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Kelvinprobeforcemicroscopy(KPFM),alsocalledsurfacepotentialmicroscopy,hasfoundbroadapplications,rangingfromcorrosionstudiesofalloys,photovoltaiceffectsonsolarcells,andsurfaceanalysis.
KPFM,togetherwithconductiveAFM,havebeenrecognizedasthetwomostusednanoscaleelectricalcharacterizationtools,complementingeachother.
1However,limitedspatialresolutionandlackofmeasurementrepeatabilityandaccuracyhaslimiteditsusefulnessinsomecriticalareas,suchasintheidentificationofdonorandacceptordomainsinbulkheterojunctionorganicsolarcells,materialdifferentiationincompositematerials,andtrappedchargesoninsulators.
ThetwomajorKPFMdetectiontechniquesareamplitudemodulationKPFM(AM-KPFM)andfrequencymodulationKPFM(FM-KPFM).
2,3Thisapplicationnotepresentsanintuitive,geometricallyrealisticprobemodeltoillustratetheirdrasticdifferencesinspatialresolutionandaccuracy.
ThismodelinghasledBrukerresearcherstocombineFM-KPFMwithaninnovativenewAFMmode,PeakForceTapping,whichoffersease-of-operationandsimultaneousquantitativenanomechnicalpropertymappingcapability(viaPeakForceQNM).
4Togetherwithanovelprobedesignandauto-optimizationsoftware,thisnewapproachhasenabledadrasticincreaseinKPFMperformance.
BackgroundUsingagold-leafelectroscopein1898,SirWilliamThomson,laterknownasLordKelvin,observedthatplatesofcopperandzincmountedoninsulatingshaftscreatedchargewhentheywerebroughtintoelectricalcontactandthenmovedapart.
Hisdiscoverycannowbeexplainedintermsofworkfunctiondifferences.
Theworkfunctionistheminimumenergy(orwork,usuallymeasuredineV),neededtoremoveanelectronfromasolid,toapointimmediatelyoutsidethesolidsurface(orenergyneededtomoveanelectronfromtheFermilevelintovacuum).
ApplicationNote#140PeakForceKelvinProbeForceMicroscopyFigure1.
EnergyandchargediagramillustratingKelvinprobetechniqueprinciple.
PeakForceTappingModeHigh-ResolutionSimultaneousAdhesion&PotentialMapsFrequency-ModulationTheaboveequationstatesthattheappliedacbiasatfrequencyωiscausingtheelectricforcetomodulateatbothωand2ω,whichcanbemeasureddirectlyusingcantileverdeflection.
Figure2showstheformsprescribedbytheaboveequation.
Mostrelevantisthefactthatoscillationamplitudeatω(shownasamplitude1)dropsto0whenVCD=VCPD,theveryideaof"nulling"electricforcetofindsurfacepotentialinamplitudemodulationKPFM.
Theelectricforcegradientisassociatedwithelectricforce,Therefore,)2cos(41)sin()()21)((Term2222Term22TermDC2222'ωωωωtVzCtVVVzCVVVzCFACACCPDDCACCPDDCel+++=Similarly,VCD=VCPDwhenthemodulationamplitudeoftheelectricforcegradientatωdropsto0,thebasisfor"nulling"theelectricforcegradienttofindthesurfacepotentialinfrequencymodulationKPFM.
AM-KPFMthroughElectricForceDetectionThemodulatedelectricforce,bytheapplicationofanacbiasbetweenthetipandsample,canbeconvenientlymeasuredusingtheoscillationofthecantilever.
TheacbiasfrequencyistypicallyselectedtobetheresonantfrequencyoftheAFMcantileverforenhancedsensitivityaffordedbycantilever'squalityfactorQ.
TheKPFMfeedback,usingtheoscillationamplitudeasinput,adjustsaDCbiasuntiltheoscillationamplitudedropsto0,whenVDCequalsCPD.
Whentwodifferentconductorsarebroughtintoelectricalcontact,forexampleviaanexternalwirecontact,electronswillflowfromtheonewithlowerworkfunctiontotheonewithhigherworkfunction,equalizingtheFermienergies.
Iftheyaremadeintoaparallelplatecapacitor,equalandoppositechargeswillbeinducedonthesurfaces.
Thepotentialestablishedbetweenthesetwosurfacesiscalledthecontactpotentialdifference(CPD),contactpotential,orsurfacepotential,whichequalstheworkfunctiondifferenceofthetwomaterials.
MeasuringtheCPDisthusquitesimple.
Anexternalpotential(alsocalledthebackingpotential)isappliedtothecapacitoruntilthesurfacechargesdisappear.
