetwointerferometerarms.Thephaseretardationoftheupperarmrelativetothatofthelowerarm,
causedtheprobeoutputtobemodulatedas
where isthelengthoftheinterferometerarms,lp,theprobe
wavelength,andDn(t)theaverageindexchange
Theprobelightof1.3µmwasinputfromportB.SinceopticalwavesoftwowavelengthsweremixedatoutputportC,theprobelightwaschoppedat270HzbeforeenteringportBandtheprobeoutputwasmeasuredbyalock-inamplifierplacedafteraphotodetector.Theprobelightintensitywaskeptbelow5µWtoensurethatnophotorefractiveeffectwascausedbytheprobe(Fujiwaraetal1989).PortDmonitoredanytemporalvariationofthe1.3µmprobelightduetoinputfibre-waveguidecoupling.
InFig.5.46,thewaveguidewidthis7µmandtheangleqofwaveguidebendingis1.7°.ThelengthLoftheinterferometerarmsis16mm.
Boththeirradiationandprobebeamswerefedthroughopticalfibresbutt-coupledtoinputportsAandBThequantitiesDneandDnocanbedeterminedseparatelybyadjustingtheinputprobepolarizationtotheTMandTEmode,
Page272
Fig.5.46ConfigurationoftheTi-diffusedwaveguidepattern
fabricatedinanLiNbO3substrateforthemeasurementofaphotoinducedindexchange(Fujiwaraetal1989).
Fig.5.47Typicaltimedependenceoftheprobeoutputofthe
Mach-Zehnderinterferometeraftertheonsetofirradiationofwavelength0.633µm(Fujiwaraetal1989).
respectively.Theirradiationbeampolarizationwasadjustedtobe45°fromtheopticalaxisofthesubstrate.Thewaveguides,designedtobesinglemodeatl=1.3µm,naturallysupportafewmodesforl=0.63-1.06µm.
Atypicalrelationbetweenprobeoutputversusirradiationtimetforlu=0.633µmisshowninFig.5.47.SincetheMZinterferometerwasinitiallysymmetrical,theoutputIpisatamaximumintheunirradiatedstate.Inthefigure,theintensityratioofthefirstmaximumandthefirstminimumcorrespondstoanextinctionratioof18dB,whichwasatypicallevelforallirradiationwavelengths.Inthe'symmetric'Ybranchinwhichtheirradiationwasfedintotheupperarm,a3dBlossofthe1.3µmprobelightwasexpected.Hence,
unequalpowerinthetwoarmswouldlimittheextinctionratioofthemodulatortoabout15dB.However,sincetheirradiationintheupperbranchinducesanindexchange,theYbranchbecomesasymmetric,reducingthebranchinglossfrom3dB.Thisopticallyinducedasymmetryexplainstheextinctionratiohigherthan15dB.Further,therelativelyhighextinctionratioindicatesthataspatiallyhomogeneousindexchangewasmeasured;scatteringduetospatialinhomogeneityofindexchangewasnotappreciable.
AphotoinducedindexchangeofDn10-5wasdetectedandafurtherimprovementofthesensitivityshouldbefeasiblewithdesignmodificationssuchasmodulatingtheprobelightbyanexternalfieldapplieduponthelowerarmoftheinterferometer.
Sincetheinterferometeroutputcanbeexpressedbyequation(5.65),theobservedtemporalchangeoftheoutputcanbeconvertedtothetimeevolutionof .ForallwavelengthslirandirradiationintensitiesIir,agoodfittoanexpression
Page273
Fig.5.48PhotorefractivesensitivitySplottedasafunctionofirradiationintensityIirforeachwavelength
(Fujiwaraetal1989).
couldbeobtained,wherethebarovern(t)denotesspatialaveragingalongthepath .Thephotorefractivesensitivitywasdefinedas
Attheinitialstage,
wheretistheirradiationtimeand isthesaturatedindexchange.InobtainingIir,thewaveguidewasassumedtobeuniformlyilluminatedinsidethecrosssectionof5×10-7cm2forallirradiationwavelengths.IndeterminingthedependenceofSontheirradiationintensity,thesubstratewasannealedat180°Cfor30minaftereachmeasurementtoerasetheinducedindexchange.Theannealingtemperaturewasfoundtocompletelyreverttheinterferometertoasymmetricone.
TheopticalintensitydependenceofSforeachwavelengthisshowninFig.5.48.TheirradiationintensitywasmeasuredatthearmoftheMZinterferometerbycutbackofthewaveguide,andthespatially
averagedirradiationintensityIiratthearmwascalculated.ThedependenceofSonIircanbedecomposedtothebehaviourof andtasisseeninequation(5.66).The wasfoundtobeinitiallyproportionaltoIirandthenshowedaslightsaturationathigherIir,whereastheinversetimeconstantofbuildup,1/t,wasnearlyconstantuptoIirof40W/cm2andthenshowedasharpupturnathigherirradiationintensities(Izutzuetal1982).InthefirstregionwhereIirissmall, isproportionaltoIirwhile1/tisconstant,renderingStobenearlyconstant.
Page274
Inthesecondregion,the vsIirrelationdeviatesfromlinearity,while1/tisstillconstant,andthereforetheratio graduallydecreaseswithincreasingIir.Inthethirdregionatstillhigherirradiationintensitylevels,thesharpincreaseof1/twithIirpredominatesthebehaviourofS .Acombinedeffectofthesecondandthethirdregionsresultsinadipinthethreecurves.Themechanismforthesharpincreaseof1/tisyettobeclarified.
Intheintensity-independentregion,SdecreaseswithincreasingwavelengthforbothTMandTEmodes.TheSfortheTMmode,STM,isaboutthreetimesgreaterthanthatfortheTEmodeforalllirandIirTheratioofthephotoinducedphasechangesfortheTMandTEmodesis ,whereGTMandGTEare,respectively,theoverlapintegralsbetweentheinternallyinducedelectricfieldandtheTMandTEopticalfields(Glass1978).At1.3µm, isabout3.2(Holmesetal1983).Althoughtheoverlapintegralscouldnotatthatstagebereliablyestimated,takingtheratio accountsfortheexperimentallyobservedratioSTM/STEof3.2-3.4.
5.7.3Relaxationofindexchange
Norelaxationoftheinducedindexchangewasobservedinbulksingle-crystalTi:LiNbO3overaperiodofdays;theindexchangepersistsforalongtimeduetothehighresistivityofcrystalsandthepresenceofdeeptrappingsites.Inwaveguides,ontheotherhand,theinducedindexchangerelaxesoveraperiodofhours.Therelaxationratedecreaseswithincreasingtime,asshowninFig.5.49.Therelaxationdoesnotfollowanexponentiallaworthesumoftwoexponentials.
ThisbehaviourhadbeenobservedpreviouslyinthedecayofX-rayinducedcentresinMgO.Inthatcasethedecaywasshowntobehyperbolicnotexponential.Thisbehaviouroccursifthermallyactivatedcarriershaveahighprobabilityofbeingretrappedinsteadof
recombiningattheequilibriumsites(SearleandGlass1968).InTi-diffusedLiNbO3therelaxationoftheindexchangewasfoundtobehyperbolic,i.e.Dnl/t(Glassetal1980).AgoodfittotheexperimentalrelaxationcurveisshowninFig.5.49.Thisbehaviour
Fig.5.49Relaxation(at300K)oftheinducedrefractiveindexchangeinplanarLiNbO3waveguides.ThepointsarecalculatedassumingabimoleculardecayDna/t
(Glassetal1980).
Page275
impliesthatthetrappedcarriersareinshallowtraps(thenatureofwhichisnotknown)andthatprobabilityofrecombinationatasimilartrappingsiteislargecomparedwithrecombinationatFe3+(excitedFe2+)centres.Inanycasethedatadosuggestamuchlowerdensityofdeeptrappingsitesinthewaveguidesthaninbulkcrystals.SinceitisknownthatFe3+ionsareindeeddeeptrapsinbulkLiNbO3crystals,therelaxationbehavioursuggestsalowdensityofFe3+ionsintheTi-diffusedlayers,thatis,allunexpectedFeionsareinthereducedstate.ThiswouldalsoaccountforabimolecularrelaxationifthedensityofshallowtrapsismuchgreaterthanthedensityofFe3+ions.
ItisprobablethatTi4+ionssubstituteforNb5+ionsintheLiNbO3crystalinwhichcasetheTi-ionsitecarriesaneffectivenegativecharge.CompensationmaybeaccomplishedbyreducingimpuritiessuchasFe3+tothebivalentstate,i.e.theTiin-diffusiontendstostabilizethereducedstatesoftheimpurities.TheFe2+-Ti4+complexisneutralifitcompensatesforaLi+-Nb5+pair.Thereducedstateofseveralions(Fe2+,Mn2+,Cu1+)isknowntoenhancethephotorefractiveeffectinLiNbO3(Petersonetal1971;StaeblerandPhillips1972).
ReductionofallmultivalentimpuritiesinthecrystalisalsolikelytoresultinincreasedphotoconductivitysinceithasbeenestablishedthatthefreecarriermobilityinFe-dopedLiNbO3singlecrystalsisgreatlyincreasedinreducedcrystalsduetothereductionoftheFe3+trapdensity(StaeblerandPhillips1974).ThisfactmayexplainthehighphotoconductivityobservedinTi-diffusedLiNbO3filmscomparedwithbulkcrystals.Itshouldbepointedoutthatindevicesrequiringanappliedfield,photoconductivityleadstospacechargefieldsandindexchangesinthesamewayasthezerofieldphotorefractiveeffect.
5.7.4Photorefractiveeffectinannealedproton-exchangedLiNbO3waveguides
Fujiwara,etal.(1992)presentedacomparativestudyofthephotorefractiveeffectinPEandAPELiNbO3waveguidesatanirradiationwavelength(lir)of488nm.Fromaquantitativemeasurementofthetemporalbehaviourofthephotoinducedindexchangeduetoirradiationatseveralintensities,theintensitydependenceofthesaturatedindexchangeaswellasthebuild-uptimeconstantinPEandAPELiNbO3waveguidesaredetermined,andthephotorefratorysensitivityinbothwaveguidesisevaluated.Theresultsindicateanincreaseinthesaturatedindexchangeofthephotorefractiveeffectduetoannealing,ahigherphotorefractivesensitivityofAPEwaveguidesthanthatofPEwaveguidesandalargercontributionofthedarkconductivitytothephotorefractiveeffectintheintensityrangeusedintheexperiments.
SevenmicrometerwidePEandAPEwaveguides,sinlgemodeatthewavelengthof1.3µm,wereusedinthemodifiedMach-Zehnderinterferometerconfiguration.ThewaveguidepatternwasdelineatedonanaluminiummaskevaporatedonthecfaceandLiNbO3substratebyetching.Proton-exchangewascarriedoutinbenzoicacidat220°Cfor88minforPEand20minforAPELiNbO3waveguides.AfterremovingtheAlmask,theAPEwaveguideswereformedbyannealingat350°Cfor6h.
Bymeasuringtheoutputintensityoftheprobelightduringirradiationexposure,theauthorsobtainedthetimedependenceofthephotoinducedindex
Page276
changeDn(t).Figure5.50showsthetypicalresultsforDn(t)forirradiationintensities(Iir)of65.4and105.3W/cm2forAPELiNbO3waveguides.Theabovevaluesoftheintensityrepresentspatialaveragesacrossthewaveguidecross-section,assuminguniformilluminationandareestimatedbytakingintoaccountthelossesatthearmintheinterferometer.Theauthorshaveusedthevaluesof7.0×10-8cm2forPEand2.7×10-7cm2andAPEwaveguidecross-sectionsinobtainingtheirradiationintensityforalltheexperimentaldata.ThebuildupoftheindexchangeshowninFig.5.50isexponentialandiswrittenas
whereDnsisthesaturatedindexchange,andtisthebuild-uptimeconstant(Fujiwara,etal.1989).ThesolidlinesrepresentthefitofthedatapointstoEq.(5.67).
BasedontheGlassmodel,Dnsisproportionaltothesaturatedspace-chargefield(Eswhichisexpressedas wherekistheGlassconstant,aistheabsorptioncoefficient,andsdandspharethedarkandphotoconoductivityrespectively.Assumingthatthephotoconductivityisproportionaltoboththeabsorptionandtheirradiationintensity, ,theauthorsobtained
whereneistheextraordinaryindex,r33istheelectro-opticcoefficient
andaisaconstantexpressedas ,whereeistheelectroncharge,
Fig.5.50Timedependenceofrefractiveindexchange
Dn(t)inAPELiNbO3waveguidesforirradiationintensitiesof65.4and105.3W/cm2atanirradiationwavelengthof488nm.Solidcurvesrepresentfitto
Eq.(5.67)(Fujiwaraetal1992).
Page277
hnthephotonenergy,µtheelectronmobility,t0thecarrierlifetimeandfthequantumefficiency.AccordingtoEq.(5.68),inthelowerintensityregionwherethedarkconductivityispredominant,thesaturatedindexchangecanbeexpressedapproximatelyas ;therefore,parameterArepresentstheresponseofthesaturaedindexchangeinthelowerintensityregiondominatedbythedarkconductivity.Inthehigh-intensityregion,wheretheresponseisgovernedbythephotoconductivity, approachesA/B,whichisindependentofboththeirradiationintensityandopticalabsorption(Fujiawaetal1989)anddependsupontheratio(r33k/a)only.
Ontheotherhand,thebuild-uptimeconstanttcanbeexpressedas,whereeristhedielectricconstant.Theintensity
dependenceof1/tisgivenby
where .Therefore,theintensitydependenceof1/t,givenbyEq.(5.69),yieldsthevaluesofbothdark-conductive(1/td)andthephotoconductive(aa/ere0)terms.
Moreover,ifwewriteEq.(5.69)as
Fujiwaraetal.(1992)havefittedthemeasureddependenceofDns,onIirtoEq.(5.68)usingAandBasadjustiveparametersandtheresultsareshowninFig.5.51.ThevalueofAisgiveninTable5.11forbothPEandAPELiNbO3waveguides.Inbothcases,thesaturatedindexchangeDns,varieslinearlywithintensityinthecornerintensityregion,andtendstodeviateslightlyfromthelinearbehaviourinthehigherintensityregion.Thisalmostlinearbehaviourindicesthatthedark-conductivitycomponentisdominantincreatingthespace-chargefieldandthecontributionofthephotoconductivityisnegligible.Inotherwords,productBIirisstilllessthanunitywithintheintensity
rangeusedintheexperiments.DnsofAPELiNbO3waveguidesisabouteighttimesthatofPEwaveguidesatirradiationintensityofupto100W/cm2ThealmostlinearbehaviourofDns(Iir)doesnotpermitanaccuratedeterminationofBbytheabovefittingprocedure.
Figure5.51alsoshowsthefitoftheintensitydependenceof1/ttoEq.(5.69).Fromtheintercept,thedarkconductivityofthePEandAPEwaveguidesisobtained,whichislistedinTable5.11.Theratiooftheslopeandtheinterceptofthe1/t(Iir)straightlinesyieldsB.ThevaluesofBarelistedinTable5.11.
FromEqs.(5.68)and(5.70),thephotorefractivesensitivityS(definedby )(Fujiwaraetal1989)isexpressedas
Figure5.52presentsaplotofthedependenceofirradiationintensityofDns/tforPEandAPEwaveguides,andinthelastcolumnofTable5.11thereis
Page278
Fig.5.51IntensitydependenceofDnsand1/t
forPEandAPELiNbO3waveguidesatanirradiationwavelengthof488nm.Solid
andbrokenlinesrepresentthebestfitofthedatatoEqs.(5.68)and(5.69),
respectively.
Fig.5.52(right)IntensitydependenceofDnsand
1/tforPEandAPELiNbO3waveguidesatanirradiationwavelengthof488nmshowinga
linearbehaviour.Theslopeofthelinesgivesthephotorefractivesensitivityforthe
correspondingwaveguide(Fujiwaraetal1992).
Table5.11ThevaluesofparametersdescribingthephotorefractiveeffectinPEandAPELiNbO3waveguidesatanirradiationlengthof
488nm(Fuyiwaraetal1992)
A×10-7(cm2/W)
sd×10-4(ohmcm)-1
B×10-3(cm2/W)
Dns×10-4
S×10-9(cm2J)
PE 0.88±0.04 1.5±0.1 0.37±0.08 2.6±0.7 0.54±0.01
APE 6.6±0.4 0.56±0.17
6.1±3.2 1.6±0.9 1.8±0.06
alistofvaluesofthephotorefractorysensitivityforPEandAPEwaveguides,obtainedfromtheslopoftwostraightlines.
Theeffectofannealingonthephotorefractivepropertiesofproton-exchangedLiNbO3waveguideswillnowbediscussed.Firstofall,theparametersAincreasesbyalmostanorderofmagnitudeasaresultofannealing.Thisiscausedbyalmostafactorof3increaseinther33coefficient(Becker1983)andadecreaseinthedarkconductivitybyalmostthesamefactor.Whilethereducedelectro-opticcoefficientinPEwaveguidesisattributedtothenear-cubicsymmetryoftheproton-richLiNbO3,thehigherdarkconductivityofPELiNbO3waveguidesmaybeaconsequenceofthepresenceofshallowdonorlevels(traps),probablyresultingfromtheincorporationofprotonsatinterstitialsites.
Page279
5.8Energylossinwaveguides
5.8.1LossesinTi-diffusedLiNbO3waveguides
Animportantconsiderationintheperformanceofanyopticalwaveguidedeviceisitsinsertionloss,L=-10logT,whereTisthepowertransmissioncoefficient.Aconvenientmethodforobtainingthewaveguidepowerattenuationcoefficienta(indB/cm)istomeasureLasafunctionofguidelength .Foratitanium-diffusedLiNbO3stripguide,however,theproblemistochange withoutchangingthecouplingintoandoutoftheguidethroughtheendfacetsofthecrystal.Polishingtheendswithoutroundingrequiresgreatcare;butcleavinghasthepotentialforprovidingreproducibleandrectangularendswithlittledifficulty(HsuandMilton1976).However,thecleavingmethodrequiresaspecialcrystalorientationand,inaddition,reflectionsfromtheparallelendfacetsleadtostanding-wavebehaviourthatmustbetakenintoaccount.KaminowandStulz(1978)describedlossmeasurementsinacleavedcrystalcontaininga4-µm-widesingle-modeTi-diffusedwaveguide.Inordertoillustratetheisolationfrommetalelectrodesprovidedbyadielectricbufferlayer,theauthorsalsomeasuredaguideovercoatedwithametallayerseparatedfromguidebyAl2O3orSiO2.
TheexperimentalsetupisillustratedinFig.5.53.ThepowerincidentontheinputmicroscopeobjectivefromthepolarizedHe-Nelaser,Pin,ismaintainedatlessthan2.5µWtoavoidopticaldamageinthecrystalandnonlinearityintheunbiasedphotodiodeusedtomeasurePinandPout.Theoutputobjective(×20,0.57N.A.)hasasufficientlylargeaperturetocollectallthelightfromtheguide.Anirisisprovidedtoisolatethewaveguidemodefromextraneousscatteredlight.Thepolarizationoftheoutputspotisobservedtobethesameasthatoftheinput.Aheater,shownschematicallyinFig.5.53,tunestheFabry-Perotformedbythecleavedendfacetsthroughmaximaand
minimabythermallyvaryingtherefractiveindexn.With ,theFresnelreflectioncoefficientR=0.14,whichiscalculatedbytheformulaR=[(n-1)/(n+1)]2.
IfT=Pout/Pin,theinsertionlossListhesumofthreecontributions:ThetwolensesintroducelossL1whichismeasuredintheabsenceofthecrystalas1.2dB.ThemismatchbetweenthecircularGaussianinputwavefunctionandthestrip-guidewavefunctionintroduceslossL2.ThecrystalintroduceslossL3duetothewaveloss, ,andtheeffectsoftheFresnelmirrors.
BurnsandHocker(1977)haveshownthatbychoosingtheGaussianinputspotradiuswtobethegeometricmeanoftheequivalentspotsizesw1andw2measuredalongtheprincipalaxesofthewaveguidemode,themismatchlossL2maybeassmallas0.8dB.Fortheguideunderinvestigation,the
Fig.5.53Intersectionlossmeasurementapparatus(KaminowandStulz1978).
Page280
value .Thecondition wasachievedbytestingvariousmicroscopeobjectivesinordertofindonethatgaveminimumL.ForanobjectivewithnominalnumericalapertureNandpupildiameterDfocusingalaserbeamofGaussiandiameterd,KaminowandStulz(1978)estimatedwusingparaxialGaussianbeamopticsas
Forthepresentmeasurementsatl=0.63µmwithd=1mm,itwasfoundthata×10lenswithnominalN=0.25andD=8mmgavetheminimumloss.Thespotdiameter2wcalculatedfromequation(5.72)was12pro,whichmaybereasonableforanominal4µm-widestripguide,allowingforlateraldiffusionandsmallguide-substrateindexdifference.
Thetransmissionthroughthecrystalwas
iftheendfacetsdonotprovidecoherentreflections,butwithFabry-Perotbehaviourthetransmissionrangesbetween
Inequations(5.73)and(5.74)thetransmissionthroughthewaveguidewas
whereaismeasuredindB/cm.ItshouldbenotedthatbyconvertingTtoL,equations(5.73)and(5.74)give
for ,sothatL0isalsotheaverageFabry-Perotloss.
TheorientationofthecleavedcrystalisindicatedinFig.5.54.The250µmthickplateisnormaltothecrystalxaxisandcontainstheopticz
axisatanangleof32.75Åfromthecleavededge.Ascribemarkismadeonthewaveguide-containingsurfaceatoneedgeoftheplate;twopairsoftweezersoneithersideofthemarkareusedtomakethebreak.Asisusualoncleavedsurfaces,anumberofterracesappears,asindicatedschematicallyinFig.5.54.TheedgesoftheterracestepsareindicatedbythedottedcurvesinFig.5.54.Thecharacteroftheterracesandthenatureofthecleavedendfacetdependuponwhetherthebreakstartsnearthenegativeorpositiveendofthezaxis.
ThecleavageplaneinLiNbO3wasidentifiedasa{102}plane.However,
Page281
Fig.5.54Cleavedcrystalorientationshowinga4µmwideguideandevaporatedelectrodespaces9µmapart.Thedottedcurvesonthecleaved
facerepresentterracesteps;thefirstfewofthesestepsstartnearthescribemarkonthesurfaceoftheplate(Kaminowand
Stulz1978).
thereissomeambiguityinassociatingthegeneric{102}planewitheitheroftheactual(102)or(012)planesinthecrystallattice.Nevertheless,examinationofacrystallatticemodel(Megaw1973)revealsthelikelyplaneastheonewhichcontainsthelayerofvacantoctahedralsitessurroundedbyalayerofLiononesideofthecleavageandalayerofNbontheother(indicatingpossiblechargeneutrality).Theatomicspacingsacrosstheproposedcleavageplanearerelativelylarge,indicatingweakbonding.
Lightpolarizednormaltothecrystalplate,paralleltothexaxis,isanordinarywave.Theguideisorientedperpendiculartotheendfacetswithin1/4°.InsertionlossLcanbeobserved(withanoscilloscopeconnectedtothephotodiode)topassthroughFabry-Perotmaximaandminima,asinequation(5.74),asthetemperaturevariesoverafewdegreesofCentigrade.Ontheotherhand,lightpolarizedintheplaneofthecrystalplateisanextraordinarywave.Inorderthatthe
Poyntingvectorbeparalleltotheguideaxis,theincidentbeammustenteratabout4.5°fromthenormal(BurnsandWarner1974).Thewave-normalvectoristheguideisthenabout2°fromtheguideaxisandthewavefrontsarenolongerparalleltothecleavedfacets.Thenthelossbehaviourcorrespondstoequation(5.73)andnomaximaorminimaareobserved.
Waveguideswerefabricatedbydiffusing4µmwide180ÅthickTistripesinflowingO2usingstandardacousticgradeLiNbO3substrates.Tiwasevaporatedfromatungstencoil.ThelossmeasurementsonsuchaguideareplottedinFig.5.55.Agoodfittothedatafortheordinary-wavemaximaandminimawasobtainedfora0=1.0dB/cm,L1=-1.2dB,L2=0.8dB,andR=0.14.Theestimatedaccuracyofthelossmeasurementswas±0.2dB.Notefromequation(5.74)thatameasurementofLmaxandLminatone issufficienttoobtaina0forgivenL1,L2,andR.However,measurementsatseveralvaluesof giveaddedprecision.Theextraordinary-wavedataisfittedbyalinewiththeslopeae=1.5dB/cm,forthesameL1,L2,andR.
Metalelectrodes(consistingof300ÅofTiplus700ÅofAg)20lainwideandspaced9µmapart,wereevaporatedalongsideasimilar4µmwideguide
Page282
Fig.5.55InsertionlossLversuswaveguidelength for
a4-µmwideTi:LiNbO3guide.Solidlinesgivemaximum,minimumandaverageloss(Lmax,
Lmin,andL0)ofFabry-Perotresonatorcalculatedfora0=1.0dB/cmandthedashed
linegivesthelossforae=2.5dB/cm.Soliddotsaremeasuredfortheordinarywaveandcirclesaremeasuredfortheextraordinary
wave(KaminowandStulz1978).
asinFig.5.54.Theattenuationcoefficientsmeasuredinthiscasewerea0=3.0dB/cmandae=2.5dB/cmindicatingthatsomeoftheopticalfieldsisincontactwiththeelectrodes.Theelectrodeswerethenstrippedoffandthemeasuredattenuationcoefficients,a0andae,werewithinexperimentalerrorofthoseobtainedinFig.5.55.
Inapracticaldevice,Rcanbereducedtozerobyantireflectioncoating,andL1andL2couldalsobemadesmallbycouplingdirectlyfromasingle-modefibrewithsuitablecircular-to-ellipticalmodetransformerortaper.Thenonlythewaveguideinsertionlossalwillremain.TheattenuationcoefficientinbulkLiNbO3isverysmall:lessthan0.1dB/cmatl=1.15µm.However,thesourceoftheexcessattenuationinthesestripwaveguidesisnotunderstoodatpresent.The
attenuationmightbeduetoabsorptionbyimpuritiesintheLiNbO3substrateorbythediffusedTi,oritmightbeduetoscatteringfromgeometricalimperfectionsintheguideoronthecrystalsurface.Thus,Ti-diffusedLiNbO3waveguideswithlosssubstantiallylessthan1dB/cmarearealpossibility.
5.8.2Absorptionlossinstripguides
TomeasuretheabsorptionlossinTi-diffusedLiNbO3(Kaminowetal1980)theguideswerepreparedbydepositing300ÅofTiontotheLiNbO3substratefollowedbyheatingfor6hat980°Cinoxygenandcoolingtoroomtemperatureforseveralhours.ThefirstarrangementwastousetheelectrodegeometryshowninFig.5.56,whichhasbeenusedforelectro-opticmodulation.Coplanarelectrodesspaced9µmapartweredepositedalongtheentirelengthofthecrystaloneachsideofthe5-µmwidewaveguide.Withabout100µWoflightmodulatedat150Hzcoupledintotheendofthewaveguide,thepyroelectricsignalduetoabsorptionoflightintheguidecouldbeeasilymeasuredwithalock-inamplifier.Thepyroelectricresponsewasverysensitivetothecouplingefficiencyintothewaveguideandcouldbeusedasamoreconvenientmeansofcouplingalignmentthanthefar-fieldpatternof
Page283
Fig.5.56ExperimentalarrangementforpyroelectricmeasurementofabsorptionlossinLiNbO3stripguides.Thepolarc-axisisintheplaneofthewaveguideat32.75°
fromthecleavedends(Glassetal1980).
thetransmittedlight.Thismethodofalignmentwouldalsolenditselftoservocontrolofthecoupling.
Thecoplanarelectrodegeometrywasnotsatisfactoryforabsolutemeasurementoftheabsorptionlossbecauseofthegeometricalcorrectionfactorforthefielddistributionbetweentheelectrodesandbecausethermaldiffusionfromthewaveguideintothesubstratewasveryrapid.Thecorrespondingattenuationofthepyroelectricsignalisalsodifficulttocalculatebecauseofthegeometry.Theattempttouseshortopticalpulsesfailedbecausetwo-photonabsorptionintheguideswasdominantatthehighintensitiesrequiredtoobtainameasurablesignal(Glass1978).
ThepreferredgeometryforabsolutemeasurementsofabsorptionlossinthewaveguidewastoevaporateelectrodesonthetwosidesofthesubstratecrystalalongtheentirelengthasshownshadedinFig.5.56.Thenthepyroelectricresponseoftheentirewaveguideandsubstratewasmeasuredwiththelock-inamplifier.Equation(5.76)canbeusedforthisgeometry,andthethermalrelaxationtimetothesurroundingsisnowlong(1s)andcanbeneglected.TodeterminethelossintheTi-diffusedwaveguide,theincidentlightisfirstinjectedintothesubstrate,andthevalueofthepowerabsorbedinacrystalofgood
quality ,wheredistheopticalpathlengththroughthecrystal.Hence,thevaluesofafortheundopedsubstratearemeasured.Thenbycouplingthelightintothewaveguide(withordinarywavepolarization)thechangeinpyroelectricresponsegivesthechangeofabsorptionlossintheTi-diffusedregiondirectly.Intheseexperimentsthesignal-to-noiseratioallowedachangeof5%inthelosstobedetected.TheexperimentaldataaresummarizedinTable5.11.
Thevaluesofalistedforthewaveguideat0.514and0.488inTable5.11representalowerlimitsincethefollowingfactorscanacttodecreasethedifferencebetweenthepyroelectricsignalsforlightcoupledintowaveguideandsubstratemodes.First,theintensityoflightcoupledintothewaveguidemodemaynotbethesameasthatcoupledintothesubstratemodeeventhoughcouplingwasoptimized(insertionlossminimized)usingthefar-fieldpatternofthetransmittedlight.Withasimilarexperimentalarrangementthisfactorhasbeenmeasuredtobe0.8dB(KaminowandStulz1978).Second,theintensityofthelightintheguidemaybedecreasedbyscatteringfromtheguideintothesubstrate.Thiscanbecorrectedbymeasuringboththeinsertionlossandelectricalresponsefortwoormoredifferentwaveguidelengths.(Thetotalinsertionlossofthe1.8-cmcrystalwas5.5dBat0.633µm,increasing
Page284
to9dBat0.488µm).Anotherfactorthatcanaffecttheaccuracyofmeasurementofwaveguidelossinthisexperimentisabsorptionofscatteredlightbythemetalelectrodes,whichinturnheatsupthecrystal.Thisdoesnotseemtohavebeensignificantintheseexperimentssincethiswouldgiveanincreasedpyroelectricresponseat0.633forlightcoupledintothewaveguidewherescatteringisgreaterthaninthesubstrates.
At0.633µm,noincreaseoflossinthewaveguideregioncouldbedetected.Thepyroelectricsignalwasthesamewhetherthelightwascoupledintothewaveguideorthesubstrate.Thusatthiswavelengththeabsorptionlossis0.3dB/cmintheguideandislimitedbythelossinthesubstrate.NoadditionalabsorptionduetoTicouldbedetectedat0.633µm.Atshorterwavelengthsincreasedlossinthewaveguidewasmeasurable.At0.515µmand0.458µmpyroelectricsignalsincreasedby50and60%,respectively,whenthebeamwascoupledintotheguidepresumablyduetotheshiftoftheabsorptionedgetothevisible.
5.8.3Lossinepitaxialwaveguides
Thelosswascalculatedfromthemeasureddistributionofscatteredlightfromthewaveguidemode.Thescatteredlightdistributionwasanalysedusingamicroscopemountedonamicromanipulator,aphotodetectorandaselectivemicrovoltmeter.ThevoltmeterreadingUwasproportionaltotheintensityofscatteredlight.HavingmeasuredthescatteredlightintensityattwopointsspacedbyadistanceL,onecancalculatetheattenuationcoefficientbytheformula
LightlossmeasurementsforseveralexaminedsampleshaveshownthatTM-modeattenuationisasarulehigherthanthatofTEmodes.ThisisevidentlyduetothefactthatTMmodesaremorecriticalto
interfacenonuniformitythanTEmodes.Itshouldbenotedthatsomeofthesamplesusedintheexperimentexhibitedadecreaseoflossto0.7dB/cmforTEmodes.
Inepitaxiallayersofsolidsolutionsoflithiumniobate-tantalatetheattenuationisequaltoldB/cmforl=0.63µmand0.8dB/cmforl=1.15µm.Thephotorefractivefilmsensitivitystudiedbycomparisonwasnohigherthanthatofthesubstrate.
Thelowestattenuationisobservedin(0001)-orientedlayers.InaLiNbO3filmonaLiTaO3substratelossesdonotexceed2dB/cmforlowermodes.ItisestablishedthatlightpropagationoccursinLiNb1-yTayO3filmsfory=0÷1fororientation(0001);y=0.3÷0.99for( )andy=0.4÷0.99for( );thelightattenuationinthewaveguidedecreaseswithincreasingtantalumcontentinthefilms(Fig.5.57).Attenuationinbestsamplesdoesnotexceed1dB/cmfory>0.2,0.6and0.9fororientations(0001),( )and( ),respectively,andincreasessharplywithincreasingorderofthemode.
Absorptioninlithiumniobate-tantalatefilmsisinsignificantanddoesnotexceed0.3-0.5dB/cm,whichshowsahighstructuralperfectionofthelayer.
Page285
Fig.5.57Waveguidepropertiesandinsertionloss
versusfilmcomposition:-effectivewaveguides;
-rapidlyattenuatingwaveguides;-nowaveguiding.
Increaseinlightattenuationwithincreasingorderofmodesisaconsequenceoflightscatteringonsubstrate-filmandfilm-airinterfaces.Thepresenceofirregularitiesoninterfacescausesenergytransferfromonewaveguidemodetoothers.Inhomogeneityoftheinterfaceisanimportantfactordeterminingefficiencyofthepracticaluseofstructures.Periodicirregularitiescanbeused(asacouplingelement)forlightoutputfromadielectricwaveguide.Butrandominhomogeneitiesthatoccurinwaveguidemanufacturingweakenapropagatingwave.Thelossfactorvariesinproportionwithroot-mean-squareroughnessofthewalls.Roughnessontheinnerfilmboundariesisapparentlyofairregularnature.Theindicatedweakattenuationoflow-ordermodesshowsthatwaveguidesobtainedthroughliquidphaseepitaxyoflithiumniobatemeetthestrictrequirementsimposedonwallsmoothnessinintegratedopticsschemes.
