1stitutoDipartimentaledi Fisica, Unit’ersità di Catania,Corso Italia, 57 195129 Catania,Italy
Heatingandcoolingratesaswell asmelting andsolidification velocity ofsurfacelayersofirradiatedsamplesby laser pulsesaresemi-quantitativelydescribedin termsof heat flowconceptsbasedon theassumptionthatlaserlight is directly convertedin latticeheating.Therangeofvalidity ofthisapproachcomparedwith amorecompleteschemetaking intoaccountthefree carrierplasmaevolution is sketchedandtheimportanceof Augereffect in theplasma--latticecoupling mechanismis detailed.The most importantconsequencesof the quencingrates achievableby short laser pulseirradiation on the structuremodificationof semicon-ductor surfacelayers are reviewedwith more detailson the liquid to amorphoussilicontransition.This is in factthemorenewandlessunderstoodfast solidification processinducedby pulsedlaserirradiation.
Introduction
Thebasisof the simplestdescriptionof laserannealingis thehypothesisthatlight energydE absorbedin a volume dV of the irradiatedsamplein a timeinterval dt is convertedinto heat“locally” and“instantaneously”giving rise toa localpositivevariationof temperaturedT=dE/pC~dV in the sametime df,p being the massdensityandC~,the specific heatof the samplematerial.Heatdiffusion, controlledby the thermal conductivity K (or the thermal diffusivityD = K/pC~),providesa redistributionin temperatureboth during the heating(i.e., during the irradiationwith a laserpulse)andduring the cooling (after thelaserswitch-off).
A thermaldiffusion equationwitha“source”termwhich describestheheatingof the sampleis generallysolvedto obtain detailedinformation on the sampletemperatureevolution [1,2]
~ (K ~3T’\ ~I(x, r)(1)
i~t ~x\pC~~xJ pC~
where~ is the light absorptioncoefficientand I the light intensity at a depth x
4 I ( 1’ Bocri -l hcrnuil i/co rip! ion o/ lao’r iinticalin~j
inside the sampleand at time i. Numerical solution of the equation is oftenneededbecauseof the involved parameters(~.(~,. K) with the temperatureandwith thestructureof thesamplewhich in manypractical easesis a layered one(amorphouslayer on crystal hulk or metal depositedon senticonductors,andso on). A numerical solution also allows one to take iilto account the localenthalpyahorption andreleaseduring phasetransition and so it is possible losimulatetheevolution of the samplemelting andsolidification 3
Heat flow concepts
WithoLit going into detailwith theheatdiffusion eqtiationsolutions,someheatflow conceptscan be very easily predicted.Assuming a planar geometry, thesampleis heatedby a laserpulseof time duration r0 througha thicknessof theorder of the light absorptionlength ~ or the heat diffusion length ~/2Dt,dependingon which of thesetwo parametersis larger.The energy density L~,requiredto reach the melting point at the samplesurface(which is normally
thehottestpoint) is proportional to themelting temperatureandto the inverseof theheatedthickness.
