2007 January • JOM 23 Overview Scanning Probe Microscopy for Materials Science Author’s Note: This paper is a contribution of the National Institute of Standards and Technology, an agency of the U.S. government, and is not subject to copyright. Tools are being developed that use the atomic-force microscope (AFM) to measure mechanical properties with nanoscale spatial resolution. Contact- resonance-spectroscopy techniques such as atomic-force acoustic microscopy involve the vibrational modes of the AFM cantilever when its tip is in contact with a material. These methods enable quantitative maps of local mechanical properties such as elastic modulus and thin-film adhesion. The information obtained furthers the understanding of patterned surfaces, thin films, and nanoscale structures. INTRODUCTION “In order to be widely used, future nanodevices will require nanomechani- cal measurements that are rapid, accu- rate, predictive, well-understood, and representative of a device or system’s environment in real time.” 1 This vision of the National Nanotechnology Initiative describes the general need for measure- ment tools for emerging nanotechnology applications, a field expected to create a multibillion-dollar market for materials within the next decade. It also emphasizes the specific need for nanomechanical information—knowledge on nanometer length scales of mechanical proper- ties such as elastic modulus, strength, adhesion, and friction. This is because applications increasingly involve several disparate materials integrated on the micro- or nano-scale (e.g., electronic interconnects, nanocomposites). The complexity of fabricating such systems dictates the use of predictive modeling to save time and money. Yet modeling can correctly predict system performance Mapping Mechanical Properties on the Nanoscale Using Atomic-Force Acoustic Microscopy D.C. Hurley, M. Kopycinska-Müller, and A.B. Kos only if the property data used as input are accurate at the relevant length scales. In addition to the achievement of nanoscale spatial resolution, there is a growing need to visualize the spatial distribution in properties instead of relying on a single “average” value. In such heterogeneous systems it is frequently the localized variation or divergence in properties that causes failure (void formation, fracture, techniques with force modulation and scanning. 3 However, the lateral resolu- tion is still limited by the radius (a few hundred nanometers) of the Berkovich diamond indenter used. Methods that use the atomic-force microscope (AFM) present an attractive alternative for characterizing mechanical properties. The AFM’s scanning ability and the small radius (typically 5 nm to 50 nm) of the cantilever tip enable rapid, in-situ imaging with nanoscale spatial resolution. The AFM was originally created to measure surface topography with atomic spatial resolution; 6 since then, a variety of AFM techniques to sense mechanical properties have been demonstrated. 7–10 Methods that show the most promise for quantitative informa- tion are dynamic approaches in which the cantilever is vibrated at or near its resonant frequencies. 11 Although more appropriately called contact-resonance- spectroscopy methods, variations are often labeled acoustic or ultrasonic corre- sponding to the characteristic vibrational frequencies involved (~100 kHz to 3 MHz). Among them are ultrasonic-force microscopy (UFM), 12 heterodyne-force microscopy, 13 ultrasonic atomic-force microscopy (UAFM), 14 and atomic-force acoustic microscopy (AFAM). 15 This article describes work toward quantitative measurements and imag- ing of nanoscale mechanical properties with contact-resonance-spectroscopy methods, in particular, AFAM. See the sidebar for a description of the principles of contact-resonance spectroscopy. SINGLE-POINT MODULUS MEASUREMENTS WITH AFAM Experiments using AFAM concepts are performed with an apparatus such as Methods that show the most promise for quantitative information are dynamic approaches in which the cantilever is vibrated at or near its resonant frequencies. etc.). Engineering these complex systems thus requires quantitative nanomechani- cal imaging to better predict reliability and performance. Many methods to obtain small-scale mechanical-property data 2–5 have draw- backs. For instance, nanoindentation (NI) 2 is inherently destructive, with each measurement creating an indent hundreds to thousands of nanometers wide. In addition, the spatial resolution afforded by conventional NI techniques may not be sufficient as dimensions shrink further and very compliant materials are increasingly used. A prom- ising method combines low-load NI
Transcript
2007 January • JOM 23
OverviewScanning Probe Microscopy for Materials Science
Author’s Note: This paper is a contribution of the National Institute of Standards and Technology, an agency of the U.S. government, and is not subject to copyright.
Tools are being developed that usetheatomic-forcemicroscope(AFM)tomeasure mechanical properties withnanoscalespatialresolution.Contact-resonance-spectroscopytechniquessuchas atomic-force acoustic microscopyinvolve the vibrational modes of theAFMcantileverwhenitstipisincontactwithamaterial.Thesemethodsenablequantitativemapsoflocalmechanicalpropertiessuchaselasticmodulusandthin-film adhesion. The informationobtained furthers the understandingof patterned surfaces, thin films, andnanoscalestructures.