Atthispoint,theexternalpotentialequalstheCPD.
ThevariousKelvinprobetechniquesdevelopedthusfardiffermainlyonlyonhowthischarge-freestateisdetected.
In1932,WilliamZismanofHarvardUniversityintroducedthevibratingelectrodetechniqueandthe"nulling"concept.
5Verticallyvibratingthetipoverasamplecausesthecapacitancetovaryasthedistancechanges.
Thisinduceschargetoflow,givingrisetoanACcurrent.
Thebackingpotential,atwhichACcurrentisataminimumorideally0,"nulled,"isfoundtoequaltheCPD.
Thistechniqueleadstodevelopmentofsystemsthatautomaticallytrackshiftsincontactpotentialduetochangesintheworkfunctionofthesample.
J.
M.
R.
WeaverandcoworkerswerethefirsttocombineKelvinmethodwithAFM.
6Theyembracedthenullingconceptinfindingthecharge-freepoint,andcapitalizedonAFM'suniquecapabilitytodetectsmallforcesandforcegradients.
Thecentralideaisthattheelectricforceandelectricforcegradientbetweenthetwoplatesofacapacitorwillbecome"0,"whenchargedisappears.
Itisfitting,forthisreason,tocallthetechniqueKelvinprobeforcemicroscopy(KPFM),asNonnenmacherdidin1991.
7KPFMopenedthedoortomeasuringCPD,thereforeworkfunction,inthenanometerregime.
AM-KPFMandFM-KPFMarebasedonelectricforceandelectricforcegradientdetectionrespectively.
ElectricForceandElectricForceGradientAconductiveprobeandaconductivesampleformacapacitor.
Theelectrostaticforcebetweenis:2)(21VzCFel=whereFelistheelectricforce,andVisthepotentialdifferencebetweentheprobeandthesample.
VisthesumoftheintrinsicCPD,anexternallyappliedDCvoltageVDCandacvoltageVAC:)sin(tVVVVACCPDDCω+=Combiningtheabovetwoequations,wearriveat:)2cos(41)sin()()21)((Term22TermTermDC22ωωωωtVzCtVVVzCVVVzCFACACCPDDCACCPDDCel+++=Figure2.
DCdeflection(top),amplitudesatfrequencyω(center)and2ω(bottom)whentheDCtipbiasissweptwhileanacbiaswithfrequencyωissuperimposed,correspondingtotheDCterm,ωtermandthe2ωtermdescribedinequation1.
2FM-KPFMthroughElectricForceGradientDetectionThedetectionofelectricforcegradientislessstraightforward.
Theforcegradientchangestheeffectivespringconstantofthecantilever.
Whenplacingaconductivecantileverinanelectricfield,itseffectivespringconstantisthesumofitsnaturalspringconstantkandtheelectricforcegradient,thesameeffectofconnectingtwospringsinparallel.
Weknowtheresonantfrequencyofacantileverdependsonthespringconstant:Thereforetheelectricforcegradientwillcausetheresonantfrequencytochange:Whentheelectricforcegradientismodulated,ascausedbyanacbias,theresonantfrequencyofthecantileverwillbemodulated.
Asimpliedintheequation,resonantfrequencywillbemodulatedatboththeacbiasfrequencyωanditssecondharmonic2ω.
Ifoneismechanicallyshakingthecantileveratitsresonantfrequencyω,andsimultaneouslyapplyinganacbiasatfrequencyωm,usuallyonlyafewkHz,themodulationoftheresonantfrequencygivesrisetotwopairsofsidebandsatω±ωm,andω±2ωm(seeFigure4).
Theamplitudeofthesidebandmeasurestheresonantfrequencymodulationamplitude;usingtheamplitudeofthesidebandatω±ωmforKPFMfeedback,andadjustingtheDCbiasuntiltheydisappearleadstothepointofVCD=VCPD.
Inpracticalimplementations,sidebandamplitudeisrarelydirectlymeasuredatthesidebandfrequencyusingasinglelock-inamplifier.
Amorecommonmethodusestwocascadedlock-inamplifiers,withthefirstonelockingattheresonantfrequency,thephaseoutputofwhichisfedintothesecondlock-in,whichlocksattheacbiasfrequency.
Theamplitudeoutputofthesecondmeasurestheamplitudesumofω±ωm,whichisthenusedforKPFMfeedback(seeFigure5).
ProbeModeling—SpatialResolutionandAccuracyofAM-KPFMandFM-KPFMProbemodelingilluminatedourunderstandingofthespatialresolutionandaccuracyprovidedbythetwoKPFMmodes.