Pulsesof energy density E greaterthan Eh will melt a layer whosethickness.within the first pm, will he proportional to F E1h. In silicon the light penetra-tion depthcanrangefrom It) ° cm in thecaseof uv irradiation to 10cm m thecaseof Neodymium 1.06gmwavelength(in this last easeit strongly varieswithtemperatureapproachingthe value of 10 ~ cm close to the niehinig point).Pulsetime durationcanhe varied from hundrednanosecondsdown to a couple
of nanosecondsin Q-switched mode, or it can he reduced to some ten pico-seconds:thecorrespondingheatdiffusion length are 30pill, 5000A and 300Arespectively. We will here neglect any discussion about fi~mtosecondlaserpulses.Theenergy densitythreshold for samplemelting is 0.2 Jcm
2 for 2.5 ns,0.347pm,pulse[4], it is also0.2 i/cm2 for a20 ps [5] 0.53gmwavelength.In thefirst casetheheatedthicknessis 5000A dueto heatdiffusion, in thesecondcaseitis i0000A dueto light absorptiondepth. This factor two is perfectlycompen-satedby a factor two in the reflectivity coefficient for thesetwo wavelengths.Theseexamplesarethecaseof thelowestenergydensity thresholdfor themelting
of Si which up till now areexperimentallyverified. For a 30 ns ruby laserpulsecrystal silicon the energy density threshold to melt the surfaceis 0.~J:cm2: it
changesveryslow with thepulsedurationdueto thefact theheatedthicknessislargely determinedby the absorptionlength. For amorphoussilicon instead.theabsorption length beinga few thousandangstronls,the melting thresholdvaries from 0.4 to 1.2 J/cm2 changingthe pulse duration (and then the heatdiffusion) from 10 to 100ns. E
15 of 4.5 i/cm2 is neededfor a nanosecondpulseat
1.06pm. due to the very low absorptioncoefficient of this wavelength in Si:hut due to the increaseof absorptioncoellicient with temperature.3 .J c111 is
P. Baeri / Thermal descriptionof laserannealing 411
enoughif the sampleis pre-heatedat 1 50CC.Heatingof the samplesurfacehappensin the sametime scaleof the pulse
itself. Heatingratesrangingfrom 1012 to lOin K/s for pulsesof 1 and lOOnstime duration respectively,can be reachedwith energy density close to E!h.Heatinginsidethe sampleis delayedby heatdiffusion (about 100ns is neededfor heatto bediffusedthrough 1 pmin hotsilicon). So,evenfor veryshortpulses,themaximumheatingratebeforemelting at 1 pm depthwill beof the order oflO”~K/s. Coolingafter the laserswitch-offis fasterthe steeperthe temperaturegradient.This temperaturegradientnear the end of the laserpulse is of theorder of Tmj~..J~.i5~or Tm x x [3], Tm being the melting temperature.It canreachseveraliO~K/cm for the extremecaseof the 2.5ns uv. Fora 30 ns ruby orneodymiumlaseron amorphoussilicon it is about7 x 106 K/s, andis about3 x 10~K/cm for ruby laseron crystal Si due to greaterabsorptiondepth incrystalcomparedwith amorphousSi, whilst it is about 5x iU~K/cm for neo-dymiumlaseron crystalSi for thesamereason.With increasingtimeor increas-ing depth inside the sample the temperaturegradient becomessmaller andsmaller.For examplein the previouscited caseof ruby laseron crystalsilicon,the temperaturegradientat the surfacebecomesa factor five smaller 200 nsafterthe pulseswitch off.
Surfacecooling rateis proportionalto the temperaturegradient.Maximumcooling ratesof severall0~K/s are easilyachievedat the surfacewhilst at 1 pmdepththeywill beaboutoneorder of magnitudesmaller.As an example,in thefollowing the first direct time-resolvedtemperaturemeasurementis reported[6].
A thin 2000A thick film thermocouple(Fe and constantan)has been invacuumdepositedontoa aluminaor Si substrate.On top of it a 1 pm thick Gefilm has beensequentiallydepositedwithout vacuumbreaking.A front andlateral view of thisdevice is showedin fig. la. The circular centralpart of thethermocouplehasa diameterof 3 mm. RegionsI and2 are the cold points atroom temperatureandare connectedto the oscilloscopeby thin copperwires.
TheGelayerwasshotby Nd glasslaserpulseswith 50 ns FWHM. Thebeamspotdiameterwas 3 mmandspatiallyuniform within 10%.The outputvoltageof the thermocoupleduring irradiation is directly measuredby a fast storageoscilloscope(fig. ib). Resultsfor a 0.3J/cm2shotareshownin fig. 2aand2b foranaluminaandSi substrate,respectively.In accordancewith a previouscalibra-tion of thethermocoupleof 16.6j.tV/ ~Ca maximumtemperatureof about600~Cis reachedin both samples.The measuredquenchingratesare 3 x 108 andiO~K/s respectively.The different values are relatedto the different thermal
conductivity of the two substrates.In Si it is aboutlW/s°Cwhile in Al203 it is
at leastoneorder of magnitudesmaller.Thetime delaybetweenthe pulsepeak(shownasa dashedline) andthe temperaturemaximumis dueto heatdiffusionprocessbecausethe sampleis heatedessentiallyat the surfacewhilst the tem-peratureis recorded1 pminsidethesample.Forsimplicity thecalculationto be
413 P. Bueri Thermaldescription of laser onnealinq
CONSTANTAN Ge Fe
Ge
CONSTAN TAN Fe
or 3
Fig. I. Plannew (a)and lateralstewIb) ofthedepositedthin ilm thermocouple.Theinsert showstheschematicelectrical circuit.