IntroductIon
“In order to be widely used, futurenanodeviceswillrequirenanomechani-calmeasurementsthatarerapid,accu-rate, predictive, well-understood, andrepresentative of a device or system’senvironmentinrealtime.”1ThisvisionoftheNationalNanotechnologyInitiativedescribesthegeneralneedformeasure-menttoolsforemergingnanotechnologyapplications,afieldexpectedtocreateamultibillion-dollarmarketformaterialswithinthenextdecade.Italsoemphasizesthe specific need for nanomechanicalinformation—knowledgeonnanometerlength scales of mechanical proper-ties suchas elasticmodulus, strength,adhesion,andfriction.Thisisbecauseapplicationsincreasinglyinvolveseveraldisparate materials integrated on themicro- or nano-scale (e.g., electronicinterconnects, nanocomposites). Thecomplexityoffabricatingsuchsystemsdictatestheuseofpredictivemodelingtosavetimeandmoney.Yetmodelingcancorrectlypredictsystemperformance
Mapping Mechanical Properties on the nanoscale using Atomic-Force Acoustic MicroscopyD.C. Hurley, M. Kopycinska-Müller, and A.B. Kos
onlyifthepropertydatausedasinputareaccurateattherelevantlengthscales.Inadditiontotheachievementofnanoscalespatialresolution,thereisagrowingneedto visualize the spatial distribution inpropertiesinsteadofrelyingonasingle“average”value.Insuchheterogeneoussystems it is frequently the localizedvariationordivergenceinpropertiesthatcausesfailure(voidformation,fracture,
techniqueswith forcemodulation andscanning.3However,thelateralresolu-tionisstilllimitedbytheradius(afewhundrednanometers)oftheBerkovichdiamondindenterused. Methods that use the atomic-forcemicroscope(AFM)presentanattractivealternativeforcharacterizingmechanicalproperties.TheAFM’sscanningabilityandthesmallradius(typically5nmto50nm)ofthecantilevertipenablerapid,in-situ imagingwithnanoscale spatialresolution. The AFM was originallycreatedtomeasuresurfacetopographywith atomic spatial resolution;6 sincethen, a variety of AFM techniques tosensemechanicalpropertieshavebeendemonstrated.7–10Methodsthatshowthemostpromiseforquantitativeinforma-tionaredynamicapproachesinwhichthecantileverisvibratedatornearitsresonantfrequencies.11Althoughmoreappropriatelycalledcontact-resonance-spectroscopy methods, variations areoftenlabeledacousticorultrasoniccorre-spondingtothecharacteristicvibrationalfrequencies involved (~100 kHz to 3MHz).Amongthemareultrasonic-forcemicroscopy(UFM),12heterodyne-forcemicroscopy,13 ultrasonic atomic-forcemicroscopy(UAFM),14andatomic-forceacousticmicroscopy(AFAM).15 This article describes work towardquantitative measurements and imag-ingofnanoscalemechanicalpropertieswith contact-resonance-spectroscopymethods,inparticular,AFAM. See the sidebar foradescriptionofthe principles of contact-resonancespectroscopy.
etc.).Engineeringthesecomplexsystemsthusrequiresquantitativenanomechani-calimagingtobetterpredictreliabilityandperformance. Manymethodstoobtainsmall-scalemechanical-propertydata2–5havedraw-backs. For instance, nanoindentation(NI)2 is inherently destructive, witheach measurement creating an indenthundreds to thousands of nanometerswide.Inaddition,thespatialresolutionaffordedbyconventionalNItechniquesmay not be sufficient as dimensionsshrink further and very compliantmaterialsareincreasinglyused.Aprom-ising method combines low-load NI
JOM • January 200724
0
50
100
150
200
250
M(G
Pa)
t (µm)
AFAMNISAWS
0.77 ± 0.01
Ni
0.28 ± 0.03
Nb
1.09 ± 0.02
a-Si1-xCx:H
1.08 ± 0.01
Al
3.08 ± 0.01
SiO:F
Figure 2. The indentation modulus M of thin supported films obtained by AFAM, nanoindentation (NI), and surface acoustic wave spectroscopy (SAWS). The thickness t of each film was determined by cross-sectional scanning-electron microscopy analysis or by stylus profilometer methods. Film materials include fluorinated silica glass (SiO:F), amorphous hydrogenated silicon carbide (a-Si1–xCx:H), aluminum, niobium, and nickel. The error bars represent the standard deviation due to scatter of multiple measurements.