5.9Ferroelectricpropertiesofwaveguides
5.9.1Dielectricproperties
Thecapacity(c)andconductivity(s)ofcapacitorsformedbythe
planarstructureofplatinumelectrodesonthefilmsurfaceweremeasuredtodeterminethetemperaturedependenceofdielectricpermittivity(e)offilms.Measurementswerecarriedoutinthetemperaturerangebetween20and970°Cinthe'weak'fieldregime(Emcas<104V/m)bythebridgemethod.Figure5.58representstypicaltemperaturedependencesofcandsfora6µmLiNb0.1Ta0.9O3filmonaLiTaO3substrateoforientation( ).
Typicalofthestructuresinvestigatedisthepresenceoftwopeaksofc(T)ands(T),thefirstlyinginthevicinityof580°Cforc(T)andat575°Cfors(T),thesecond,amoresmearedone,at770°Cforc(T)andat750°Cfors(T).Thepeaksofc(T)ands(T)near580°Careduetophasetransitioninthesubstrate,whichisclearfromasmallersmearingandarathersmalldisplacementofthemaximumofc(T)relativetos(T).ThisfactisalsoconfirmedbywellknowndataindicatingthatforasinglecrystalLiTaO3thephasetransitiontemperaturelieswithintherangeof550÷680°C(ed.byShaskol'skaya1982).SincephasetransitioninLiNbO3crystalsoccursat1140÷1180°C,itisnaturaltoexpectthephasetransitioninLiNb01Ta0.9O3tooccurwithintherangeof550÷1190°C,thatis,smearedmaximainc(T)ands(T)at770(750)°C
Page286
Fig.5.58Temperaturedependenceofdielectricpropertiesof
LiNb01Ta09O3/LiTaO3:a)capacity(1)andconductivity(2);b)dielectricpermittivityofsubstrate(1)andfilm
(2),calculatedvalues.
maybeduetophasetransitioninthefilm.
Assumingthedielectricpermittivitiesofthefilme1andsubstratee2tohaveonlyonemaximum(each)thatcorrespondstotheirphasetransition,onecansolvetheproblemofestimatinge1(T)ande2(T)bymeasuringthecapacityCstofthestructure.ThefollowingfactsandassumptionsareusedtodetermineCst
1.Itcanbeeasilyshownthat
whereCstisthecapacityofthestructure, thestructureperiod(300µm),atheelectrodewidth(100µm),dthefilmdepth(6÷20µm).
2.IntherangeT>750°C, and,asfollowsfrom(5.78),e1(T)canberestoredwithasatisfactoryaccuracy.
3.Knowingthebehaviourofe1(T)forT>750°Cande(20°C)=46(WangHongandWangMing1986)onecaninterpolatee(T)totheregionT<700°Cand,usingthisinterpolation,restoree2(T)inthistemperaturerange.Fortherelationsbetweenfilmthicknessandlattice
period,e2alwaysrestrictsthestructurecapacityfromabove.TheresultsofthecalculationsforthedielectricpermittivityofthefilmandsubstrateispresentedinFig.5.58b.
ThebehaviourofthestructureinstrongelectricfieldswasinvestigatedforT>750°C,wheretheinfluenceofthesubstrateissmall,sinceatthesetemperaturesitisintheparaelectricphase.AtypicaloscillogramofthedependenceofspontaneouspolarizationPsonthestrengthoftheelectricfieldEispresentedinFig.5.59.
Analysisofdielectrichysteresisloopsshowsthatat750-800°CthestrengthofthecoercivefieldforLiNb0.1Ta0.9O3filmsonLiTaO3( )makesup(2-3)×105V/mandPs=0.46C/m2.Theobservedeffluentonhysteresisloopsisobviouslyduetochargeescapefromsmalltrapsduetoredistributionoftheappliedelectricfieldcausedbyadecreaseofferroelectricimpedanceatthemomentofrepolarization(LinesandGlass1977).
Page287
Fig.5.59OscillogramofahysteresisloopofaLiNb0.1Ta0.9O3
film.T=750°C,f=60Hz,[email protected]/m2,Ec2.3105V/m.
5.9.2Pyroelectricproperties
Thepyroelectricpropertiesoffilmsweremeasuredbythethermalpulseandlow-frequencysinusoidaltemperaturemodulationmethods(Antsygin1987).
5.9.2.1Thelow-frequencysinusoidaltemperaturemodulationmethod
TheabsolutevalueofthepyroelectriccoefficientgwasfoundusingasetupshownschematicallyinFig.5.60(Antsyginetal1986).ThebasicelementofthisdevicesetupisathermoelectricdeviceenablingthesampletemperaturetochangeaccordingtoastrictlysinusoidallawwithamplitudeDT.Thetemperaturemodulationfrequencywischosentobesuchthatitcouldprovideauniformtemperaturedistributionthroughouttheentiresamplethicknessd,thatis, ,where isthethermalrelaxationtimeofthesample.ThenatureofpyroelectriccurrentissuchthatmagnitudeofpyroelectriccurrentJpisproportionaltodT/dt.Thisisjustwhatdiffersthepyroelectriceffectfromallotherphysicalphenomenathatarecharacterizedbyvariationofcurrentthroughaspecimenwithvaryingtemperatureandpermitsdistinguishingthecontributionofpyroelectriccurrentintothetotaltemperature-inducedcurrent.Temperaturevariationinasamplebysinusoidallawisresponsibleforthesamelawforvariationof
pyroelectriccurrentJpbutwithaphaseshiftp/2.
Thismethodhasbeenemployedtoinvestigateferroelectriccrystals(CarnandSharp1982).Uniformtemperaturedistributionthroughoutthecrystalthicknesscanbeattainedonlyatverylowmodulationfrequencieswsince .Determinationofthephaseshiftbetweenpyroelectricandnonpyroelectriccurrentsischaracterizedbylowsensitivity.Thephaseshiftj,ascanbereadilyshown(CarnandSharp1982),isequaltoarctan(Jpmax/Jnpmax).Examinationofthinferroelectricfilmsbythismethodhasmadeitpossibletosingleoutthecontributionofpyroelectriccurrentandtomeasurelvaluesuptoabout3%.Thepyroelectriccoefficientisfoundfromtherelationl=Jp.max/(SDTw),wheresisthesamplearea.
5.9.2.2Thethermalpulsemethod
Thedirectionofpyroelectriccurrentinaferroelectricisdeterminedbythe
Page288
Fig.5.60Schematicofadeviceformeasuringpyroelectriccoefficient.
1)thermalbath;2)sample;3)temperaturegauges;4)meansampletemperaturegauges;5)heatconductingbufferlayer;6)thermocouple;7)electrometer;8,9)amplifiers;
10)two-coordinatex,yrecorder;11,12)unitsforthermocouplecontrol;13)printer;14)crate'Camak';15)computer;16)display;
17)monitor.
spontaneouspolarizationvectorPs,whichfactcanbeusedininvestigationofpolarizationdistributionthroughoutthesamplethickness.
Themethodconsistsinprobingasamplebyshortradiationpulsesthatheatthethinabsorbingelectrode.Movingfromtheheatedelectrodeinthesampletowardstheoppositeelectrode,thethermalfluxinducestheoccurrenceofpyroelectricsignal.Theinitialpolarityofthiscurrentisdeterminedbythepolarizationdirectioninthevicinityoftheabsorbingelectrode.Ifinabulkferroelectricthepolarizationdirectionreverses(head-ondomainstructure),thisisexpressed,beginningfromsomeinstantoftime,asasharpdecreaseinthemagnitudeofofpyroelectriccurrentevenreachingpolarizationreversal.Thethermalpulsemethodshowsahigherresolutioninfilmstudiesthanincrystalstudies(Chynoweth1956).Thispromotedinvestigationofpyroelectricprocessesdirectlyneartheelectrodesurface.Thetimeresolutionofabout10-9sattainedinthe
measurementscorrespondstothethicknessresolutionof3-5×l0-8m.Analysisoftheeffectofradiationonbothelectrodesmadeitpossibletodirectlydiscoverthehead-ondomainstructureinthesample.Suchastructurecausesoppositepyroelectriccurrentpolarityuponirradiationofeachoftheelectrodes.Currentpolarityisdeterminedonlybythepolarizationdirectionanddoesnotdependontheheatdistributiondirection.
Structureswiththecaxisnormaltothesubstrateplanewereusedinmeasurements;chromiumfilms(10-7minthicknessand(1-3)×10-6m2inarea)manufacturedbythethermalsputteringmethodwereusedaselectrodes.
AtypicaloscillogramofpulsepyroelectricsignalsispresentedinFig.5.61.Analysisofthebehaviourofpulsepyroelectriccurrentresponseofthestructuretothelightpulsebothfromthefilmandsubstratehasshownthatspontaneouspolarizationofthefilmisalignedalongthesubstratepolari-
Page289
zationdirection,andthepyroelectriccoefficientoffilmsestimatedbytheinitialslopeofthecurrentresponseis grad.Thisvalueagreeswellwith gradobtainedforsolidsolutionsofthesamecomposition(WangHongandWangMing1986),whichisindicativeofhighqualityoftheepitaxialstructure.
Theobserveddecreaseofpyroelectricresponsewith s,aswellasthenonlineardependenceofpyroelectricstressonloadimpedanceatsubsonictemperaturemodulationfrequenciesindicatetheexistenceofanonferroelectriclayerinthestructure.Theabsenceofcurrentresponsedelayrelativetothelightpulse(under10-8s)uponlightabsorptionbyelectrodesbothonthesideofthefilmandsubstrateimpliesthatthislayerislocatedonthefilm-substrateinterface.
5.10Temperaturedependenceofthermoelectriccoefficientsoflithiumniobateandlithiumtantalate
Thermoelectriceffectsinlithiumniobateandlithiumtantalateferroelectricsaffectgreatlythefilmcrystallizationconditions.
Khachaturyanetal(1988)investigatedthermoelectricSeebeck,ThomsonandPeltiereffectsforLiNbO3andLiTaO3singlecrystalsandtheirtemperaturedependenceintherangeof300-1400K.
Themainresultsofthethermodynamictheoryofthermoelectricphenomenacomedowntoestablishingrelationshipbetweenvariousthermoelectriceffects(SamoylovichandKorenblit1953),namely:
wheretisThomson'scoefficient,IIisPeltier'scoefficient,aisSeebeck'scoefficientandTistemperature.
So,havingmeasuredtheSeebeckcoefficientforaparticularmaterialonecanreadilyobtainthevaluesofPeltierandThomsoncoefficients.
TheexperimentalsetupfordeterminationofSeebeckcoefficientincludedamainfurnace,upperandlowermicroheaters,thermocouplesandaspecimen(RekasandWierzbicka1983).
Fig.5.61Oscillogramofapyroelectricsignaltolightpulse.1)lightpulse,2)pyroelectricresponseofthefilm,
3)responseofthesubstrate.
Page290
Fig.5.62TemperaturedependenceofSeebeckcoefficientsofLiNbO3andLiTaO3.
Table5.12Thermoelectriccoefficientsoflithiumniobateandtantalate
LiNbO3 LiTaO3
T,K amV/deg IImV tmV/deg amV/deg IImV tmV/deg
700 0.3 210 -5.2 0.04 28 1.2
750 0.05 37.5 -5.1 0.13 97.5 5.52
800 -0.65 -520 -5.0 0.91 728 6.9
850 -0.65 -552.5 -5.0 1.12 952 7
900 -0.2 -180 5 1.5 1350 7.1
950 0 0 5.1 1.69 1605.5 7.2
1000 0.2 200 5.1 1.66 1660 1.1
1050 0.35 367.5 5.2 1.6 1680 -1.6
1100 0.2 220 -2.5 1.44 1584 -1.5
1150 0.1 115 -2.4 1 1150 -9
1200 0.1 120 -0.37 0.8 960 -9.1
1250 0.1 125 -0.36 0.53 662.5 -9.1
SamplesofLiNbO3andLiTaO3crystals(10×10×10mm)werepositionedbetweentwoplatinumelectrodes.Thecrystalsurfacescontactingtheelectrodeswascoveredwithplatinumniello.Twoinnermicroheatersweremountedonrodsandenabledtemperaturegradientstooccurthroughoutthespecimenthickness.Temperaturewascontrolledbythreeplatinum-rhodiumthermocouples,measurementswerecarriedoutbythecompensationmethodinairataconstantnormalpressure,thetemperaturegradientwas10deg/cm.Thethermo-electromotiveforceofcrystalswasmeasuredwithinexperimentalerror
Page291
of1-3%.Figure5.62presentsthetemperaturedependenceoftheSeebeckcoefficient(a)forLiNbO3andLiTaO3singlecrystals.Withintheexperimentalerror,nodependenceofaoncrystallographicorientationofthecrystalwasobserved.Thedislocationdensityof(2-4)×104cm-2remainedunalteredinallthespecimens.
AsisseeninFig.5.62,the300-1400KtemperaturevariationoftheSeebeckcoefficientforLiNbO3canbedividedintothreetemperatureranges.Intherangeof300-750KtheSeebeckcoefficientstartsincreasingandthenfallssharply,whichsuggestsanintricatenatureofconductionofLiNbO3singlecrystalsintheindicatedtemperaturerange.AtlowtemperaturesthereprevailstheimpurityconductionofLiNbO3(Kuz'minov1987;Kuz'minov1975).Inthetemperaturerangeof750-950K,achangessign,whichisindicativeofthecontributionoftheelectroncomponenttotheintrinsicconduction.AsubsequentsignchangeintheSeebeckcoefficientinthetemperaturerangeof950-1400KagreeswiththefactthatthemaincarriersareLi+ions(D'yakovetal1985).
ThevaluesofthecoefficientaforLiTaO3arepositiveintheentiretemperaturerangeunderexamination.Atthephasetransitiontemperature(T=933K)amaximumisobserved,whichsuggeststheinfluenceofthephasetransitionuponthecharacterofconduction.ItisobviousthatthemaincarriersinLiTaO3singlecrystalsareLi+ions.ComparingthevaluesofSeebeckcoefficientsforlithiumniobateandtantalatesinglecrystalswithintheinvestigatedtemperaturerangeonecanassumethatthehighertheavalue,thehighertheconductionofthematerial.For
ThecalculatedvaluesofPeltierandThomsoncoefficientsintheindicatedtemperaturerangearetabulatedinTable5.12whichshowsthatforlithiumniobatethePeltiercoefficientchangesfrom-662.5
mVto367.5mV,whileforlithiumtantalateitchangesfrom28mVto1680mV.Attemperaturesabove1200K,Thomsoncoefficientsforlithiumniobateandtantalatedonotchangeappreciably.
Page292
6Thin-FilmStructuresinIntegratedOpticsIntegratedopticsismainlydevelopedinthedirectionofintegrationofwaveguideandoptoelectroniccomponentsonasinglesubstratetotheeffectofcreationofmultifunctionaldevices.
Opticalfilmwaveguidesarethebasiccomponentsofintegro-opticalmodulators,switchers,filters,nonlinearopticalfrequencyconverters,commutators,andlightbeamdeflectorsforcorrelationandspectralanalysisoflightsignalsduringtheirprocessing.Hybridbistableopticaldevicesonthebasisofchannelwaveguidesoperatingatsmalllevelsofopticalpowerareusedassensorsoflightintensityinautomaticsystemsandopticalmultivibrators.
Forintegralnonlinearopticaldevices,channelwaveguidesareofgreatinterestandhaveadvantagesoverplanarones.Propagationofalightbeamalongachannelincreasestheluminousenergyconcentrationand,accordingly,theefficiencyofnonlinearconversion.Thephasematchingconditionscanbemaintainedbyvaryingthegeometricalsizeofwaveguides.
Inthischapter,wearemainlyconcernedwithdevicesbasedonwaveguidelithiumniobateandtantalatestructuresandinvolvingelectro-opticeffect.
Asdistinctfromthediffusionmethod,liquid-phaseepitaxyforobtaininglightguidestructuresinlithiumniobate-tantalatesystemsisveryflexibleandsuggestsnewpossibilitiesforcreatingintegro-opticschemeswithintegrationofelementsbothinhorizontalandverticalplanes.Inaverticallyintegratedstructure,waveguidelayersareseparatedbylayersofasolidsolutionoflithiumniobate-tantalatewith
alowerrefractiveindexwhichplaystheroleofanopticalinsulator.Nootherinsulatinglayersofothermaterials(SiO2,Al2O3)appliedinanumberofintegratedsystemsareneededheresinceseparatinglayersaregrowninaunifiedtechnologicalcycleofobtainingdevicestructures.
WeshallnowcarryoutacomparisonstudyofTi-diffusionandepitaxialtechniquesofintegro-opticdevicesonanexampleofelectro-opticswitchingelementsincrossing-channelwaveguidesorelectro-opticX-switchers(Betts
Page293
etal1986).Single-modeswitchersareoftheutmostpracticalinterest.Inthiscase,forasufficientlysmallwidthofwaveguides,theoperationofsuchaswitcherisbasedoninterferenceofevenandoddmodesintheintersectionregionandonelectriccontroloftheirphaserelations(Neyer1984).Switchersofthistypehavearathersimpledesignandarefairlystableascomparedtoothertypesofswitchers(Bettsetal1986).Thecontrolstructureconsistsoftwometallicelectrodeswithagapof1÷3µmpositionedonthelightguidestructureandorientedalongthelongdiagonalofarhombforanefficienteven-modecontrol.Toreducethetotallossesthistypeofdevice,thereisabufferlayerbetweenmetallicstripsandthelightguidelayer.
Thetechnologicalprocessofmanufacturingsuchlightguidesusingthediffusionmethodincludesthefollowingoperations:
-depositionofacontrolledwidthoftitanium,
-photolithographyforobtainingapictureofchannellightguides,
-titaniumdiffusionforobtainingthelightguidestructure,
-depositionofaSiO2orAl2O3insulatinglayer,
-surfacemetallizationfortheformationofacontrolledstructure,
-placinginsidethedevice.
Itshouldbenotedthatthediffusionprocessallowstheformationofonlynonsymmetriclightguidestructures,whichsuggestsdifficultiesinafurthermatchingofsuchastructurewithfibrespossessingaxialsymmetry.Thecalculationsshow(Lazarev1986)thatevenuponaprecisiondiffusionofTiwiththepurposeofobtaininganoptimalprofileofachannellightguideformatchingwithaxial-symmetricfibresthereoccurmorethan10%oflossesduetomatching.Fibresarenowtypicallyface-adjustedtointegro-opticaldevices,whichrequires
polishingofdevicefaces.ThepositionofTi-diffusivelightguidesdirectlyinthenear-surfaceregionimposesstrictrequirementsupontheprocessingofplatefacestoremoveoravoidpossiblechippingsintheregionofthelightguidingstructure.
Whenadeviceismadeusingepitaxialtechnique,thenaftertitaniumisdeposedandphotolithographyisperformed,theimmersedlightguidingstructuresareformedbythediffusion-filmmethod.Thisyieldssymmetriclightguidingstructuresallowingadecreaseoflossesinthecourseoffibreadjustment.Italsolowerstherequirementsonthesizeofchippingsduringfacepolishing,andaninsulatinglayerneednotbespeciallydepositedsinceitisformedinthetechnologicalprocessofobtainingimmersedlightguidingstructures.
6.1Principalcharacteristicsofwaveguidingelectro-opticmodulators
Modulatorsarecharacterizedbyacontrolvoltage,bythebandwidth,bythemaximalmodulationdepthandbyinsertionlosses(Tamir1979;MustelandParygin1970).WeshallconsiderthesecharacteristicsfollowingAlferness(1982).
6.1.1Controlvoltage
Animportantcharacteristicofmodulatoriscontrolvoltage(aminimalvoltageforwhichthemodulationdepthismaximal).Inspiteofthefactthatthe
Page294
Fig.6.1Integro-opticphasemodulator.a)generalview;b)sideview(Alferness1982).
magnitudeofcontrolvoltagedependsonaspecificmodulatorscheme,thebasicconclusionsontheeffectoftheexternalfieldcanbemadeonthebasisofasimplephasemodulator(Fig.6.1).Ifelectrodesareplacedonbothsidesofawaveguide,thehorizontalcomponentoftheelectricfield isused,whileifanelectrodeliesonthewaveguidesurface,theverticalcomponentoftheelectricfield isused.Inthelattercase,todecreaselightlossundertheelectrodes,especiallyforpolarizationoftheperpendicularplaneofthecrystal(TM-modes),abufferlayerofSiO2orAl2O3shouldnecessarilybedepositeduponthewaveguidesurface(Ucharaetal1975).Inbothcases,crystalorientationissochosenthattheelectro-opticcoefficientr33hasthehighestvalue.Whenlightpropagatesbetweentheelectrodes,thecoefficientr33isusedforTE-modesonthey-cut,whereaswhenlightpropagatesundertheelectrodes,r33isusedforTM-modesonthez-cut.
Therefractiveindexvariationundertheactionofthefieldduetoelectro-opticeffectisgivenbytheexpression
wheredistheinterelectrodegap,Gistheoverlapintegraloftheelectrodefieldandthemodefield: dA,whereEisanormalizedfieldofthemode,xisanappliedelectricfield,Visvoltage.
Theconditionfora100%modulationdepthcanbewrittenas
whereDb=(2p/l)dn*,Listheinteractionlengthbetweentheappliedfield
Page295
andthelight,p=1anddependsonthetypeofmodulator.So,
ThetransmissionbandwidthcanbeshowntobeinverselyproportionaltoL(Alferness1982).So,tobroadenthebanditisnecessarytodecreasethequantityV×Lbyminimizingthegeometricparameterd/G.Tothisendoneshouldknowhowtheoverlapintegraldependsontheinterelectrodegap,onthemagnitudeofthemodefield,ontheelectricfieldcomponent( or )andonthepositionofthewaveguiderelativetotheelectrodes.Thedependenceoftheoverlapintegralontheseparameters(forhalf-infiniteelectrodes)wasconsideredbyMarcuse(1982).Themodefielddistributioninwidth(withdimension )isassumedtobedescribedbytheGaussianfunctionandindepth(withdimension )bytheHermitian-Gaussianfunction.Forawaveguidelyingbetweentheelectrodesinagapdequaltoorslightlygreaterthanthemodedimension,symmetricpositionrelativetotheseelectrodesisoptimal.Iftheverticalcomponentoftheelectrodefieldisused,thenoptimalisthecaseofcoincidentinneredgeoftheelectrodewiththemodefieldedge(withdimension (Fig.6.1)).Figure6.2illustratesthedependenceoftheproductofthefield-inducedchangeoftheeffectiverefractiveindexbythemodewidth ,onthenormalizedgapsize forthecasewhenboththeverticalandhorizontalfieldcomponentsareused(Marcuse1982).Thesedependencesshowthatanincreaseofdn*requiresadecreaseofthewaveguidemodeandofagapbetweentheelectrodes, .Forthecaseoftheuseofthis requirementislesscriticalthaninthecaseof (Alferness1982).
Aphotorefractiveeffectmayresultinasignificantincreaseofthecontrolvoltage(ataconstantvoltage)duetocompensationoftheappliedfieldbyphotoelectrons.Therearetworeasonsforthis:first,thephotoconductivityintheexternalfieldand,second,the
photogalvaniceffect(Schmidtetal1980;YamadaandMinakata1981).
6.1.2Bandwidth
Thewidthofthemodulatorfrequencybandisdeterminedbyelectrodecapacitanceprovidedthattheelectrodelengthismuchsmallerthanthewavelengthoftheradiofrequencysignal.Itcanbeshownthatthecapacitanceofthesystemofelectrodesperunitlengthisequalto(Alferness1982)
wherers=(d+1)/2G, ,Gistheelectrodewidth,for(LiNbO3)isthedielectricconstantandKisthe
ellipticintegral.
TheratioC/Ldecreasesandthebandwidthincreases(Df=(pRC)-1,Ris
Page296
Fig.6.2Theproductofthefield-inducedeffectiverefractiveindexbythewidthofthemode andtheoverlapintegralFasfunctionsofnormalisedvalueofthegapforfields
(a)and (b)(Alferness1982).
Fig.6.3CapacityofanelectrodesystemperunitlengthC/Land
productofthebandwidthbytheelectrodelengthDfRC.Lversusthevalueoftheinterelectrodegap-electrodewidthsratiod/G(Alferness1982).
theloadresistance)withincreasingratiod/G(Fig.6.3).Sincetheproductofthecriticalfrequency,whichisdeterminedbythesignalpassagetime,bytheelectrodelength cm(cishespeedoflight),itisinexpedienttoused/G>0.8.
Itisknownfromtheforegoingthattolowerthecontrolvoltage,thegapbetweentheelectrodesshouldbesmall.Thus,toobtainawideband,itisnecessarytoreducetheelectrodewidth(since ).A
reductionoftheelectrodewidthis,however,limitedbytwofactors.First,itshouldnotbemademuchlessthanthewaveguidewidthlesttheoverlapoftheelectricandopticalfieldsshouldbesmall.Second,whentheelectrodewidthissmall,theresistanceincreasesandthebandwidthdecreasesaccordingly.
Sincethecontrolvoltageandthebandwidthareinverselyproportionaltothedevicelength,thecontrolvoltage-to-thebandwidthratiocanbethoughofasafigureofmerit:
Page297
TheratioV/Dfdecreaseswithdecreasinggap(downto )becauseC/Lincreasesslower(Fig.6.3)thandecreasesthecontrolvoltage(Fig.6.2).Butastheinequality decreases,anincreaseofC/Lwillnotbecompensatedbytheloweringofthecontrolvoltage.So,V/Dfhasaminimumford/w<0.5and .InsofarasC/Ldependslogarithmicallyond/G,theelectrodecanbewidenedwithoutanoticeableincreaseofV/Df.
Thesmallestattainablegapisrestrictedbythesmallestattainablemodedimension(Alferness1982): andfrom therefollows
[email protected],Dn=0.01,l=0.63µm:dmin=1µm.Thus,
(since ford/G=0.5),wheretheoverlapintegralG=0.3or0.2formodulatorsthatemploy or ,respectively.Assumingp=1,R=50Ohmandneglectingtheelectroderesistance,onecanobtaintheminimalvalueV/Df:0.5V/GHzand1.5V/GHzforl=0.63µmand1.32µm,respectively(Alferness1982).
6.1.3Modulationdepthandinsertionlosses
SupposethatwithoutanappliedvoltagetheintensityoflightcomingoutofthemodulatorisequaltoI0.Thenthemodulationdepthisdeterminedas(Barnoski1974):
whereIistheintensityoflightatacorrespondingvoltage.Whenacontrol(halfwave)voltageisapplied,themodulationdepthiscalledamaximalmodulationdepth.Theactionofthemajorityofmodulatorsisbasedonthephasechange( )whichistransformedintothechangeofintensity.Forinterferentionalmodulators,thedependence
ofthemodulationdepthonthephaseshifthastheform(Barnoski1974):
whileforwaveguidingdevicesemployingphasechangeintheconnectionoftwowaveguidesortwowaveguidemode
Page298
whereListheinteractionlengthandkisthecouplingconstant.
Thetheoreticallyadmissiblemodulationdepthis100%,whileinexperimentitisnormallyalittleless(about96%)duetolightscatteringonwaveguidedefectsandontheelectrodestructure,andalsoduetoconversionoflightpolarization.Thefirstreasonresultsfromthetechnologicaldifficultiesofmanufacturingawaveguidemodulator(micronsize,highclassofsurfacepolishing,etc.).Thesecondisduetothephotorefractiveeffectandtheassociatedlightpolarizationconversion.Thedependenceofthemodulationdepthofawaveguidemodulatoronthepolarizationoflightis,inturn,aconsequenceoftwofacts.First,theelectro-opticcoefficientsarenotthesameforTE-andTM-waves:inthecaseofz(y)-cutoflithiumniobate,whenthefieldisdirectedalongthezaxisforaTE(TM)-waveDb~r13V,andforaTM(TE)-waveDb~r33Vandr33/r13=3;second,theincrementoftherefractiveindex,Dn,isnotthesameforTE-andTM-waves(Dne>Dno),andthereforethemagnitudeofthemodefieldandthecouplingcoefficientdepend,inthecaseofmatchedwaveguides,onthepolarizationoflight(Leonberger1983).
Adecreaseinthemodulationdepthduetoconversionofpolarizationoflightonthepassivepartofthemodulator(unaffectedbytheelectricfield)canbestoppedbyplacingatthemodulatorexitananalyserallowingonlyonepolarizationoflight(eitheraTM-oraTE-wave).Butthiswillstimulatetheinsertionloss.
Theinsertionlossisdeterminedasfollows(Barnoski1974):
whereIinistheintensityoflightenteringthemodulator.Insertionlossesalsoincludetheinputandoutputlossesandthosedueto
propagationalongthemodulatingstructure.
Itshouldbeemphasizedthattheinsertionlosseswillalsobeincreasedbyaphotoinducedradiationoutputfromthewaveguides.
6.2Photoinducedpolarizationconversion
Ifvoltageisappliedtoelectrodesplacedonbothsidesofawaveguide(forthey-cutoflithiumniobate),thenalongwiththephasemodulationtheamplitudemodulationofradiationmayoccur.RadiationintensityvariationmustbearesultofphasemismatchbetweenTE-andTM-wavesand,therefore,ofachangeinthedegreeofpolarizationconversion.Theestimationbyformula(6.1)yieldsacontrolvoltageofabout7VforL=10mm,d=10µm,l=0.63µmandG=0.3.SuchamplitudemodulationwasexperimentallydiscoveredbyZolotovetal(1983).
Thewaveguidesweremanufacturedbytitaniumthermodiffusionintolithiumniobatecrystals(they-cut)fromstrips,15µmwideand300Åthick,depositedalongthexaxis.Thediffusionwascarriedoutfor6hinairatatemperature
Page299
of960°C.Thentheelectrodestructure(twoparallelaluminiumstrips15µmwideand14mmlongwerephotolithographicallydepositedonbothsidesofthewaveguideonthecrystalsurface.Thedistancebetweentheelectrodeswas10µm(Fig.6.1).
Atthewavelengthoflaserradiation,0.63pro,an wasexcitedwhosepolarizationcorrespondedtothatofanordinarywave.Withanincreaseofthepoweroflightintroducedtothewaveguide,thepowerwasloweredandan appearedwhichcorrespondedtoanextraordinarywave.ThedegreeofpolarizationconversiondependedonthepoweroflightintroducedtothewaveguideP,andforP@25µWtheconversionwaspracticallycomplete( ).
Thenthepotentialdifferencewasappliedtotheelectrodes,andthepowerofthe wasmeasuredasafunctionofvoltageV.Thevoltageatwhichtheconversionstopped(thecontrolvoltage)andthe onlywasobservedattheoutputincreasedwithincreasingpoweroflightfedintothewaveguide.Thisisevidentlyassociatedwithanincreaseinthemodulationdepthoftherefractiveindexintheholographicgratingand,therefore,withanincreaseofthecouplingconstantbetweenthe and .Whenthelightpowerwasabout5µW,thedegreeofconversion(Pe/Po~60%)wasabout60%andthecontrolvoltagewasequalto~2.5V.Butaftersometime(~30s)thepolarizationreturnedtoitsinitialstatewhichwaslikelyduetothenewlyinducedholographicgratingrestoringphasematchingbetweenthe and modesandduetoacompensationoftheappliedfieldbyphotoelectrons.Ifthepotentialdifferenceofoppositepolaritywasappliedtotheelectrodes,thenwithanincreaseofthevoltagethepowerofthe firstgrew(themaximumwasobservedforV@-3V)andthenstartedfalling.Thisislikelytosuggestthatwhenradiationpolarizationconversionisincomplete,theholographicgratingdoesnotyieldaperfectmatchingbetweenmodesoftheordinaryandextraordinarypolarizationintheabsenceofvoltage
betweentheelectrodes.Whenthepoweroflightwasabout25µW,thedegreeofconversionmadeup95%andthecontrolvoltageincreasedupto7V.Themodulationcurvewasobservedonanoscillographscreentotheinputofwhichasignalwassentfromthephotomultiplierthatregisteredthepoweroflightcomingfromthewaveguide,andasawtoothvoltagewiththeamplitudeof8Vwasappliedtotheelectrodesduring1µs.Thepowerofthe fell( µw)asshowninFig.6.4a,whilethepowerofthe
Fig.6.4Extraordinary(a)andordinary(b)wave
polarizationpowervsvoltage(Kazansky1985).
Page300
-modegrewasshowninFig.6.4b.Whileattheinitialinstantoftimethepowerofthe felltotheminimumatavoltageof7V,afterafewsecondsthemodulationcurvebecamemoregentle(thecontrolvoltageincreased)anditsmaximumwasdisplacedtowardsthehighervoltage.Suchabehaviourofthedependenceofthepoweronthevoltagecanbeexplainedbytheinfluenceofthefieldofspacechangesinducedbytheeffectoftheconstantcomponentofthesawtoothvoltageuponthepolarizationconversionmechanism.Itshouldbenotedthatthemodulationbandwasdeterminednotbytheslowphotorefractionprocesscausedbythechangedriftbutratherby
theelectrodecapacitancewhichinthegivencasemadeup7picofarads,whichcorrespondstothebandwidthof900MHz
calculatedforalodeof50Ohm.
Thepoweroflightcomingfromthewaveguideafterananalysertransmittingradiationpolarizedatanangleof45°tothedirectionofpolarizationofthe and wasmeasuredasafunctionofthevoltage.Herechangedthecharacterofpolarizationoflightundertheactionofvoltagewhichaffectedthephasedifferencebetweenthe
andthe transformedfromthe bymeansofthephotorefractiveeffect(Fig.6.5).
Fig.6.5Thepoweroflightpolarisedatananglep/4tothewaveguideplaneversusvoltage(Kazansky1985).