Nd aser puEse : -50 ns 03 3/cm Ge~1Substrat~
fhermocoup~e
C ~ — ~ 3d0~
Orbubstisie
ME (p S
Fig. 2. Oscilloscope traceof theoutpui soltagevs time obtainedby irradiaii~nol a 1.2gmthick (ic
layerdepositedontoa thin iron -constantanthermocoupleon Al2O~(a) andon Si (b) substrate.The
i~ulseshapeis shownasa dashedline for comparison.
P. Baeri/ Thermaldescriptionof laserannealing 413
comparedwith the experimentaldataweremadeusinga heat flow procedureassuminga bulk Ge sampleof infinite thicknessand irradiatedwith 50 ns1.06gmlaserpulse.The temperature—timedependenceat the samplesurface(upperpart)and at 1 pm depth(lower part) computedfor 0.3 and 0.15 i/cm2energydensityvaluesare reportedin fig. 3. The thresholdfor surfacemelting is0.27J/cm2andthe maximumtemperaturecomputedat the surfaceandat 1 pmdepthdiffers about500K for the 0.3J/cm2irradiation.Thedifferencebecomesnegligible0.5 psafterthe pulse.Theaveragequencingrateis about4 x 108 K/swhich is comparableto the valuesextractedfrom the experimentalresultsoffig. 2.
Theliquid—solid interfacevelocity during the epigrowth,following the lasermelting, plays an important role in many nonequilibrium thermodynamicquestions,as impurity trapping and metastablephaseformation. It is thenimportant,within the frameworkof the heatflow computations,to understandhow to control it.
At the liquid—solid interfacetheheatflow mustbeequalto the releaseof thelatentheat,so
KdT/dx=Hpv, (2)
::: ~ SAMPLE SURFACE
~ 3O0T~
.2gm DEPTH
300 ~
0 0.5 1.0 1.5 20
LME (ps)
Fig. 3. Computedtemperaturevs time curvefor a bulk Ge sampleirradiaiedwiih 5t) ns Nd laserpulseat 0.3 and0.15 J/cm2.The upperfigure representsthe temperaiureai I gm insidethesample.
41 4 P. Boeri - I hernial description of laser aiiiiealitip
wherer is solidification velocity, lithe melting enthalpy,dT;dx the tempera-
ture gradientin the solid behind the liquid solid interface.Another term taking into account the temperaturegradient in the liquid
layer should be included in eq. (2) but it can be neglecteddue to the muchlower valueof dT1dx in the liquid [10].
Thetemperaturegradientjust at theend of the pulse is stronglydeterminedby the energydepositiondepth as previouslydiscussed.It turns out that thevelocity, at leastfor energy densitiescloseto the melting threshold,is inverselyproportionalto the squareroot of the pulseduration,or directly proportionalto theabsorptioncoefficient,dependingon which of the two is moreinfluencingthe energydepositionlength.Due to the largevariationof ~and t~.it hasbeenpossible to control the liquid solid interface velocity from less than I msto 20 rn/s. As an examplein fig. 4 are shown the calculatedmeltfront positionvs time for four different cases.Case(a) is a free running neodymiumlaseronamorphoussilicon, case(b) is a Q-switched Nd 30 us laserpulse on crystalsilicon pre-heatedat 300 C, case(c) is thesameascase(b) but on an amorphoussilicon and case (d) is an ultraviolet (ruby double frequency2.5 us pulse oncrystal Si). The energy densitiesare 30. 3.2, 2.5 and0.45 Jcm
2for case(a). (b),(c) and(d) respectively.The velocity of the liquid solid interfacedecreasesalsoon increasingthe energydensityabove the threshold.