Figure 1. The schematics of experimental apparatus used for (a) AFAM modulus measurements at a fixed sample position and (b) contact-resonance-frequency imaging.
a
b
Equations
(1)
(2)
(3)E Ek
ks refs
ref
n
* **
*=
1 1 1E M Mtip s*
= +
k* = 6F RE*C23
theoneshownschematicallyinFigure1a.Theapparatusisbasedonastandard,commerciallyavailableAFMwithafewadditional off-the-shelf instruments.Notethataccesstotheunfilteredphoto-diode output signal from the AFM isrequired.ForAFAMmeasurements,thespecimen is bonded to an ultrasonicpiezoelectrictransducermountedontheAFMtranslationstage.Thetransducerisexcitedwithacontinuoussinewavevoltage by a function generator. TheamplitudeofthecantileverdeflectionismonitoredbytheAFM’sinternalposi-tion-sensitive photodiode. Lock-intechniquesareusedtoisolatethecom-ponentofthephotodiodesignalattheexcitation frequency. In this way, aspectrum of the cantilever responseversus frequency can be obtained bysweepingthetransducerexcitationfre-quencyandrecordingthelock-inoutputsignal. Contact-resonance spectra areacquiredfortransducerexcitationvolt-agessufficientlylowthatthetip-sampleinteractionremainslinear.Asdescribedinthesidebar,spectrafortwodifferentresonantmodesareneededinordertodeterminetheeffectivetippositionL
1.
Mostcommonly,thetwolowestflexural(bending) modes are used, althoughtorsional and lateral modes have alsobeen examined.20 Frequency measure-ments are made on two samples inalternation:thetestorunknownsampleandareferenceorcalibrationspecimenwhose elastic properties have beendeterminedbyanothermeans.Themea-suredcontact-resonancefrequenciesareusedtocalculatevaluesofk*forboththetestandreferencematerialswiththebeam-dynamicsmodelmentionedinthesidebar.Fromthecalculatedvaluesofk*
Figure 3. Quantitative AFAM images for an Nb/SiO2 thin-film sample. Contact-resonance frequency images of (a) first (f1) and (b) second (f2) flexural modes, respectively. (c) Normalized contact stiffness k*/kc calculated from (a) and (b). (d) Map of indentation modulus M calculated from (c) assuming Hertzian contact mechanics.
a
c
b
Figure 4. Imaging of film/substrate adhesion. (a) Schematic of sample in cross section. (b) Map of the normalized contact stiffness k*/kc calculated from contact-resonance-frequency images. (c) Average stiffness versus position across the center of (b).
42
40
38
36
34
32
k*/K
c
ba
c d
625 675 725 775 1.51 1.60 1.69 1.79f1 (kHz)
33 41 50 58 67 35 64 93 121 150
f2 (kHz)
k*/kc M (GPa)
culatedbyEquation3,24whereE*ref
isthe reduced Young’s modulus of thereference material (all equations arelistedintheEquationstable).Theexpo-nent n depends on the model used todescribethecontactmechanicsbetweenthetipandsample.22Usually,aspherical(n=3/2)orflat-punch(n=1)tipgeom-etryisassumed.Theindentationmodu-lusM
softhetestsampleisthendeter-
minedfromE*susingEquation2and
knowledgeofMtip
.Multipledatasetsareobtained by comparing measurementsontheunknownsampletothosemadeon the reference sample immediatelybeforeandafterward.Averagingthedatasetsyieldsasinglevaluefortheindenta-tionmodulusofthetestmaterial,M
s,for
whichtheeffectsoftipweararemini-mized. Comparison measurements with areference material of known elasticpropertieseliminatetheneedforpreciseknowledgeofthetipradiusR(seeEqua-tion1),whichisverydifficulttodeter-
minedirectly.Theuseofmultiplerefer-encesampleshasalsobeendemonstratedasawaytoimprovemeasurementaccu-racy.18,25 Because k* depends on thecontact area, the comparison methodreliesontheassumptionthatthecontact
geometry is identical for the test andreference materials. An alternativeapproachthatavoidsthisassumptionbymeansofatipshapeestimationprocedurehasalsobeendeveloped.26
The accuracy of this experimentalapproachhasbeenexaminedbycompar-ingAFAMmeasurementswithvaluesobtainedbyothertechniques.18,27Figure2showstheresultsofsuchexperiments.Measurementsoftheindentationmodu-lusMweremadeonthinsupportedfilmsof several different materials withAFAM,NI,andsurfaceacousticwavespectroscopy (SAWS). As mentionedpreviously,NIisdestructivetothesampleandhassomewhatpoorerspatialresolu-tionthanAFAM,butiswidelyusedinindustry. The SAWS method5 is usedprimarily in research laboratories;although nondestructive, the valuesobtainedrepresent theaveragesamplepropertiesoverafewsquarecentimeters.Figure2showsthattheresultsfromallthreemethodsareinverygoodagreement(differencesoflessthan10%andwithinthemeasurementuncertainty)forallofthesamples. ResultssuchasthesedemonstratethevalidityofAFAMmethodsforquantita-tivedeterminationofelasticproperties.Additionalresearchisongoingbothtoimprove measurement precision andaccuracyandtomorefullyunderstandtheextenttowhichthemethodscanbeapplied.Forexample,theeffectoffilmthicknessonAFAMmeasurementaccu-racy was examined with a series ofnanocrystalline nickel films depositedonsiliconsubstrates.28Theresultsindi-
JOM • January 200726