Itisnoteworthythatontheonehandthediscoveredamplitude
radiationmodulationisundesirablefortheoperationofaphasemodulator,butontheotherhand,theelectro-opticcontroloveraphotoinducedradiationpolarizationconversionconfirmsthemechanismofthisneweffectbasedonphasematchingoftheordinaryandextraordinarypolarizationmodesusingabulkphasegrating;theelectro-opticcontrolcanalsobeusedforlightmodulation.
Thephasemodulatorbelongstosometypesofamplitudeintegro-opticmodulatorsusingcoupledwaveguides(Papuchonetal1975;KogelnikandSchmidt1976)andinterferentionalmodulators(Papuchon1977).
6.3WaveguidemodulatorsonthebasisofTi:LiNbO3
6.3.1Electro-opticmodulatoroncoupledchannelwaveguideswithavariableDb
Themainshortcomingofthemodulatoroncoupledwaveguidesisalowcontrastof90%(Bozhevil'nyetal1981).Toreachahighcontrast,thecouplinglengthbetweenthewaveguidesshouldbeequaltoanintegral(odd)number
Page301
ofpumpinglengths(Papuchonetal1975),whichisdifficultfromapracticalpointofview.Toeliminatethisdefect,suchelectrodesweresuggestedthatcreateincoupledwaveguidesthedifferenceofpropagationconstantsDb=b2-b1whichreversessignanintegralnumberoftimesequaltothenumberofpumpinglengths.Usingthismethodinatwo-sectiondevicegaveanon-offratioof27dBforacontrolvoltageof30V(SchmidtandKogelnik1976).
Thesolutionofthesystemofequations(Kazinsky1985)
forcoupledwaveguideswithavariablesignofDbinthematrixformis(KogelnikandSchmidt1976)
where isthematrixforthemodulatorregionwith
; ;
sin
B1=ksin[x(k2+d2)1/2]/(k2+d2)1/2,wherek=2p/listhecouplingconstant,
Fig.6.6Modulatoronthebasisofcoupledwaveguides
withavariableDb.1,2)waveguide(Zolotoveta11982).
Page302
Fig.6.7Statediagramofamodulatoronthe
basisofcoupledwaveguides(KogelnikandSchmidt1976).
x=L/2,listhepumpinglength,R0andS0arethewaveamplitudesatthewaveguideinput.IfS0=0,thentheconditionforthecrosstalk,thatis,forlightpumpingfromwaveguide1towaveguide2(Fig.6.6)canbeobtainedprovidedthatA2=0:
Forthestraightforwardstate(B2=0)onecanaccordinglywrite
Figure6.7showsastatediagramforasystemofcoupledchannelwaveguideswithavariablesignofDb.Inthisdiagram,thepointslyingonthecurvecorrespondtothestateinwhichthelightiscompletelypumpedoverfromwaveguideItowaveguide2(Fig.6.6),whilethepoints onthecurvecorrespondtothestatewhenthepumpingisstopped.
Theelectro-opticmodulatoronthebasisofcoupledchannelwaveguideswasmanufacturedonaz-cutlithiumniobateplate(Fig.6.6)(Zolotovetal1982).Thesystemofwaveguideswascreated
bywayofsputtering300Å.oftitaniumontotheplatesurfacewithasubsequentetchingoftitaniumthroughaphotoresistivemaskandbydiffusioninairatatemperatureof960°during6h.Thebandwidthofthetitaniummadeup3.5µm,whichprovidedobtainingsingle-modewaveguidesattheradiationwavelengthof0.63.Thedistancebetweenwaveguideswas4.5µm.Todecreasepropagationlossesundertheelectrodes,thewaveguidesurfacewassputteredwithaSiO2film2000Åthick.Theelectrodestructureonthewaveguides(Fig.6.6)wasfabricatedbyetchingthe2000ÅthickAllayersputteredontothecrystalsurfacethroughaphotoresistivemask.Thelength,widthandthedistancebetweentheelectrodeswererespectively8mm,20µmand4.5µm.
Toestablishthepumpinglength,theHe-Nelaserradiationwas,usinga
Page303
Fig.6.8Modulationcharacteristicofmodulatoron
thebasisofcoupledwaveguides(Kazansky1985).
×20microlens,introducedinturnineachofthefivesystemsofcoupledwaveguides,andtheintensityoflightatthewaveguideoutputwasregisteredbyaphotomultiplier.Themaximumintensityoflightinthecaseofthe modewasobservedatacouplinglengthof7mm.Lightpumpingbetweenthewaveguideswasalsoobservedasamodetrackunderamicroscope.Thepumpinglengththusdeterminedwas3.5mm.Theexperimentonlightmodulationwascarriedoutoncoupledwaveguideswithacouplinglengthof7.5µm.Forzerovoltage,theradiationaftertwopumpingswaspropagatedinwaveguide1(Fig.6.6).Whenacorrespondingvoltagewasappliedtotheelectrodes,thephasemismatchontheregion0<x<L/2ofcoupledwaveguideswasresponsibleforadivisionofthelightintensityintotwoequalpartsbetweenthewaveguides.IntheregionL/2<x<Lofcoupledwaveguidestheelectro-opticallyinducedphasedifferencehasareversesignascomparedtothephasedifferenceontheregion0<x<L/2.Thisaffectsthevariationintheenergypumpdirectionanddecreasesthelightintensityinwaveguide1.
Toobtainthemodulationcharacteristicofelectrodes,asawtoothvoltagewithanamplitudeof20Vwasappliedtotheelectrodes.Theoutputradiationwasappliedtoaphotomultiplierwhosesignalwasobservedontheoscillographscreen(Fig.6.8).Themaximalmodulationdepthwas14dBandwasreachedatavoltageof~9V.
Thetotallightlosseswere8dB.Thecapacitanceoftheelectrodesystemmadeup4.4picofarad.
Whenaconstantcontrolvoltageisapplied,thelightpoweratthemodulatoroutputwasfirstdecreased,butafter10sitincreaseduptotheinitialvalue;therelaxationtimewasindependentofthelightintensity.SucharelaxationislikelytobeduetotheconductivityofthebufferlayerofSiO2resultedfromanincompleteoxidationofSiO2(Tangonanetal1978).
Thebasisoftheeffectiverefractiveindexmethodmodefielddistributionallowedcalculationofthemodefielddistributioninawaveguideandpumpinglengthsweredetermined.Forthe thepumpinglengthwas3.6µmandforthe itwas60mm.
Thelargepumpinglengthofthemode ascomparedtothepumpinglengthofthe isexplainedbythefactthattheincrementoftherefractiveindexDnand,therefore,modelocalizationwithanextraordinarypolarizationof largerthatthemodeswithanordinarypolarizationof (Alfernessetal1979).Thus,theexperimentalvalueofthepumpinglengthinthecaseof isincloseagreementwiththetheoreticalvalue,while
Page304
Fig.6.9Interferometertypemodulatorwith
aninducedchannelwaveguide(Zolotovetal1982).
inthecaseof thetheoreticalcalculationisindicativeofthepracticallackofcouplingbetweenthewaveguides,whichwasobservedinexperiment.
TheoverlapintegralofthemodefieldwiththefieldofelectrodeswasevaluatedfromthestatediagramsofthesystemofcoupledchannelwaveguideswithDbelectrodes(Fig.6.7)
Whenthelightintensityincreasesupto5µW,thepoweroflightatthemodulatoroutputwasdecreased,andnophotoinducedpolarizationconversionwasobserved,whichislikelyduetolargelossesoflightofextraordinarypolarization(oftheTM-mode)undertheelectrodes(6dB/cm)becauseofimperfectionofthebufferlayerofSiO2.Adecreaseoflightintensityisevidentlyconnectedwiththephotoinducedvariationoftherefractiveindexofthewaveguides,whichleadstophasemismatchbetweenmodesofcoupledwaveguides.
6.3.2Interferometricandperfectinnerreflectionmodulators
Zolotovetal(1982)consideredthemechanismoftheactionofatechnologicallysimpleinterferometertypemodulator(Fig.6.9).When
voltageisappliedwithapolaritycorrespondingtoanincreaseoftherefractiveindexinacrystal,intheregionundertheelectrodesthereformsachannelwaveguide(Channin1971).Themodeofthiswaveguidehasasmalltransversedimensioncointhewaveguideplaneand,therefore,alargerdiffractiondivergence~l/w.InthefartherregionthismodemustinterferewiththemodeofaplanarTi-diffusedwaveguide(whichbelongstothecontinuumofradiationmodesofthechannelwaveguide)havingasubstantiallylargertransversedimensionWandasmallerdivergence~l/W(i.e.asmallangulardimensioninthefarregion).Thephasedifferenceofthese
twowaves ,wheredn*isthedifferenceofeffectiverefractiveindices)dependsonthemagnitudeoftheappliedvoltage.Inthecasewhenwavesareinthecounterphase
Page305
( ),inthecentreoftheinterferencepatternaminimummustbeobserved,whereasattheboundariesofthispicturenocompletemutualwaveextinctionwilloccursincetheirangulardimensionsdifferstronglyfromoneanother.Bytheestimates(6.1)thecontrolvmakesup(forl=0.63µm,d=6µm,L=5mm):
Toobtainthemaximalmodulationdepth,weshallfindtherelationbetweenthewidthoftheGaussianbeamWincidentonthemodulatorandthewidthcoofthemodefieldoftheinducedchannelwaveguide.Thenormalizedfieldoftheincidentbeamhastheform
Accordingly,thenormalizedfieldofthemodeofthechannelwaveguideweapproximatebytheGaussianfunction
whereh=2/[w/W)+(W/w)]istheefficiencyoflightinputintothechannelwaveguide.
ForthelightpropagatingoutsidethechannelwaveguideErad=Einc-Echan.Theintensityoflightinthefarregion isrelatedtothe
fieldinthenearregionas
where ,(herey1isthecoordinateinthedirectionperpendiculartothelightpropagationdirectionatadistancexfromthemodulator.Thentheinterferencepatterninthefarregioninthecaseofinphasewaveinterferencehastheform
andinthecaseofcounterphasesubtraction,accordingly(Fig.6.11)
Page306
Fig.6.10Modulationcharacteristicofaninterference
typemodulator(Kazansky1985).
Fig.6.11Interferencepatternsinthefarregion.Inphasewaveinterference(/+)andcounterphasesubtraction
(/-)(Kazansky1985).
Fromthisweimplytheconditionwheninthecentreoftheinterferencepatternthelightintensitywillbeequaltozero
Toperformanexperimentonasubstrateoflithiumniobate(y-cut),aplanarwaveguidewasmanufacturedbywayoftitaniumdiffusion(theTilayerthickness300Å).Theelectrodestructurewasdepositedphotolithographicallyonthecrystalsurface,asshowninFig.6.9.Thiselectrodestructureconsistedoftwoparallelaluminiumstrips5mmlongand4µmwide.Thedistancebetweentheelectrodeswas6µm.
He-Nelaserradiationwasintroducedintothewaveguidebymeansofarutileprism.Beamfocusingbyalensewithafocusdistanceof20cmmadeitpossibletoobtainthedimensionoftheGaussianbeamWatthewaveguideinputequalto60µm.Asthepotentialdifferenceontheelectrodeschangesfrom0to5V,thefieldpatterninthefarregionchangesaccordingtothemodelconsideredabove,andthemaximalmodulationdepthobtainedforV=5Vwas95%(Fig.6.10).Figure6.11presentsthemodulationcurveofsuchamodulatorobservedonthescreenofanoscillograph(theappliedvoltagevariedfrom0to20V).Themodulationcurvehasmaximaandminimatypicalofinterferentialphenomena.Itshouldbenotedthatalowvalueofthecontrol
Page307
Fig.6.12Totalinnerreflectionmodulator(Kazansky1985).
voltage,alargemodulationdepthandthepossibilityofrealizingawide(~1GHz)modulationbandmakethistypeofmodulatorsfairlypromisingforpracticaluse.
Tsaietal(1978)andSheem(1978)consideredthemechanismofoperationofthetotalinternalreflectionmodulator,shownschematicallyinFig.6.12.
Whenvoltageofanappropriatepolarityisappliedtotheelectrodes,intheregionbelowtheelectrodestheelectro-opticeffectresultsintheformationofalayerinwhichtheeffectiverefractiveindexofthewaveguidemodeisdecreasedbythevaluedeterminedbytherelation(6.3).MakingallowanceforthisrelationonecancalculatethereflectionfactorofthewaveguideH-modeincidentontheperturbedlayeratanangleq1(BornandWolf1979)
where
Undertheconditionn'*<n*sinq1thereoccursatotalinternallightreflection.So,varyingthevoltageappliedtotheelectrodesonecanchangethedn*valueand,therefore,thelightreflectioncoefficient.
Radiationwithawavelengthof0.63µmwasintroducedintothewaveguideusingarutileprismandwasdirectedtotheelectrodesatanangleof89.5°.Thedependenceofthepowerofthereflectedlight,Prefonthevoltageappliedtotheelectrodeswithintherangefrom0to20VisillustratedinFig.6.13.Forthepotentialdifferenceof15Vthereflectioncoefficientwas95%±3%.Thisvalueagreescloselywiththe94%calculatedbyformulae(6.3)and(6.21).Thecapacitanceoftheelectrodestructuremadeup2pF,whichadmits
Page308
Fig.6.13Modulationcharacteristicoftheinnerreflection
modulator(Kazansky1985).
inprinciplethebandwidthof>1GHzfortheloadresistanceof50Ohm.
Whenlightofpower1mWwasintroducedintothemodulators,inthewaveguidesthereoccurredastronglightscatteringinthem-line(Tangonanetal1977)causedbyinducedopticalinhomogeneities,whichissimilartothescatteringwithoutpolarizationreversalinbulkcrystals(MagnussesandGaylord1974;Voronovetal1980).Suchascatteringwasresponsibleforadecreaseofthemodulationdepth(to~50%).Butnophotoinducedradiationpolarizationconversionwasobserved,whichisalsoassociatedwithaphotorefractivebeamscatteringinaplanarwaveguideand,therefore,withadecreaseofoflightintensityinthiswaveguide.
6.4Practioalexamplesofwaveguideelectro-opticmodulators
6.4.1Opticalwaveguideswitchmodulator
Fastwaveguideopticalswitchmodulatorsareimportantcomponentsforfuturewidebandlightwavecommunicationsystems.High-speedswitchingmaybeespeciallyusefulfortimedivisionmultiplexing.Severalhigh-speedswitches(CrossandSchmidt1979;Mikamietal1978)andmodulators(NeyerandSohler1979;AuracherandKiel1980;Leonberg1980)usingTi-diffusedlithiumniobatewaveguides.Mostofthesedeviceshavedemonstratedmodulationbandwidthof
about1GHz(approximately500psswitchingtime)andrequirerelativelylongdevicelengthof3to10mm.Highsinusoidalmodulationrateshavebeenachievedusingatravelingwavegeometry,againwithlongdevicelength(Izutsuetal1977).Auniquelydesignedandfabricatedopticaldirectional
Fig.6.14Schematicdrawingofopticalwaveguidedirectionalcouplerswitchmodulator(Alfernessetal1981).
Page309
couplerswitchwithademonstratedswitchingtimeof110pswasdescribedbyAlfernessetal(1981).High-speedswitchingwasachievedbyusingveryshort(750µm)electrodeswithasmall(1µm)interelectrodegap(Fig.6.14).Thesmallcapacitanceresultingfromtheshortdevicelengthyieldshigh-speedswitching.Atthesametime,thesmallinterelectrodegapallowsalowswitchingvoltageinspiteoftheshortdevicelength.
AschematicofthewaveguidedirectionalcouplerswitchisshowninFig.6.14.Thedirectionalcouplerwasdesignedsothat ,wherekisthecouplingcoefficientandnistheoddintegersothatintheabsenceofanappliedfieldmostofthelightincidentinonewaveguidecrossesovertotheother.Formodulatorapplications,thisconditionneednotbestrictlysatisfied.Applicationofanappropriatevoltagesufficientlymismatchesthetwowaveguidessothatthelightstaysintheincidentwaveguide.
Theopticalswitchingtimecanbeminimizedbyfixingthecontrolvoltage(power)atsomeacceptablelowlevel.ForthelumpedelectrodesconsideredheretheswitchingtimeisgivenbytheRCtimeconstant,whereCiselectrodecapacitanceandR=50isaparallelresistancetomatchtoanexternaldrivingcircuit.Theelectrodecapacitanceisgivenapproximatelyby(KaminowandStulz1975)
whereLandWaretheelectrodelengthandwidth,respectively,anddistheinterelectrodegap.NotethatthecapacitanceincreaseslinearlywithLbutitincreasesonlylogarithmicallywithdecreasinggap.
Clearlyforhigh-speedswitching,shortdevicelengthisdesirable.However,thedevicelengthmustbesufficientlylargetoyieldanacceptablylowswitchingvoltage.Therequiredelectro-opticallyinducedphasemismatchtoswitchthelightbacktotheincident
waveguide(assumingonecouplinglength)is
wherethepush-pulleffectforelectrodesplacedontopofthewaveguides(Fig.6.14)hasbeeninduced.Visthemaximumadmissiblecontrolvoltage,nistherefractiveindex,lthewavelengthandathegeometricaloverlapbetweentheopticalandappliedelectricfields.Therequiredlengthistherefore
Fromequations(6.22)and(6.24)theRCswitchingtimeis
Page310
Fig.6.15Calculatedrequiredelectrodelengthandresultingmodulationbandwidthversusinterelectrodegap.AdrivevoltageV=5V,electrodewidthW=30µm,
opticalwavelengthl=0.6328µm,andoverlapparametera=0.5areassumed(Alfernessetal1981).
Theresultsofequations(6.24)and(6.25)areshowninFig.6.15,wheretherequiredLandtheresultingmodulationbandwidthDf=1/ptareplottedversustheinterelectrodegap.ItisassumedthatV=5V,r=r33(lithiumniobate)=30×10-12m/V,l=0.6328µm,W=30µm,anda=0.5andthatineachcaseLcorrespondstoonecouplinglength.Clearlyforfixedswitchingvoltagethemodulationbandwidthismaximizedbyusingasmallinterelectrodegapd.Asmalldisdesirablebecausealthoughitresultsinalargercapacitance/length,theresultinglargerelectricfield(forafixedappliedvoltage)allowsashorterdevicelength.Becausetheelectrodecapacitancedependslinearlyuponlengthandonlylogarithmicallyupond,thesmallgapmakespossibleanetenhancementoftheswitchingspeed.Ofcourse,theresultingshortlengthisalsodesirableforincreasedpackingdensityindcswitchingnetworksandresultsinloweropticalandelectricalloss.
Specialfabricationcareisrequiredtoachievethedesiredone-micronelectrodegapalignedoverthewaveguides.Thislimitationwas
overcomeusingthenoveltwo-stepalignmentprocedureoutlinedinFig.6.16.First,theelectronbeamwrittenelectrodemaskwith1µmgapwasintentionallymisalignedlaterallybyabout1µm.Thepatternwasexposed,developedandchrome/aluminiumelectrodespatternedbyliftoff.Theresultisthatwhileoneelectrodeisproperlyalignedoveronewaveguide,becauseoflinebroadening,theotherisnot.Thesameelectrodepatternisthenalignedoverthewaveguidesasecondtime,howeverwithanintentional1µmshiftintheoppositedirection.Afterasecondevaporationandliftoff,thedesired1µminterelectrodegapalignedovertheinterwaveguidegapisachieved.Inaddition,toprovidethedesired1µmgap,thedoublemetalthicknessobtainedbythistechniqueisbeneficialtoreducetheelectroderesistance.
Thedevicewasevaluatedatl=0.6µmusingtheTMpolarizationwhichseesther33coefficient.Usingdcconditionswithasix-voltbias,anadditional6-Vmodulationresultsinanabout-7dBmodulationinthelightoutputfromthecrossoverwaveguide.Theswitchingspeedofthisdevicewhendrivenbyashortelectricaldrivepulsewasmeasuredwithanovelopticalsamplingtechniquereportedindetailelsewhere(Alfernessetal1980).Asequenceof
Page311
Fig.6.16Fabricationstepsforachieving1µmelectrodegap
alignedoverthe1µminterwaveguidegap(Alfernessetal1981).
shortelectricaldrivepulsesfromanelectricalcombgeneratordrivesthemodulator.Thesepulsesareinsynchronismwiththepicosecondopticalpulsesfromasynchronouslypumpedmode-lockeddyelaser.Theopticalpulsesarecoupledintothedevice.Themodulatorresponseismappedoutviasamplingbyusinganelectricalphaseshiftertosweeptheopticalpulsetraintemporallyacrosstheelectricalpulsetrainandmeasuringthemodulatoroutputversustimeshift.
6.4.2Thin-filmelectro-opticlightmodulator
Kaminowetal(1973)demonstratedtheutilityofthinfilmsbybuildingandtestinganefficientwide-bandLiNbO3phasemodulatorwhosecharacteristicscanbesatisfactorilyaccountedforbythebulk
electro-opticcoefficientofLiNbO3.
Thepowerperunitbandwidth,P/Df,requiredtodriveabulkmodulatorrodoflengthLandsquarecrosssectiond2wasproportional(KaminowandTurner1966)tod2/L.Theminimumvalueofthisfactorisdeterminedbydiffractionofthelaserbeampassingthroughthemodulatorcrystal.Withthebeamfocusedsothatthewaistoccursatthecentreoftherod,theminimumvalueford2/Lis4l/np,wherelistheopticalwavelengthandnistherefractiveindex.Forthisminimumcondition,thepowerdensityattheedgesofthe
Page312
apertureislessthan1/e2timesthepowerdensityatthecentreoftheaperture.Inordertoalleviatethealignmentproblem,modulatorsareusuallydesignedwithasafetyfactorS(KaminowandTurner1966)suchthat
withS>3.
Inaplanarwaveguide,thereisnobeamspreadingnormaltotheplane,butdiffractionintheplanestilllimitselectrodespacingaccordingto(6.26).However,sincealignmentissimplerandreflectionsfromcrystalsurfacesarenotaproblem,onemayemploytheminimumvalue intheplanarstructure.
Kaminowetal(1973)haveusedthesimplemodulatorstructureillustratedinFig.6.17:aLiNbO3planarwaveguidewithaluminiumelectrodesevaporatedonthesurface,andinputandoutputrutileprismcouplers.Theout-diffusedcrystalhasdimensionsof15×2×5mmalongthea,b,andccrystalaxes,respectively.Theextraordinaryindexprofileisgivenby
wherexisthedepthbelowthesurface,A=4×10-3,andB=530µm.Theguide,whichcansupportabout198modes,isexcitedinTEmodesviatheinputcouplerbya0.633µmlaserpolarizedalongthecrystalcaxis.
Theelectrodeswereformedphotolithographicallywithdimensionschosensothat
wherebistheelectrodespacingand .Theextraordinaryindex,ne,measuredonasampleatl=0.633µm,is2.214.
AsindicatedinFig.6.18,thewidthoftheelectrodes,a,ischosensothat .ThecapacitanceCforacoplanarcondenserwitha=bonauniaxialcrystallikeLiNbO3havingdielectricconstantsea=43andec=28along
Fig.6.17Thin-filmLiNbO3electro-opticphasemodulator(Kaminovetal1973).
Page313
Fig.6.18CoplanarelectrodeonLiNbO3guiding
layer(Kaminovetal1973).
theaandcaxes,respectively,isgivenapproximatelyby(ProkhorovandKuz'minov1990)
Themodulatingfieldcomponentsjustbelowthesurfaceofthecrystalare
whereVisthevoltagebetweenelectrodes.TheEycomponentdecreaseswithdepthatleastasfastas(Engan1969)exp(x/x0),where
Formosteffectiveuseofthemodulatingfield,thepenetrationdepthoftheopticalbeamshouldbecomparablewithx0.TheelectrodedimensionswereL=6.2mm,a=44µm,andb=57µm,yieldingS=1.22,x0=45µm,andC=2.0pF.Themeasuredcapacitanceat50MHzwasabout3pF.
IfaloadresistanceRisplacedinparallelwithCandthecombinationisdrivenbyamatchedvoltagegeneratorwithimpedanceR,thebasebandwidthisgivenby(KaminowandTurner1966)
ForR=50WandthecalculatedC=2pF,themaximumbandwidthis
Df=3.2GHz.Transit-timelimitationsareabove3.2GHzforL=6.2mm.
Forthecrystalcaxisorientedalongy,thephasemodulationindexis
wherer33istheelectro-opticcoefficientand istheeffectivemodulatingfield.Thefactoruisanumberlessthanunitythattakesaccountofthefact
Page314
Fig.6.19Apparatusforheterodynemeasurementofthephase
modulationindex(Kaminovetal1973).
thatEyvariesacrossthebeam.Withr33=31×l0-12m/V,thecalculationyieldsh/V=0.18u/V.
Themodulationindexcanbemeasuredbyusingtheheterodynesystem(Kaminow1965)illustratedinFig.6.19.ThestabilizedHe-Nelaseroscillateinonlyonelongitudinalmodebecauseoftheirrestrictedlength.Thelocal-oscillatorlasercanbesweptovera500-MHzrangewithoutappreciablevariationinamplitudebyvaryingthemirrorspacing.Thespectrumofthemodulatedcarrierlasermixeswiththelocaloscillatorinaphotodiode;thephotocurrentispassedthrougha70-MHz-i.f.amplifierandisdetectedanddisplayedonanoscilloscope.TheratioofsidebandtocarrieramplitudesisJ1(h)/J0(h),whereJnisthenthorderBesselfunction.Theamplituderatioismeasuredwiththeaidofcalibratedopticalattenuatorsplacedinfrontofthelocaloscillator,andhiscalculatedfromtheresult.Theuseofinputandoutputprisms,ratherthanfocusingthebeamintoandoutoftheedgesofthelayer,ensuresthatonlyguidedlightisdetected.
Intheexperiment,aGeneralRadiooscillatorfeedsaminiature50Wcoaxialcableleadingtoapanelconnectoradjacenttothemodulatorcrystal.Thingoldwiresfromtheconnectorconnectthevoltagetotheelectrodesonthecrystal.Thecapacitanceoftheconnector,leads,andelectrodesmeasuredattheconnectorisabout4pF.Inordertoobtain
acorrectreadingofVathighfrequency,itisnecessarytoplacethevoltmeterprobeindirectcontactwiththeelectrodes.
Themeasurementsyieldh/V=0.13V-1,constanttowithin10%overtheavailablemeasuringrangeoftheapparatus,50-500MHz.Voltagewasalsovariedfrom0.7to7Vwithoutalteringh/V.Themeasuredandcalculatedvaluesofh/Vagreeiftheeffectivefieldfactoruissetequalto0.7,whichisreasonablyclosetounity.Thus,Kaminowetal(1973)confirmthatthebeampassescleanlybetweentheelectrodesinthex=0planeanddoesnotpenetratemuchdeeperthanx0,justifytheassumptionthattheelectro-opticcoefficientsintheguidinglayerandbulkcrystalarepracticallythesame,anddemonstrateexperimentallyabasebandwidthatleastasgreatas500MHz.
Theobservedvalueofumayseemsurprisinglyclosetounityinviewofthefactthatthepenetrationofthemodulatingfieldisapproximatelyx0=45µmwhilethethicknessoftheguidinglayerisapproximately
Page315
B=530µm.Thelikelyexplanationisthat,byadjustingtheinputangletotheprismcouplerformaximummodulation,onlytheshallowlow-ordermodesareselectivelyexcited.Theexperimentalerrorinthemeasurementofh/Visprobablylessthan15%.Thepeakvoltagerequiredtoobtainh=1radis7.7V.ThecorrespondingpowerP=V2/2Rconsumedinthe550Wloadis590mW,and,forDf=3.2GHz,P/Df=0.19mW/MHz.IfoneusesthecapacitancemeasuredattheconnectorratherthanthecalculatedC,DfwillbehalvedandP/Dfdoubled.
InordertoimproveP/Df,theopticalbeamandmodulatingfieldsmustbeconfinedtosmallercrosssectionsovertheirinteractionlength.Opticalconfinementinthey=0planecanbeimprovedbyreducingtheout-diffusiontimeand/ortemperatureinordertoreducethelayerthickness(KaminowandCarruthers1973).Otherschemesarebeingconsideredthatwillguidetheopticalbeaminthex=0planeinordertoeliminatediffractioneffects;thenb2/Lmaybereducedindefinitely.Inordertousethemodulatingfieldmosteffectively,themodulatingfielddistributionshouldbetailoredtojustoverlaptheopticalbeam;forthecloselyconfinedopticalbeam,thiscanbeachievedbyreducingtheelectrodespacing.
6.4.3Braggdiffractionmodulator
Intheirwork,HammerandPhillips(1974)reportedtheproductionoflow-lossLiNbxTa1-xO3opticalwaveguidesandtheiruseasthebasisofelectro-opticmodulatorswithover80%modulationatvoltagesbelow5V.
AsimpletechniqueofdiffusingmetallicniobiumintotheLiTaO3substratesproducesahigh-indexsurfacelayerofLiNbxTa1-xO3whichactsasanopticalwaveguide.Theeffectivethicknessandindexcanbecontrolledtoreadilyproducesingle-modewaveguides.Lossesofabout1dB/cmat6328Ahavebeenmeasuredonasingle-mode
guideofthistype.
Usingaperiodicelectrodestructure,Braggdiffractionmodulation(Hammeretal1973)isobtainedwhichswitchesover80%oftheguidedlightatvoltagesof3.5,4.5,and6.5Vforlaserlinesat4976,5592,and6323A,respectively.Theseresultsholdforbothoperationatdcandwithpulserisetimesoflessthan3nsec.Frequencyresponseinthemicrowaverangewithpowerrequirementsbelow0.2mW/MHzisexpected.
Thelowpowerandvoltagerequirementsoftheseopticalwaveguidemodulatorsarecompatiblewithintegratedcircuittechnology.This,plustheexcellentandcontrollablewaveguideproperties,makesthesedevicesextremelyattractiveforuseinavarietyofopticalcommunicationandintegratedopticapplications.
LaserlightiscoupledintothefilmwithSrTiO3prismcouplers.Theeffectiveindexfortheguidedlightmaybecalculatedfromthecouplingangle(Tienetal1969).ThevaluesfoundfallintherangeexpectedforopticalwaveguideswithindicesbetweenthoseofLiNbO3andthoseofLiTaO3.
Forexample,inasingle-modex-zplanesampletheeffectiveindexfortheTE0modepropagatingat51°tothezaxisismeasuredtobe2.188atl=6328Å.Thisfallsintherangebetween2.179and2.237whicharetheindicesinthisdirectionforpureLiTaO3andLiNbO3,respectively.Propagationat51°ischosentooptimizetheelectro-opticcoefficientandretainrelatively
Page316
strongguidingasdescribedbelow.Foraguideofthistypetohaveonlyonemodethethicknessatwhichthegradedindexdifferencebetweenfilmandsubstratefallsto10%ofitsmaximumvalueis0.7-1.6mm(Marcuse1973).
Thelossisdeterminedbymeasuringtheintensityoflightscatteredoutofthewaveguideasafunctionofdistanceusingafibreopticprobe.At6328ÅthelossinthesolitaryTE0modeislessthan1dB/cm.Atthe5592-and4845-ÅHe-Nelaserlinesthelossesare4.3and6.7dB/cm.ThisrepresentsamorerapidincreaseinlossthanthedependenceexpectedforRayleighscattering(l0isthefree-space
wavelength).Itispossiblethatimpurityionabsorption,particularlyFe2+,isresponsible.
HammerandPhillips(1974)notedthatforthex-zsubstratesandtransverseelectricfieldsusedinthemodulator,propagationofaTEmodeinthecdirectiongivesrisetothelargestindexdifferencebetweenlithiumniobateandlithiumtantalate(Dn0=0.113)butanelectro-opticcoefficientisequaltozero.PropagationalongthexdirectionreversesthesituationwithDne=0.021andr33=3×10-12m/V.PropagationintheplaneatanarbitraryanglefwithrespecttothezaxisgivesanindexdifferentialDn'suchthat andaneffectiveelectro-opticcoefficientr'whichisalinearcombinationofr13,r33,andr51.maybechosentomaximizer'.TheresultingvaluesforLiNbO3canbeshowntobef=±51°,r'=±34.4×10-12m/V,andDn'=0.058.Thus,theoperatinganglecanbechosentomaximizetheelectro-opticcoefficientwithoutminimizingtheindexdifferentialrequiredforwaveguiding.
ThewaveguidemodulatorisproducedbyapplyingavoltagetoaninterdigitalelectrodepatterndepositedonthewaveguidesurfaceasshowninFig.6.20a.
Applicationofavoltagetotheelectrodesresultsinanelectro-
opticallyinducedBraggdiffractiongrating.LightenteringthegratingatanangleqBisdiffractedthroughanangle2qBinthewaveguideplanewheresinqB=l0/4Sng.ngistheeffectiverefractiveindexfortheguidedmodebeingconsidered.ThefractionoftheenteringlightdiffractedisI/I0=sin2(Df/2)andtofirstorderinr' ,whereEistheaverageinplanefieldcomponentcausedbythevoltageV0.Thus,I/I0hastheformsin2(BV0).
ThepercentagediffractionasafunctionofvoltageforthreelaserwavelengthsisshowninFig.6.20b.Thesquares,crosses,andcirclesarethedatapointsfor4976,5592and6328Ålaserlines,respectively.Thesolidcurvesareplotsofsin2(BV0)normalizedtothedataI/I0=75%.Thefunctionalagreementisgood.Novariationwasobservedinthesepercentagesfromdcuptopulseswithrisetimesbelow3nsec.Theobservedvariationofvoltagewithwavelength,however,isgreaterthanthefirst-ordertheorypredictsifdispersionintheelectro-opticcoefficientsisignored.ThisdispersionforLiNbxTa1-xO3isunderstudy.Themeasuredcapacitanceofthissampleis20pFwhichgivesindicatedcapacitivepowerrequirementsbelow0.2mW/MHz.Thetotallossintroducedbytheelectrodesisunderstudybutappearstobelessthan1dB.