WeutilizedarealisticyetstraightforwardapproachtomodelingtheprobeinanattempttounderstandhowmuchFigure3.
AM-KPFMdiagram.
Anacbiaswithafrequencyω,typicallytheresonantfrequencyofthecantilever,isappliedbetweentheprobeandthesample,givingrisetoanalternatingelectricforcebetweentheprobeandsamplethatcausestheprobetooscillate.
Figure5.
FM-KPFMdiagram.
AnacvoltageisappliedtothetappingpiezotooscillatetheAFMcantileveratitsresonantfrequencyω.
Anacbiasatfrequencyωm,usuallyafewkHz,isappliedbetweentheprobeandthesample,modulatingtheresonantfrequency.
Twocascadedlock-inamplifiersareusedtodetectthesumamplitudeofsidebandpairω±ωm.
Figure4.
Amplitudevs.
frequencyplotoftheverticaldeflectionsignalrecordedwithhigh-speeddatacapturewhenaMESP-RCprobeisshaken,nearasamplesurface,bythetappingpiezoatitsresonantfrequencywhileanacbiasof2kHzisapplied,illustratingtheemergenceofsidebandsduetoacbias-inducedfrequencymodulation.
3decaystoaround200nm,whichdemonstratesthesharpdependenceofspatialresolutiononprobe-sampledistance.
Whiletheabovemodelingisonlyafirstorderapproximation,itisusefulforconceptualunderstandinganditdoesreachthesameconclusionasColchero,whousedadifferentsetofassumptions.
2Ithasbeenrecognizedthattheelectricforcefromthetipconeandcantileverpredominateoverthatfromthesmalltip-apex,therefore,AM-KPFMisnotatallaquantitativenanoscalemeasuringtool.
OnlyFM-KPFM,wheredominatingelectricforcegradientsignalcomesfromthetipapex,offershighspatialresolutionandaccuratelocalCPDinformation.
Theeffectoftipgeometryonspatialresolutionisonlysecondary.
ModesOverviewandComparisonKPFM,asacombinationoftheKelvinprobetechniqueandAFM,makessurfacepotentialmeasurementsaccessibleonthenanometerscale.
KPFMtraditionallyoperatesinconjunctionwithTappingMode,however,therearemanyreasonstocombineitwiththetriedandprovenPeakForceTappingmode(seeBrukerapplicationnoteAN135).
ThefourpossiblecombinationsarechartedinTable1(thenamingofeachcombinationwillbeusedthroughthisapplicationnote).
Someofthesecombinationsmaybedoneeitherinasingle-passfashion,whereAFMimagingandKPFMmeasurementrunsimultaneouslyononescanline;orinadual-pass(orlift-mode)fashion,whereAFMimagingmodeisrunonthefirstpassandKPFMonthesecondpassusinglift-mode.
PeakForceKPFM,thecombinationofPeakForceTappingmodeandFM-KPFM,integratesthebenefitsofthetipneedstobeincludedtoaccountfor(1)halfofthetotalelectricforceinAM-KPFM,or(2)halfofthetotalelectricforcegradientinFM-KPFM.
Wesetoutwiththecapacitormodelofprobeandsample,andapproximatedtheprobeasconsistingofamicro-cantileverandatipconewithapointend(seeFigure6).
Asagoodconductor,thepotentialisthesameallovertheprobe,andchargesareonlypresentonthesurfaces.
Theintegratedcapacitanceofthecantileverandtipconecanbeanalyticallyexpressed.
Electricforceandelectricforcegradientarededucedfromthefirstandsecondderivativesofcapacitance.
(SeeAppendixIforthemathematicdeductions.
)Figure7showsthesimulationresultofthewidelyusedSCM-PITprobe,whichhasthefollowingnominalgeometry:cantilever225mlong,30mwide,tip10mtall,andconehalfangleof22.
5°.
Therelativecontributionofthetipcone,integratedtoheighth,versustotalinteraction,isplottedagainsttipheight.
ToquantifythespatialresolutionofKPFM,weadoptedthesimilardefinitionusedbyCohchero,2theradiusoftheringattheheightuptowhichtheintegralcontributionofthetipconeaccountshalfthetotalelectricforceincaseAM-KPFM;orhalfthetotalelectricforcegradientforFM-KPFM.
ForAM-KPFM,whenliftheightis5nm,thecontributionofthewholetipconeremainsbelow50%,indicatingitsspatialresolutionisdominatedbythewidthofthecantilever-onthemicrometerscale,alsoimplyingtheCPDobtainedisnotlocal,butaconvolutionoverthelargeareacoveredbythecantilever.