PrIncIPleS oF contAct-reSonAnce SPectroScoPy Contact-resonance spectroscopy techniques—methods that use the resonant modesof the atomic-force microscope (AFM) cantilever in order to evaluate near-surfacemechanical properties—have been utilized by several groups.15–18 For clarity, thediscussionhereislimitedtotheatomic-forceacousticmicroscopy(AFAM)techniquefirstdevelopedbyU.Rabeandcoworkers.15,19,20ThebasicconceptsofAFAMareshowninFigureA.Resonantvibrationalmodesofthecantileverareexcitedbyeitherthebuilt-inpiezoelectricelementoftheAFMcantileverholderorbyanexternalactuatorsuchasanultrasonictransducer.Whenthetipofthecantileverisinfreespace,asinFigureAa,theresonantmodesoccuratspecificfrequenciesthatdependonthegeometryandmaterialpropertiesofthecantilever.WhenthetipisplacedincontactwithaspecimenasinFigureAb,thefrequenciesoftheresonantmodesincreaseduetotip-sampleforcesthatstiffenthesystem,asillustratedschematicallyinFigureAc.Atomic-forceacousticmicroscopy and other contact-resonance-spectroscopy methods exploit the fact thatmechanicalpropertiesofthesamplecanbededucedbymeasuringthese“free-space”and“contact-resonance”frequenciesandinterpretingthemwithsuitablemodels. Thefirstmodelneededtointerpretcontact-resonancespectrainvolvesthedynamicsofthevibratingcantilever.Bothanalytical19,20andfinite-element18,21analysisapproacheshavebeenused.Thesimplestmodel todescribe the interaction,showninFigureAd,contains a rectangular cantileverbeamof lengthLand stiffnessk
Thevaluesofk*areusedtocalculate theelasticpropertiesof thesamplewith the
catedthatfornickelfilmsevenasthinas about 50 nm, AFAM measures thepropertiesof thefilmaloneandisnotaffectedbythepropertiesofthesubstrate.Thefilmthicknessforwhichthesubstratebegins to play a role depends on theelastic properties of both the tip andsample.Inaddition,recentstudieshavebeguntodelvemoredeeplyintothetruenatureofthenanoscalecontactmechan-icsbetweenthetipandsample.29,30Otherresearchinvolveseffortstoincludetheeffectsofadamping(inelastic)terminthetip-samplecontact,due,forinstance,to capillary forces from thin surfacelayers.31Furtherworkisneededtoincor-poratetheresultsofsuchstudiesintoanimprovedAFAMprocedureforquanti-tativemeasurements.
StIFFneSS IMAgIng And MAPPIng
Contact-resonance spectroscopymethods may also be used for two-dimensional imaging of near-surfacemechanical properties. Qualitative“amplitudeimages”indicativeoflocalvariations in stiffness16,32 are obtainedwithanapparatuslikethatinFigure1aandafixedexcitationfrequency.Asthetip is scanned across the sample, thelock-indetectorsensesvariationsinthecantilever vibration amplitude causedby changes in the local stiffness. Theoutputsignalofthelock-inisusedasanexternalinputtotheAFMforimaging.Amplitude imaging has been used toinvestigatethenanoscaleelasticproper-ties of systems such as piezoelectricceramics,15 carbon-fiber-reinforcedpolymers,16 anddislocations ingraph-ite.33
Correct interpretation of amplitudeimagesisdifficult,20especiallyformate-rial systems with several phases orcomponents.Moreusefularenanome-chanicalmaps—quantitativeimagesofnanoscale properties. To obtain suchmaps, it isnecessary to rapidlydetectthecontact-resonancefrequencyateachpointonthesampleasthetipisscanned.Recently,severalapproacheshavebeendemonstrated to achieve contact-reso-nance frequency imaging.14,15,34 Nowmapsoffrequency,contactstiffness,andmodulus27,35 are emerging as tools formaterialscharacterization. In contrast to other methods, theauthors’approachtocontact-resonance
frequencyimagingisbasedonadigitalsignalprocessor(DSP)architecture.27ADSPapproachfacilitatesfutureupgradesbecausechangesaremadeinsoftwareinsteadofhardware.Aschematicofthefrequency-trackingapparatusisshowninFigure1b.Thecircuitappliesaswept-frequency sinusoidal voltage to thepiezoelectric transducer. The AFMphotodiodesignalisconvertedtoadirectcurrent(DC)voltageproportionaltotheroot mean square (rms) amplitude ofvibration (rms-to-DCconverter, band-width from 1 kHz to 3.2 MHz) andsupplied toananalog-to-digital (A/D)converter.Fromthermsvoltageversusfrequencyresponse,thecircuitconstructsaresonancespectrumandfindsitspeak.Adigitalfeedbackcontrolloopusesthisinformation to adjust a voltage-con-trolledoscillatorsothatthefrequencysweepwindowremainscenteredonthe
contact-resonance frequency as itchangeswithsampleposition.Thecon-trol voltage is also sent to the AFMthroughanauxiliaryimagechannel.Theacquiredvoltageimagethusrepresentsthevalueofthecontact-resonancefre-quencyateachposition.Withthespecificcircuit components used, the currentsystemacquires a complete128-pointcantileverresonancespectrumevery2.7ms(375Hzrepetitionrate).TheAFMscanspeedmustbeadjustedtoensurethatseveralspectrumsweepsaremadeateachimageposition.Forscanlengthsuptoseveralmicrometers,animagewith256×256pixelsisusuallyacquiredinlessthan25min. Results obtained with contact-reso-nance-frequencyimagingtechniquesareshowninFigure3.Thesamplecontaineda silica (SiO
2) blanket film (thickness
~350nm)depositedonasiliconwafer.