TheLiNbxTa1-xO3opticalwaveguidesdescribedinthisreportarerelativelysimpletomake,haveexcellentandcontrollablewaveguideproperties,andcanbeorientedtomakeoptimaluseofthestrongelectro-opticeffectofbothLiNbO3andLiTaO3.Thehighefficiencyandlowvoltageandpowerrequirementsofthegratingmodulatorformedonthistypeofguiderepresentatleast
Page317
Fig.6.20(a)SchematicofgratingmodulatorinLiTaxNb1-xO3waveguide.Guidedlightisdiffractedthroughanangle2qBwhena
voltageisappliedtotheinterdigitalelectrodes.Sis7.6mmandLis0.3cm.(b)Thecurveshowsthepercentageoflightdiffractedasafunctionofvoltage.Opensquares4976
Å(He-Selaser),crosses5598Å(He-Selaser),andsolidcircles6328Å(He-Nelaser).Thesolid
curvesareplotsofsin2(BV0)normalisedtothedataat75%(HammerandPhillips,1974).
anorder-of-magnitudeimprovementinperformanceoverbulkdevicesandearlierwaveguidegratingmodulators.Similarimprovementsmaybeexpectedforotherformsofelectro-opticandpossiblyacousto-opticwaveguidemodulatorsandswitchesiftheLiNbxTa1-xO3guideisemployed.
6.4.4Ridgewaveguidemodulator
Kaminowetal(1974)reportedanexperimentalLiNbO3ridgewaveguidemodulatorrequiringamodulatingpowerofonly0.02
mW/MHz/rad.
ALiNbO3crystalhavingdimensions25mm×6mm×3mmalongthecrystallographicX,Y,andZaxes,respectively,wasout-diffusedtoproduceaplanarguidewithextraordinaryindexprofilebasedontheintegralerrorfunctioncomplement
where .Inordertoapproachsingle-modeoperation;theresultantcoefficientswerea=2×10-4,b=33mm.Iftheprofile(equation(6.34))isapproximatedbyanexponentialfunction
thencalculations(Conwell1973)indicatethattheplanarguidewillsupportjusttwomodes.FortheTE0andTE1modes,respectively,
Page318
wherebandkarethepropagationconstantsintheguideandinfreespace,respectively.
Aridgewasproducedbyion-beametchingthe6×25mmsurfaceofthecrystaleverywhereexceptforanarrowcentralstripalongthe25mmdimension.Aquartzfibreofsquarecrosssectionadheredtothecrystalsurfacewithphotoresistorservingasthemask.Aniongunfiredargonionsat30°fromthenormalontothecrystalsurface.With100mAionbeamcurrent,theetchingrateforthisconfigurationwasapproximately1mm/hforboththeLiNbO3crystalandquartzfibre.Afterionetchingandwiththefibremaskstillinplace,thesamplewascoatedwithCr(250Å)andAl(3000Å)electrodesbyevaporation.Inordertoensurecoatingthesidewallsoftheridge,thesamplewastiltedfirsttoonesideandthentheotherduringevaporation.Afterexaminationofthecompletedridge,thebestregionwasselectedandtheremainderofthecrystalwasgroundoffandtheendspolished.
Ascanningelectronmicrographofthesampleshowsthatthewallsoftheridgearesmoothandrectangular.Althoughthecross-sectiondimensionsmayvaryby±1mmalongthelengthoftheridge,theaverageheighthis7.5mmandaveragewidthwis19mm.ThelengthLoftheridgeis11.5mm.
Aheterodynemeasuringsetwasusedtodeterminethephasemodulator.A0.633-mmlaserbeamwasinjectedintotheendoftheridgewitha×20microscopeobjective;a×40objectivewasusedtoimagetheoutputendontoascreenandlatertocollimatethebeaminthemeasuringset.Thebeamappearstobesingle-mode,slightlyellipticalincrosssection,andisalmostcompletelyconfinedwithintheridgeitself,ratherthanpenetratingintotheplanarwaveguideregionbelowtheridge.
Ifoneassumestheexponentialindexprofile(6.35)fortheoriginalplanarguideandthenremoves7.5mmtoformtheridge,theplanarguideoutsidetheridgewillhaveanexponentialprofilewithcoefficientsap=aexp(-2h/b)=1.3×10-4andbp=b.ThenusingthecurvesofFig.5.15(Carruthersetal1974)oneobtainsforTE0andTE1modes,respectively,
Thentheeffectiveindexapproximationcanbeused(Ramaswamy1974)todeterminetheconfinementwithintheplane.Theeffectiveindexchangeforthesymmetricalguidewithintheplaneis(fromequations(6.36)and(6.37))
Page319
Fig.6.21SchematicdiagramoftheLiNbO3ridgewaveguide
modulator(Kaminovetal1979).
forTE0andTE1modes,respectively.Ineithercase,computationshowsthatonlythefundamentalmodeisguidedintheplane.TheplanarTE1modeisprobablynotstronglyexcitednorisittightlyconfinedintheridgeguide.Otherapproachestotheanalysisofridgeguide(orequivalentlyribguide)modesgivesimilarresults.
TheridgewaveguidemodulatorisshownschematicallyinFig.6.21.Theelectrodesareattachedbythinwirestoaminiaturecoaxialconnector.Avoltmeterand50Wloadareplacedinparallelwiththecrystalattheconnectorandthemodulationindexhismeasuredatfrequenciesbetween50and200MHz.TheseriesinductanceoftheleadsandstraycapacitanceoftheconnectorinterferewiththemeasurementofpeakmodulatingvoltageVathighfrequency.However,theseunwantedimpedancescanbeeliminatedorreducedinapracticaldevice.
Thecapacitancemeasuredattheconnectoris19pF,whilethecapacitanceCofthemodulatorcrystalalone,obtainedbysubtractingthecapacitancemeasuredwhentheleadsaredisconnectedatthecrystal,is10pF.Thecalculatedcapacitanceoftheridgecapacitorinparallelwiththeassociatedplanarcapacitorisonly5pF,sothata
furtherreductionofCandanincreasedbandwidthmustbepossible.
Themeasuredvalueofh/Vis0.85V-1.Thevaluecalculatedassumingthebeamtobecompletelyconfinedwithinaridgeofwidthw=19mmis0.98V-1.Thisexcellentagreementisfurtherevidencethatthebeamiswellguidedwithintheridge.Foraplanarmodulator,h/Vwas0.13V-1.ThatdevicewasdiffractionlimitedsothatthesafetyfactorSwasunity.Fortheridgeguide,ifw=dinequation(6.26),thenS=0.28.SincemodulatingpowerPperunitbandwidthperunitmodulationindexisproportionaltoS2,theridgeguidemodulatorrepresentsapotentialthirteenfoldimprovementinefficiencyoverthediffraction-limitedplanarmodulatorandanadditionalorder-of-magnitudeimprovementoverbulkmodulatorsforwhichthesafetyfactorisusuallygreaterthan3.
Page320
ThemodulatorbandwidthisDf=(pRC)-1and,withR=50WandmeasuredC=10pF,Df=640MHz.Thenusingthemeasuredh/VandP=V2/2R,Kaminowetal(1974)obtainedP/Df=20mW/MHzforh=1rad.
Theopticalattenuationduetoabsorptionbythemetalwallsontheridgeguidemaybeestimatedfromcalculationsforaplanarsymmetricalmetal-cladguideoperatingintheTM2mode(Kaminowetal1974).Thecalculatedlosseswere4and3dB/cmforCrandAlelectrodes,respectively.Agelectrodeswouldintroducealossofonly0.2dB/cm.Themajorsourceoftransmissionlossinthedeviseatpresent,however,isimperfectinputcouplingintothedominantmetal-cladridgeguidemode.Theridgewaveguidephasemodulatoriswellsuitedtoincorporationinabalancedbridgearrangementinanintegratedopticalcircuitforuseasswitchoramplitudemodulator.
6.4.5Ti-diffuseddiffractionmodulator
Tangonanetal(1978)describedthedesignandfabricationofthin-filmBraggdiffractionmodulatorsinTi-diffusedLiTaO3waveguides.Themodulatorperformancewasadequatefornear-termsystemsapplicationswithademonstrateddiffractionefficiencyof98%atthevisibleandnearIRwavelengths,ahighextinctionratio(<250:1),andadesignbandwidthof GHz.LiTaO3wasswitchedasthewaveguidematerialbecauseofthemuchhigherimagethresholdofwaveguidesformedbyTi-diffusedinLiTaO3thaninLiNbO3(Tangonanetal1977).
Beamdiffraction,asamechanismforintensitymodulationbyelectro-opticmeansinthethinfilms,isachievedbyproducinganelectricallycontrolledphasegratinginthepathofthepropagatingbeam.Thediffractionprocessresultsfromaperiodicperturbationoftherefractiveindextransversetothebeampropagationdirection.Ausefulmethodforelectro-opticallygeneratingthedesiredphasegratingis
showninFig.6.22.Themechanismforinteractionreliesonthefringingelectricfieldsextendingbelowthesurfacebetweeninterdigitalstripelectrodesformedonthecrystalsurface.Thelocalfringingfieldstrengthshouldbereasonablyuniformacrosstheguidedbeamandapproximatelysinusoidalintheplaneoftheguidinglayer,transversetothebeam.Thismaybemostreadilyachievedbyapplyinganisolatinglower-indexlayerabovetheguidinglayer.Thisservestheaddedfunctionofminimizinginteractionoftheopticalbeamevanescenttailwiththelossymetallicsurfaces.Bragg
Fig.6.22Phasegratingformationbythe
electro-opticeffect(Tangonaneta11978).
Page321
diffractioninvolvesintroducingtheinputbeamataspecificangleqB,theBraggangle,withrespecttotheelectrodearray(HammerandPhillips1974;Nodaetal1974).DiffractionoccursreflectivelyinasingleoutputattwicetheinputanglewhentheBraggconditionissatisfied.
Thephasechangef,inradians,inducedbytheelectricalsignalfieldoverapathlengthLis
whereDnistherefractive-indexincrementcausedbytheelectro-opticeffect,l0andisthefree-spacewavelength.ThestrongestinteractioninLiTaO3andLiNbO3occurswhentheappliedelectricfieldandopticalelectricpolarizationarebothparallel(ornearlyparallel(HammerandPhillips1974))tothecrystallinecaxis(theopticaxis).Forthiscondition,therefractive-indexincrementis
wheren3istheextraordinaryrefractiveindex,r33istheappropriateelectro-opticcoefficient,andE3istheappliedelectricfield(Chen1970).Thus,thecrystalmustbecutwithitscaxisintheplaneofthewaveguideessentiallytransversetothebeampropagationdirection,andthepropagatingopticalmodemusthaveTEpolarization.Thispolarizationhastheleastlosscharacteristicsinproximitytothemetalelectrodesurfaces.Hence,thisminimizestheinsertionlossofthemodulatorcausedbyabsorption.
Combiningequations(6.39)and(6.40)yields
Assumethatthecaxis-orientedelectricfieldintheregionoftheguidedlayerisapproximatelysinusoidalinthetransversedirection(areasonableassumptionforaregionaboutadistancesbelowthe
surface).ForBraggdiffraction,thezero-andthefirst-orderpowersareproportional,respectively,tocos2(f/2)andsin2(f/2).Formodulation,correspondingto100%depletionofthezero-orderbeamintheidealizedcase,themaximumrequiredvalueoffisp.
Todesignasuitablediffractionmodulator,onehastodeterminetheallowabledimensionsoftheelectrodearray,basedonbandwidthrequirementsanddriverpowerlimitations.Thiscanbedoneinafairlystraightforwardmanner,andboththepowerandthecapacitancecanbeeasilyexpressedintermsoftheratiooftheelectrodespacingtoelectrodelength,s/L.
Withoptimizedvideopeaking,thepowerrequiredtodriveacapacitanceCoverabandwidthBwithpeakdrivervoltageVmis
Page322
where istheshuntresistanceneededtodissipatethepowerandprovideanRC-limitedbandwidthB.ThecapacitanceofaninterdigatedelectrodearrayhavingNfingerpairsonanx-ory-cutuniaxialcrystalsuchasLiTaO3is(JoshiandWhite1969)
whereKisacorrectionfactor(BarrosandWilson1972)determinedfromtheratioofelectrodewidthtospacingw/s.ForLiTaO3intheclampedcondition(whichisexpectedtoobtainovermostoftheoperatingband),thecapacitanceis
Thenumberofelectrodepairsisreadilydeterminedfromthetotalwidthoftheelectrodearray.Foraninputlaserbeamhavinga1/e2diameterDequaltoabout1mm,itturnedouttobesufficienttoassumeanelectrodearraywidthof1.5D,whichyields
whereSistheperiodicity(expressedincentimeters).
TheappliedelectricfieldE3intheactiveregionofthebeamisestimatedtobeapproximately(JoshiandWhite1969;BarrosandWilson1972)
whenthedistancebelowthesurfaceiscomparabletos.Thisistheassumeddesignconditionthatleadstoareasonablyuniformfieldstrengthacrosstheopticalbeam.ItisconvenienttoexpressVmintermsofthecommonlyusedelectro-opticparameterE3L,thefield-lengthproduct
where
Table6.1liststherelevantelectro-opticanddielectriccharacteristicsofLiTaO3andLiNbO3at0.53mmand1.06mm.ThesedataareusefulinthedesignofadoubledNd:YAGcommunicationlink.Thechangesine1ande2forLiNbO3ingoingfromtheunclampedtoclampedconditionarequitelarge,
Page323
Table6.1Propertiesofelectro-opticmaterials(Tangonaneta11978)
Quantity LiTaO3 LiNbO3
0.53mm 1.06mm 0.53mm 1.06mm
n3 2.21 2.14 2.23 2.16
~31 ~29 32.2 ~32
30.3 ~29 30.8 ~30
33.5 ~28.4 35.7 ~32
32.7 ~28.4 34.1 30
51 78
41 43
45 32
43 28
(T)=unclamped
(S)=clamped
Table6.2Resultsofdesigncalculations(Tangonan,Persechini,Lotspeich,Barnoski,1978)
Parameter 0.53mm,3Wdrive 1.06mm,24Wdrive
B=0.7GHz B=1.4GHz
K=1,s=w
E3×L,V 1606 3732
L,mm 2.5 5
s,mm 4.6 6.9
S,mm 18.4 27.5
N 81 54
C,pF 77 104
Rs,W 6 2.2
Q 11 20
afactwhichadverselyaffectsthefrequencyresponsecharacteristics.Similarly,thechangeinr33issubstantiallygreaterthanthatofLiTaO3,thusproducingastrongereffectontheelectro-opticfrequencyresponse.
Forw/s=1,amaximuminteractionlengthof2.5mmwaschosen0.53mmtokeepwithinreasonablelimitsofopticalloss.Itwasfoundthatthewaveguidelossat5145ÅforTi-diffusedLiTaO3guideswas3-5dB/cm.Forthe1.06-mmcase,whereopticallossesaresubstantiallylower( dB/cm),alengthof5mmwasarbitrarilychosenasareasonableupperlimit.
Table6.2givestheresultsderivedfromtheprecedingequationsforthetwowavelengthsofinterest.TheTableincludesaparameterQdefinedby
Page324
Fig.6.23SerieselectrodemodificationforBraggdiffractiongrating(Tangonanetal1978).
Fig.6.24(right)Splitelectrodepatternofmodulator
(Tangonaneta11978).
whichdescribesthesamenatureofthediffraction.BraggdiffractionoccursmostefficientlywhenQ>10.
ExaminationofthevaluesofshuntresistanceRsforthetwocasesshownclearlyindicatestheneedforimpedancematchingfroma50Wdriversource.Somedevelopmentsinthedesignofwidebandrfimpedancetransformershaveledtoverywidebanddevicescapableofoperatingfrombelow1MHztowellabove500MHzwithinsertionlossesof0.5dBandless,providedtheimpedanceratiosdonotexceedabout3or4to1.Forlargerstep-downratios,theinsertionlossesaresubstantiallyhigher.Asanalternative,adifferentelectrodedesignmaybeusedtoprovidematchingtoa50Wdriver.Forthecaseof0.53mmdesign,themodificationfollowsaschemeproposedbyNodaetal(1974)inwhichtheelectrodearrayisdividedintoseveralsections,say3,eachoflengthL/3,arrangedinseriesbothelectricallyandoptically.Thisdevicereducesthecapacitancebyafactorof9,whichincreasesshuntresistanceinthesameproportion.This
modificationisshowninFig.6.23.Forthecaseofthe0.53mmmodulatordesign,thisclearlyyieldsashuntresistanceof0.54Wandacapacitanceof8.6pF.Thepenaltypaidbythisapproachisthatthedrivervoltageisincreasedbyafactorof3.
Opticalwaveguideswereformediny-cutLiTaO3wafersbyTiin-diffusionfollowingtheprocessingtechniquedescribedinchapter1.InterdigitalelectrodesemployingthedesignparametersinTable6.2for0.53mmoperationwerefabricatedonthewaferswiththefielddirectionsalignedwiththecaxis.Diffractionefficiency,measurementsweremadeat6328Å(He-Ne),5145Å(Ar),andat10.640Å(Nd:YAG).Diffractionmeasurementsindicatethatthesearethemostefficientelectro-opticBraggmodulatorstodate:98%efficiencywithextinctionratiosashighas300:1.
Forthemodulatorstructuresfabricated,theelectrodepatternswereformedbyphotoetching1500ÅAlfilmsthathadbeenevaporateddirectlyonthe
Page325
waveguidesampleoronabufferfilmofSiO2(1500Å).Thisthicknessofthebufferlayerhasbeenfoundtobeeffectiveinprovidingthenecessaryisolationtopreventdirectinteractionsoftheopticalfieldwiththemetalgrating.Figure6.24isaphotographofaportionofasplitelectrodedesignusedtoreducetheeffectivecapacitancebyafactorof9.Thewidth-to-spacingratioachievedwascloseto0.5forallthesamplesstudied.
Thediffractionefficiencyofmodulatorswithandwithoutelectrodebufferlayerswasstudiedtodeterminethedegreeofenergytransferfromthem=0undiffractedbeamtothedifferentgratingorders.Electricalleakagecanhinderdeviceevaluation,andsevereleakagecurrentswereobservedinseveralsamples.TheleakagecurrentsoriginatefromincompleteoxidationoftheSiO2.Theappliedvoltagewassimplyturnedonandkepton.Itisclearfromthetracethattheeffectivefieldoverthewaveguidestructuregoestozeroinashorttime.TheseresultswereobtainedformodulatorswithasputteredSiO2bufferlayer.ThesesamesampleswerestrippedoftheAlelectrodepatternandplacedinanoveninanoxygenatmosphereat500°Cforafewhours.Thesampleswerethenreprocessedandnewmodulatorpatternsfabricatedonthem.Thesesampleswerefoundtoexhibitgooddcproperties:noleakagewasobserved,andmodulationtestscouldbecarriedout.
Diffractionefficiencymeasurementsweremadeat5145Å.Thismodulatorhadnobufferlayeronitandwasusedtodeterminetheeffectsofthemetalgrating.ThemetalgratinginducedadeflectedspotattwiceqBofintensityequalto15-25%oftheundeflected(m=0)spot.Themeasuredvoltageformaximumdiffractionwas17.5V,whichisquiteclosetothecalculatedvalueof17.0Vfor5145Åoperation.ThecalculatedvaluefordoublesNd:YAGoperation(0.53mm)is17.7V.Thediffractionefficiencymeasuredinthisexperimentwas95.3%.
Theresultsofmeasurementsmadeat1.06mmareplottedinFig.6.25.Themeasureddiffractionefficiencywas98%withanextinctionratioof300:1,or24.7dB.
Fig.6.25Resultsofdiffractionmeasurementsat
1.06mmshowing98%maximumfirstorderdiffractionanda300:1extinctionratio
(Tangonaneta11978).
Page326
Table6.3Characteristicsofelectro-opticinterferencetypemodulator
Controlvoltage 2V
Operatingfrequencybands 50Hz-500MHz
Operatingwavelength 0.85mm
Opticalinsertionloss,notmorethan 12dB
Controlinputcapacity 10pF
6.4.6InterferometricMach-Zehndermodulator
Anopticalinterferometer-typemodulatorwasrealizedinpracticeusingtheepitaxialthin-filmtechnique.
ThemodulatorwasmanufacturedbytheMach-ZehnderinterferometerschemeonanY-LiTaO3substrate.Single-modechannellightguideswiththedistributionprofileDnclosetoacylindricalonewereformedbythefilmdiffusionmethod.Thesizeofthemodespotatawavelengthof0.85mmmadeup~9mm.Analuminiumelectrodestructurewithdimensionsl(length)20mm,d(width)5mmwasformedonthefilmsurface.
TheLi(Nb,Ta)O3filmthicknesswash=13mm,L=20mm,theinterelectrongapwidthd=3mm,l=0.85mm,n=2.18,r=20×10-12m/V.UndersuchconditionstheoverlapintegralG=0.8.ThecalculationsshowthatthevalueofthecontrolvoltagewillbeequaltoV=1V,whileexperimentalvalueswere2V.Theexperimentalmodulationdepthm(equation(6.8))wasequalto82%whenweworkedwithlinearlypolarizedradiationattheinput.
A100%modulationdepthwhichistheoreticallyadmittedistypicallysomewhatlessinexperimentduetolightscatteringonwaveguidedefectsandontheelectrodestructure.Inourexperimentsmwasequal
to82%whenweworkedwithlinearlypolarizedradiationattheinput.
Theinsertionlossesincludeinputandoutputradiationlossestopropagationaboutthemodulatingstructure.Themeasuredvalueofawas12dB.Forlinearlypolarizedradiationthisvaluefallsdownto9dB.Thelossesoflightscatteredfromchannellightguidesonthestructurewere6dB,andthelosseson'Y'brancheswereequalto2dB.
Themodulatorsweremanufacturedintegro-opticallyonalithiumtantalatesubstratesmeasuring20×30×2mm3onwhichtwoMach-Zehnderinterferometerswereplaced.Themodulatorsaredistinguishedinthattheirlightguidestructureisformedinanepitaxialfilmofasolidsolutionoflithiumniobate-tantalateandrepresentschannellightguidesobtainedbythecombinedfilmdiffusionmethod.Suchlightguides,ascomparedwithlithiumniobate,arehighlyresistanttoopticaldamages.Thecontrolstructureofthemodulatoriswellprotectedfromtheinfluenceoftheatmosphere.
Themodulatorsaremountedintoametallicframemeasuring75×15×35mm3.Thecontrolvoltageisappliedthroughjoints.Thereexiststwoversionsofadjustmentwithexternalopticalchains.
Themodulatorcanbefabricatedintwomodifications.First,asemicon-
Page327
Fig.6.26Thinfilmintegro-opticmodulator(generalview).
ductorlasermatedwithamodulatormayserveasalightsource.Thelightistransmittedthroughasingle-modefibreadjustedimmediatelytothemodulatorend.Inthesecondversionthelightisputinandoutofthemodulatorthroughasingle-modefibrejoinedtothesubstrateends.
TheprincipalparametersofthemodulatorarepresentedinTable6.3.
Figure6.26givesapictureofthemodulator(Dubrovennazetal1988).
Significantinterestliesinproducingopticalwaveguidedevicesinmaterialwithahigherelectro-opticcoefficientwhichcouldbeusedformakingcompactlow-voltageelectro-opticmodulatorsandswitches(EknoyanandSwenson1991).AsuitablechoiceforthisisSr0.6Ba0.4Nb2O6(SBN:60),becauseitsr33electro-opticcoefficient(420×10-12m/V)ismorethananorderofmagnitudelargerthanthatforLiNbO3andLiTaO3(ProkhorovandKuz'minov1990(a)).OtherrelevantparametersofSBN:60areitsrelevantdielectricconstantvaluese11=470ande12=880,andrefractiveindiceswhichat0.83mmwavelength(ProkhorovandKuz'minov1990(b))arene=2.2435andn0=2.2375.Theinterestinthismaterialisparticularlyattractiveduetomajoradvancesinitsgrowthtechniques,whichnowmakesitpossibletoproducecrystalsinlargesizes(2-3cmindiameter)ofexcellentquality(Neurgaonkar1989).
OpticalwaveguideshavebeenproducedinSBN:60byZndiffusionfromvapourphase.Usingelectronmicroprobewavelength-dispersivespectroscopy,theZndistributionwasdeterminedandavalueof7.3mmforthediffusiondepthwasobtained.Thebestwaveguideswererealizedbydiffusionat1000°Cfor30minfollowedbyannealingat600°Cfor~100h.
TheopticalwaveguideswereproducedbyZndiffusionfromthevapourphaseinto1mmthickZ-cutSBNsubstrates,inaprocesssimilartoonedescribedearlierwithLiTaO3crystals.TungstenbronzeSBN:60istetragonalatroomtemperatureandexhibitstheCuriepointTcat78°C.ThecrystalsweregrownbytheCzochralskitechniqueandthesurfaceswerepreparedaccordingtocurrentneeds.WaveguidingwasobservedforbothTEandTMpolarizationsbyend-firecouplingat0.83mmwavelength.Electro-opticmodulationatawavelengthof0.83mmonaMach-Zehnderinterferometerwasdemonstratedforthefirsttimeinthismaterial.Withelectricfieldappliedtobotharmsoftheinterferometer,avoltage-lengthproductof0.48Vcmwasobtained.LowervaluesofVpcanbeexpectedbyfurtheroptimizingthepolingprocedureorusingmaterialofhigherelectro-opticcoefficientlikeSBN:75.Electro-optic
Page328
Fig.6.27(a)Geometryusedforwritingaholographicgrating
intoaTi-diffusedLiNbO3waveguidewith0.5145mmlight;(b)beamsplittingofaguidedwave(l=0.6328mm)bya
holographicgrating;(c)modulationofaguidedbeambytheapplicationofanelectricfieldacrossaholographicgrating
(1.59mmgapelectrodes)(Goruketal1981).
modulatorsandswitchesinSBNareattractiveastheymightpavethewaytocompactlow-voltagedevices.
6.4.7Electro-opticphotorefractivemodulator
Goruketal(1981)describedanovelmodulatorbasedonacombinationofthephotorefractiveandelectro-opticeffects.Itisessentiallyanintegratedopticsversionoftheelectro-opticswitchfirstdemonstratedinbulkLiNbO3byKenanetal(1974).LightincidentontoaphotorefractivegratingatandneartheappropriateBraggangleisfirstsplitintotwobeamswhoserelativeintensityvarieswiththeexposuretimeusedinwritingthegrating.Theelectro-opticeffectisthenusedtomodulatetemporallythesebeamsviaaninputelectricalsignal.Theresultingmodulatorisausefullowcostlaboratorytoolwhichdoesnotrequireelaboratefabrication.Furthermore,byusingstandardholographictechniques,variousopticalelementssuchaslensesandcouplersmaybewrittenintothewaveguideandswitched
onandoffbythismethod.
ThephotorefractivemethodofwritinggratinghologramsinplanaropticalwaveguideshasbeenreportedbyChenetal(1968)andWoodetal(1981).Goruketal(1981)madeuseofthelargephotorefractiveeffectknowntooccurinLiNbO3whenlightinthebluegreenregionofthespectrumisincident.Twoguidedwaves(writingbeamsatl=0.5145mmfromanAr+laser)withwavevectorsb1andb2interferetoproduceagratingwithperiodicity .ForthecaseillustratedinFig.6.27a,bg=2b0sinq0,where ,q0istheanglebetweenb(orb2)andthexaxis,andbgliesalongthezaxis.Theeffectivewaveguiderefractiveindexisgivenby
Page329
andthemodulationdepthDndependsonthenumerousfactorssuchasthewritingbeamintensitiesandduration,waveguide,andmodeparameters.
ConsidernowasetofelectrodesdepositedontothewaveguidesurfaceasindicatedinFig.6.27c.WhenavoltageVisappliedtotheelectrodeswhichareseparatedbyadistanced,aneffectiveindex(Marcuse1975)changeDN,
issuperimposedontothephotorefractivegratingviatheelectro-opticeffect.(Thereisanadditionaleffectduetothematerialpiezoelectricity,butthisisbelievedtobeasecondarymechanismhere.)Theparameterr33istheappropriateelectro-opticcoefficientforthegeometryshowninFig.6.27(c).Hence,thetotalrefractiveindex
AsimilarphenomenonhasbeenanalysedpreviouslyviaacoupledmodeapproachbyKenanetal(1974).(Intheircaseasurfacecorrugationinsteadofaholographicgratingwasusedtoobtaintheinitialdivisionoftheincidentguidedwaveintotwobeams.)TheyshowedthatthediffractedlightintensityIdisgivenintermsoftheincidentguidedwavelightintensityIiby
HereLgisthelengthofthegratingwithperiodicityL,anddisthephasemismatchtermduetoboththeelectro-opticeffectand(or)misalignmentDqoftheincidentbeamfromtheBraggangleqB,i.e.
Theparameterkeisgivenby
wherekisthecouplingcoefficientwhichappearsinthecoupledwaveequations(Kenanetal1974).Maximumdiffractionoccurswhend=0,whichisusuallyobtainedbyensuringthattheguidedwaveisincidentattheBraggangle.Itisalsousefultonotethatamisalignmentinthedirectionoftheincidentlightcanbecompensatedforbyapplyinganappropriatevoltage.Furthermore,
Page330
thevoltageDVwhichmustbeappliedtogofromthemthtothem+lminimumisgivenapproximately(keL<p/2)by
Thewaveguidesstudiedwerey-cutandx-propagatingTiin-diffusedLiNbO3waveguidescharacterizedapproximatelybyexponentialrefractive-indexprofiles(equation(6.35)).GratingswerewrittenintothewaveguideasindicatedinFig.6.27bycouplingtwocwlaserbeamsfromanargon-ionlaser(l=0.5145mm)intoTE0waveguidemodesviafutileprisms.Twoseparategratingswerestudied;theanglesbetweenthewritingbeamswhichweresymmetricaboutthexaxiswere3°(1.59mmspacingbetweenelectrodes)and4°(0.3mmspacing).Typicallytheincidentpowersineachbeamwere1mW,andthegratingwerewrittenin1sexposures.Theseparameterswereadjustedtoproduceapproximatelya50:50splittingratiowhenHe-NeguidedwavelightwasincidentattheappropriateBraggangle.Thefirstsetofelectrodesconsistedoftwostripsseparatedby1.6mmpaintedonwithsilverpaint.Thesecondhadasetofevaporated1500Åthickaluminiumelectrodeswitha0.3mmspacing.
Themodulatorcharacteristicswerestudiedwith0.1mWofHeNelaserlight.LightwascoupledintoandoutoftheTE0modeviarutileprisms.Thegratingswerestudiedwithinafewmonthsoftheirfabrication,anditwasverifiedsixmonthslaterthatthegratingswerestillpresent.Modulationwasobtainedbyapplyingavoltagevaryingwithtimeacrosstheelectrodes,andthedeflectedandundeflectedbeamintensitiesweremeasuredwithacalibratedphotodiode.
SomeofthepertinentoperatingcharacteristicsofthemodulatorareshowninFigs.6.27cand6.28.Whentheincidentanddeflectedbeamswerekeptawayfromtheelectrodeedges,thequalityofbothbeamswasgood,asindicated
Fig.6.28Modulatorefficiency(100%=completeextinction)versusappliedvoltageacrossthe1.59mmelectrodegap.Solidline
correspondstotheory(seethetext)(Goruketal1981).
Page331
inFig.6.27c.ForlightincidentattheBraggangle,theoutputsignalistheharmonicofthefundamental.AwayfromtheBraggangle,theoutputcanbechosentobeeitherinphaseoroutofphasewiththemodulationsignal.
Detailedmeasurementsofthemodulatorresponsefunction(modulatorefficiencyarereproducedinFig.6.28.(100%efficiencycorrespondsinthiscasetoacompleteextinctionofthediffractedbeam.)AsisevidentfromFig.6.28,theagreementbetweenexperimentandtheoryisexcellent.Thebestextinctionratioobtainedwas20dB,andtheappliedvoltagecorrespondedtoanappliedelectricfieldof0.22×106V/m.
Thebeamqualitydisplayedanomalousbehaviourwhenevertheincidentand(or)deflectedbeamswerepropagatedneartheelectrodeedges.Goruketal(1981)hypothesizedthatthefieldsattheelectrodeedgesaresufficientlyhightocausethewaveguidetoapproachthecutoffcondition,andhencethebeamqualityismuchmoresusceptibletolaserdamage.
Basedontheseobservations,itwasimportanttokeeptheguidedwavebeamsawayfromtheelectrodestomaintainreasonablebeamquality.
6.4.8KNbO3inducedwaveguidecut-offmodulator
Potassiumniobate(KNbO3,pointgroupsymmetrymm2atroomtemperature)isaveryinterestingelectro-opticalmaterialforbothbulkandwaveguideapplications,becauseofitslargeelectro-opticandnonlinearopticcoefficients,goodphotorefractiveproperties,andhighdamagethreshold(60MW/cm2pulsedatl=0.86mm)(ProkhorovandKuz'minov1990).ThesepropertiesmakeKNbO3attractiveforthin-filmwaveguides,suchaselectro-opticmodulators,whichwouldbenefitfromhighfiguresofmeritnr33=680pm/Vandnr42=4350pm/V(n3=2.1683isaprincipalrefractiveindex,n4=2.254isan
averagerefractiveindexinthebcplane,andr42=380pro/V)comparedtonr33=341pm/VforLiNbO3,oranefficientfrequencydoublerforAlxGa1-xAssemiconductorlasers,allowingcollinearphase-matchedtypeIinteractionaroundroomtemperaturewithinthiswavelengthrange.Tuckeretal(1974)observedopticalwaveguidinginnaturallyformedplanarsheetdomainsinKNbO3.Moreusefulwaveguideswouldrequeststructureswithcontrollableparametersinpreferredorientationsofsingledomaincrystals.Baumertetal(1985)reportedonthefirstwaveguidesinKNbO3inducedbytheelectro-opticeffect.KNbO3needslow-temperatureprocessing(Curietemperaturearound+220°C)andcarefulhandling,otherwiseferroelectricdomainsmayappear.Uptonow,ithasnotyetbeenpossibletoprepareopticalwaveguidesbyin-diffusionofTiionsfromthecrystalsurface.