1__
a) 5:2cm/S
E b) V:1 rn/s
c( V:4 rn/sa.a,
b dl V:lsrn/s
a,
C
0’ -— -
0 1 2 3 4 5
Time ps)
Hg. 4. Melt front position vs iime for severaldifferent irrudiations in Si as clcscrihcd in the text As
7erotime hasbeentakenthesian of soliditication in all cases.
P. Bueri Thermaldescription of laser annealing 415
Energycoupling
Till now we haveneglectedall the intermediatemechanismsof energytrans-formation from laserlight to sampleheating,but thepreviousschemeis validin the following hypothesis:
(1) Thediffusion length of freecarriersbeforerecombinationmustbe shorterthan the light penetrationdepth or the heat diffusion length during pulseduration.
(3) Thelifetime of free carriersmustbeshorterthanpulseduration.If theseconditionsare not fulfilled a morecomplicatedschemeof calculation
which include spaceandtime evolutionof free carrier densityandenergy likethe oneproposedby Lietoila andGibson[7] mustbeused.Two characteristictime constantsare important in this scheme:the electron---phononrelaxationtime te andthe Augerdecaytime tA. te hasbeenestimatedto beof theorder ofi--lOps although Yoffa [8] hascalculatedthat underconditionspertinenttolaserannealingthe rateof energy releaseof the carrier to the lattice is sloweddown; recentexperimentsof time-resolvedreflectivity in thepicosecondregimeby Liu, Kurtz andBloembergen[9] haveshownthat 1 Ps ~5a suitablevalueforte soits influence on the simplest“thermal” schemeis negligible.
The Auger decayrate tA is relatedto the free carrier concentrationN bythe Auger decayconstant~‘3. t~= 1/y3N
2. An evaluationof the value of ‘~‘~
in silicon canbe doneby a transmissionmeasurementwith Nd 1.06pm wave-length laserpulses.This wavelengthcancreateelectron—holepairsbecausetheenergyassociatedwith a photon is just abovethe silicon bandgap;moreoverfreecarrier absorptionbecomescomparablewith latticeabsorptionat concen-tration levels exceedingsome 1018 carriers/cm3.The pulse which createstheplasmais then a suitable probe to determineits concentrationthrough themeasurementof transmittance.In fig. 5 is plotted the transmittedagainsttheincident energy density measuredin the range 0.1- 3 i/cm2 of a 25 ns laserpulse. The silicon sample was a 10~cm,100pm thick single crystal (100)
oriented with both faces optically polished. The trend is clearly not linear,thetransmittedincidentenergyratio being 0.25at li/cm2 and0.16at 2.8 i/cm2.Although lattice heatingplays some role for this nonlinearity,mainly respon-sible for the absorptionincreasewith energydensity is the free carrier plasma.Calculationsbasedon the previousquotedmodel [7] assuminga free absorp-tion crosssectionof 5 x 10— iS cm2 at this wavelengthare reportedin the samefig. 5 for severalvaluesof the Augerdecayconstanty~.
The best fit is found for y~==8x 10—31 cm6s~.Freecarrier diffusion isnegligible becauseof the in-depthlight penetration.(Lattice absorptionrangesfrom 10 cm - to 110cm- from R.T. to 450K.) Latticeabsorptiontemperaturedependencewas previously determinedat low intensity incident light in the
416 P. Baeri Thermaldescriptionof laser annealing
25 ~ Ndpi )~ /
-~
Incident Energy Density l/cni
Fig. 5. Transmittedenergydensii~ihrough a 100gmSi samplefor a 25 its 1.06pm pulsevs incident
energydensity (black dots). Full lines refer to calculations assumingdifferent valuesof the Auger
decayconstani
range300 500 K. in the caseof 3J/cm2pulsea maximumcarrier concentrationof 3 x lOi~/cm)is reached10 usafter the pulse peakand at this concentrationtheAuger lifetime is 1.38 ns. A maximumtemperatureof 450 K is reached35 us
afterthe pulsepeak.A temperaturerisewithout taking into accountfreecarrierabsorptionwould havebeen,instead,much lower.This exampleshowsthat theAugerdecaymechanismcanbe a limit in theenergyexchangebetweenelectronsandlattice.In table I, for different laserpulseson Si characterizedby the first 4columns (energy density. time duration, wavelengthand lattice absorptioncoefficient) are reportedthe energydepositiondepthL (the maximumbetweenthe absorptionlength andthe heatdiffusion length); the maximumfree carrierconcentration,N, reachedduring thepulse;thecorrespondingminimumAugerdecaytime, TA; the averagediffusion length,Li), of carriersduring the time tA.