2007 January • JOM 27
helpofasecondmodelforthetip-samplecontactmechanics.22Mostcommonlyusedare Hertzian contact mechanics, which describe the elastic interaction between ahemisphericaltipofradiusRpressedagainstaflatsurfacewithanappliedforceF
Figure A. Concepts of AFAM contact-resonance spectroscopy. Resonant modes of the cantilever are excited by a piezoelectric actuator mounted beneath the sample when the tip is (a) in free space and (b) in contact with the sample. Flexural (bending) modes of the cantilever are illustrated here. (c) Resonant spectra. The first contact resonance [shown in (b)] occurs at a higher frequency than the first free-space resonance [shown in (a)], but is lower than the second free-space resonance. (d) An AFAM beam-dynamics model. A rectangular cantilever beam with stiffness kc is clamped at one end and has a total length L. It is coupled to the surface through a spring of stiffness k* (contact stiffness) located at a position L1 with respect to the clamped end.
tively. The narrow, bright, and darkvertical lines indicate relatively large,spuriousfrequencychangesthatoccurfromsuddenchangesinthetip-samplecontactareaattheedgesoftheniobiumstrip.Otherwise, the frequencyvaluesfortheindividualmaterialsareuniformand repeatable from line to line. It isclearthattheaveragecontact-resonancefrequenciesofthecentralniobiumstriparegreaterthanthoseoftheSiO
by-pixel basis with the AFAM pointapproachdescribed.TocalculateamapoftheindentationmodulusMfromthecontact-stiffnessimage,Hertziancontactmechanicswereusedanditwasassumedthatthemeanvalueofk*/k
cfortheSiO
2
regioncorrespondedtoMSiO2
=75.1GPa.This value of M was obtained fromAFAMfixed-pointmeasurementsmadeontheSiO
2filmusingbulkfusedsilica
asthereferencesample.TheresultingmodulusmapisshowninFigure3d.Themean value for M in the entire SiO
2
regionisMSiO2
=75.5±7.1GPa,whilethe mean value for the niobium filmregionisM
Nb=118.5±7.1GPa.These
results are consistent with the valuesM
SiO2=72GPato77GPaandM
Nb=116
GPato133GPagivenintheliteratureforthebulkmaterials.Theyalsoagreewith AFAM point measurements thatyieldedM
Nb=112.7±15.0GPa.Fur-
thermore,therelativelysmallstandarddeviation of the values (5% to 10%)indicatesthatthetip-samplecontactisconsistentandrepeatable.