Inordertousetheelectro-opticalcoefficientr33inKNbO3,acrystalplatewascutnormaltothebaxis,andtwoelectrodeswithawidthof(s-h)=100mm,separatedbyagapofwidth2h=10mm,weredepositedonthepolishedbface(seeFig.6.30).Theedgesoftheelectrodeswereparalleltotheaaxis.Thehorizontal(paralleltothecaxis)componentEx(x,y)oftheappliedelectricfieldyieldsanincreaseoftherefractiveindexncofthecrystalinthegapregiongivenby
Page332
withA=3.262×10-4mm/Vforl=0.63mm.TherefractiveindexchangeDnb,duetotheverticalelectricfieldEy(x,y),hasbeenneglectedbecauseofthesmallelectro-opticcoefficientr23=1.3pm/V(ProkhorovandKuz'minov1990).Therefore,withthistypeofwaveguideonlyTEmodespropagatingalongtheaaxisareguided.InordertoevaluatetheworkingvoltageandthelightfielddistributionofthepropagatingmodesBaumertetal(1985)havecalculatedtherefractiveindexdistributionnc+Dnc(x,y)asafunctionoftheappliedvoltage.TheelectricfieldcomponentsEx(x,y)andEy(X,y)insidethecrystal,belowtheelectrodegap,wereobtainedbysolvingtheLaplacepotentialequationusingtheconformalmappingtechnique(VandenbulckeandLagasse1976;Wei1977)andaregivenby
wherez=x+iy,k=h/s,K(k)isthecompleteellipticintegralofthefirstkind,and
Uisappliedvoltage, and arethefreedielectricconstants(at25°C)ofKNbO3alongthec-andb-axes,respectively.
ApreferentiallysingledomainKNbO3crystalwasgrownbyatopseededhigh-temperaturemeltpullingtechnique(FluckigerandArend1978).Chipswithasizeof4×3.4×0.7mmwerecutfromthecrystalandorientedbyx-rayandpreferentialetchingmethods(Wiesendanger1973).AftersurfacepolishingtheremainingdomainswereremovedinastrongpolarizingdcfieldneartheCurietemperature.Oppositeendsofthesinglecrystalswerepolishedinordertoallowforend-fire
couplingoflaserlight.Thisprocess,however,hascausedstress-inducedmicrodomainsalongtheedgesofthefacetthatcouldnotentirelyberemovedbypoling.Forelectrodepreparation,athinchrome/goldfilmwasdepositedbyelectronbeamevaporationontheb-cutsurface.Apositiveelectricfieldwasappliedandthesurfacewasbakedverycarefullytopreventcreationofnewdomains(heating/coolingcyclewithdT/dt<2°C/min).Theelectrodestructurewaspatternedandthemetalfilmetched.Theelectrodeshadalengthof3mm(Fig.6.29).Thesamplesweremountedonaceramicsubstrateandcontactedusingcopperwireandsilverpaste.
LightofaTE-polarizedHe-Nelaserbeamwascoupledintotheelectro-opticallyinducedwaveguide.Fortheend-firein-andout-coupling,two20×
Page333
Fig.6.29Designoftheelectro-opticallyinduced
waveguide(Baumerteta11985).
Fig.6.30Near-fieldlightdistribution(l=0.633mm)
(Baumerteta11985).
Fig.6.31Calculatedintensitydistributionforan
appliedvoltageof35V(l=0.633mm)(Baumert
etal1985).
microscopelenseswereused.Withnoelectricfieldapplied,onlysomelightspotscausedbydiffractionatstress-induceddomainsatthecrystalendfaceswereobserved.Increasingtheappliedvoltageupto30V,anon-offratioof12dBcouldbemeasured,clearlydemonstratingafield-inducedincreaseoftherefractiveindexncbetweenthetwoelectrodes.Baumertetal(1985)measured
Page334
thewavelengthdependenceofthenear-fieldlightdistribution.Thefollowinglaserlightsourceswereused:InGaAsP/InPdiode(1.3mm),Nd:YAG(1.064mmand0.532mm),argonpumpeddye(0.86mm),andHe-Ne(0.633mm).Figure6.30showsthenear-fieldlightdistributionsat0.633mmforanappliedvoltageof0and35V.Foravoltageof35Vtheintensitydistributionofthefundamentalmodeoftheelectroopticinducedwaveguidewascalculated(Fig.6.31).Goodagreementbetweencalculated(Fig.6.31,10mm)andmeasured(Fig.6.30,3.8±0.5mm)widthoftheintensityprofileswasfounddespitethemicrodomainsattheedges.
6.5Waveguideelectroopticpolarizationtransformer
Polarizationtransformationisanessentialfunctionforopticalsignalprocessing.Itisespeciallyimportantforsingle-modefibresystemsbecause,althoughshortlengthsofspeciallyfabricatedpolarizationpreservingbirefringentfibreshavebeenreported(Ramaswamyetal1978a;Stolenetal1978),typicalsingle-modefibresdonotmaintainlinearpolarization(Ramaswamyetal1978b;Kapronetal1972).Formanycommunicationapplication,thepolarizationindependentswitch(Alferness(1979)andon/offmodulator(Burns1978)canbeeffectivelyusedinspiteofanincidentsignalofunknownandtemporallychangingpolarization.However,forinterferometricsignalprocessingapplicationssuchas,forexample,heterodynedetectionorfibresensors,areceivedsignaloffixedpolarizationidenticaltothatofsomereferencesignalisrequired.Inthesecases,activepolarizationstabilization(Ulrich1979)maybenecessary.Polarizationtransformationsuitableforsuchstabilizationhasbeenachievedbybulkmechanicalelementswhichsqueeze(Johnson1979)ortwist(UlrichandJohnson1979)thefibretoinducelinearbirefringenceoropticalactivity,respectively.Thesedevicesarebulkyandmayresultinfibrefatigue.However,becauseitreliessolelyuponchangingthe
birefringence,twoelectroopticalcrystalswithproperrelativeorientationarerequired.Furthermore,becauseitisabulkdevice,alargecontrolvoltage(~425V)isrequired.ThewaveguideelectroopticpolarizationtransformerdescribedbyAlfernessandBuhl(1981)iscompact,nonmechanical,capableoffastresponse,hashighfidelityandneedsonlylowcontrolvoltage.
Thepolarizationstateofanopticalwavecanbedefinedbytwoparameters,qandf.IntermsoftheseparameterstherelativeTEandTMfieldcomponentsofanopticalguidedwaveare
Thus,qdefinesthemagnitudeoftherelativeTEandTMamplitudesandqtherelativephasebetweenthesecomponents.Forq=0,thelightislinearlypolarizedatanangleq;q=0representspureTEpolarizationandq=½ppureTM.Rightcircularpolarizationisgiven,forexample,byq=0.25pandf=0.5p.
Page335
Fig.6.32Schematicdrawingofpolarizationtransformer
(AlfernessandBuhl1981).
Thedemonstratedpolarizationtransformer,whichunderelectroopticalcontrolprovidesanydesired transformation,isshownschematicallyinFig.6.32.Itiscomprisedofasingle-modewaveguidewiththreeelectroderegions.Theoutertwoelectrodepairs(Fig.6.32)providetheE/Ochangeofthebirefringence.ForthecrystalorientationshowntheelectricallyinducedphaseshiftbetweentheTEandTMmodesis
whereVistheappliedvoltage,d1theinterelectrodegap,Ltheelectrodelength,ltheopticalwavelength,no,etheordinaryandextraordinaryrefractiveindicesandrthee/ocoefficients.Thecentreelectrodeprovides modeconversionbyutilizinganoffdiagonalelementofthee/otensortocoupletheotherwiseorthogonalTEandTMmodes(Alferness1980).Theeffectofthemodeconverterupontheamplitudecomponentsinequation(6.60)isgivenbythematrix
Fig.6.33Calculatedoutputpolarizationangleq0vs
themodeconvertercouplingstrengthkLforvariousinputpolarizationanglesq1.TheincidentrelativeTE/TMphaseisassumedtobezero(AlfernessandBuhl1981).
Page336
wherethecouplingcoefficientis
whered2istheinterfingerseparationandatheoverlapparameter(Alferness1980).Periodicelectrodesarerequiredbecauseofthematerialbirefringenceoflithiumniobate.
AlfernessandBuhl(1981)outlinedsomekeyfeaturesofthedeviceoperationbeforepresentingexperimentalresults.First,themodeconverterwasessentialbecausetherelativeTE/TMamplitudescannotbealteredbysimplechangingthebirefringence.However,themodeconverteralonewas,infact,alsoinsufficienttoproducegeneralTE/TMamplitudechanges,thatisthearbitrarychange .ThisfactisdemonstratedinFig.6.33,wherethecalculatedoutputpolarizationangleq0isplottedversustheelectricallyinducedmodeconvertercouplingstrength(proportionaltoV2)forseveralinputpolarizationanglesq1.Theresultswerecalculatedusingthetransformationmatrixofequation(6.62)withtheassumptionthattherelativeTE/TMphaseuponincidencetothemodeconverter iszero.Ofcourse,foreitherpureTEorTMinput(qi=0or½p,respectively)withpropervoltage,anarbitraryangleq0canbeachieved.However,astheangleqiincreasesfrom0ordecreasesfromp,theresultsofFig.6.33showthattherangeofachievableq0becomesgreatlylimited.Indeed,for ,regardlessofthevoltage(V2)appliedtothemodeconverter,theangleq0remainsequalto¼p.
Thekeytoovercomingthislimitationistheuseofthee/ophaseshifterbeforethemodeconvertertoadjusttherelativeTE/TMphaseofthesignalincidentuponthemodeconverterto±p.Inthesecases,apropervalueofthemodeconvertervoltagecanbeshowntoexist,sothatany changeispossible.Indeed,onlyforthesespecialrelative
phasevaluescansucharbitrarytransfomationsbeachieved.Fortunately,forthesecasesthemodeconverteractsasalinearrotatorwithrespecttothepolarizationangle.For p,forexample,
wherekaV2isthesubjectoftheequation(6.62).Thus,controloverqisachievedbythecombinationofthefirstphaseshifterandthemodeconverter.
Thedesiredoverallrelativephasetransformationisthenachievedwiththefinalphaseshifter.ItshouldbenotedthatiftherelativeTE/TMinputphasetothemodeconverteris-0.5p,thentheoutputphasefromthemodeconverterisalso-0.5p.Furthermore,thebirefringentsubstratesthereisarelativephaseshift ,whereLTisthetotalcrystallength,andNTEandNTMaretheeffectiveindicesoftheTEandTMmodes,respectively.Thus,
Page337
Fig.6.34Measuredresultsofthedeviceasalinearpolarizationrotator,therequiredmodeconvertervoltagetoachieveanoutputTEfieldvsinputpolarizationangle
V1=-4.1VandV3=0(AlfernessandBuhl1981).
toachievethedesiredvalueoff0thevoltageofthesecondphaseshiftermustbeadjustedtoobtainaphaseshiftDf2,sothat,
whereDf2isthechangeinducedbythefirstphaseshifter.ThevalueofDf2doesnotaffectq0.
Thedevicewastestedinseveralmodesofoperation.First,thenecessityofthefirstphaseshifterwasverified;forV1=0arbitrary
transformationscouldnotbeachievedregardlessofthemodeconvertervoltage.Next,thedevicewasoperatedasalinearrotatorwiththegoaloftransforminganarbitraryinputlinearpolarizationtoanoutputwave,thatis,pureTE.TofindthepropervalueofV1toachievea½pTE/TMphaseshiftatthemodeconverter,theangleqiwassetto¼pandV1adjustedtomaximizetheoutputTEcomponent.Oncedetermined,thisvalueofV1wasfixed.TherequiredmodeconvertervoltagetoachieveapureTEoutputpolarizationversustheinputpolarizationanglewasthenmeasured.Theresultsareshownin
Fig.6.34.Aspredicted(equation(6.63)),alinearrotationisobservedand,indeed,anyvalueofq1canbetransformed.Therotationrateis15°/V.Theorthogonalpolarizationcomponent(TM)wastypicallygreaterthan23dBdownfromthedesiredone.Withcareinvoltageadjustmentvaluesof-27dBcouldbeachieved.
Becausethelargebirefringenceoflithiumniobatenecessitatesperiodicelectrodesforthemodeconverter,thedemonstrateddeviceiseffectiveonlyoveralimitedspectralbandwidthof~10Å(AlfernessandBuhl1980).However,thedevicecanbebroadbandedeitherbyshorteningthemodeconverterelectrodelengthorbylinearlyvaryingtheelectrodeperiod.Effectivespectralbandwidthsofseveralhundredangströmsshouldbereadilyachievable.Alternately,thedevicecanbefabricatedusingalessbirefringentsubstratelikelithiumtantalateoranonbirefringentone.Althoughthreecontrolvoltagesarerequiredforthemostgeneralpolarizationtransformation,formanyapplicationsonlyoutputlightthatispureTEorTMisrequired.Inthiscase,onlythefirstphaseshifterandthemodeconverterarerequired.
Page338
6.6Lightbeamscanninganddeflectioninelectro-opticwaveguides
Tienetal(1974)reportedamethodoflightbeamscanninganddeflectioninwhichtheangleofdeflectionvarieswiththeappliedfield.Inoneoftheexperimentstheauthorswereabletoscanalightbeamcontinuouslyupto4°intheplaneofthefilm.Theexperimentswerecarriedoutinanelectro-opticwaveguideofasingle-crystalLiNbO3filmgrownepitaxiallyinLiTaO3.
Thetheoryandexperimentforthelightbeamdeflectionandtheconditionsthatoptimizethedeflectionefficiencyarediscussedbelow.
Ageneralequationofalightpathinamediumofvariableindexofrefractionisconsidered.Theequation(BornandWolf1959;Tienetal1965)is
Heredsisanelementofthelightpathandristhepositionvectorofds.Letthefilmlieintheyxplane.Therefractiveindexofthefilmvariesinxandyasitisexcitedbytheelectro-opticeffect.Theoriginofthecoordinatesarechosentolieonthexaxis(Fig.6.35(a)),andthelightpathisconsideredwhichdeviatedfromthexdirectionbyanangleqnotmorethan10°.Thentan andqissmall.Thus,
wherexandyaretheunitvectorsalongthexandydirections,respectively.Equation(6.66)nowbecomes
Fig.6.35(a)Lightbeaminamediumofvariablerefractiveindexn(x,y).(b)Diagramshowingtheprocessofoptimisingthedeflectionofalightbeam.
(c)Experimentalarrangementusedtodeflectalightbeamthroughrefractions.(d)Experimentalarrangementusedtodeflectalightbeamthroughincompletereflection(DqT)and
refractions(DqR)(Tienetal1974).
Page339
Aftersimplification,wehave
Sincedy/dx(=tan )issmall,equation(6.68)becomes
Here,inthefirstintegral,dxisreplacedby(dx/dy)dywhichis(1/tanq)dy.Equation(6.69)isageneralequationfordeflectingalightbeamandDqisthedeflectionangleoccurringafterthelightbeamhastracedapathfrom(x1,y1)to(x2,y2).Theanglesq1andq2aretheentranceandexitanglesofthelightbeamat(x1,y1)and(x2,y2),respectively.Thequantitiesn,tanq, ,and areevaluatedalongthelightpath.Equation(6.69)hasseveralintersectingfeatures:First,thefirstintegralinvolves( )whereasthesecondintegralinvolves( ).Next,thefirstintegralcontainsafactorof(1/tanq)andthesecondintegralcontainsafactoroftanq.Sincetanqissmall,thefirstintegralin(6.69)isusuallymuchlargerthanthesecondone.Todemonstratetheprocessleadingtotheoptimizationof ,letusconsiderinFig.6.35balightbeamwhichisdeflectedbypassingthrougharectangularregionofrefractiveindex(n+Dn)surroundedbyauniformmediumoftherefractiveindexn.Tobespecific,thecasewheredx,dy,tanq,DnandDqareallpositive.ForoptimizingDqintheportionofthelightpathwheretherefractiveindexisincreasing,theconditionsare , ispositive,andtanqshouldbesmall.Byplacing ,theentireamountofDnhastobecontributedby
alone.Consequently, canhavethelargestpossiblevalueforagivenDnandsoisthefirstintegralin(6.69).Moreover,because
,thesecondintegralin(6.69)iszero.Otherwise,thisintegralwouldbenegativeandwouldreducethevalueofDq.Usingasimilar
argument,Tienetal(1974)foundthatfortheportionofthelightpathwheretherefractiveindexisdecreasing,theconditionsare and
isnegative.AsillustratedinFig.6.35b,alltheaboveconditionsaresatisfied,ifalightbeamwhichentersintotheregionof(n+Dn)throughthebottomleavesitattherightwithouttouchingthetopsideoftherectangle.Thesamelightpath(Fig.6.35b)optimizedanegativeDq,ifDnisnegative.
Toproduceaproperdistributionofelectricfieldonthefilm,Tienetal(1974)usedthecircuitshowninFig.6.35d.Itconsistsoftwomainelectrodes,AandB,andfourparallelfingerseach5mmwide.Thespacingsbetweenthefingersare20mmandthetotalspacingbetweenAandBis120mm.TheelectrodesandthefingersareL=2.7mmlongalong .Byapplying
Page340
Fig.6.36ThedotsarethemeasurementofDqvstheintensity
oftheappliedfieldusingtheexperimentalarrangementshowninFig.6.35(c).Solidlineindicatedtheresult
calculatedfromequation(6.71)usingr33=28.5×10-12m/V(Tienetal1974).
propervoltagestotheelectrodesandthefingers,avarietyofelectricfielddistributionscanbeproducedbetweenAandB.ThecircuitisfabricatedonaglasssubstratebytheusualphotolithographictechniqueandisthenattachedontopoftheepitaxialLiNbO3film.AcoatofEUKITTisappliedbetweenthefilmandthecircuitinordertoavoidelectricbreakdowninair.Thefilmhasthecaxisparalleltoandtherefractiveindicesofthefilmaren0=2.290andne=2.220.Intheexperiments,al=0.6328mmHe-Nelaserbeamwascoupledintothefilmbyarutileprismcoupler.Thelightbeaminthefilmwas60mmwideandpropagatednearlyparallelto intheTE(m=0)waveguidemode(Tien1971).Tosimplifythecomputation,themodeindexwastakentobeequaltoneofthefilm.
ThefirstexperimentisillustratedinFig.6.35c.ByapplyingavoltageacrossAandB,auniformelectricfieldEyisexcitedbetweentheelectrodes.TheelectricfielddistributionisillustratedinthisFig.bydashedlines.Duetotheelectro-opticcoefficientr33ofLiNbO3,therefractiveindex(extraordinary)ofthefilminthespacebetweenAandBisincreasedbyanamountDnsuchas
ThiswasareproductionofthesituationshowninFig.6.35b-aregionof(Dn+ne)surroundedbyamediumofne.Here,DnispositiveornegativedependinguponthesignofEy.WhenEyvariesfrom7.0to-6.7V/mm,thelightbeamscansfirstover rad(whenDnisnegative)andthenover rad(whenDnispositive),asshowninfigures6.35cand6.36.Tocalculatethesedeflections,itcanbeshownfromequations(6.68)and(6.69)that
Page341
whereq1andq2areexpressedinradians.FromtheexperimentalvaluesofDqandusing(6.70)and(6.71)Tienetal(1974)obtainedr33=28.5x10-12m/Vfortheirfilm,whichwassubstantiallylargerthanthatreportedbyFukunishietal(1974)fortheirLiNbO3films.Infact,thevalueofr33obtainedbyTienetal(1974)wasonlyabout10%lessthanthatofbulkLiNbO3.Usingtheexperimentalvaluer33ofthefilm,themeasuredvaluesofDqarecomparedinFig.6.36withthosecomputedfromequations(6.70)and(6.71);theagreementisexcellent.
Tienetal(1974)discussedaphenomenonofrefraction.Thelightwavewasrefractedasitenteredintotheregionof(ne+Dn)andwasrefractedagainasitlefttheregion.Foroptimizing theauthorsarrangedthelightpathsothatthesetworefractionsadded.Itisevidentfrom(6.71)thatthismodeofoperationappliesonlyfor
.Otherwise,thelightbeamwouldbetotallyreflected.
ThesecondexperimentisillustratedinFig.6.35d.ConsideragainthegapbetweentheelectrodesAandB.Byapplyingpropervoltagestothefingersandtheelectrodesanindexdistributionwasexcited,suchthatDn(=Dn)-wasnegativeinthetoppartofthegapandDn(=Dn)+waspositiveinthelowerpart.Theoverallvariationoftherefractiveindexinthegapwas .Alightbeamwithanentranceangleq1facesanegativegradientoftherefractiveindexwhichcausesthelightpathtobend.IfthenegativeDnislargeenough,thelightbeamtracesacirculararcinsidethegapandfinallyemergesattherightwithanexitangleq2=q1.Thisiswhatonewouldexpectforatotalintegralreflection.However,whenAnislessnegative,thearctracedbythelightbeambecomeslarger.Soon,onefindsthatthegapisnotlongenoughforthelightbeamtocompletethisarc.This
Fig.6.37Schematicdiagramofthepolarization-independentopticalfilter(WMC,polarizationconvertervoltage;VTbirefringencetuningvoltage;Vc,polarizationsplittertuningvoltage)(Waranskyetal1988).
Page342
incompletetotalreflectionmakesq2againvarywithDnwhichofcoursedependsontheintensityoftheappliedelectricfield.Itcanbeshownfurtherthat,forvaluesof(2Dn/n)muchlessthan ,thelightbeaminsidethegapisdeflectedthroughtheincompletetotalreflection(illustratedinFig.6.35(d)by ).Inthismodeofoperationthedeflectionislinearwith fromq2=0toq2=-q1andthenstaysatq2=-q1forafurtherincreaseof .Ontheotherhand,intherangebetween and0(orpositive),thelightbeamisdeflectedbyrefractionsasdiscussedearlierinthefirstexperiment(illustratedinFig.6.35dby ).Theseparatinglinebetweenthesetwomodesofoperation, ,issimplytheconditionofthecriticalangle.
6.7Electro-opticallytunablewavelengthfilter
Wavelengthdivisionmultiplexing(WDM)isaveryattractiveschemetoincreasetheinformationbandwidthoffibreopticcommunicationsystemsandnetworks.WavelengthdemultiplexingandchannelselectioninsuchWDMsystemsrequiretunablenarrow-bandopticalfiltersthatarecompatiblewithsingle-modefibres.Furthermore,applicationswithfibresthatdonotpreservepolarizationrequireopticalfiltersthatoperateindependentlyoftheinputpolarization.Variousschemesoftunableopticalfiltershavebeendemonstratedwithsingle-modewaveguides,suchaswavelengthselectiveintegratedopticaldirectionalcouplers(AlfernessandSchmidt1978)andinterferometers(RottmanandVoges1987)orfibreopticBraggreflectors(Whalenetal1986)andFabry-Perotresonators(StoneandStulz1987).Waranskyetal(1988)proposedanddemonstratedthefirstpolarization-independentelectro-opticallytunablewavelengthfilterwithsingle-modewaveguides.TheLiNbO3wavelengthfilterhasabandwidthofonly12Åandatuningrangeofatleast110Å.Ithadtwooutputportsservingasabandpassandanotchfilter,anditcanbeusedforwavelengthdemultiplexingaswellasfor
multiplexing.
Thepolarization-independentfilteremploystwoidenticalwavelength-de-pendent polarizationconvertersandtwoidenticalTE/TMpolarizationsplittersintheinputandoutputofthepolarizationconverters.Theinputpolarizationsplitterdemultiplexesthequasi-TEandquasi-TMpolarizedcomponentsofinputlightandrouteseachcomponentseparatelythroughoneofthetwoparallelpolarizationconverters,wherethetwopolarizationcomponentsexperiencethesamewavelength-dependent polarizationconversionbeforetheyarerecombinedattheoutputpolarizationsplitter.Figure6.37showsaschematicdiagramofthefiltreimplementedwithsingle-modestripwaveguidesonx-cuty-propagatingLiNbO3.Thetwoelectro-optic polarizationconvertersarewavelengthtunableandconsistofacascadeofshortsectionsofpolarizationconverterelectrodesalternatingwithshortsectionsofbirefringencetuningelectrodes(AlfernessandBuhl1985).ThetwopolarizationsplittersareidenticalwaveguidedirectionalcouplerswithDb-reversaltuningelectrodesandaredesignedtocoupleTM-polarizedlightcompletelyintothecrossoverwaveguidewhileleavingTE-polarizedlightintheinput(straight-through)waveguide(AlfernessandBuhl1984).
Thefilteroperatesasfollows.Arbitrarilypolarizedlightentersthefilter
Page343
intheinputwaveguide(No.1inFig.6.37)ofthefirstpolarizationsplitter,whereallTM-polarizedlightiscompletelycoupledintothecrossoverwaveguide(No.2inFig.6.37),whileallTE-polarizedlightstaysinthestraight-throughwaveguide(No.1).Thetwoseparatedpolarizationcomponentspassthroughidenticalnarrow-bandpolarizationconverters.Iftheirwavelengthisatthecentrewavelengthofthepolarizationconverters,thentheTE-polarizedlightofwaveguideNo.1iscompletelyconvertedintoTM-polarizedlight,andlikewise,theTM-polarizedlightinwaveguideNo.2iscompletelyconvertedintoTE-polarizedlight.TheoutputpolarizationsplittercouplesthenowTM-polarizedlightofwaveguideNo.1completelyintothecrossoverwaveguide(No.2)whileleavingthenowTE-polarizedlightinwaveguideNo.2.ThusthetwopolarizationcomponentsarerecombinedandexitthefilterinwaveguideNo.2(thecrossoverwaveguide).
Onthecontrary,ofthewavelengthoftheinputlightisoutsidethebandwidthofthepolarizationconverters,thenthetwopolarizationcomponentspassthepolarizationconverterswithoutchangeinpolarization,andtheoutputpolarizationsplittercouplestheTM-polarizedcomponentofwaveguideNo.2completelybackintoinputwaveguide(No.1),whereitisrecombinedwiththeTE-polarizedinputlight.Inthiscase,bothpolarizationcomponentsexitthefilterinwaveguideNo.1(theinputwaveguide).
ThuslightatawavelengthwithinthebandwidthofthepolarizationconvertersexitsthefilterinwaveguideNo.2,whereaslightatotherwavelengthsexitsthefilterinwaveguideNo.1.ThedevicethereforeactsasabandpassfilterwhentheoutputistakenfromwaveguideNo.2andasanotchfilterwhentheoutputistakenfromwaveguideNo.1.Notethatbothoutputportscanbeusedsimultaneously,thusallowingapplicationsasawavelengthtapinabus-typenetworkorasawavelengthmultiplexer.
Thedetailsoftheelectro-optic polarizationconvertersandtheTE/TMpolarizationsplittersusedinthefilterweredescribedbyHeismannandAlferness(1988),Habara(1987),HeismannandBuhl(1987).InthewaveguideorientationofFig.6.37,theTE-andTM-polarizedmodeshavedifferentpropagationconstantsbecauseofthelargebirefringenceofLiNbO3,thusrequiringperiodiccouplingforefficient polarizationconversion.Periodiccouplingofthetwomodesisachievedelectro-opticallybyinducingaperiodicgratingofindexperturbationsinthewaveguideviaaspatiallyalternatingelectricfieldExandther51electro-opticcoefficient( m/V).Mostefficient polarizationconversionisobtainedatafree-spacewavelength ,whereListhespatialperiodoftheappliedelectricfieldEx,andDnphisthedifferenceoftheeffectiveindicesofthetwopolarizationmodes( ).Theopticalbandwidthoftheefficient conversionisdeterminedbytheoverallinteractionlengthL(HeismannandAlferness1988):
Page344
where isthegroupindexdifferenceofthetwomodesatl0.
Tuningofthecentrewavelengthl0isaccomplishedelectro-opticallybychangingthebirefringenceDnphinthewaveguideviaaspatiallyuniformelectricfieldEz,andther33andr13electro-opticcoefficients( m/Vand m/V).Herethefieldsforpolarizationconversion,Ex,andforbirefringencetuning,Ez,areappliedalternatelyoveralargenumberofshortsections.Inthisdevice,45sectionsofuniformbirefringencetuningelectrodesareperiodicallyinterleavedbetween46sectionsofperiodicpolarizationconverterelectrodes,whereallbirefringencetuningelectrodesaredrivenbyacommonvoltageVTandallpolarizationconverterelectrodesbyacommonvoltageVMC.Thetuningrateofthecentrewavelengthl0isgivenby(HeismannandAlferness1988)
where istheshiftofthecentrewavelength,GisthenormalizedoverlapintegraloftheappliedelectricfieldEzwiththeopticalfields,Gisthegapofthebirefringencetuningelectrodes,and and arethelengthsofasinglepolarizationconverterandbirefringencetuningsection,respectively.
Operationofsuchtunable polarizationconverterasawavelengthfilterrequireslinearTE-(orTM-)polarizedinputlightandalinearTM-pass(TE-pass)polarizationfilterintheoutputbeam.Notethatthewavelengthdependenceofelectro-opticconversionisindependentofthedirection,i.e. conversionhasthesamecentrewavelength,bandwidth,andtuningrateasconversion.This symmetryofthewavelengthresponseisessentialfortheoperationofthepolarizationindependentfilter.HereidenticalwavelengthresponsesforTE-andTM-polarizedinputlight
areobtainedbyusingidenticalpolarizationconvertersinthetwobranchesofthefilter.Inthepresentdevice,thetwopolarizationconverterssharethesameinterdigitalfingerelectrodes,asshowninFig.6.37,toobtainthesamecentrewavelengthsforTE-andTM-polarizedinputlight.Thebirefringencetuningelectrodesofbothconvertersaredesignedtohaveexactlythesamelengthstoobtainidenticaltuningrates.Thetuningelectrodesarearrangedinsuchawaythatnocrossconnectionsareneededwithintheelectrodestructure.However,thiselectrodelayoutrequirestwotuningvoltages,VTand2VT.toobtainaneffectivetuningvoltageofVTforbothpolarizationconverters.
Thepolarizationsplittersareconventionalwaveguidedirectionalcouplersdesignedtohavecouplingcoefficientsof forTM-polarizedlightand forTE-polarizedlight,whereLcisthecouplinglength.Polarizationsplittingwithlowcrosstalkisachievedbydetuningthecouplersviatwo-sectionDb-reversalelectrodesutilizingther33(forTE)andr13(forTM)electro-opticcoefficientssothatTM-polarizedlightiscompletelycoupledintothecrossoverwaveguide,whileTE-polarizedlightstaysintheinputwaveguide(Habara1987).
Page345
Fig.6.38Normalizedfiltertransmissionoftheuntuned(VT=0V,solidandthindashedlines)andtunedbandpassfilter(VT=+100and-100V,bolddashedlines)measuredforTE-andTM-polarizedinputlight(Waranskyetal1988).
Thefiltreisrealizedinx-cutandy-cutpropagatingLiNbO3usingstandardfabricationtechniques.The polarizationconvertersaredesignedforoperationaround mm.ThebasicperiodoftheinterdigitalfingerelectrodesisL=21mm( ),andthetotalinteractionlengthis19mm.Thepolarizationsplitter/directionalcouplershaveacentre-to-centrewaveguideseparationof17.5mmandatotalcouplinglengthof8mm.Polarizationsplittingwithcrosstalkoflessthan-18dBisachievedbyapplyingvoltagesof-37and+40VtothetwosectionsoftheDb-reversalelectrodes.Theoveralllengthofthefiltreis52mm.
PolarizedlightfromatunablecolorcentrelaserisusedtotestthefilterresponseseparatelyforTE-andTM-polarizedinputlight.Fig.6.38showsthetransmissionofthebandpassfiltre(outputportNo.2)versuswavelengthforTEaswellasforTMinputlight.Forbothinputpolarizationsthecentrewavelengthoftheuntunedfiltre(VT=0)is1.5254mmandtheopticalbandwidthis12Å,asexpectedforthe19mmlongpolarizationconverters( ).Thevoltageforcomplete conversionisVMC=+37grV.AlsoshowninFig.6.38isthefiltretransmissionwhentuningvoltagesofVr=-100and+100
Vareappliedtothebirefringencetuningelectrodes.Herethecentrewavelengthisshiftedby55Åtoshorterandlongerwavelength,respectively,whereidenticalresultsareobtainedforbothinputpolarizations.Thusthefiltrecanbetunedoverarangeofatleast110Å.
6.8Flip-chipcouplingbetweenfibresandchannelwaveguides
Efficientcouplingbetweensingle-modefibresandTi-diffusedLiNbO3channelwaveguidesisessentialfortheinclusionofLiNbO3waveguidedevicesinsingle-modefibresystems.Suchcouplingisdifficulttoachievebecauseofcriticalpositioningandpreparationtolerances.Micromanipulatorscanbeusedforthefibre/channelalignmentforend-firecoupling(Nodaetal1978;KeilandAuracher1979;FukumaandNoda1980).Hsuetal(1978)demonstratedfibre/channelend-firecouplingusingtheflip-chipapproachwhereV-groovesarepreferentiallyetchedinaSiwafer.TheLiNbO3end-faceswerecleaved.Infibre/fibrecoupling,improvedaltitudinalalignmenthasbeendemonstratedwithtaperedfibrespositionedingroovesatrightanglestotheinputandoutput
Page346
Fig.6.39SchematicofSiV-groove/flip-chip
couplingstructure(Bulmeretal1980).
fibregrooves(SheemandGiallorenzi1978).Bulmeretal(1980)usedtaperedfibresintransversegroovesinSiV-groove/flip-chipcouplingmethodandhaveconsistentlymeasuredcouplingefficienciesof>70%,correspondingtoan~3dBtotalthroughputloss(Bulmeretal1980)forTE-andTM-modepolarizations.ThecouplingstructureisindicatedschematicallyinFig.6.39.Itiscompactandcanbemaderigid.