assumingan ambipolardiffusioncoefficientof 100cm2/s;andthe maximumfreecarrier absorptioncoefficient. Conditions1, 2 and3 statedat the beginningofthis paragraphare fulfilled in all the us pulsecasesexceptthe 1.06pm pulse in
Table I
A r1, / xi 1. 5 r5 I.e, xi,
IJ,cm) (s) 1gm) cm ) gm) cm Is) (pm) (ciii ‘I
3 3 x I)) .06 10 1 0~ 2 x 0 3 x 10 3.4 I3 x 10 0.64 l0~ 10 6.4x it)’ 3 x It) ‘~ 1.7 32))
P. Baeri / Thermaldescriptionof laser annealing 417
which absorptionby free carrier is greaterthan latticeabsorption.In thepico-secondregimetheAugerdecaytimeis comparablewith thepulsedurationitself;plasmaevolutionmust betakeninto accountfor a correctpredictionof latticeheating.It mustbepointedouthoweverthat in anycasethefinal resultisheatingor melting of the lattice evenif somewhatdelayedin respectof the light pulseitself.
Structure modification of surface layers
The very high heatingand cooling ratesachievableby short laserpulsesassumerelevancebecausethey allow theformationof particularstructurein theirradiatedsurfacelayers. In fact by the fast heating,it is possibleto reachthemelting pointpreventingotherphasechangesin solid phaseof any metastabiestructurepresentat the samplesurface.An exampleof thiseffect is the meltingof theamorphoussilicon. Amorphoussilicon is ametastablestructurewhosefreeenergyis higherthan thatof crystalsilicon[11]. It undergoesspontaneouslythe transitionto poly or singlecrystal in solid phase.The maximum velocityfor epygrowth for amorphouslayers on a single crystal is about iO~A/ps.To melt anamorphouslayerof about1000A without regrowinga singlecrystalin solidphase,a heatingrateof at least iO~K/s must thenbe employed.Themeltingtemperatureof amorphousSi is somehundreddegreebelowthecrystalmelting point, the liquid producedby the previousmelting can then be at atemperaturemuchlower than the crystal—liquid equilibrium temperature.
Recrystallizationfrom suchan undercooledliquid mayproduceverypeculiarstructures[12] andits behaviouris still underinvestigation.A quitegoodunder-standingof this kind of phenomenais presentedby D.H. Lowndesin theProceedingof this conference;for precision’ssakereferencemustbemadeto aquite different interpretationof the samephenomenareportedby Thompsonet al. [13].
Anotherimportantaspectis relatedto thecooling rateand thesolidificationvelocity. Solidification velocity of several rn/s can result in some metastablestructureformation;quencingof this structurefrom the melting pointdown toroom temperaturein some hundrednanosecondsis enoughto preventanychangein a thermodynamicallymorestablestructure.The diffusion coefficientof dopantsin silicon has a maximum valueof the order of 10~2cm2/scloseto themelting temperature.Theaveragediffusion length in the hundrednano-secondtime scaleis only 1 A, which meansthat any long-rangeatomicreorder-ing is prevented.
The first effect studiedasa functionof the liquid—solid interfacevelocity wasthe impurities surfaceaccumulation.After the completesolidification of theirradiatedsampleimplantedwith somedopant,partof the impurity is rejectedon the samplesurface.