APPlIcAtIonS oF contAct-reSonAnce
IMAgIng
Onlyrecentlyhavecontact-resonance-spectroscopytechniquesblossomedintovaluable tools for nanoscale materialscharacterization.Recentresultsfortwodifferent applications illustrate thepotentialofthesetechniques.Thefirstexampleconcernstheinterfacialadhe-sionbetweenathinfilmanditsunderly-ingsubstrate.36Inthesecondstudy,theelasticpropertiesoftinoxidenanobeltsareexamined.37
Contact-resonance-spectroscopymeth-odscanbeusedtoevaluateothermechan-icalpropertiesbesideselasticmodulusif they influence the contact stiffnessbetweenthetipandthesample.Onesuchpropertyoftechnologicalinterestistherelativebondingoradhesionbetweenafilmandasubstrate.Toexperimentallyinvestigatethesensitivityofthesemeth-odstovariationsinfilmadhesion,36theauthors fabricated a model system ofgoldandtitaniumfilmson(001)silicon.Figure4ashowsacross-sectionalsche-maticofthesample.Arectangulararrayof5µm×5µmsquares(10µmpitch)ofAu/TisurroundedbyagridofTi/Au/Tiwasfabricatedonsiliconbystandardmicrofabricationtechniques.Thesamplewasintendedtocontainvariationsintheadhesionofaburiedinterfacewithonlyminimal variations in topography andcomposition at the surface. A crudescratch test was performed by lightlydraggingoneendofatweezeracrossthesample. Optical micrographs showedthatthistreatmenthadremovedthefilminthescratchedregionswithoutatita-nium interlayer (squares) and left thegoldintactinthescratchedregionscon-tainingatitaniuminterlayer(grid).Theresultconfirmedtheexpectationthatthefilm adhesion was much stronger inregions containing the titanium inter-layer.ThetitaniumtopcoatwasincludedmerelytopreventcontaminationoftheAFMtipbythesoftgoldfilm. To understand how AFAM sensesvariationsinaburiedinterface,notethatexperimentsprobethesamplepropertiestoadepthzroughlythreetimesthatof
JOM • January 200728
the tip-sample contact radius a.22 ForHertzian contact mechanics, a3 =(3RF
c)/(4E*).Forz>3a,thestressfield
beneath the tip is sufficiently smallrelativetothevalueatthesurface(<10%)thatthemeasurementisnotsensitivetoproperty variations. In this way, therelativedepthsensitivityofmethodssuchasAFAMisaffectedby thechoiceofexperimentalparametersRandF
obtainedfrom40linesinthecenterofthe image is shown inFigure4c.Themeanvalueofk*/k
cis39.1±0.6inthe
gridregionsand37.1±0.5inthesquare,adifferenceof5%.Severalothercontact-stiffness images acquired at differentsamplepositionsconsistentlyshowedadecreaseof4%to5%ink*/k
cforthe
regionsofpooradhesionthatlackedatitaniuminterlayer. Theresultsareconsistentwiththeo-reticalpredictionsfor layeredsystemswithdisbonds.38Animpedance-radiationtheorymodeledthedisbondedsubstrate/filminterfacebyachangeinboundaryconditions(i.e.,zeroshearstressattheinterface). For a disbond in a 20 nm
aluminumfilm(M=78GPa)on(001)silicon(M=165GPa),areductionofapproximately4%inthecontactstiffnesswas predicted, very similar to thedescribedresults.Thesystemmodeledin Reference 38 contained a differentfilmmaterialthanusedintheseexperi-ments.However,theoverallcombinationofconditions(filmandsubstratemodu-lus,appliedforce,etc.)wassufficientlysimilartotheauthors’thatacomparisonisvalid.Theseresultsrepresentprogresstowardquantitativeimagingofadhesion,agoalwithimportantimplicationsforthedevelopmentofthin-filmdevicesinmanytechnologicalapplications. In another application, tin oxide(SnO
2)nanobeltswereexaminedwith
contact-resonance methods.37 Quasi-one-dimensional structures such asnanotubes,nanowires,andnanobeltsaresubjecttomuchresearchinterestduetothepromisetheyshowfornewnanoscaledevices.Becausesuchdevicesarestillin the earliest stages of development,fundamentalmaterials-propertydataforthe component materials are needed.However,thespatialresolutionofmanyconventionalmethodsissimplyinade-quateforthesenanoscalestructures.Forthisreason,AFMmethodsareanattrac-tiveoption. Nanobeltsweresynthesizedbyheattreatmentoftinpowderinaquartztubefurnace.Thenanobeltsformedbythismethodwereremovedfromthealuminasubstratesanddepositedon(001)siliconsubstratesbysolventmethods.Ion-mill-ing techniqueswereused tomark thesubstratenearspecificnanobeltsofinter-estsothattheycouldbereliablyidenti-fied.TopogaphicimagesobtainedwithcontactAFMmethodsindicatedthatthe
nanobeltsweretypically0.5µmto1.0µm wide, 30 nm to 50 nm high, andseveral tensofmicrometers in length.Electron-backscatter-diffractionanalysisindicatedthatthecrystallinestructureofthenanobeltswastetragonal,asexpectedforsingle-crystalSnO
2.Thenanobelts
studiedinthisworkhadasurfacenormalparallel to the (102) reciprocal latticevector. Auger-electron spectroscopyrevealedthatthechemicalcompositionofthenanobeltswasthesameasthatofbulkSnO
2.