Thereareseveralverystringentrequirementsforefficientcoupling:(i)accuratehorizontal,vertical,andangularpositioning;(ii)planar,defect-freewaveguideandsurfaces,normaltothepropagationdirection;and(iii)forcompletecoupling,matchingofthewaveguidefielddistributions.Bulmeretal(1980)aimedtoachievetranslationalalignmentof<1mmandangularalignmentof<10.OnlyLiNbO3waveguideorientationswereusedinordertoavoidanisotropicleaky-mode(Sheemetal1978)anddoublerefractioneffects(KaminowandStulz1978)whichoccurwhenwavesarepropagatingalonganonaxialdirection,andsoachievepolarization-independentpropagationlossesandcouplingefficiencies.AsLiNbO3hasonlyonecleavageplane,alonganonaxialdirection,itisnecessarytopreparethecubicandfacesoftheLiNbO3substratesbypolishing.TheLiNbO3substrateedgesshouldhaveminimalrounding.
Accuratepositioninginthehorizontalplaneisachievedbyaligningmatchingregistrationlines(groovesandchannels)whichareregisteredalongthecouplingfibreV-groovesintheSiwaferandalongthechannelwaveguidesintheLiNbO3.Theregistrationlinesareseveralmicronswideandareregisteredwithanaccuracybetterthan0.5mm.Accurateverticalpositioningisprovidedbytaperedalignmentfibres,withdiameterstaperedby0.5-1mm/mm,placedunderthecouplingfibresindeepV-grooves,atrightanglestothecouplingfibregrooves.Thehightoftheinputoroutputfibreiscontinuouslyadjustedbypushingorpullingthetaperedfibreinitstransversegroovesothatthecouplingismaximized.Withoutsuchfinealtitudinalalignment,ahighcouplingefficiencycouldbeachievedonlywithcouplinggroovespreciselytothedepthappropriateforafibreofknowno.d.(opticaldamage)andperfectconcentricity.
Bulmeretal(1980)usedhigh-resistivity<100>Siwafers,withan1mmthickmaskinglayerofSiO2,andalignedthephotolithographicgroovemask
Page347
tothewaferaxestobetterthan1°.Themaskhastworegistrationgroovesalongeithersideofeachcouplinggroove.Inthealignmentoftheflipped-overLiNbO3ontopoftheSiwafer,acorrespondingTi-diffusedlineintheLiNbO3,toeithersideofeachchannelwaveguideorwaveguidedevice,isarrangedtoliebetweenthesetworegistrationgrooves.InthecentralregionwhereLiNbO3substrateistobelaid,onlyhalfwaythroughtheSiO2masklayerwasetchedsothattheregistrationlinesarenotoveretchedduringtheSiV-grooveetchingprocess.ThecouplingandalignmentcouplinggrooveswerethenetchedintheSiusinganethyl-enediamine-pyrocatechol-watermixture(FinneandKlein1967).IftheregistrationgroovesareetchedintheSi,theydeteriorategreatlyowingtoundercuttingandthefinitepreferentialetchratio,whichmakesexactalignmentverydifficult.ThecompletepatternontheSiwaferconsistedofsixcouplinggrooveswithdeepertransversealignmentgroovestoeithersideofsubstrateregion.Couplinginturntoeachofsixdifferentchannelwaveguidesisthereforepossiblewithasingleunit.
TheLiNbO3endsurfaceswerepreparedbyanopticalcontactpolishingmethod.TheTi-diffusedLiNbO3substratewasopticallycontactedtoadummyLiNbO3substrate,theinputandoutputedgeswerepolished,andthesubstrateswerethenseparatedbymildthermalshock.Toallowopticalcontact,TiwasdiffusedovertheentireLiNbO3substrateexceptclosetothechannelwaveguidepattern.Asthereisnogapbetweenthesubstrates,chip-freeedgeswithnoroundingareobtained.Veryflatfibreends,withlittleornolip,normaltothefibreaxis,wereobtainedusingtheconventionalcleavingtechnique.Ifthewaveguidefielddistributionsareperfectlymatched,100%couplingispossible(neglectingreflectionlosseswhichcanbeminimizedwithantireflectioncoatings).However,perfectmatchingisnotpossiblebecausethechannelwaveguidefielddistributionhasanon-unityaspectratio,isasymmetricperpendicular
tothesurface,andisnotexactlyGaussianeitherparallelorperpendiculartothesurface,whereasthefibrefieldisessentiallyGaussian(BurnsandHocker1977).ThechannelwaveguidefieldcanbeoptimizedsomewhatbyanappropriatechoiceofTidiffusionconditions(Fukudaetal1979).
Bulmeretal(1980)defined3and4mmwidestraightchannelwaveguidesand3mmwidechannelwaveguideMach-Zehnderinterferometersin170-220Å.Tionz-cut,x-propagatingLiNbO3substrates.ThediffusionwasperformedinO2for6hat1000°C,andinsomecasesinthepresenceofLiNbO3powdertoreduceLi2Oout-diffusion.Thechannelswereperpendicular,to1°,totheedgeswhichwerethenpolished.An4000ÅSiO2layerwassputteredoneachsubstrateandthenoxidizedfor9hat600°C.ItwasneededtoisolatetheopticalwaveguidesfromtheA1electrodeslaterdepositedalongtheinterferometer.Toobtainpolarization-independentbehaviour,authorsusedhorizontalandverticalfieldelectrodes.Theauthorsusedsingle-modefused-silicafibrewithNA0.1andcoreandcladdingdiametersof4.5and88mm,respectively.Theouterplasticjacketwasremovedinthecouplingregionandalongsectionsoftheinputandoutputfibreswherecladdingmodeswerestripped.Thefibrebeatlengthwas~20m.Measurementsweremadeat633nm,separatelyforeachopticalpolarization.Thepolarizationwasrotatedwithahalf-waveplateattheinputtothe0.5mlonginputfibreanditwascheckedatthefibre
Page348
output.Thepolarizationwasmaintainedto~99%.
Bulmeretal(1980)entirelyneglectedanymodepropagationlossesincalculationsofflip-chipcouplingefficiencies.Usingtheflip-chiparrangementdescribedabove,theauthorsobtained76and72%couplingbetweenthesameinputfibresandthe3and4mmchannels,respectively,foreachopticalpolarization.Thus,theflip-chipcouplingefficiencieswereashighasthosemeasuredwiththemicropositioner.Thecouplingcouldbesmoothlyvariedbetweenmaximumandnearzerobymovingthetaperedalignmentfibre.Ifthecouplingfibregrooveswereetchedtoodeeply(byseveralmm),therewassomefrictionbetweenthetwofibres,resultinginappreciablehorizontalmotionofthecouplingfibre,whichaidscouplingiftheLiNbO3-Siwafertransversealignmentisimperfect.
With3and4mmwidechannelsoneachsubstratecementedtoaSiwafer,andwithfibre/channelseparationof<10mm,Bulmeretal(1980)havemeasuredTE-andTM-modecouplingefficienciesof70-88%,correctedforreflectionlosses.ProvidedthattheinitialSi/LiNbO3alignmentisaccurateto1mm,themeasurementswererepeatablewithin10%andthesamecouplingefficiencieswereobtainedforcouplingwithoneinputfibreorwithinputandoutputfibres.ThevaluesforsubstratesweredeterminedallowingforsmallFabry-Perotresonances(BornandWolf1970)usingtheexpression
HerePmax(mm)isthemaximum(minimum)outputpower,Pinistheinputpower,kisthefibre/channelcouplingefficiency,and arethereflectivitiesateitherendoftheFabry-Perotcavity;representsthefractionofpowerreflectedateitherendofthecavitywhichremainsguidedinthechannelwaveguide( indicatescompletelossonreflectionbecauseofnonperpendicularchannelend
facets).Inthecasesunderconsideration, .Equation(6.74)wasderivedintheassumptionofzeromodeattenuationinthecavityandwithdisregardofanyeffectofthe7.5cmlasercoherencelength.Foroneofthesamples,fromcomparisonsoftheoutputswithindexmatchingoilandairbetweenthefibreandLiNbO3,theLiNbO3itselfappearedtobeactingasaresonantcavity.ThiswasverifiedbyheatingandcoolingtheLiNbO3tovarytheopticalpathlengthandobservingtheresultantoscillatoryvariationinoutputofupto7%duetothermalexpansionandrefractiveindexchange.
Inordertoestimatethemaximumcouplingefficiencyforperfectalignmentlimitedonlybythemodefieldmismatch(BurnsandHocker1977),modedistributionsweremeasuredbyscanningwitha100mmdiam.pinholeinthehorizontal(x)andvertical(y)directionsacrossthemagnifiednear-fieldimagesofthechannelwaveguideandfibreoutputs.Alltheprofileswereextremelysmooth,andshowednoindicationofimperfectionsinthechannelandsurfaces.Fromthe1/epointsoftheseintensityprofiles,theGaussianmodefieldhalfwidthwasdetermined(seeTable6.4).Forthechannel,thesewerewx,
Page349
Table6.4Measuredchannelmodefieldhalf-widthswx,wyandcorrespondingtheoreticalmaximumcouplingefficiencieskmand fromnumericaloverlapofbeamprofiles(Bulmer,Sheem,Moeller1980)
Mode wx(mm) wy(mm) km(%) k'm(%)
2.9 2.2 88 92
3.6 3 91 93
2.9 2 86 89
3.2 2.3 89 92
wyoftherectangularGaussian(BurnsandHocker1977)(where,e.g.,whichapproximatesthewaveguidemodeelectricfield
(wxisparallelandwyperpendiculartothesurface).Forthefibre,assumingacircularGaussianfield,themoderadiuswasa=3.0mm.Thenforaperfectalignment,azeroseparationandnoreflectionlosses,thepowercouplingcoefficientwasestimatedas
wherethefactor0.93isacorrectionforthedeviationoftherealmodefieldsfromtheirGaussianapproximations.Table6.4presentsthekmvaluescorrespondingtothemeasuredmodewidths.Theyareafewpercenthigherthantheexperimentalcouplingefficiencies.Themaximumcouplingefficiencieswerealsoestimatedbyanumericaloverlapofthenormalizedmodeprofilesandareshownas inTable6.4.Thevaluesare2-4%higherthanthecorrespondingkmvalues.Sincetheoryintends itcanbeconcludedthatthecorrectionfactor0.93isslightlyconservativeforthiscase.
6.9KTiOPO4waveguidedevicesandapplications
KTPhasseveralpotentialadvantagesforopticalwaveguidedevice
comparedwithothermaterialsinadditiontohavingamuchlargermodulatorfigureofmerit.ItshighopticaldamagethresholdsuggeststhatKTPwaveguidedevicescouldbeusedtocontrolorconverthigh-intensityopticalbeamswithinputwavelengthsextendingfromthevisibletotheIR.KTPwaveguidedevicesshouldbemuchlesssusceptibletopiezoelectricandpyroelectricinstabilitiesbecausetheseeffectshavenotbeenobservedinbulkdeviceapplications,andhencedevicethermalandmechanicalstabilityshouldbemuchbetter.
Severaldemonstrationelectro-opticandnonlinearopticdeviceshavebeenfabricatedbyusingKTPwiththewaveguidefabricationprocessdescribedinchapter2.Themeasured forseveralsingle-channelphasemodulatorsindicatesthatthewaveguidefabricationprocessdoesnotaltertheelectro-opticcoefficient.Usinga6mmwidechannelwaveguideanda0.2mmMgF2bufferlayer,andcouplingtotheelectro-opticcoefficientrc2,BierleinandVanherzeele
Page350
(1989)observeda of6Vcmat6328Å,whichisclosetothetheoreticallypredictedvalueforKTP'sbulkelectro-opticanddielectricconstants(Bierleinetal1989).Thesedevicesaredcstableforbothhydrothermallyandflux-grownsubstrates.The waslowerthan6Vcmatlowfrequenciesandincreasedto6Vcmathighfrequency.Theoccurrenceofionic-conductioneffectssuggeststhatthedcconductivityoftheRb-richopticalwaveguideislowerthanthatofbulkKTP.LimiteddataonthedielectricpropertiesofbulkRbTiOPO4indicatesuchalowerconductivity,aresultthatisnottotallyunexpectedbecauseRbhasalargerionicradiuscomparedwithK,givingalowerionhoppingrate.
AMach-Zehndermodulatorwasalsofabricatedona1mmthick,z-cutKTPsubstratebyusing6mmwideRb-exchangedwaveguidesandtraveling-waveelectrodesthatshowabandwidthofnearly16GHz(Laubacheretal1988).Thismodulatorwasfabricatedwitha0.4mmSiO2bufferlayer,a1cmelectricfieldinteractionlength,anda25mmelectrodegapandhada of10Vata1.3mminputwavelengthand5Vat0.633mm.Thismodulatordidnotshowanyinstabilitiesduetoopticaldamageorphotorefraction,whicharecommonlyobservedinothermaterials,evenwithinputsofasgreatas1mW.
Thenonlinear-opticalpropertiesofKTPwaveguideshavealsobeenevaluatedbymeasuringtheSHGoutput,usingadiode-pumpedNd:YAGinputat1.064and1.31mm.Usinga6mmwideRb-exchangedchannelwaveguide,Bierlein(1989)measuredconversionefficienciestothegreeninthe4%W-1cm-2range.Thisconversionefficiencyisclosetothebestvaluesmeasured(4.8%)forTi:LiNbO3waveguides.At1.31mminputconversionefficienciesofapproximately1%W-1cm-2wereobtained.
ForfrequencydoublingexperimentsconductedbyRisk(1991)awaveguidewasfabricatedonthec-sideofaKTPsubstratewitha
depthofd~2mmandfoundtobesinglemodeattheinfraredwavelengthusedforSHG.InbulkKTP,typeIInonlinearprocessesareused,sincethesehavehigheffectivenonlinearcoefficients.Theseprocesses,suchasfrequencydoublingof994nmlight(Risketal1989),orsum-frequencymixingof809and1064nmlight(Baumert1988),requirebothx-andz-polarizedfieldsattheIRwavelengthsforpropagationalongthey-axis.ThegeneratedSHfieldispolarizedalongx.ThephasematchingconditionforSHGisthus1/2
.Inthewaveguide,theanalogousinteractioncorrespondsto ,wherem,n,andparemodenumbers.Themostdesirableinteractionisform=n=p=0,whichinvolvesonlythelowest-ordermodes.Interactionsinvolvinglowest-ordermodesatthefundamental(m=n=0)andhigher-ordermodesatthesecond-harmonic( )permitgenerationofblue/greenwavelengthsshorterthanthoseobtainedusingthebulkmaterial.
Figure6.40showscalculatedvaluesfortherefractiveindicesinvolvedinthebulkinteractionandforeffectivemodeindicesintheguided-waveinteraction.ThebulkrefractiveindexvaluesarecalculatedfromSellmeierequations.TheeffectivemodeindiceshavebeencalculatedbytheWKBmethodusingtheparametersofthewaveguidemeasuredbyprismcouplingat633nm.Thedashedcurvesrepresent1/2[ ],correspondingtofundamental
Page351
Fig.6.40Phase-matchingcharacteristicsforfrequency
doublinginaplanarKTPwaveguide.Lowerhorizontalscalereferstofundamentalwavelengths;upper
horizontalscalereferstocorrespondingsecond-harmonicwavelengths(Risk1991).
Table6.5Wavelengthsofphase-matchedinteractions(Risk1991)
Interaction Calculatedwavelength Measuredwavelength
1130nm N/A
966nm 969nm
913nm 923nm
905nm 906nm
wavelengthsonthelowerhorizontalscaleandnx(2w),correspondingtosecond-harmonicwavelengthsontheupperhorizontalscale.Attheintersectionofthesetwocurves,thebulkphase-matchingconditiongivenaboveissatisfied;thiscorrespondstoSHGwithafundamentalwavelengthof994nm(Risketal1989).ThesolidcurvesinFig.6.40showthedispersionoftheeffectiveindicesforwaveguidemodes.Theintersectionsofthecurverepresentingtheaverageofthe andmodeindiceswiththecurvesrepresentingthemodeindicesforthe
modesdefinewavelengthsforwhichguided-modeSHG
interactionsarephasematched.Ascanbeseenfromthefigure,blue/greenlightcanbegeneratedatwavelengthsconsiderablyshorterthanthatobtainedbySHGinthebulkcrystal.
Lightfromatitanium-sapphirelaserinthe900-1000mmrangewasusedtosimultaneouslyexcitetheTE0andTM0modesofthewaveguide.Asthewavelengthofthelaserwastuned,SHGinteractionsinvolvingexcitationofhigher-orderTEmodesatthesecondharmonicwereobserved.ThemeasuredwavelengthsatwhichtheseinteractionsoccurredareshowninTable6.5,alongwiththecalculatedvaluesfromFig.6.40.Themeasuredandexpectedwavelengthsforthevariousinteractionsareingoodagreement.ExcitationoftheTE0modeatthesecondharmonicwasexpectedtooccurforafun-
Page352
damentalwavelengthof1130nm,butcouldnotbeobservedsincethiswavelengthwasoutsidethetuningrangeofthetitanium:sapphirelaser.Forwavelengthsshorterthan905nm,excitationofradiationmodesatthesecondharmonic(Cherenkovdoubling)wasobserved.
6.9.1PhasematchinginperiodicallysegmentedKTiOPO4waveguides
Bierleinetal(1990)describedanewtechniqueusedforachievingphasematchinginKTiOPO4(KTP)waveguidesbutequallyapplicableforbothbulkandotherwaveguidesystems.Thisschemecannotonlygivephase-matchedsecond-harmonicconversionefficienciesbutcansignificantlyextendprocessinglatitudewhichisparticularlyimportantforpracticalnonlinearopticalchannelwaveguidedevices.
Intheconventionalphasematchinginvolvingthenonlinearinteractionofthreebeamsinacrystalwherethefrequenciesofthethreebeamsarerelatedas ,eitherthedirectionofpropagationorthetemperatureistunedsothatthepropagationconstants ofthesebeamsobeytherelation ,or
.Herethe arethebeampropagationconstants,n'stherefractiveindices,andl'sthecorrespondingwavelengths.Thecrystalorwaveguideisdividedintosegments,eachsegmentconsistingofsectionsoflength andpropagationconstantmismatch suchthatforeachsegment ,wherethesumisoverallsections.Thelengthofeachsectionislessthanitscorrespondingcoherencelength,thatis .Whentheseconditionsaremet,eventhoughthebeamsarenotphasematchedisthesectionsindividually,theyarephasematchedattheendofeachsegmentandthegeneratedoutputpowerwillincreaseasthesquareofthenumberofsegments.
Eachsegmentcouldinprincipleconsistofmanysections,mightdiffer
instructurefromtheprevioussegment,orcouldevenbeasinglesectionwithcontinuouslyvaryingpropertiessuchthat .Toillustratethemethod,thesimplifiedcasewasconsidered,wherethesecond-harmonicgenerationinaperiodicwaveguidestructureconsistedoftwosectionspersegmentasshowninFig.6.41.Forthiscase,afairlysimplequantitativerelationforthegeneratedoutputpowercanbeobtained.Inthestructuresconsidered,thelengthofthesectionsdeviatedstronglyfromtheBraggconditionandtherefractiveindexdifferencesbetweenthesectionsweresmall.Therefore,thereflectioneffectsfromthesubsequentsectionsandthefundamentalbeamdepletioncouldbeignored.Withtheseapproximationsandextendingthisanalysis
Fig.6.41Segmentedwaveguidestructure(Bierlein1990).
Page353
toincludeferroelectricdomainreversals,thesecond-harmonicpowergeneratedfromthesegmentedstructure,P,normalizedtothepowergeneratedinaperfectlyphase-matcheduniformwaveguideofequallength,P0,isgivenby
whereGdescribestheeffectsoftheperiodicgratingandItheinternalSHGwithinasingleperiod.TheeffectsofoverlapbetweenfundamentalandharmonicguidedmodeswereassumedtobeidenticalforbothPandP0.
Thegratingfunction,G,inequation(6.76)isgivenby
whereNisthetotalnumberofperiodsinthewaveguideand
isthephasematchingbetweenthefundamentalandsecond-harmonicwaveguidemodesinasingleperiod.The and arethelengthsandcorrespondingpropagationconstantmismatchesofthetwosegments.ThefunctionGwillpeakifthesecondharmonicwavesfromsubsequentperiodsaddinphase,thatis,at ,whereM=0,±1,±2,etc.andthephase-matchingconditionbecomes
Theinternalfunction,I,inequation(6.76)describeshow,withinasingleperiod,thesecond-harmonicfieldsofneighbouringsegmentsinterfere.Atphasematching,Iisgivenby
where arethecoherencelengthsofthetwosections.The+signinequation(6.80)correspondstothecasewhereadjacent
segmentshaveinvertedferroelectricdomains,the-signcorrespondstoapurerefractiveindexgrating.Withthelowindexstepsusableinpractice,itcanbereadilyshownfromequation(6.80)thatthelattersituationleadstomuchlowerconversionefficienciesascomparedtothedomaininvertedcase.
Balancedphasematching(BPM)occurrswhenM=0inequation(6.79)andislimitedtophase-matchedSHGinKTPforawavelengthlongeraboutthat1mm(Bierlein,etal.1990).With theblueregionofthevisible
Page354
Fig.6.42Second-harmonicgenerationin5mmRb/Baflux
KTPsegmentedwaveguides.(a)Absoluteconversionefficiencyat850.5nmfora4mmperiod,4mmwaveguide.(b)Wavelengthscanfora5mmperiod,4mmwaveguide.Pwistheguidedfundamentalpower(Poeletal1990).
Fig.6.43Phase-matchingwavelengthvssegment
periodof4mm-widewaveguides.Solidlinesand()arefor interactions,dashedlines
and(x)arefor interactions.Misdefinedinequation(6.79)(Poeleta11990).
spectrumbecomesavailableforphase-matchedsecond-harmonicgeneration.Thewaveguidedepthcanbechosentominimizetheeffectsofdepthvariationsontherefractiveindexmismatchsuchthat
optimumfabricationtolerancesforphasefunctionresult.Thispropertyofthesegmentedstructureconstitutesamajoradvantageoveruniformwaveguides,wherethisdegreeoffreedominfabricationisabsent.Intheexperiments,onesegmentwasbulkKTPandtheotherwasanion-exchangedwaveguide.Withthismask24differentwaveguidewidth/segmentperiodcombinationscanbefabricatedonasinglesubstrate.Inatypicalexamplesegmentedy-propagatingwaveguideswerefabricatedonthez-surfaceofaflux-grownKTPsubstrate.UsingatunableTi:A12O3laser,thephase-matchingwavelengthsandconversionefficienciesforthesewaveguidesaregiveninFig.6.42.Overallfundamentalbeamthroughputfromthelasertothewaveguideoutput(includinglenses,couplingandwaveguidelosses)
Page355
Fig.6.44Phase-matchedwavelengthbandwidthsfor
segmentedKTPwaveguides.(a)M=0,typeII,5mmperiod,5mmwidth.(b)M=1,typeI ,4mmperiod,5mmwidth.(c)M=2,typeI ,4mm
period,4mmwidth(Poeleta11990).
isabout40%.Twowaveguidemodesareobservedtogivephase-matchedSHG.Fromthenear-andfar-fielddistributions,thesemodescorrespondtocouplingsbetweenthelowestorderguidedfundamentalmodeand,respectively,thelowestandfirst-orderguidedharmonicmodes,asindicatedinFig.6.42.
AtypicalefficiencyplotisalsoshowninFig.6.42which,atlowfundamentalpowers,indicatesanefficiencyof80±5%/Wcm2.Dependingonwaveguideprocessingconditions,significantlylowerphase-matchedtypeIefficienciescanalsooccurwithbothhydrothermalandflux-grownsubstrates.Forexample,loweringtheexchangetemperatureby20°Cdecreasestheconversionefficiencybynearlythreeordersofmagnitude.
Forawaveguidewidthof4mm,theSHGphase-matchingwavelengthsweremeasuredforfourdifferentsegmentperiodspresentonthesameKTPsubstrate.InFig.6.43,themeasurementsarecomparedwiththeoreticalpredictionsforvariousphase-matchingM
valuesandnonlinearinteractions.TheinteractionsincludetypeIcouplingthroughthed33nonlinearopticalcoefficient( )andthroughthed32coefficient( ).EfficientSHGphase-matchedoutputisobservedfromdeeppurpleat0.38mmtoblue-greenat0.48mm.ForKTP,thiswavelengthrangeisnormallynotaddressablebyconventionalphase-matchingtechniques.Forperiodsof3,4,5and6mm,theobservedphase-matchingwavelengthsforthesevariouscombinationsareingoodagreementwiththosepredictedfromequation(6.79)usingbulkKTPrefractiveindices(BierleinandVanherzule1989).Thedifferencesbetweenthecalculatedandexperimentalwavelengthsarequitesmallconsideringthatinthecalculationbulkrefractiveindicesratherthaneffectivewaveguideindiceswereusedinequation(6.79).
Thewavelengthbandwidths,asmeasuredin5mmsegmentedwaveguides,aresummarizedinFig.6.44andcomparedtoatypicalresultusingBPM.From
Page356
aTaylor'sexpansionofequation(6.77),usingequation(6.79)andtheSellmeierequationsforbulkKTP(Bierleinetal1989),wavelengthbandwidthsfullwidthathalfmaximumof0.67nmcmfortypeIIat1.06mmand0.06nmcmfortypeI, at0.80mmarepredicted.Thecloseagreementbetweenthepredictedandmeasuredbandwidthsindicatesthatnearlyperfectphasematchingoccursoverthefull5-mmsamplelength.Thisalsoaccountsforthehighabsoluteconversionefficiencyobserved(3%at100mWfundamentalpowerforM=1).Themeasuredtemperaturebandwidthisabout3°C.AlsoshowninFig.6.44isthetypeI phase-matchedpeak.ThispeakcorrespondstophasematchingforM=2,withanexpectedwavelengthbandwidthof0.05nmcm.
Preliminaryresultsfromlow-temperatureelectrostatictuningandfromsurfaceSHGexperimentsindicatethattheoriginoftheselargetypeIconversionefficienciesisferroelectricdomainreversalinducedbythewaveguideprocessingwhenBaispresentintheexchangebath.AssumingthatthedepthoftheferroelectricdomaincorrelateswiththeBaionconcentrationinthewaveguideand,sincetheeffectiveSHGmodeoverlapisexpectedtovarystronglywithdomaindepth(ArvidssonandJaskorzynskii1989),thismechanismwouldalsoexplainthelargechangesinconversionefficiencythatoccurwithchangesinion-exchangetemperature.Ion-exchangeexperimentswithdifferentsubstratematerials,differentsurfacepolarities,andavarietyofmoltensaltcompositionsareinprogresstoclarifythemechanismfordomainreversalinthesematerialsandtogainimprovedunderstandingofandcontroloverthefabricationprocess.
ConclusionsInasinglebook,evenofthisvolume,itisdifficulttoembraceallaspectsofferroelectricthin-filmwaveguides,fromalargenumberof
methodsoffabricationtoevenalargernumberofpossibleapplicationsindevicesforlaserradiationcontrol.Asindicatedbythecontents,thebookexaminesmainlytheeffectofthephysico-chemicalfactorsontheopticalandwavepropertiesofthinfilmswhichareofprimaryimportanceforpracticalapplication.Wehavealsopresentedseveralmethodsofexaminingthethinfilmsandtheoreticalconclusionsregardingthevariationoftherefractiveindicesandthelawsoflightpropagationinthefilm.Onlyinthefinalchapterwehaveexamined,asexamples,severaldevicesforelectro-opticallightmodulation.,deviationsandtransformationstothesecondharmonics.Inthisperiodcharacterizedbytheappearanceofalargenumberofpublicationsinmanyscientificjournalstheauthorssometimesomitinitialstudiesinwhichthefundamentalresultsfortheexaminedproblemwereobtained.Wehavethereforetriedtostresstheroleofinitialpublicationsinwhichthephenomenonunderexaminationisoftenstudiedinconsiderabledetail.Wehopethebookwillbeusefulforexpertsworkingintheareaofproducingandapplyingthinlightguidefilmsforlaserradiationcontrol.
Page357
ReferencesAbrahamsS.C.,HamiltonW.C.andSequeiraA.(1967),J.Phys.Chem.Solids,28,1963.
AbrahamsS.C.,ReddyJ.M.andBernsteinJ.L.(1966),J.Phys.Chem.Solids,27,977.
Abul-FadlA.andStefanakosE.K.(1977),J.CrystGrowth,39,341-344.
Abul-FadlA.,StefanakosE.K.andCollisW.J.(1981),J.Cryst.Growth,54,279-282.
AcousticCrystals,ed.byM.P.Shaskol'skaya(1982),Nauka,Moscow,632.
AdachiM.,HoriM.,ShiosakiT.andKawabataA.(1978),Jap.J.Appl.Phys.,17,2053.
AdachiM.,ShiosakiT.andKawabataA.(1977),Jap.J.Appl.Phys.,18,No.1,193.
AgostinelliJ.andBraunsteinG.H.(1993),Appl.Phys.Letters,63,123.
Al-ChalabiA.M.(1985),Appl.Phys.Letters,47,564.
AleksandrovL.N.andEntinI.A.(1971),Izv.VUZ,Fizika,No.9,34-39.
AleksandrovL.N.(1978),TransitionRegionsofEpitaxialSemiconductorFilms,Nauka,Novosibirsk,240.
AlfernessR.C.(1979),Appl.Phys.Lett.,35,748.
AlfernessR.C.(1980),ApplPhys.Lett.,36,513.
AlfernessR.C.(1982),IEEETrans.onMTTv.MTT-30,No.8,1121.
AlfernessR.C.andBuhlL.L.(1980),Opt.Lett.,5,473.
AlfernessR.C.andBuhlL.L.(1981),Appl.Phys.Lett.,38,655.
AlfernessR.C.andBuhlL.L.(1984),Opt.Lett.,10,140.
AlfernessR.C.andBuhlL.L.(1985),Appl.Phys.Lett.,471137.
AlfernessR.C.andSchmidtR.V.(1978),Appl.Phys.Lett.,33,161.
AlfernessR.C.,EconomouN.andBuhlL.L.(1980),Appl.Phys.Lett.,37,597.
AlfernessR.C.,EconomouN.andBuhlL.L.(1981),ApplPhys.Lett.,38,216.
AlfernessR.C.,SchmidtR.V.andTurnerE.H.(1979),Appl.Opt.,184012-16.
AlferovZh.(1976),VestnikANSSSR,7,28-40.
AndreevV.M.,DolginovL.M.andTretyakovD.N.(1975),LiquidPhaseEpitaxyinTechnologyofSemiconductorDevices,Sov.Radio,Moscow,328.
AntsyginV.D.(1987),Candidatedissertation,Novosibirsk,178.
AntsyginV.D.andKostsovE.G.(1986),Ferroelectric-typethin-filmradiationdetectors,PreprintNo.311,Novosibirsk,29.
AntsyginV.D.,KostsovE.G.andSokolovA.A.(1986),AvtometriyaNo.2,30-40.
ArmeniseM.N.,CanaliC.,DeSarioM.,CarneraA.,MazzoldiP.andCelottiG.(1983),J.Appl.Phys.,54,No.1,62.
ArmeniseM.N.,CanaliC.,DeSarioM.,CarneraA.,MazzoldiP.andCelottiG.(1983),J.Appl.Phys.,54,No.11,6223.
ArutyunyanV.M.,GambaryanK.M.andGevorkyanV.A.(1986),ZhETF,56,No.11,2145-2151.
ArvidssonG.andLaurellF.(1986),ThinSolidFilms,136,28-34.
AtuginV.V.andZakharyanT.I.,(1984),ZhETF,54,No.5,977-979.
AtuginV.V.,ZilingK.K.andShipilovaD.(1984),KvantovayaElektronika,11,No.5,934-938.
AuracherF.andKeilR.(1980),Appl.Phys.Lett.,36,626.
AvakyanM.S.,KurginyanR.G.,MadoyanR.S.andKhachaturyanO.A.(1986),ElektronnayaPromyshlennost',No.10,55-57.
AvakyanM.S.,MadoyanR.S.,KhachaturyanO.A.andShchekinYu.G.,(1986),ElektronnayaPromyshlennost',issue1(149)27-29.
BallmanA.A.andTienK.,PatentU.S.3.998.687.
BallmanA.A.,BrownH.,TienP.K.andMartinR.J.(1973),J.Cryst.Growth,20,251.
BallmanA.A.,BrownH.,TienP.K.andRiva-SanseverinoS.(1975),J.Cryst.Growth,29,184.
BallmanA.A.,BrownH.,TienP.K.andRiva-SanseverinoS.(1975),J.Cryst.Growth,29,289-295.
BallmanA.A.,BrownH.,TienP.K.andRiva-SanseverinoS.(1975),J.Cryst.Growth,30,37.
BallmanW.(1983),Crys.Res.Technol.,18,No.9,1147.
BarchukA.N.andIvashschenkoA.I.(1982),ZhEFT,52,No.9,1978-1982.
BarchukA.N.,IvashchenkoA.I.andKopanskayaF.Ya.(1979),ZhETF,49,No.3,643-647.
BarnoskiM.(1974),IntroductiontoIntegratedOptics,PlenumPress,
NewYork.
BarrosM.A.R.andWilsonM.G.F.(1972),Proc.Inst.Electr.Eng.,119,807.
BashkirovA.N.,ShandarovV.M.,ShandarovS.M.andShvartsmanT.I.(1985),Pis'mavZhETF,11,No.5,302-305.
Page358
BaudrantA.,VialH.andDavalJ.(1975),J.Cryst.Growth,10,No.12,1373-1378.
BaudrantA.,VialH.andDavalJ.(1978),J.Cryst.Growth,43,197-203.
BauerE.(1966),Single-CrystalFilms[Russiantranslation],MirPublishers,Moscow.
BauerE.(1969),in:TechniquesofMetalResearch,vol.2,ed.BunshakR.F.,Wiley-Interscience,NewYork.
BaumertJ.C.,WaltherC.,Buchman,KaufmannH.,MelchiorH.andGunter(1985),Appl.Lett.,46,1018.
BeckerR.A.(1983),Appl.Phys.Lett.,43,No.2,131-133.
BeckerR.A.andWilliamsonR.C.(1985),Appl.Phys.Lett.,47,1024.
BeckerR.A(1982),in:ElectromagneticFieldsandInteraction,Dover,NewYork,1982,75.