41 5 P. Boeri I licrmal descriptionof laser a,inea)ini/
According to theclassicaltheoryof normal freezingthis hasbeenexplained
as follows: whilst themelt front comestoward tile surface,tile impurity profileis broadenedby the diffusion ill the liquid, a fraction of dopant is rejectedby
the advancinginterfaceit the phasecharacterizedby the highersolubility. i.e.,in the liquid, and then accumulatesthe samplesurface. At the interface theconcentrationsof impurities in liquid. to. andin the solid, c,. will stay in agivenratio K0 = c5~c. K0 is the equilibriun3 distribution coefficient defined as theratio of the concentrationin thesolid and the liquid phasedeterminedby thephasediagramat a fixed temperaturecloseto the melting point. But far fronlthermodynamicequilibrium, al thevery high speedreachedin thecaseof laserirradiation, theprocessof surfacerejectionof impurity can he describedstill interms of normal freezing but using instead of K1 an interface distributioncoefficientK’(i) which is velocity dependent.
Usually K0 is much less than unity and the very common result at highvelocity reachedby laserannealingis thai. K’ is severalordersof magnitudegreaterthan K0 anddependstrong1~on thevelocity. With all theotherparam-etersfixed, the amount of impurity rejectedon the sample surfaceincreaseswith decreasinginterfacesegregationcoefficient K’. Tile amount of impuritywhich is retainedin the solid is locatedinto the latticesitesof thesilicon crystalat a concentrationfar abovethe solid solubility limit thus forming a super-saturatedsolid solution.
To determineK’),) one has to comparethe measureddopant profile afterlaserirradiationwith theresultsofamodel calculationfor dopantredistribution[3] usingK’ as a fitting parameter.Thekinetic of the melt front remaiil fixed bythe irradiation conditiontilrough the heal flow calculation. As an exampleofdifferent redistributionsdue to different solidification ratesfig. 6 reports thedepthprofilesof Te implantedin Si andirradiatedwith a Nd laserpulseat 1.06pm. The lower part shows the profiles after irradiation with a Nd laserpulseat 1.06pm. The lower part shows the profiles after irradiation with 2.0 J1cm
2of the implanted sample.The amount of’ surfaceaccumulationis 20%. thecalculatedsolidificationvelocity is about3 ms. If the implantedsampleis firstthermally annealedso that a single crystal is obtainedbefore the Nd laserirradiation, the Te profile reported in the upperpart of the figure shows aconsiderablylargersurfaceaccumulation.
Thesmall absorptioncoefficientof the 1.06pm wavelengthin Si crystalgivesriseto a small temperaturegradientandthe calculatedsolidificationvelocity is
about 0.8ms. The correspondingK’ fitting valuesare ~-~0.5and0.03 for tilehigherandthe lower velocity, respectively.Severaltheories[14,15,16.17]havebeeildevelopedto describenonequilibriumdopantsegregationat a fastmovingliquid--solid interface,It is far from the purposeof this work to review them andthe readeris referredto the original papersor to recentreviews[18].
Tile commonfeatureto thesemodelsis aquantityD1 definedas the impurity
diffusion coefficient in the nearinterfaceregion. It has beenshown [19,20] that
P. Baeri/ Thermaldescriptionof laserannealing 419
Si <tOO> Nd 30
~ )5OkeV Te
3.23/cm’CRYSTAL
3.ci
z0
R-4
2.03/cm’AMORPHOUS
~
DEPTH (pm)
Fig. 6. Thedepthprofile of a Si) 100)sampleirradiatedwith t 50 keV Te afterirradiationwith 30 nsNd laser pulse for a single crystal(up) and with 1500A amorphouslayer(down). The R~arrowrepresentsthe averagepenetrationof Te beforethe irradiation.
assumingD, =(D8D1)U2 D
5 and D1 being the diffusion coefficientsin the solidandliquid phaserespectively,bothat themelting point, it is possibleto predictif a given impurity will be trappedor rejectedon the surface. If u.= D1/)L ?)L beingthe interfacethickness(i.e. few monolayers)the impurity is fasterthantheinterfaceandwill accumulatein the highsolubility phase,i.e. the liquid, thefinal result will be a K’ valuevery closeto the equilibrium K0 vaiue. If r~=A ~ v then the impurity will befrozen by the fast advancingsolid phaseandK’will reacha valueveryclose to unity.