Thiscallsitsaccuracyintoquestion,exceptonlargeuniformsamples.
Ontheotherhand,forFM-KPFM,whenthetipislifted5nmabovethesurface,halfofthesignalisgatheredfromupto15nmabovethetipend,correspondingtoadiameterof12nm.
Thissuggestsapossibleresolutionof10nmmaybeachievedwithFM-KPFM.
TheCPDinformationcollectedislocaltothearearightunderneaththetipaffordingcredibleaccuracy.
Liftingthetiphigher,forinstance,50nmabovethesurface,thespatialresolutionFigure6.
ModelofaKPFMProbewitharectangularcantilever.
Thecapacitanceofthecantileverisanintegrationofcapacitanceofeachtinyrectanglealongthecantilever.
Asthesameforcewouldcausedifferentdeflectiondependingonitsdistancetothebaseofthelever,thecapacitanceisnormalizedtorecognizethis.
Figure7.
Thecontributionofthetipconeintegrateduptoheighthovertotalelectricforce(blue)andelectricforcegradient(purple)areplottedversusheightfromtipendforaSCM-PITprobe.
Geometriesare:cantilever225mlong,30mwide,tip10mtall,andconehalfangleof22.
5°.
The"BLUE"plotsareelectricforceattip-sampleseparation5nmand50nm.
The"purple"plotsareelectricforcegradientattip-sampleseparation5nmand50nm.
4andcapabilitiesofPeakForceTapping(easeofuseandsimultaneousPeakForceQNMcapability)andthesuperiorspatialresolutionandaccuracyofFM-KPFM.
Itisbestdoneinadual-passfashion.
ItispossibletoimplementPeakForceKPFMinasingle-passfashionbutnotwithoutsacrificingperformance,asinterferencefromPeakForceTappingcansometimesbesevere.
KPFM-FMisdoneinasingle-passfashion.
Thoughitcanalsobedoneinadual-passfashion,thereisnobenefitthatisnotcoveredbyPeakForceKPFM.
Itishelpfultoclearsomeconfusionintheliterature,wheresingle-passKPFMissometimesimproperlyusedtoreferexclusivelytoKPFM-FM,albeitKPFM-AMcanalsobedoneinasingle-passfashion.
PeakForceKPFMandPeakForceKPFM-AMBrukeroffersastandardKPFMsample,whichispatternedwithAu,Si,andAlstrips.
BoththeAlandAufilmsare50nminthicknessdepositedonann-dopedsiliconsubstrate.
Intheory,whenthetipisonanyoneofthethreedifferentregions,aconstantpotentialvalue(CPD)shouldberead.
Astaircasepotentialprofileisthereforeexpectedacrossthethreedifferentmaterials.
Thereisanoticeableslope,however,presentoneachofthestairsofthepotentialprofileacquiredwithPeakForceKPFM-AM.
Thiscanbereadilyexplainedbytheprobemodelingdescribedabove.
Thepotentialdataisaconvolutionfromthetip,thetipcone,andthecantilever.
Althoughthetipisononesinglematerial,therelativelygiganticcantilevercoversothermaterialsandthuscontributesalargeportionofthetotalvalue.
Forinstance,whenthetipisonthetheAl/Siinterface,onlyhalfofthecantileverisoverAl,andwiththemajorityoftheotherhalfoverSi(andsmallerportionextendingovertheAu).
Thefinalmeasuredvalueendsupaweightedaverageoftheworkfunctionofthethreematerials.
Asthetipmovesawayfromtheedge,morecontributioncomesfromtheAl,andlessfromSiandAu,givingrisetotheslope.
Thisistrueofalloftheinterfaces,andnotonlyspeaksofthepoorlateralresolutionofAM-KPFM,butalsoitsinaccuracyasaresultofconvolution.
Incontrast,thestairsonthepotentialprofileacquiredusingPeakForceKPFMarelargelylevel,amanifestationthatthedominantcontributionisfromthetipapex.
Thus,thecantilevercontributionbecomesnegligible.
ThedataconfirmsthatFM-KPFMoffersmuchhigherlateralresolution,duetotheminimalcontributionfromthecantilever,andmuchbetteraccuracythanAM-KPFM.
DataonaSn-Pballoyfurtherillustratesthispoint.
Thetopographyrevealsdifferentdomainsinthealloy(seeFigure9,right).
TheyareclearlyresolvedonbothpotentialmapsacquiredwithPeakForceKPFM-AM(seeFigure9,left)andPeakForceKPFM(seeFigure9,middle)withlittledifferenceperceivablebyqualitativeevaluationofthepotentialmaps.