BerkowizJ.,ChupkaW.A.,BlueG.D.andMargaveJ.L.(1959),J.Phys.Chem.,63,644.
BergmanJ.G.,AshkinA.,BallmanA.A.,DziedzicJ.M.,LevinsteinH.J.andSmithR.S.(1968),Appl.Phys.Lett.,12,92-94.
BierleinJ.D.(1989),in:Proc.oftheInternationalMeetingonAdvancedMaterials(Pittsburgh)12,81.
BierleinJ.D.,FerrettiA.andRoelofsM.(1989),Proc.Soc.Photo-Opt.Instrum.Eng.,944,160.
BierleinJ.D.,FerrettiA.,BrixnerL.H.andHsuW.Y.(1987),Appl.Phys.Lett.,50,1216.
BierleinJ.D.andArweilerC.B.(1986),Appl.Phys.Lett.,49,917.
BierleinJ.D.andGierT.(1976),U.S.PatentNo.3.949.323.
BierleinJ.D.,LaubacherD.B.,BrownJ.B.andPoelC.J.(1990),Appl.Phys.Lett.,56,1725.
BierleinJ.D.andVanherzeeleH.(1989),J.Opt.Soc.Am.,B6,622.
BierleinJ.D.,VanherzeeleH.,andBallmanA.A.(1989)Appl.Phys.Lett.,54,783.
BiryulinYu.F.,VorobjevaV.V.andGolubevL.V.(1984)ZhETF54,issue1,1394-1399.
BocharovaN.G.(1986),Thestudyofphasenucleationonlithiumniobatecrystalsurface,Candidatedissertation,InstituteofCrystallography,Moscow.
BoikoT.M.,Gan'shinV.A.andKorkishkoYu.N.(1985),ZhETF,55,1441-1444.
BolkhovityanovYu.B.(1977),in:Semiconductingfilmsformicroelectronics,ed.AleksandrovL.A.,Nauka,Novosibirsk,170-197.
BolkhovityanovYu.B.andYudaevV.I.(1986),Initialstagesofnucleationunderhetero-LPEofA3B5compounds,IPF,Novosibirsk,114.
BolkhovityanovYu.B.andChikichevS.I.(1982),Resistanceofanequilibriummelt-crystalinterfacetohetero-LPEofA3B5compounds,IPFPreprint5-82,Novosibirsk.
BoltaksB.I.(1972),Diffusionandpointdefectsinsemiconductors,Nauka,Leningrad,384.
BorduiP.F.,JaccoJ.C.,LoiaconoG.M.,StolzenbergerR.A.andLollaJ.J.(1987),J.CrystGrowth,84,403.
BornM.andWolfE.(1970),PrinciplesofOptics,PergamonPress,
NewYork.
BortzM.L.andFejerM.M.(1992),Opt.Letters,17,704.
BoydG.D.(1972),IEEEJ.QuantumElectronics,QE-8,788.
BoydG.D.,MillerR.C.,NassauK.,BondW.L.andSavageA.(1964),Appl.Phys.Letters,5,234.
Bozhevol'nyS.I.,ZolotovE.M.andShcherbakovE.A.(1981),Pis'mavJETP,7,656-659.
BremerT.,HeilandW.,HellermannB.,Hertel,KratzigE.andKolleweD.(1988),FerroelectricsLett.,9,11.
BrownH.(1974),Appl.Phys.Letters,24,503.
BryskiewiczT.(1985),J.Appl.Phys.,57,No.8,Pr.1,2783-2787.
BryskiewiczT.,LagowskiJ.andGatosH.C.(1980),J.Appl.Phys.,51,No.2,988-996.
BulmerC.H.,SheemS.K.,MoellerR.andBurnsW.K.(1980),Appl.Phys.Lett.,37,351.
BurfootJ.C.andTaylorG.W.(1979),PolarDielectricsandTheirApplication,TheMacmillanPressLtd.
BuritskiiK.S.,DianovE.M.,GrjaznovYu.M.,DobryakovaN.G.,ChernykhV.A.andShcherbakovE.A.(1991),Sov.LightwaveCommun.,1,107.
BurnsW.KandWarnerJ.(1974),J.Opt.Soc.Am.,64,441.
BurnsW.K.andHockerG.B.(1977)Appl.Opt.16,2048.
BurnsW.K.,BulmerC.H.andWestE.J.(1978),Appl.Phys.Lett.,33,70.
BurnsW.K.,GiallorenziT.G.,MoellerR.P.andWestE.J.(1978),Appl.Phys.Lett.,33,944.
BuzhdanYa.M.,KuznetsovF.A.,BraslavskyB.I.andBelyaevaL.N.(1982),in:ElectricTransferanditsApplications,Nauka,Novosbirsk,80-88.
CanaliC.D.,DeBernardiC.andDeSarioM.(1986),J.LightwaveTechnol,LT-4,No.7,951-955.
Page359
CanaliC.,CameraA.,DellaMeaG.,MazzoldiP.,AlshukriS.M.,NuttA.C.G.andDeLaRueR.M.(1986),J.Appl.Phys.,59,2643.
CaoX.,SrivastavaR.,RamaswamyR.andNatourJ.(1991),IEEEPhotonTech.Letters,3,25.
CarslawH.S.andJaegerJ.C.(1971),ConductionofHeatinSolids,OxfordUniversityPress,75.
CarruthersJ.R.,PetersonG.E.,GrassoH.andBridenbaughM.(1971),J.Appl.Phys.,42,No.5,1846.
CarslawH.C.(1945),IntroductiontotheMathematicalTheoryoftheConductionofHeatinSolids,DoverPublications,NewYork.
ChandlerJ.,LamaF.L.,TownsendP.D.andZhangL.(1988),Appl.Phys.Letters,53,89.
ChandlerJ.,ZhangL.andTownsendP.D.(1989),Appl.Phys.Letters,55,1710.
ChanniD.G.(1971),Appl.Phys.Lett.,19,128-130.
ChenB.U.andPastorA.C.(1977),Appl.Phys.Lett.,30,No.11,570-572.
ChenF.S.(1970),ProcIEEE,58,1440.
ChenF.S.,MacchiaJ.T.andFrazerD.B.(1968),Appl.Phys.Lett.,13,223.
ChenY.X.,ChangW.S.,LauS.S.,WielunskiL.andHolmanR.L.(1982),Appl.Phys.Lett.,40,10.
ChengL.K.,BierleinJ.D.andBallmanA.A.(1991),J.Cryst.Growth,110,697.
ChengL.K.,BierleinJ.D.,ForisC.M.andBallmanA.A.(1991),J.
Cryst.Growth,112,309-315.
ChernovA.A.andTrusovL.I.(1969),Crystallography,14,No.2,218-226.
ChernovA.A.,GivargizovE.I.andBagdasarovKh.S.(1980),in:ModernCrystallography,Nauka,Moscow,v.3,408.
ChernykhV.A.andShcherbakovE.A.(1991),Sov.LightwaveCommun.,1,107.
ChiangK.S.(1985),J.LightwaveTechnol.,3,385.
ChopraK.L.(1969),ThinFilmPhenomena,McGraw-Hill,NewYork.
ChowK.,McKnightH.G.andRothrockL.R.(1974),Math.Res.Bull.,9,No.8,1067.
ChynowethA.G.(1956),Phys.Rev.,102,No.3,705-714.
ClarkD.F.,NuttA.C.G.,WongK.K.,LaybournJ.D.andDeLaRueR.M.(1983),J.Appl.Phys.,54,No.11,6218.
ConwellE.M.(1973),Appl.Phys.Lett.,23,328.
ConwellE.M.(1973),IEEEJ.QuantumElectr.,QE-9,867.
CrankJ.F.(1970),MathematicsofDiffusion,OxfordUniversityPress,Oxford,31.
CrossS.andSchmidtR.V.(1979),IEEEQuantumElectron.,QE-15,1415.
CurtiesB.J.andBrunnerH.R.(1975),Math.Res.Bull.,10,515.
D'AmicoA.,PetroccoG.,LucchesiniA.andGianniniF.(1984),Mater.Lett.,3,No.1-2,33-36.
D'yakovV.A.,ShumovD.,RashkovichL.N.andAleksandrovskyA.L.(1985),Izv.ANSSSR,Ser.Fiz.,49,No.12,2418-2420.
DanieleJ.J.(1975),Appl.Phys.Lett.,27,373-375.
DanieleJ.J.(1975),J.Electrochem.Soc.,124,1143-1144.
DaviesJ.E.,WhiteE.A.D.andWoodJ.D.C.(1974),J.CrystGrowth,27,227.
DeMatteiR.C.,HugginsR.A.andFeigelsonR.S.(1976),J.CrystGrowth,34,1-10.
DeMatteiR.C.andFeigelsonR.S.(1978),J.CrystGrowth,44,No.2,115-120.
DeGrootS.R.andMazur(1962),NonequilibriumThermodynamics,Amsterdam.
DeSarioM.,ArmeniseM.N.,CanaliC.,CarneraA.,MazzoldiP.andCelottiG.(1985),J.Appl.Phys.,57,No.5,1482.
DeMicheliM.,BotineauJ.,NeevenS.,SibillotP.,OstrowskyD.B.andPapuchonM.(1983),Opt.Lett.,8,114.
DeMicheilM.,BotineauJ.,SibillotP.,OstrowskyD.B.andPapuchonM.(1982),Opt.Commun.,42,110.
DeLaRueR.M.,LoniA.,LambertA.,DuffigJ.F.,Al-ShukriS.M.,KopylovYu.L.andWinfieldJ.M.(1987),in:Proc.4thEur.Conf.onIntergratedOptics,Glasgow.
DeminV.N.,BuzhdanYa.M.andKuznetsovF.A.(1978),ZhETF,48,1442-1445.
DeryuginL.N.,MarchukA.N.andSotinV.E.(1967),Izv.VUZ,Radioelektronika,10,No.2,134.
DhanasekaranR.andRamasamyP.(1986),ILNuovoCimento,7D,No.4,506-512.
DickB.,GierulskiA.,MarowskyG.andReiderG.A.(1985),Appl.Phys.Letters,38,107.
DickeR.H.andWittkeJ.P.(1960),IntroductiontoQuantumMechanics,Addison-Wesley,Reading,Mass.
DiDomenicoM.andWempleS.H.(1968),Appl.Phys.Letters,12,352.
DigonnetM.,FejerM.andByerR.(1985),Opt.Letters,10,235.
DistierG.I.(1975),in:ProblemsofModernCrystallography,Nauka,Moscow,197-207.
Page360
DolginovL.M.,EliseevG.andMilvidskyM.G.(1976),QuantumElectronics,3,No.7,1381-1393.
DorfmanV.F.(1974),Gas-PhaseMicrometallurgyofSemiconductors,Metallurgiya,Moscow,190.
DubrovskayaI.M.,LazarevM.V.,MadoyanR.S.,RyzhevninV.N.,KhachaturyanO.A.andShlykovV.V.(1988),Staticintegro-opticmodulator,Inform.Bull.(ArmenianResearchInstituteofScientificandTechnicalInformation),No.88-54,4.
DudnikE.,LevinzonD.I.,PetrikA.G.andSeminV.V.(1973),Izv.ANSSSR,Ser.Fiz.,37,No.11,2286-2287.
EgorovL.,ZatulovskyL.M.,ChaikinM.etal.(1971),Izv.ANSSSR,Ser.Fiz.,35,No.3,466-468.
EnganH.(1969),IEEETrans.ElectronDevices,ED-16,1064.
FayH.,AlfordW.J.andDessH.M.(1968),Appl.Phys.Lett.,12,No.3,89.
FeisstA.A.andRaüberA.(1983),J.Cryst.Growth,No.2,337-342.
FejerM.M.,DigonnetM.J.andByerR.L.(1986),Opt.Lett.,11,No.4,230-232.
FinakJ.,JerominekH.,OpilskiZ.andWotjalaK.(1982),Opt.Acta,12,No.1,11-17.
FinneR.M.andKleinD.L.(1967),J.Electrochem.Soc.,114,965.
FirtsakYu.Yu.LukshaO.V.andFennichA.(1984),in:GrowthofSemiconductorCrystalsandFilms,Part2,Nauka,Novosibirsk,69-84.
FluckD.,Gunter,IrmscherR.andBuchalCh.(1991),Appl.Phys.Letters,59,3213.
FlückigerU.andArendH.(1978),J.Cryst.Growth,43,406.
FosterN.F.(1969),J.Appl.Phys.,40,No.1,420.
FosterN.F.(1971),J.Vac.Sci.andTechnol.,8,No.1,251-255.
DeFourquetJ.L.,RenouM.F.,dePapeR.,TheveneauH.,ManP.P.,LucasO.andPannetierJ.(1983),SolidStateIonics,9/10,1011.
FujiwaraT.,CaoX.,SrivastavaR.andRamaswamyR.V.(1992),Appl.Phys.Letters,61,743.
FujiwaraT.,MoriH.andFujiiY.(1989),Ferroelectrics,95,133.
FujiwaraT.,SatoS.andMoriH.(1989),Appl.Phys.Lett.,54,975.
FujiwaraT.,SatoS.,MoriH.andFujiiY.(1988),J.LightwaveTechnol.,LT-6,909.
FujiwaraT.,TerashimaA.,MoriH.(1989),Appl.Phys.Letters,55,2718.
FukudaT.andHiranoH.(1975),Mat.Res.Bull.,10,801.
FukudaT.andHiranoH.(1976),Appl.Phys.Lett.,28,No.10,575-577.
FukudaT.andHiranoH.(1980),J.CrystGrowth,50,No.1,291-298.
FukumaM.andNodaJ.(1980),Appl.Opt.,19,591.
FukumaM.,NodaJ.andIwasakiH.(1978),J.ApplPhys.,49,3693.
FukunishiS.,UchidaN.,MiyazawaSh.andNodaJ.(1974),Appl.Phys.Lett.,24,424.
FushimiS.andSughK.(1974),JapanJ.Appl.Phys.,13,No.11,1895.
GabrielyahA.I.andKhachaturyanO.A.(1984),Izv.ArmenAkad.Nauk,Fizika,19,No.3,158-162.
GabrielyanA.I.,EritsyanG.G.andKhachaturyanO.A.(1990),Izv.Akad.NaukElektrokhimiya,26,No.3,345-348.
GabrielyanA.I.(1988),Cryst.Res.Technol.,23,No.5,621-627.
GabrielyanV.T.(1978),Investigationofgrowthconditionsandsomephysicalpropertiesofelectro-opticandacousticsinglecrystalsoflithiumniobate,lead,molybdateandleadgermanate.Candidatedissertation,Moscow.
GambaryanK.M.,GevorkyanV.A.andGolubevL.V.(1984),ZhETF,54,No.10,2011-2015.
Gan'shinV.A.,IvanovV.Sh.KorkishkoYu.N.andPetrovaV.Z.(1986),ZhETF,56,No.7,1354.
Gan'shinV.A.,KorkishkoYu.N.andPetrovaV.Z.(1985),ZhETF,55,No.11,2224-2227.
GaponovS.V.andSalashchenkoN.N.(1976),ElektronnayaPromyshlennost',issueI(49),11-20.
GarnL.E.andSharpE.J.(1982),J.Appl.Phys.,53,No.12,8974-8987.
GaryE.Betts.,WilliamsS.,andChangC.(1986),IEEEJ.Quant.Electron.,OF-22,No.7,1027-1038.
GearyJ.M.(1979),BellSyst.Tech.J.,58,No.2,467.
GevorkyanV.A.,GolubevL.V.,KaryaevV.N.,etal.(1979),ZhETF,49,No.10,2206-2210.
GevorkyanV.A.,GolubevL.V.,KhachaturyanA.E.andShmartsevYu.V.(1983),ZhETF,53,No.3,545-549.
GevorkyanV.A.,GolubevL.V.,PetrosyanS.G.,ShikA.Ya.andShmartsevYu.V.(1977),ZhETF,47,No.6,1306-1318.
GierT.E.(1980),U.S.PatentNo.4.231.838.
GlassA.M,KaminowI.P.,BallmanA.A.andOlsonD.H.(1980),Appl.Opt.,19,275.
Page361
GlassA.M.(1978),Opt.Eng.,17,470.
GlavasE.,ZhangL.,ChandlerP.J.andTownsendP.D.(1988),Instrum.Methods,B32,45.
GolubenkoG.A.,LyndinN.M.,SychugovV.A.andShipuloG.P.(1980),Kvant.Elektronika,7,No.3,577-582.
GolubevL.V.,KhachaturyanO.A.,ShikA.Ya.andShmartsevYu.V.(1974),Phys.Star.Sol.a,22,203-204.
GolubevL.V.,OychenkoV.M.andShmartsevYu.V.(1982),ZhETF,52,No.1,400-402.
GoncharenkoA.M.(1967),ZhETF,37,822.
GoncharenkoA.M.GusakN.A.andKarpenkoV.A.(1969),ZhETF,11,104.
GorskyF.K.(1969),in:TheMechanismandKineticsofCrystallization,NaukaiTekhnika,Minsk,328-332.
GorukW.S.,VellaJ.,NormandiR.andStegemanG.I.(1981),Appl.Opt.,20,4024.
GriffithsG.J.(1981),PhDThesis,Dept.ofElectricalEngineering,UniversityofQueensland,Australia.
HabaraK.(1987),ElectronLett.,23,614.
HammerJ.M.andPhillipsW.(1974),Appl.Phys.Letters,24,545.
HammerJ.M.,ChanningD.T.andDuffyM.T.(1973),Appl.Phys.Letters,23,176.
HauseH.A.(1984),WavesandFieldsinOptoelectronics,EnglewoodCliffs,NewYork.
HayataK.andKoshibaM.(1989),Electron.Letters,25,376.
HayataK.,SugawaraT.andKoshibaM.(1990),IEEEJ.QuantumElectron.,26,No.1,123-132.
HayataK.,YanagawaK.andKoshibaM.(1990),Appl.Phys.Letters,56,206.
HaycockW.andTownsendP.D.(1986),Appl.Phys.Letters,48,698.
HeismannF.andAlfernessR.C.(1988),IEEEJ.QuantumElectron.,QE-24,83.
HeismannF.,BuhlL.L.andAlfernessR.C.(1987),Electron.Letters,23,572.
HoffmannD.andLangmannU.(1981),in:ProceedingsoftheFirstEuropeanConferenceonIntegratedOptics(London),IEE.
HolmanR.L.(1978),Mat.Sci.Res.,11,343.
HolmanR.L.andGressmanJ.(1982),Opt.Eng.,21,No.6,1025-1032.
HolmanR.L.,GressmanJ.andRevelliJ.F.(1978),Appl.Phys.Letters,32,No.5,283.
HolmesR.J.,KimY.S.,BrandleC.D.andSmythD.M.(1983),Ferroelectrics,51,41.
HolzbergF.,ReismanA.,BerryM.andBerkenblitM.(1956),J.Amer.Chem.Soc.,78,No.8,1538.
HsuH.andMiltonA.F.(1976),Electron.Lett.,12,404.
HsuH.,MiltonA.F.andBurnsW.K.(1978),Appl.Phys.Lett.,33,611.
HsuW.Y.,BraunsteinG.,GopalanV.,WillandS.andGuptaM.S.(1992),Appl.Phys.Letters,61,3083.
HsuW.Y.,WillandC.S.,GopalanV.andGuptaM.(1992),Appl.Phys.
Letters,61,2263.
HugginsR.A.andElwellD.,(1977),J.Cryst.Growth,37,No.2,159-162.
HungL.S.,AgostinelliJ.A.,MirJ.M.andZhengL.R.(1993),Appl.Phys.Letters,62,3071.
HunspergerR.G.(1984),IntegratedOpticsTheoryandTechnology,SpringerVerlag,Berlin-Heidelberg-NewYork-Tokyo.
HurleD.l.,MullinI.B.andPikoE.R.(1964),Phil.Mag.,No.9,423.
IkonnikovaT.M.andIvlevaO.M.(1974),Izv.ANSSSR,Neorgan.Mater.,No.3,397-401.
IngleS.G.andMishraM.V.(1977),J.Appl.Phys.,10,149.
IntergratedOptics,ed.byT.Tamir(1975),SpringerVerlag,Berlin-Heidelberg-NewYork.
IoffeA.F.(1956),J.Techn.Phys.,26,478-482.
IrmscherR.,FluckD.,BuchalCh.,StritzkerB.andGunter(1991),Mater.Res.Soc.SymProc.,v.201,399.
IshidaM,MatsunamiH.andTanakaT.(1977),J.Appl.Phys.,48,No.3,951-953.
ltoH.,TakyuC.andInadaJ.(1991),Electron.Letters,27,1221.
ItoH.,UesugiN.andInabaH.(1974),Appl.Phys.Lett.,25,385.
IvlevaL.I.andKuz'minovYu.S.(1985),LPEmethodsforsinglecrystalfilmsofoxideferroelectricmaterials,PreprintNo.185,InstituteofGeneralPhysicsoftheUSSRAcad.ofSci.,Moscow,44.
IwasakiH.,YamadaT.,NiizekiN.andToyodaH.(1968),Rev.ECL,16,385.
lyerS.,StefanakosE.K.,Abul-FadlA.andCoilisW.J.(1984),J.
Cryst.Growth,67,337-342.
lyerS.,StefanakosE.K.,Abul-FadlA.andCoilisW.J.(1984),J.Cryst.Growth,70,No.1-2,162-168.
IzutsuM.,NukaiY.andSuetaT.(1982),Opt.Letters,7,136.
Page362
IzutsuM.,YamuneY.andSuetaT.(1977),IEEEJ.QuantumElectron.,QE-13,287.
JackelJ.L.(1980),Appl.Phys.Lett.,37,739.
JackelJ.L.(1982),J.Opt.Commum.,3,82.
JackelJ.L.andRiceC.E.(1981),Ferroelectrics,38,804.
JackelJ.L.andRiceC.E.(1982),Appl.Phys.Lett.,41,508.
JackelJ.L.andRiceC.E.(1984),SPIEGuidedWaveandOptoelectronicMaterials,460,43.
JackelJ.L.,OlsonD.H.andGlassA.M.(1981),J.Appl.Phys.,52,4855.
JackelJ.L.,RamaswamyL.andLymanS.(1981),Appl.Phys.Lett.,38,No.7,509-511.
JackelJ.L.,RiceC.E.andVeselkaJ.J.(1982),Appl.Phys.Lett.,41,No.7,607-608.
JackelJ.L.,RiceC.E.andVeselkaJ.J.(1983),Electron.Lett.,19,No.10,387.
JackelJ.L.(1985),Electron.Letters,21,509.
JarmanR.H.andGrubbS.G.(1988),Proc.SPIESoc.Photo-Opt.Instr.Eng.968,108.
JarzebskiZ.M.(1974),Mat.Res.Bull.,9,No.3,233.
JastrzebskiL.,GatosH.C.andWittA.F.(1976),J.Electrochem.Soc.,123,1121-1122.
JastrzebskiL.,ImamuraYandGatosH.G.(1978),J.Electrochem.Soc.,No.7,1140-1146.
JastrzebskiL.,LagowskiJ.,GatosH.G.andWittA.F.(1978),J.Appl.Phys.,49,No.12,5909-5919.
JetschkeS.andHehlK.(1985),Phys.Stat.Sol.a,88,No.1,193.
JohnsonM.(1979),Appl.Opt.,18,1288.
JoshiS.G.andWhiteR.M.(1969),J.AccousticSoc.,4617.
KaminovI.P.(1965),Appl.Phys.Lett.,7,123;(1966)Appl.Phys.Lett.,8,54.
KaminowI.P.andCarruthersJ.R.(1973),Appl.Phys.Lett.,22,No.7,326.
KaminowI.P.andStulzL.W.(1978),Appl.Phys.Lett.,33,62.
KaminowI.P.andTurnerE.H.(1966),Proc.IEEE,54,1374.
KaminowI.P.,MammelW.L.andWeberH.(1974),Appl.Opt.,13,396.
KaminowI.P.,StulzL.W.andTurnerE.H.(1975),Appl.Phys.Lett.,27,555.
KaminowI.P.,RamaswamyV.,SchmidtR.V.andTurnerE.M.(1974),Appl.Phys.Lett.,24,No.12,622
KapronF.,BorrelliN.F.andKeckD.B.(1972),IEEEJ.QuantumElectron.,QE-8,222.
KarpovE.Yu,MilvidskyM.G.,NikishinS.A.andPortnoyL.(1986),ZhTF,56,No.2,533-360.
KazanskyP.G.(1985),Photo-inducedradiationpolarizationconversioninintegrated-opticelementsonthebasisoflithiumniobate.Thesis,InstituteofGeneralPhysicsoftheUSSRAcademyofScience,Moscow.
KenanR.,VeberC.M.andWoodV.E.(1974),Appl.Phys.Lett.,24,
428.
KeysR.W.,LoniA.,DeLaRueM.,IronsideC.N.,MarshJ.H.,LaurelF.,BrownJ.B.,BierleinJ.D.(1992),Appl.Phys.Letters,60,1064.
KhachaturyanO.A,PetrosyanS.G.andKhachaturyanS.G.(1977),Uch.Zap.Erevan.Univ.No.2,(135)54-59.
KhachaturyanO.A.(1974),Growthofsemiconductingfilmsusingelectro-LPE,Candidatedissertation,154.
KhachaturyanO.A.(1988),in:GrowthofSemiconductorCrystalsandFilms,Nauka,Novosibirsk.
KhachaturyanO.A.andMadoyanR.S.(1978),ElektronnayaTeknika,Ser.6,issue4,41-42.
KhachaturyanO.A.andMadoyanR.S.(1980),VlInternationalConferenceonCrystalGrowth,vol.3,Moscow,332.
KhachaturyanO.A.andMadoyanR.S.(1984),Cryst.Res.Technol.,19,No.4,461-466.
KhachaturyanO.A.,MadoyanR.S.andAvakyanM.S.(1984),EpitaxialFilmsofLithiumNiobate,ArmNIINTI,Erevan,60.
KhachaturyanO.A.,AvakyanM.S.andArakelyanV.B.(1987),InfluenceofDirectElectricCurrentuponLPE,ArmNIINTI,Erevan60.
KhachaturyanO.A.,GabrielyanA.I.andKolesnikS.(1988),ZhETF,30,No.3,888-890.
KhachaturyanO.A.,MadoyanR.S.,AvakyanM.S.andShchekinYu.S.(1984),CapilaryLiquid-phaseEpitaxyofFerroelectrics,ArmNIINTI,Erevan,48.
KittelC.(1956),IntroductiontoSolidStatePhysics,WileyInc.,NewYork.
KogelnikH.(1969),Bull.Syst.Tech.J.,48,2909.
KogelnikH.(1974),TheoryofDielectricWaveguidesinIntegratedOptics,ed.T.Tamir,TopicsAppl.Phys.7,SpringerVerlag,Berlin-Heidelberg-NewYork.
KogelnikH.andRamaswamyV.(1974),Appl.Opt.,13,1857.
KogelnikH.andSchmidtR.V.(1976),IEEEQuantumElectron.,QE-12,396-401.
KolobovH.A.andSamokhvalovM.M.(1975),DiffusionandOxidationofSemiconductors,
Page363
Metallurgiya,Moscow,456.
KolosovskyE.A.,PetrovD.V.andTsarevA.V.(1981),Quant.Electr.,8,No.12,2557-2568.
KondoS.,MiyazawaS.,FushimiS.andSugiiK.(1975),Appl.Phys.Lett.,26,No.9,489-491.
KondoS.,SugiiS.,MiyazawaS.andUeharaS.(1979),J.Cryst.Growth,46,No.3,314-322.
KopylovYu.L.,KrachenkoV.B.,MirgorodskayaE.N.andBobylevA.V.(1983),Pis'maZhTF,9,No.10,601-604.
KorobovO.E.,MaslovV.N.andNechaevV.V.(1977),in:CrystalGrowth,12,ErevanStateUniversity,Erevan,332-337.
KosminaM.B.,VoronovA.andTkachenkoV.F.(1983),ReportsofVIIAll-UnionConference,partI,Donetsk,41.
KovacsL.,SzalayV.andCapellettiR.(1984),SolidStateCommun.,52,1029.
KrylovA.S.andIvanovG.A.(1980),Izv.Akad.Nauk.SSSR,FizikaMetalloviMetallovedenie,49,No.2,425-427.
KuhnL.,DakssM.L.,HeidrichF.andScottV.A.(1970),Appl.Phys.Lett.,17,265.
Kuz'minovYu.S.(1987),Electro-OpticandNonlinearOpticCrystalsofLithiumNiobate,Nauka,Moscow.
Kuz'minovYu.S.(1975)LithiumNiobateandTantalate.MaterialsforNonlinearOptics,Nauka,Moscow.
Kuz'minovYu.S.,LyndinN.M.,ProkhorovA.M.,Spikhal'skyA.A.,SychugovV.A.andShipuloP.G.(1975),KvantovayaElektronika,2,No.10,2309-2399.
KuznetsovF.A.,DeminV.N.andBuzhdanYa.M.(1983),in:MaterialsforElectronTechnology,partI,Novosibirsk,45-62.
LapitskyA.V.(1952),ZhurnalObshcheiKhimii,22,36.
LaubacherD.B.,GuerraV.L.,ChouinardM.,LiouJ.Y.andWyatN.(1988),Proc.Soc.Photo-Opt.InstrumEng.,993,80.
LaurellF.,RoelofsM.G.andHsiungH.(1992),Appl.Phys.Letters,60,301.
LazarevM.V.(1986qAcousto-andElectro-OpticLightControlinDielectricWaveguides,Candidatedissertation.
LeeW.E.,SanderN.A.andHeuerA.H.(1986),J.Appl.Phys.,59,2629.
LemonsR.A.,GearyJ.M.,ColdenL.A.andMattesH.G.(1978),Appl.Phys.Lett.,33,No.5,373.
LeonbergerF.J.(1980),Opt.Lett.,5,312.
LeonbergerF.J.(1983),Ferroelectrics,50,161-164.
LernerP.,LegrasC.andDumasJ.(1968),J.Cryst.Growth,No.3/4,231.
LevanyukA.andOsipovV.V.(1975),Izv.Akad.NaukSSSR,Ser.Fiz.39No.4,686-689.
LevinzonD.I.(1969),in:SiliconandGermanium,issue1,Metallurgiya,Moscow,105-110.
LiM.J.,deMicheliM.P.,OstrowskyD.B.,LallirE.,BreteauJ.M.,PapuchonM.andPocholleJ.P.(1988),Electron.Lett.,24,No.15,914.
LichtensteigerM.,WittA.F.andGatosH.G.(1971),J.Electrochem.Soc.,118,No.6,1013-1015.
LidlardA.(1957),IonicConductivity,SpringerVerlag,Berlin.
LimE.J.,FejerM.M.andByerR.L.(1989),Electron.Lett.,25,174.
LimE.J.,FejerM.M.,ByerR.L.andKozlovskyW.J.(1989),Electron.Lett.,25,731.
LinesM.E.andGlassA.M.(1977),PrinciplesandApplicationofFerroelectricsandRelatedMaterials,ClarendonPress,Oxford.
LitvinA.A.andMaronchukI.E.(1977),Kristallografiya,22,425-428.
LiuY.S.,DontzD.andBeltR.(1984),Opt.Letters,9,76.
LiuY.S.,XuB.,HanJ.,LiuX.andJiangM.(1986),ChinesePhys.Letters,13,502.
LoniA.,DeLaRueR.M.andWinfeldJ.M.(1987),J.Appl.Phys.,61,No.1,64.
LoniA.,DeLaRueR.M.,ZavadaJ.M.,WilsonR.G.andNovakS.W.(1991),Electron.Letters,17,1245.
LoniA.,HayG.,DeLaRueR.M.andWinfeldJ.M.(1989),J.LightwaveTechnology,7,No.6,91.
LoniA.,KeysR.W.andDeLaRueR.M.(1990),J.Appl.Phys.,67,3964.
LotschH.K.(1968),J.Opt.Soc.Am.,58,551.
LozovskyV.N.(1972),ZoneMeltingwithaTemperatureGradient,Metallurgiya,Moscow.
LuffB.J.TownsendD.(1991),Electron.Letters,26,188.
LukshaO.V.,FirtsakYu.Yu.andDovgosheyN.I.(1982),Izv.Akad.NaukSSSR,Neorgan.Mater.,18,No.2,231-234.
LundbergM.(1971),ActaChem.Scand.,25,No.9,3337.
Page364
LyutovichA.S.,KharchenkoV.V.andAbdurakhmanovB.M.(1971),in:TheMechanismandKineticsofCrystallization,NaukaiTekhnika,Minsk,131.
MadoyanR.S.(1984),LPEofLithiumNiobate,Candidatedissertation,IFIAkad.Nauk.Arm.SSR,Ashtarak.
MadoyanR.S.andKhachaturyanO.A.(1985),EpitaxialSingleCrystalFilmsofLithiumNiobate-TantalateSolidSolutions,ArmNIINTI,Erevan.
MadoyanR.S.,GabrielyanA.I.andKhachaturyanO.A.(1983),in:Abstr.VIIIntern.Conf.onCrystalGrowth,Stuttgart,488.
MadoyanR.S.,SarkisyanG.N.andKhachaturyanO.A.(1985),Cryst.Res.andTechnol.,20,No.8,1031-1040.
MadoyanR.S.,SarkisyanG.N.andKhachaturyanO.A.(1982),UchenyeZapiskiEGU,ErevanStateUniversity,Erevan,No.2,68-73.
MadoyanR.S.,SarkisyanG.N.,PetrosyanYu.G.andKhachaturyanO.A.(1979),Izv.Akad.NaukSSSRZh.Neorgan.Khimii,24,No.2,3088-3091.
MagnussenR.andGaylordT.(1974),Appl.Opt.,13,1545-1548.
MakioS.,NitandaF.,ItoK.andSatoM.(1992),Appl.Phys.Letters,61,3077.
MalininA.Yu.andNevskiO.V.(1978),Cryst.Res.andTechnol.,13,No.8,921-927.
MarcatiliE.A.J.(1969),Bell.Syst.Tech.J.,48,2071.
MarcuseD.(1973),IEEEJ.QuantumElectron.,QE-9,1000.