Severalnanobeltswereexaminedbothbysingle-pointmodulusmeasurementsand contact-resonance modulus map-ping. The (001) silicon substrate wasusedasthereferencematerial,withthevalueM
Si(100)=165GPaused.Valuesfor
theindentationmodulusMnb1
=154±18GPaandM
nb2=184±13GPawere
obtained for two nanobelts from thesingle-point measurements. In theseexperiments, the Hertzian stress fieldpenetrationwasestimatedtobe45nmto60nm,equaltoorslightlygreaterthanthenanobeltthickness.Thusacontribu-tiontothemeasurementfromthesiliconsubstrate is possible. However, theAFAM results are in good agreementwith the value M
nb1 = 151 ± 14 GPa
obtainedwithdifferentialUFM,37whichused sufficiently low forces that thesubstratewasnot interrogated.There-fore, theeffectof thesubstrateon themeasurementwasnotconsideredtobesubstantial. The measured values aresignificantlylowerthanthevalueof358GPacalculatedfor(102)SnO
2fromthe
second-order elastic tensor. However,the results are consistent with otherexperimental and theoretical findingsthat report nanobelt modulus valuessignificantlylower(upto75%)thanthatof bulk SnO
2.37 The reason for these
finite-sizeeffectsisstillunderinvestiga-tion. Figure5showsresultsfromcontact-resonanceimagingexperimentsonthenanobeltpreviouslyidentifiedas#1.AtopographyimageisgiveninFigure5a,whileFigure5bcontainsthecorrespond-ing modulus map. Two contact-reso-nancefrequencyimageswereacquiredandanimageofthenormalizedcontactstiffnessk*/k
Figure 5. (a) A topography image and (b) modulus map of SnO2 nanobelt.
30
20
10
0
220
180
140
100
60
Hei
ght (
nm)
M (G
Pa)
2007 January • JOM 29
asareference.Darkerareascanbeseenattheright-handedgesofthenanobelt.At first impression, this suggests thattheseareashavealowermodulus.How-ever, theauthorsbelieve theyactuallyrepresent regions of reduced contactstiffnessduetocontaminationbetweenthe nanobelt and the substrate. Thishypothesiswasformedfromanalysisofthe sample topography. Although notclearintheimage,individualtopographyline scans reveal that these areas areslightlytaller(~3nmto5nm)thantherestofthenanobelt.Likethethin-filmadhesion effects discussed previously,contaminationcouldcausevariationsinthe nanobelt-substrate contact, whichwouldappearasareductionincontactstiffness. Averaging over the entirenanobeltregionoftheimageincludingthedarkregionsyieldsameanmodulusvalueM
nb=145±28GPa.Ifthedark
regionsareomitted,themeanisMnb
=164±10GPa.Theseresultsareconsis-tentwiththedescribedpointmeasure-ments within the measurement uncer-tainty.
concluSIonS And outlook
Knowledgeofmechanicalpropertiesatthenanoscalewillbeessentialtothesuccessfuldevelopmentofnewnanos-calematerialsandstructures.The resultsTheresultsdiscussedhere,aswellasothersfromgroups worldwide, show significantprogress in advancing the state of the in advancing the state of theart.However,true quantitative nanome-truequantitativenanome-chanical imaging requires furtherresearchefforts.AdeeperunderstandingAdeeperunderstandingofthedynamicsofnonidealAFMcan-tileverbeamsasthetipinteractswiththesample is needed for improved dataanalysis. To increase measurementTo increase measurementaccuracyandrepeatability,itisimportanttobetterunderstandandcontrolissuessuchassurfacetopography,wearofthesilicon tip, and the actual tip-samplecontact mechanics. Resolving suchissueswillresultinrefinementstocon-tact-resonance-spectroscopytechniquesandthusenhancetheirvalueasaquan-
titativemeasurementtools.It is antici-Itisantici-patedthatthesetypesofdynamicAFMtechniqueswillcontinuetodevelopandwillplayacrucialroleinfuturenanote-chnologyeffortsbyprovidingquantita-tivenanomechanicalinformation.information.
AcknowledgeMentS
The authors thank W. Arnold, S.Hirsekorn,U.Rabe(Fraunhofer�nstitut�nstitutfür zerstörungsfreie Prüfverfahren,Saarbrücken,Germany),andJ.Turner(University of Nebraska–Lincoln) forvaluableinteractions.Thenanoindenta-tionmeasurementswereprovidedbyN.Jennett(NationalPhysicalLaboratory,UnitedKingdom),A.Rar(UniversityofTennessee–Knoxville), and D. Smith(National �nstitute of Standards andTechnology[N�ST]).TheSnO
2nanobelt
experimentswereperformedincollabo-rationwithY.ZhengandR.Geer(CollegeofNanoscaleScienceandEngineering,Albany,NewYork),whoalsoprovidedthosesamplesandperformedthesupple-mentalcharacterization.WearegratefultoG.Pharr(UniversityofTennessee–Knoxville), Y. Dzenis (University ofNebraska–Lincoln),N.Barbosa,P.Dres-selhaus,G.Hilton,E.Langlois,W.Rip-pard,andS.Russek(N�ST)forprovidingthe samples used in this work. TheTheessentialcontributionsofothercurrentandformerN�STcoworkers(M.Fasolka,R.Geiss,D.Julthongpiput,R.Keller,J.Müller,andP.Rice)arealsoacknowl-edged.