Quencing of the amorphous phase
Anotherexampleof a fast quencedmetastablestructureis theamorphizationof silicon singlecrystals.It hasbeenshownin fact that for solidificationvelocityapproaching15 rn/s [21] amorphoussilicon is obtained.The picture of this
420 P. Bueri Thermaldescriptionof laserannealing
phenomenonis notyet completelyunderstoodas the oneof thesupersaturatedsolutionspreviouslydiscussed.
In fig. 7 [22] the measuredregrowth velocity is shown as a function of themaximum meltdepth for a 2.5 us 0.347pm wavelengthlaserpulseorientedona silicon single crystal (100) and for energy densitiesranging from 0.2 to 0.8i/cm2. The melt front kinetics has been followed by meansof time resolvedconductivity measurementsand closely agreewith the one computedOil thebasisof the thermalmodel.The blackdotsrefer to samplesin which the amor-phouslayerwasproducedafter irradiation. A maximum liquid solid interfacevelocity of 15 rn/s thenexistsfor theregrowthof a singleSi crystalfrom themeltin the (100) dlrectioil. A possibleapproachto the explanationof this effectcomes from thermodynamicconsiderations.A finite solidification velocity
canbe obtainedonly by freezingthe liquid at a temperaturebelow the meltingpoint.
Theoreticalevaluation[23,24] predictedabout 15K undercoolingfor I msvelocity.In fig. 8 is plottedthefreeenergyvstemperaturefor crystal,amorphousandliquid crystal.The liquid curve intersectsthe solid curve at two differenttemperaturesfor the amorphousandthe crystal phases.
Liquid to amorphoustransitionis possibleonly at a temperatureabout300 Kbelow thecrystal meltingpoint. Following the previousestimate,a liquid solidinterfacevelocity of 20 rn/s will producean undercoolingof about300 K thatis enoughto bring the liquid silicon at the energylevel requiredto undergothetransitionto theamorphousphase.Butkinetic limitation concerningthe nuclea-
25 ~ ~ ~ ‘, \ ‘ .,,,
--..-....••..
\ \.,\ \ \~... ‘\ \ - -.--‘ -,.,---
20 \ ~ -, .. Amorphization -,
\ \\ \S ~-, ‘- - I\ \ — .,, .., ~.
E \ \ \S\
5 \ \ ~•~‘\ N -‘ ... \ N --.
.1
~-2.5nS,~lO “fl OO—~9O /
—.--- p~ ~
0 0T~O
~ 5 IOnS-----~
0 ~0 50 tOO 50 200 250
Me)t depth (nm)
Fig. 7. Regrowthvelocity vs maximum melt depthfUr uv pulseirradiation measuredby transientconductancemeasurements.Solid dots indicate that amorphousSi forms from the melt (from ref.
[22]).
P. Baeri / Thermaldescriptionof laser annealing 421
V////iTEMPERATURE T~ TM
ENERGY PULSE E1 E2
I.. ~iUNDER COOLING
RANGE
Fig. 8. Freeenergyvs temperature(schematic)for amorphous,crystalandliquid silicon. T~and 7~,,differ by about300 K.
tion of the amorphousphasemust be also takeninto accountto explain thiseffect.
Furtherindicationscanbe obtainedfrom a comparisonbetweenthe amor-phousformationin a dopedandundopedSi crystal.
In fig. 9 [25] areshownthealignedspectrafora2 MeV Heincidenton Si (111)samplesirradiatedwith 0.33 J/cm
2 2 ns 347 nm laserpulse doped (full dots)with 50 keY Te 2 x i0’~cm2 andundoped(opendots).
The thicknessof the amorphouslayer is almosta factor 2.5 greaterfor thedopedsample.It canbeinterpretedasaninfluenceof thedopantatomsthatactasheterogeneousnucleationcentersfor the amorphousphase.