MarcuseD.(1974),TheoryofDielectricOpticalWaveguides,AcademicPress,NewYork.
MarcuseD.(1975),IEEEJ.QuantumElectron.,QE-11,759.
MarcuseD.(1982),IEEEJ.QuantumElectron.,QE-18,No.3,393-398.
MarcuseD.(1969),Bell.Syst.Tech.J.,48,3187;48,3233;(1970),49,273.
MargolinA.M.,ZakharchenkoI.N.,EremkinV.V.etal.(1983),Izv.VUZ,Fizika,25,No.6,102-103.
MaslovV.N.(1977),GrowthofProfileSemiconductorSingleCrystals,Metallurgiya,Moscow.
MaterialsforOptoelectronics(1976),TranslationfromtheEnglish,ed.E.I.GivargisovandS.N.Gorin,MirPublishers,Moscow.
McClureD.S.(1959),SolidStatePhys.,9,399.
MeekR.,TownsendD.andHollandL.(1986),ThinSolidFilms,141,No.2,251-259.
MegawH.D.(1954),ActaCryst.,7,187.
MegawH.D.(1973),CrystalStructures:AWorkingApproach,Saunders,Philadelphia.
MidwinterG.E.(1968),J.Appl.Phys.,39,3033.
MikamiO.,NodaJ.andFukumaM.(1978),TransIECEJn.,E-61,144.
MilvidskyM.G.(1986),SemiconductorMaterialsinModernElectronics,Nauka,Moscow.
MilvidskyM.G.,NikishinS.A.andSeysyanR.P.(1982),Kristallografiya,27,No.4,742-750.
MilvidskyM.G.,OrlovV.andTsepilevichV.G.(1980),Izv.Akad.NaukSSSR,Neorgan.Mater.,16,1159-1163.
MinakataM.,KumagiK.andKawakamiS.(1986),Appl.Phys.Lett.,49,992.
MinakataM.,SaitoS.,ShibataM.andMiyazawaS.(1978),J.Appl.Phys.,49,4677.
MinakataM.,UeharaS.,KubotaK.andSaitoS.(1978),Rev.Electr.Commun.Lab.,26,1139.
MiyasawaS.,FushimiS.andKondoS.(1975),Appl.Phys.Lett.,26,8.
MiyazawaS.(1973),Appl.Phys.Lett.,23,No.4,198-200.
MiyazawaS.(1979),J.Appl.Phys.,50,4599.
MiyazawaS.(1980),J.Inst.ElectronandCommun.Eng.ofJapan,63,No.4,354-360.
MiyazawaS.andIwasakiH.(1971),J.Cryst.Growth,10,276.
MiyazawaS.,CuglielmiR.andCarencoA.(1977),Appl.Phys.Lett.,31,742.
MizuuchiK.andYamamotoK.(1992),Appl.Phys.Lett.,60,1283.
MizuuchiK.,YamamotoK.andTaniuchiT.(1991),Appl.Phys.Lett.,58,2732.
MoonR.T.(1974),J.Cryst.Growth,27,No.1,62-68.
MorrisA.,FerrettiA.,BierleinJ.D.andLoicanoG.M.(1991),J.Cryst.Growth,109,367.
MukhortovV.M.,TolstousovS.V.andBiryukovS.V.(1981),ZhETF,51,No.7,1524-1529.
MustelE.andParyginV.N.(1970),MethodsofLightModulationandScanning,Nauka,Moscow.
NaitohH.,NunoshitaM.andNakayamaT.(1977),Appl.Opt.,16,2546.
NakayamaT.(1979),JapanJ.ofAppl.Phys.,18,No.5,897-902.
NakajimaK.,YamazaskiS.andUmebuI.(1984),JapanJ.ofAppl.Phys.,23,No.1,126-128.
NashF.R.,BoydGD.,SargentM.andBridenbaughP.M.(1970),J.Appl.Phys.,41,2564.
NassauK.andLinesM.E.(1970),J.Appl.Phys.,41,No.2,533.
NelsonD.F.andMcKennaJ.(1967),J.Appl.Phys.,38,4057.
Page365
NelsonH.(1963),RCARev.,24,No.4,603.
NeurgaonkarR.R.andBelykhL.(1960),RussJ.Phys.Chem.,34,399.
NeurgaonkarR.R.andStaplesE.J.(1981),J.Cryst.Growth,54,572.
NeurgaonkarR.R.,KalisherM.N.,StaplesE.J.andLimT.S.(1979),Appl.Phys.Lett.,35,No.8,606.
NeurgaonkarR.R.(1980),AnnualTechnicalReport,ContractNo.F49620-77-C-0081July(1980).
NeurgaonkarR.R.,LimT.C.andStaplesE.J.(1978),Mater.Res.Bull.,13,635.
NeurgaonkarR.R.,LimT.C.,StaplesE.J.andCrossL.S.(1980),Ferroelectrics,27-28,63.
NeurgaonkarR.R.,OliverJ.R.andWuE.T.(1987),J.Cryst.Growth,84,407.
NeyerA.andSohlerW.(1979),Appl.Phys.Lett.,35,256.
NeyerA.(1984),IEEEJ.Quant.Electron.,QE-20,No.9,999-1002.
NikishinS.A.(1983),ZhETF,53,No.3,538-543.
NikishinS.A.(1984),ZhETF,54,No.5,938-942.
NikishinS.A.(1984),ZhETF,54,No.6,1128-1132.
NinomukaK.,IshikaniA.,MatsubaraJ.andHayashiI.(1978),J.CrystalGrowth,45,No.2,355-360.
NishiharaH.,HarunaM.T.andSuharaT.(1989),OpticalIntegratedCircuits,McGraw-Hill,NewYork,136.
NodaJ.,FukumaM.andItoY.(1980),J.Appl.Phys.,51,No.3,1379-
1384.
NodaJ.,MikamiO.,MinakataM.andFukumaM.(1978),Appl.Opt.,17,2092
NodaJ.,SakuT.andUchidaN.(1974),Appl.Phys.Lett.,25,No.5,308.
NodaJ.,UchidaN.,andSakuT.(1974),Appl.Phys.Lett.,25,13.
NodaJ.,UchidaN.,SaitoS.,SakuT.andMinakataM.(1975),Appl.Phys.Lett.,27,19.
NovakS.W.,MatthewsP.,YoungW.andWilsonR.G.(1992),ProceedingsofSIMS,VIIInternationalConferenceonSIMS,England,1992.
NuttA.C.G.,GopalanV.andGuptaM.(1992),Appl.Phys.Lett.,60,2828.
NyeJ.F.(1964),PhysicalPropertiesofCrystals,ClarendonPress,Oxford.
O'BrienR.J.,RosascoG.J.andWeberA.(1970),J.Opt.Soc.Am.,60,716.
OhmachiY.andNodaJ.(1975),Appl.Phys.Lett.,24,544.
OhnishiN.andlizukaT.(1975),Appl.Phys.,46,1063.
OkuyamaM.(1981),Ferroelectrics,33,235-241.
OkuyamaM.andHamakawaY.(1986),Avtometriya,No.2,17-29.
OstrowskyD.V.andVannesteC.(1978),ThinFilmsAdv.Res.Devel.,NewYork,10,248.
PalienkoA.N.,SechenovD.A.andChristyakovYu.D.(1971),Izv.ANSSSR,Neorgan.Mater.,7,No.7,1253-1254.
PanishM.B.andSumskiS.A.(1971),J.Cryst.Growth,11,No.1,
101-103.
PapuchonM.andCombemaleY.(1975),Appl.Phys.Lett.,27,289.
PapuchonM.,RoyA.andOstrowskyD.B.(1977),Appl.PhysLett.,31,266-267.
PastukhovE.A.,MusikhinV.N.andVatolinN.P.(1984)ElectricPropertiesofNonstoichiometricOxideMelts,Nauch.TsentrAkad.Nau,Sverdlovsk.
PearsallT.,ChiangS.andSchmidtR.W.(1976)J.Appl.Phys.,47,4794.
PearsallT.,ChiangS..andSchmidtR.W.(1976),TopicalMeetingonIntegr.Optics,TechDigestTuC2-1,SaltLakeCity,Utah.
PetersonG.E.andCarnevaleA.(1972),J.Chem.Phys.,56,4848.
PetersonG.E.,BridenbaughM.andGreenP.(1967),J.Chem.Phys.,46,4009.
PetersonG.E.,CarruthersJ.R.andCarnevaleA.(1970),J.Chem.Phys.,56,2436.
PetersonG.E.,GlassA.M.andNegranT.J.(1970),Appl.Phys.Lett.,19,130.
PetrossoG.(1983),VuotoSciezaeTechnologia,B4,99-101.
PetrosyanS.G.,ShikA.Ya.andShmartsevYu.V.(1974),Fiz.TverdogoTela,16,No.2,392-397.
PeuzinJ.C.andMiyazawaS.(1986),Appl.Phys.Lett.,48,1104.
PfannW.G.(1966),ZoneMelting,NewYork.
PfannW.G.,BensonK.E.andWernickJ.H.(1957),Electronics,No.2,597.
PhillipsW.,AmodeiJ.J.andStaeblerD.L.(1972),RCARev.,33,94.
Photonics(1975),ed.M.BalkanskiandLallemand,Gauthier-Villars,Paris.
PoelC.J.,BierleinJ.D.,BrownJ.B.andColahS.(1990),Appl.Phys.Lett.,57,2074.
PostnikovV.S,levlevV.M.,ZolotyukhinI.V.andRodinG.S.(1973),Izv.ANSSSR,Neorg.Mater.,9,No.8,1455.
Page366
ProkhorovA.M.andKuz'minovYu.S.(1990)FerroelectricCrystalsforLaserRadiationControl,AdamHilger,Bristol-NewYork.
ProkhorovA.M.andKuz'minovYu.S.(1990),PhysicsandChemistryofCrystallineLithiumNiobate,AdamHilger,Bristol-NewYork.
PunE.Y.B.,WongK.K.,AndonovieI.,LaybornP.J.R.andDeLaRueR.M.(1982),Electron.Lett.,18,740.
PunE.Y.,LollK.K.,ZhaoS.A.andChungP.S.(1991),Appl.Phys.Letters,59,662.
RamaswamyV.(1974),Bell.Syst.Tech.J.,53,697.
RamaswamyV.andStandleyR.D.(1975),Appl.Phys.Lett.,26,10.
(a)RamaswamyV.,KaminovI.P.,KaiserP.andFrenchW.G.(1978),Appl.Phys.Lett.,33,814.
(b)RamaswamyV.,StandleyR.D.,SzeD.andLawleyK.L.(1978),BellSyst.Tech.J.,57,635.
RamerO.G.(1982),IEEEJ.QuantumElectron.,QE-18386.
RanganathT.andWangS.(1977),Appl.Phys.Lett.,30,376.
RaschA.,RottschalkM.andKartheW.(1985),J.Opt.Commun.,6,No.1,14-117.
RäuberA.(1976),Mat.Res.Bull.,No.5,497-502.
RäuberA.(1978),ChemistryandPhysicsofLithiumNiobate:CurrentTopicsinMaterialScience,1,North-Holland,Amsterdam,481-601.
RedfieldD.andBurkeW.(1974),J.Appl.Phys.,45,4566.
RegenerR.,SohlerW.andSucheH.(1981),in:FirstEur.Conf.onIntegr.Opt.,lEE,Conf.publ.201,London.
ReiberL.,RoyA.M.,SejourueB.andWernerM.(1975),Appl.Phys.Lett.,27,289-291.
ReismanA.andHoltzbergF.(1955),J.Amer.Chem.Soc.,77,2117.
ReismanA.andHoltzbergF.(1958),J.Amer.Chem.Soc.,80,35.
ReismanA.andHoltzbergF.(1965),J.Amer.Chem.Soc.,80,6503.
ReismanA.andMineoJ.(1962),J.Phys.Chem.,66,1184.
RekasM.andWierzbickaM.(1983),PolonaisedesSciences,29,No.9-10,431-436.
RiceC.E.(1986),SolidStateChem.,64,188.
RiceC.E.andJackelJ.L.(1982),SolidStateChem.,41,No.3,308-314.
RiceC.E.andJackelJ.L.(1984),MatRes.Bull.,19,591.
RiskW.(1991),Appl.Phys.Lett.,58,19.
RottmanF.andVogesE.(1987),Electron.Lett.,23,1007.
RubininaN.N.(1976),StudyoftheMechanismsofIronInsertionintoFerroelectricCrystalsofLithiumMetaniobate,Candidatedissertation,Moscow.
SafarovV.I.andKhachaturyanO.A.(1976),Fiz.Tverd.Tela,18,No.9,1790-1791.
SamoylovichA.G.andKorenblitL.L.(1953),Usp.Fiz.Nauk,19,No.2,244-271.
SanfordN.A.andRobinsonW.C.(1989),J.Appl.Phys.,65,1429.
SanfordN.A.andConnorsJ.M.(1989),J.Appl.Phys.,65,1429.
SaridD.,CressmanP.J.andHolmanR.L.(1978),Appl.Phys.Lett.,31,514.
SashitalS.R.,KrishnakumarS.andEsenerS.(1993),Appl.Phys.Letters,62,2917-20.
SavageR.(1966),J.Appl.Phys.,37,3071.
SchahM.L.(1975),Appl.Phys.Lett.,26,652.
SchittH.,KortheinR.andKleinG.(1984),Ferroelectrics,56,No.1,1145-1148.
SchmidtR.V.andKaminovI.P.(1974),Appl.Phys.Lett.,25,No.8,458.
SchmidtR.V.andKogelnikH.(1976),Appl.Phys.Lett.,28,503-305.
SchmidtR.V.,CrossP.S.andGlassA.M.(1980),J.Appl.Phys.,51,90-93.
SchwarzK.K.(1986),PhysicsofOpticalRecordinginDielectricsandSemiconductors,Zinaite,Riga,62-63.
SchwynS.,LehmannH.W.(1992),J.Appl.Phys.,72,1154.
ScottB.A.andBurnsG.(1972),J.Amer.Ceram.Soc.,55,No.5,225-229.
SearleT.M.andGlassA.M.(1968),J.Phys.Chem.Solids,29,648.
ShapiroZ.N.,FedulovS.A.,VenevtsevYu.N.andRigerman(1965),Izv.ANSSSR,ser.Fizika,39,No.6,1047-1050.
ShashkinV.V.(1983),Fiz.Tverd.Tela,25,No.12,3719-3721.
SheemS.K.(1978),Appl.Opt.,17,3679-3678.
SheemS.K.andGiallorenziT.G.(1978),Opt.Lett.,3,73.
SheemS.K.,BurnsW.K.andMiltonA.F.(1978),Opt.Lett.,3,76.
SheftalN.N.(1983),in:MaterialsforElectronicEngineering,partI,Nauka,Novosibirsk,83-103.
ShewmonG.(1963),DiffusioninSolids,McGraw-Hill,NewYork.
Page367
ShimaokaG.(1985),Appl.SurfaceSci.,22,No.2.
ShimuraF.(1977),J.Cryst.Growth,42,579-582.
ShinozakiK.,FukunagaT.,WatanabeK.andKamijohT.(1991),Appl.Phys.Lett.,59,510.
ShiosakiT.,AdachiM.andKawabataA.(1982),ThinSolidFilms,96,129-140.
ShubnikovA.V.(1956),CrystalsinScienceandEngineering,Izdatel'stvoAkad.NaukSSSR,Moscow.
ShumovD.(1986),InvestigationofTransportProcessesingrowingLithiumNiobateCrystalsfromtheMelt,Candidatedissertation,MoscowStateUniversity,Moscow.
SinghR.,WittA.F.andGatosH.C.(1968),J.ElectrochemSoc.,No.1,112-113.
SirotaN.N.(1971),in:CrystallizationandPhaseTranformations,NaukaiTekhnika,Minsk,333-351.
SmithgallD.H.,DablyF.W.andRunkR.B.(1977),IEEEJ.QuantumElectron.,QE-9,1023.
SmolenskyG.A.(ed)(1985),PhysicsofFerroelectricPhenomena,Nauka,Leningrad.
SmolenskyG.A.,BokovV.A.,IsupovV.A.,KraynikN.N.,PasynkovR.E.andShurM.S.(1971),FerroelectricsandAntiferroelectrics,Nauka,Leningrad.
SochilinaI.N.andKhachaturyanO.A.(1975),FTP,9,No.2,367-368.
Spikhal'skyA.A.(1984),Quant.Electron.,11,No.9,1812-1823.
StaeblerD.L.andPhillipsW.(1974),Appl.Opt.,13,788.
StegemanG.I.andStolenR.H.(1989),J.OptSoc.Am.,136,652.
StepanovA.V.(1963),ProspectsofMetalWorking,Lenizdat,Leningrad
StoneJ.andStulzL.W.(1987),Electron.Lett.,23,787.
StrohkendlF.,BuchalCh.,FluckD.,GunterPandIrmscherR.(1991),Appl.Phys.Lett.,59,3354-7.
StrohkendlF.,GunterP.,BuchalCh.andIrmscherR.(1991),J.Appl.Phys.,69,84.
SucheH.,HampelB.,SeibertH.andSohlerW.(1985),Proc.SPIE,578,156-161.
SuchoskiG.,FindaklyK.andLeonbergerF.J.(1988),Opt.Lett.,13,1050.
SugiiK.,FukumaM.andIwasakiH.(1978),J.Mater.Sci.,13,523-533.
SugiiK.,FukumaM.andIwasakiH.(1980),J.Mater.Sci.,19,No.21,1997-2001.
SuharaT.,TazakiH.andNishiharaH.(1989),Electron.Lett.,25,1326.
SvaasandL.O.,EriksrudM.,NakkenG.andGrandeA.(1974),J.Cryst.Growth,22,No.3,230-232.
SwartzJ.C.,SurekT.andChabmersC.(1975),J.Electron.Mater.,4,255.
SychevV.V.(1970),ComplicatedThermodynamicSystems,Energiya,Moscow.
TakadaS.,OhnishiM.,HayakawaH.andMikoshibaN.(1974),Appl.Phys.Lett.,24,No.10,490-492.
TakeiW.I.,FarmigoniN.P.andFrancombeN.M.(1969),Appl.Phys.Lett.,15,No.8,256-258.
TamadaH.,YamadaA.andSaitohM.(1991),J.Appl.Phys.,70,2536.
TamirT.(1979),IntegralOptics,2ndTopics,Appl.Phys.7,Springr-Verlag,Berlin-Heidelberg-NewYork.
TangonanG.L.,BarnoskiM.K.,LotspeichJ.F.andLeeA.(1977),Appl.Phys.Lett.,30,238.
TangonanG.L.,PersechiniD.L.,LotspeichJ.F.andBarnoskiM.K.(1978),Appl.Opt.,17,3259-3263.
TaniuchiT.andYamamotoK.(1987),ConferenceonLasersandElectro-Optics,Apr26-May1,Baltimore,Maryland.
TaylorH.F.andYarivA.(1974),Proc.IEEE,62,1044.
TaylorH.F.,MartinW.E.,HallD.B.andSmileyV.J.(1972),Appl.Phys.Lett.,21,95.
ThaniyavarnsS.,FindaklyT.,BooherD.andMoenJ.(1985),Appl.Phys.Lett.,46,933.
ThinFilmsInterdiffusionandReaction(1978),ed.J.M.Poate,K.N.TuandJ.W.Mayer,J.WileyandSons,NewYork.
ThonyS.S.,LehmannH.W.andGünterP.(1992),Appl.Phys.Lett.,61,373-376.
TienP.K.(1971),Appl.Opt.,10,No.11,2395-2415.
TienP.K.andUlrichR.(1970),J.OptSoc.Am.,60,1325.
TienP.K.,GordonJ.P.andWhinneryJ.R.(1965),ProcIEEE,53,129.
TienP.K.,MartinR.J.andSmolenskyG.(1972),Appl.Opt.,11,637.
TienP.K.,MartinR.J.,BanksS.L.,WempleS.H.andVarnerinL.J.
(1972),Appl.Phys.Lett.,21,207.
TienP.K.,Riva-SanseverinoS.andBallmanA.A.(1974),Appl.Phys.Lett.,25,563.
TienP.K.,Riva-SanseverinoS.,MartinR.I.,BallmanA.A.andBrownH.(1974),Appl.Phys.Lett.,24,503.
Page368
TienP.K.,UlrichR.andMartinR.J.(1969),Appl.Phys.Lett.,14,291.
TienP.K.,UlrichR.andMartinR.J.(1970),Appl.Phys.Lett.,17,447.
TillerW.A.(1963),J.Appl.Phys.,34,No.9,2757-2763.
TimofeevaV.A.(1978),CrystalGrowthfromSolutioninMelt,Nauka,Moscow.
Tomashpol'skyYu.Ya.(1982),Izv.Akad.NaukSSSR,Neorg.Mater.,18,No.10,1662-1666.
Tomashpol'skyYu.Ya.(1984)Film-TypeFerroelectrics,RadioiSvyaz',Moscow.
TownsendD.(1984),Vacuum,34,No.3-4,395-398.
TsaiC.S.,KimB.andEl-AkkariF.R.(1978),IEEEJ.QuantumElectron.,QE-14,513-517.
TuckerJ.R.,ChaseA.B.andKingS.R.(1974),Dig.Tech.Pap.MB12,1.
UeharaS.,TakamotoK.,MatsuoS.andYamauchiY.(1975),Appl.Phys.Lett.,26,296-298.
UematsuU.(1974),Jap.J.Appl.Physics,13,No.9,1362.
UesugiN.(1980),Appl.Phys.Lett.,36,178-190.
UesugiN.andKimuraT.(1976),Appl.Phys.Lett.,29,572.
UesugiN.,DaikokuK.andKimuraT.(1978),J.Appl.Phys.,49,4945.
UlrichR.(1979),Appl.Phys.Lett.,35,840.
UlrichR.andJohnsonM.(1979),Appl.Opt.,18,1857.
VanDerZielJ.,MikuljakR.M.andChoA.Y.(1975),Appl.Phys.Lett.,27,71.
VandenbulckeP.andLagasseE.(1976),WaveElectron.,1,295.
VeberS.M.,HartmanN.F.andGlassA.M.(1977),Appl.Phys.Lett.,30,272.
VohraS.T.,MichelsonA.R.andAsherS.E.(1989),J.Appl.Phys.,66,5161.
VojdaniS.,DabiviA.E.andTavakoliM.(1975),J.ElectronSoc.,122,No.10,1400-1404.
VonDerLindeD.,GlassA.M.andRodgersK.F.(1974),Appl.Phys.Lett.,25,155.
VorobjevaV.V.,GolubevL.V.,NovikovS.V.andShmartsevYu.Yu.(1985),Pis'mavZhETF,11,No.4,224-226.
VoronovV.V.,DoroshI.,Kuz'minovYu.S.andlachenkoN.V.(1980),Kvant.Elektron.,7,2312-2317.
VoskresenskayaE.N.,GavrilovV.A.,KutvitskyV.A.andDemidochkinaS.I.(1985),in:Proc.VllthAll-UnionConf.GrowthandSynthesisofSemiconductorCrystalsandFilms,Novosibirsk,98-99.
WalkerR.G.(1981),Ph.D.thesis,UniversityofGlasgow.
WangHongandWangMing(1986),J.Cryst.Growth,79,No.1-3,527-529.
WargoM.J.andWittA.F.(1984),J.Cryst.Growth,66,289-298.
WaringJ.L.andRothR.S.(1965),J.Res.Nat.Bur.Std.,69A,2.
WarzanskyjW.,HeismannF.F.andAlfernessR.C.(1986),Appl.Phys.Lett.,53,13.
WebjörnJ.,LaurellF.andArvidssonG.(1989),IEEEPhotonTechnol.Lett.,1,1579.
WebjörnJ.,LaurellF.andArvidssonG.(1989),IEEEPhoton.TechnolLett.,1,316.
WeiJ.S.(1977),IEEEJ.QuantumElectron.,QE-13,152.
WeisR.S.andGaylordT.K.(1985),J.Appl.Phys.,A37,193-203.
WellerM.T.andDickensG.(1985),J.SolidStateChem.,60,139.
WernerA.W.,OnoeM.andCoquinG.A.(1967),J.Acoust.Soc.Am.,42,1223.
WhalenM.S.,TennantD.M.,AlfernessR.C.,KorenU.andBosworthR.(1986),Electron.Lett.,22,1307.
WiesendangerE.(1973),CzechJ.Phys.,B23,91.
WilkinsonC.D.W.andWalkerR.G.(1979),ElectronLett.,14,599.
WolkensteinF.F.(1973),Physico-ChemistryofSemiconductorSurface,Nauka,Moscow.
WongK.K.(1975),G.E.C.J.Res.,3,No.4,243.
WongK.K.,Clark,D.F.,NuttA.C.,WinfieldJ.,LayboumP.J.R.andDeLaRueR.M.(1986),Proc.InstElectr.Eng.J.,113,No.133,1986.
WongK.K.,DeLaRueR.M.andWrightS.(1982),Opt.Lett.,7,546.
WoodE.(1951),ActaCrystallogr.,4,353.
WoodV.E.,HartmanN.F.,VeberC.M.andKenanR.(1975),J.Appl.Phys.,46,2114.
YakovlevV.A.(1985)OpticsofAnisotropicMedia,MFTI,Moscow,27.
YamadaA.andTamadaH.(1992),Appl.Phys.Lett.,61,2848.
YamadaM.andKishimaK.(1991),Electron.Lett,,27,828.
YamadaM.,NodaN.,SaitohM.andWatanabeK.(1993),Appl.Phys.Lett.,62,435.
YamadaS.andMinakataM.(1981),Jap.J.Appl.Phys.,20,733-737.
YamamotoK.,YamamotoH.andTaniuchiT.(1991),Appl.Phys.Lett.,58,1227.
YanA.Y.(1983),Appl.Phys.Lett.,42,633.
YarivA.(1976),IntroductiontoOpticalElectronics,2nded.,Holt,RhinehartandWinston,NewYork.
Page369
YarivA.(1985),OpticalElectronics,Holt-SaundersInternationalEditors,NewYork-Philadelphia,295.
YarivA.andYehP.(1984),OpticalWavesinCrystals,J.WileyandSons,NewYork,513
YatsenkoA.V.andSergeevN.(1985),UFZh,30,No.1,118-120.
ZakhlenyukN.A.andZhovnirG.I.(1985),ZhETF,55,No.7,1406-1413.
ZernikeF.andMidwinterJ.E.(1973),AppliedNonlinearOptics,J.WileyandSons,NewYork,261.
ZhangL.,ChandlerJ.P.andTownsendP.D.(1988),Appl.Phys.Lett.,53,544.
ZhangL.,ChandlerJ.P.andTownsendP.D.(1990),FerroelectricsLett.,11,89.
ZhovnirG.I.andMaronchukE.I.(1980),Avtometriya,No.6,22-32.
ZhovnirG.I.andZakhlenyukN.A.(1985),ZhETF,55,No.5,902-904.
ZilingK.K.,NadolinnyV.A.andShashkinV.V.(1980),Izv.Akad.NaukSSSR,Neorg.Mater.,16,701-706.
ZolotovE.M.,KazanskyP.G.andChernykhV.A.(1982),Pis'mavZhETF,8,1413-1417.
ZolotovE.M.,KazanskyP.G.andChernykhV.A.(1983),Pis'mavZhETF,9,360-363.
ZolotovE.M.,KiselevV.A.andSychugovV.A.(1974),Usp.Fiz.Nauk,112,No.2,231-273.
ZolotovE.M.,KiselevV.A.,ProkhorovA.M.andShcherbakovE.A.
(1976),Quant.Electron.,3,1672.
ZolotovE.M.,PlekhatyjV.M.,ProkhorovA.M.,AmiletovS.A.andShcherbakovE.A.(1977),Pis'mavZhETF,3,241.
ZolotovE.M.,PlekhatyiV.M.,ProkhorovA.M.andChernykhV.A.(1979),ZhETF,76,1190.
ZolotovE.M.,ProkhorovA.M.andChernykhV.A.(1980),Kvant.Elektron.,7,No.4,843-848.
ZumsteyF.C.,BierleinJ.D.andGierT.E.(1976),J.Appl.Phys.,47,4980.
ZverevG.M,KolyaginS.A,LevchukE.A.andSkvortsovaL.A.(1977),Kvant.Elektron.,4,No.9,1882-1889.
ZytkiewiczZ.(1983),J.Cryst.Growth,61,665-674.
FurtherReading
1.HausH.A.(1988),WavesandFieldsinOptoelectronics,EnglewoodCliffs,Prentice-Hall,NewJersey.
2.HunspergerR.G.(1984),IntegratedOpticsTheoryandTechnology,SpringerVerlag,Berlin,Heidelberg,NewYork.
3.ProkhorovA.M.andKuz'minovYu.S.(1990),PhysicsandChemistryofCrystallineLithiumNiobate,AdamHilger,Bristol,NewYork.
4.ProkhorovA.M.andKuz'minovYu.S.(1990),FerroelectricCrystalsforLaserRadiationControl,AdamHilger,Bristol,NewYork.'
5.PropertiesofLithiumNiobate(1990),EMIS,England.
6.SmolenskyG.A.(ed)(1985),PhysicsofFerroelectricPhenomena,Nauka,Leningrad.
7.YarivA.andYehP.(1984),OpticalWavesinCrystals,NewYork.
8.YarivA.(1985),OpticalElectronics,Holt-SoundersInternationalEditors,NewYork.
Page371
Index
A
absorptionloss282
activationenergyforvaporization29
actualvaporizationflux30
angularmatching241
annealedproton-exchangedwaveguides56
autodiffusedlayers25
B
bandwidth295
Braggdiffractionmodulator315
Braggreflector247
bufferedmelts59
Bulkcrystallization131
C
capillaryliquidepitaxialtechnique78
channelwidth255
Cherenkovradiation245
cinnamicacid64
coherencelength248
controlvoltage293
conversionefficiency245
copperdiffusion49
coupledchannelwaveguides302
criticalsupersaturation135
crystallizationfromagasphase6
Curietemperature16
Curie-Weissbehaviour16
Czochralskimethod132
D
degreeoffilmperfection1
dielectricimpermittivitytensor35
dielectricproperties285
diffusiondepth123
diffusionoftransitionmetals37
diffusion-induceddefects188
directelectron-beamwriting203
dislocationstructure191
domainconfiguration198
domaininversion203
domainstructure195
doublewaveguide23
double-exchange'technique66
Dufoureffect139
E
effectivesegregationcoefficient110
electro-opticcoefficient259
electro-opticeffects258
electro-opticmodulators293
electro-opticphotorefractivemodulator328
electro-opticX-switchers292
electro-opticallytunablewavelengthfilter342
electrodiffusion49
electronpolarizability36
electrostrictioneffect36
energylossinwaveguides279
epitaxialferroelectricfilms118
epitaxialgrowth151
epitaxialgrowthofLiNbO397
equilibriumsegregationcoefficient142
evaporationcoefficient33
exchangetime66
extraordinaryrefractiveindex215
F
Fabry-Perotloss280
Fabry-Perotresonator260
Fermifunction229
Fermilevel135
ferroelectricfilms210
Fick'ssecondlaw27
filmgrowthrate141
flip-chipcoupling345
G
gas-transportepitaxy1
gas-transportepitaxy6
Gaussiannucleardamage24
Gaussianprofiles39
Glassconstant276
Glassmodel276
Gratingformation267
gratings266
H
holographicwriting267
homoepitaxialLiNbO3films178
hydrogenisotopicexchange58
I
in-diffusioncoefficient65
indexchange274
insertionlosses293
interferometricMach-Zehndermodulator326
isothermalepitaxy105
J
Jouleeffect133
Page372
K
Kerreffect48
Kikuchilines207
KLNcrystal121
KNbO3,inducedwaveguidecut-offmodulator331
L
Langmuirrelation28
Langmuirvapourpressure29
lasersputteringmethod17
layercomposition173
layerprecipitationtime124
lightresistance2601
LiNbO3birefringence245
liquid-phaseelectroepitaxy136
liquid-phaseepitaxy74
liquid-phaseepitaxy(LPE)technique83
lithiumniobate165
Lorentz-Lorenzformula36
M
Mach-Zehnderinterferometer271
Marcatili'sapproximation246
maximalmodulationdepth293
MFESstructurexvi
micro-channelslab125
microdomains199
micromorphologyoffilmsurface186
modenumber231
modulationindex260
monocrystallinity175
N
negativebirefringence215
nucleationrate146
O
one-dimensionalwaveguides22
opticalmodes224
opticalproperties213
opticalswitchingtime309
opticalwaveguideswitchmodulator308
ordinaryrefractiveindex215
out-diffusedlayers26
out-diffusioncoefficient65
out-diffusionindexprofiles26
out-diffusionkinetics27
out-diffusionsuppression34
P
partitioncoefficient128
PDRwaveguide247
PEwaveguide65
Peltiercoefficient132
perovskite118
phasematching239
photoelasticcoefficient47
photoinducedpolarizationconversion298
photorefractiveeffect269
photorefractiveproperties264
photorefractivesensitivity270
planarion-exchangedKTiOPO4waveguides68
planarwaveguides20
Pockelscoefficient68
potassiumlithiumniobate121
prismcouplingtechnique65
propagationconstant230
propagationloss12
protondiffusion62
proton-lithiumexchange52
proton-exchangedLiNbO3182
proton-exchangedLiNbO3waveguides51
pseudo-Kosselpattern11
pulsedlaserdeposition17
pumpingpower240
pumpingwavelength240
pyroelectricproperties287
Q
QPM-SHGdevice202
quasi-phasematching200
R
Raoultlaw3
refractiveindexgradient31
rfsputtering8
ridgewaveguidemodulator317
Rutherfordbackscatteringspectroscopy16
S
'sandwichmethod'5
schemeofthegrowthcell95
Schröderequation91
secondharmonicgeneration237
Seebeckcoefficient289
Sellmeierrelation215
Snelllaw217
spikelikedomains201
stationarycrystallizationmodel97
Stepanovmethod132
striplinestructures123
stripwaveguides21
substratemodes222
sum-frequencygeneration253
supersaturation101
surfaceindex72
symmetricwaveguides124
T
polarizationconversion345