references
1. Instrumentation and Metrology for Nanotechnology, Report of the National Nanotechnology Initiative Workshop (27–29 January 2004, Gaithersburg, MD); available at www.nano.gov/NNI_Instrumentation_Metrology_rpt.pdf .2. W.C. Oliver and G.M. Pharr, J. Mater. Res., 7 (6) (1992), pp. 1564–1583.3. S.A. Syed Asif et al., J. Appl. Phys., 90 (3) (2001), pp. 1192–1200.4. O. Kraft and C.A. Volkert, Adv. Engng. Mater., 3 (3) (2001), pp. 99–110.5. A.G. Every, Meas. Sci. �echnol.,�echnol., 13 (5) (2002), pp. R21–R39.6. G. Binning et al., Phys. Rev. Lett., 56 (9) (1986), pp. 930–933.7. P. Maivald et al., Nanotechnology, 2 (2) (1991), pp. 103–106.
8. M. Troyon et al., Nanotechnology, 8 (4) (1997), pp. 1630–171.9. N.A. Burnham et al., J. Vac. Sci. �echnol. B., 14 (2) (1996), pp. 794–799.10. A. Rosa-Zeiser et al., Meas. Sci. �echnol.,�echnol., 8 (11) (1997), pp. 1333–1338.11. Q. Zhong et al., Surface Science, 290 (1-2) (1993), pp. �688–�692.�688–�692.12. R.E. Geer et al., J. Appl. Phys.,Phys., 91 (7) (2002), pp. 4549–4555.13. M.T. Cuberes et al., J. Phys. D: Appl. Phys., 33 (19) (2000), pp. 2347–2355.14. K. Yamanaka et al., Appl. Phys. Lett., 78 (13) (2001), pp. 1939–1941. 15. U. Rabe et al., J. Phys. D: Appl. Phys., 35 (20) (2002), pp. 2621–2635.16. K. Yamanaka and S. Nakano, Appl. Phys., A 66 (1) (1998), pp. S313–S317.17. K.B. Crozier et al., Appl. Phys. Lett., 76 (14) (2000), pp. 1950–1952.18. D.C. Hurley et al., J. Appl. Phys., 94 (4) (2003), pp. 2347–2354.19. U. Rabe et al., Ultrasonics, 38 (1-8) (2000), pp. 430–437.20. U. Rabe, “Atomic Force Acoustic Microscopy,” Applied Scanning Probe Methods II, ed. B. Bushan and H. Fuchs (New York: Springer, 2006), pp. 37–90.21. R. Arinero and G. �évêque, Rev. Sci. Instr., 74 (1) (2003), pp. 104–111. 22. K.�. Johnson, Contact Mechanics (Cambridge, U.K.: Cambridge University Press, 1985), pp. 84–99.23. J.J. Vlassak and W.D. Nix, Phil. Mag. A, 67 (5) (1993), pp. 1045–1056.24. U. Rabe et al., Surf. Interface Anal., 33 (2) (2002), pp. 65–70.25. M. Prasad et al., Geophys. Res. Lett., 29 (8) (2002), pp. 1172 1–4.26. K. Yamanaka et al., Rev. Sci. Instr., 71 (6) (2000), pp. 2403–2408.27. D.C. Hurley et al., Meas. Sci. �echnol., 16 (11) (2005), pp. 2167–2172.28. M. Kopycinska-Müller et al., Nanotechnology, 16 (6) (2005), pp. 703–709.29. D. Passeri et al., Rev. Sci. Instr., 76 (9) (2005), pp. 093904 1–6.30. M. Kopycinska-Müller et al., Ultramicroscopy, 106 (6) (2006), pp. 466–474.31. D.C. Hurley et al., Appl. Surf. Sci., 253 (3) (2006) pp. 1274–1281.32. U. Rabe et al., J. Vac. Sci. �echnol. B, 15 (4) (1997), pp. 1506–1511.33. T. Tsuji and K. Yamanaka, Nanotechnology, 12 (3) (2001), pp. 301–307. 34. D. Passeri et al., Appl. Phys. Lett., 88 (12) (2006), pp. 121910 1–3.35. T. Tsuji et al., Appl. Phys. Lett., 87 (7) (2005), pp. 071909 1–3.36. D.C. Hurley et al., Appl. Phys. Lett., 89 (2) (2006), pp. 021911 1–3.37. Y. Zheng et al., J. Appl. Phys., in press (2006).38. A.F. Sarioglu et al., Appl. Phys. Lett., 84 (26) (2004), pp. 5368–5370.
D.C. Hurley, M. Kopycinska-Müller, and A.B. Kos are currently with the National Institute of Standards and Technology, 325 Broadway, Boulder, Colorado 80305-3328 USA. D.C. Hurley can be reached by e-mail at [email protected].