The effect canalso be explainedwith somedifferencein the undercooling—velocity relationship betweena doped and an undopedcrystal but kineticconsiderationsabout nucleationrates are strongly proposedby this otherfollowing effect [26].
A samplewas first implanted with 120keY, 2 x i0~~at. cm3 In ions and thenannealedby a 2 J/cm230 nsq-switchruby laserpulse.The resultingstructurewasa singlecrystalfreeof defectswithanaverageconcentrationof substitutional
422 P. Buert Ihcr,nal description of laser atiiicaliiiq
2 ns fd RUBY (347nm) 033 jcm-2
500 — tOO 0...1~
DEPTH (nm) .
.
.I~U)0I,) -
~ 1000 sSi<til>5OkeVTe
2x10’5Cm2
500 -
. • •.
1Cc~b~d”W~•• • •••
- t. ~ i
250 300 350
CHANNEL NUMBER
Fig. 0. (II 1)channelinganalysisof a Si sampleperformedby 2 Me’s’ He. Opeii dois refer to a pure
sampleand black dots io a sampleimplanied with 5)) keV, 2 x
In atomsof 4 x IO~° at cm in the outer2000A anda strong peakof about1.5 x l0’~cm
2 of In atomsrejectedon tile samplesurface.Backscatteringspectrumof the indium signalis shownin hg. 10 (triangles).
Following an irradiation with 0.36 J/cm22 ns 0.347 nm laserpulseswhichproducea 500 thick amorphouslayerit changes.In thesamefig. l0(opencircle)the backseatteningspectrumof this new distribution is shown: thesurfacepeakdisappearedand anotherpeak appearsat lower energy indicating a strong
which producedan amorphouslayer,800A thick ) ~.)(from ref. [26]).
surface
Fig. Ii. TEM micrographof thesamesampleoffig. 10 afterthe2 nspulseirradiation(from ref. [26]).
423
424 1’. Biicri / /icrmaI dc.scripi viii n/íascr ,imicaliiiii
concentrationof In locatedat 160A from tile samesurface.A crosssectionalTEM of this sampleis shownin thenextfig. ii. The7~,peakresultsin anarrow
(20A thick) buried layerof In imbeddedin 500A thick aillOrpilous silicon layer.This appearsas a clear evidencethat a solid amorphousliquid interface,nucleatedat the samplesurfaceandsegregatedthe In toward tile inside,until asecondliquid solid interface starting from the intericr of tile sample is en-
counteredat 160A from the surface.Nucleation processesof the amorphousphaseis then important to determinethekineticsof the amorphouslayerforma-
tion following laserpulse irradiation.
References
I] I’. Baeri. S.F. (. ampisano.(I. l—i’ti and F. Rimini AppI. Pbs. 5)( 11070)788.
12] RI-’. Wood and (~E.Giles, Phys. Rev. B 23(19S02923.[3] 1’. Baeri and S.I.). ( ‘ampisano.ii,: Laser A incatins’ of Scmiconduetor,.cds..J . W. Mayer and
J.M. Poate(AcademicPress.Ness York. 1982) chap.4.
[4] AG. Cullis. HF. Webber.N.G. (‘hess,J.M. Poateand P. Bacri. Phys.Rev. Lett. 49(1982(219.
[5] R. Yen, J.M. Liii, H. Kuri and N. Bloembergen,Appl. Phys. ‘s 27U982( 153.
[6] P. Baeri. S.F. (‘ampisano. F. Rimini and J.P. Zhang.AppI. Phys. Lett. 45(1984)398.[7] Lietoila and iF. Gibbons.J. AppI. Phyv. A 27(1982(153.
[8] F. Yoffa. Phys. Rcv. 21 (1980)3415,[9] L.A. Lompr~.J.M. [,iu. H. Kurtt and N. Bloembergen. AppI. Phys. Leit. 44(1984)3.
I I 0] P. Baeri, in Laserand Electron Beam Interaction svith Solids, eds.. B. Appleton and G.K.Celler (North-Holland. Amsterdam. 1982) p. IS).