Theircrosssection,however,revealsastarkcontrast.
PeakForceKPFMgivesadifferenceof240mVbetweenthetwoselecteddomains,consistentwiththeworkfunctiondifferencebetweenSn(4.
42eV)andPb(4.
25eV),whereasKPFM-AMgivesonlyadifferenceof97mV,whichislessthanhalfoftheexpectedtheoreticaldifference,andhalfofwhatisseenfromPeakForceKPFM.
Again,thishighlightsthebetteraccuracyofFM-detectionTable1.
ChartsummarizingthefourmajorcombinationsbetweentwomajorKPFMmodes,AM-KPFMandFM-KPFM,andtwomajorAFMmodes,TappingModeandPeakForceTapping.
Allmodesareimplementedinadual-passfashion(lift-mode),exceptKPFM-FM,whichisdoneinsingle-pass.
Figure9.
PeakForceKPFMandPeakForceKPFM-AMpotentialmapsandcrosssectionprofileofaSn-Pballoy(60:40byweight,atrightisthetopography(4mscan).
Figure8.
Height(top)andpotentialprofilesusingPeakForceKPFM-AM(middle)andPeakForceKPFM(bottom)ontheBrukerKPFMstandardsample,onthesamelocationandwiththesametip(PFQNE-AL).
5values,however,differbyabout100mV,whichisnotyetfullyaccountedfor.
MechanicalPropertyMapping:TheadhesionchannelfromPeakForceKPFMshowsadistinctcontrastbetweentheSnandPbdomainsandalsohasgoodcorrelationwithpotentialdata,renderingadditionalassuranceindomainidentification.
Ontheotherhand,littlecontrastisshownonthephasemapbyTappingMode.
Thesimultaneousquantitativenanomechanicalpropertymapping(PeakForceQNM)isanoutstandingcapabilitythatonlyPeakForceTappingcanoffer.
Thisisfurtherillustratedonapolymerfilmcomprisedofpolystyrene(PS)andlow-density-polyethylene(LDPE)castonasiliconsubstrate.
Inadditiontothepotentialmap,modulus,deformation,andadhesiondatawereobtained.
ArtifactsinTappingModeKPFM-FM:Figure11showsthatthetappingphaseimagefromKPFM-FMdoesnotdisplaymuchcontrastontheSn-Pballoysample.
WhilethiscanbeinterpretedasashortcomingofTappingModeinrevealingmechanicalproperties,asmallphasecontrastprovesmandatoryforfaithfulKPFMmeasurement.
FrequencymodulationKPFMusesphaseasameansoffrequencyshiftdetectionandanysharpphasechangefromtip-sampledirectcontactcanbeasourceoferrorleadingtoartifactsinthepotentialmap.
Inlightofthis,ifthereisasharpphasecontrast,caremustbetakentoensurethatthepotentialmapisleastaffected.
Onemeasureistouselighttapping(adefaultsettinginBruker'simplementation),thatis,toKPFMoverAM-detectionKPFM.
Thelateralresolutionisthusdefinedasthesmallestdimensiononwhichacertainaccuracy(90%)canbeachieved,thedistinctionherebeingbetweenwhetheryoucanresolvethedifferenceandwhetheryoucanresolvethedifferenceaccurately.
Figure10isaheightandPeakForceKPFMpotentialmapofsingle-walledcarbonnanotubes(SWCNTs)laidonaSisubstrate.
The30nmpartsuggestsaCNTbundle,withasinglestrandCNT(~2nmindiameter)stickingoutatthetop,whichcanbeseenonthepotentialmap.
Notea30mVdifferencefromthesubstrateisobtainedonthesinglestrandCNT,whichisonlyathirdofthatreadontheCNTbundle(105mV).
PeakForceKPFMcanindeedresolvenanometerfeatures,butisnolongeraccurate.
Thesmallerdimensioncontributesonlyanon-dominantportiontothetotalelectricforcegradient,withtherestcomingfromthesubstrate,endingupwithamuchsmallercontrastduetosignalconvolution.
NoteanevensmallervaluewouldbereadwhenusingPeakForceKPFM-AM,asthecontributionfromthetip-apexdiminishes.
ThisexemplifiesthatPeakForceKPFMhasnanometerresolvingpower,butisonlyaccurateonfeatures10nmorlarger.
PeakForceKPFMandKPFM-FMPeakForceKPFMisacombinationofPeakForceTappingmodeAFMwithFM-KPFM,whereasKPFM-FMisacombinationofTappingModeAFMwithFM-KPFM.
Inprinciple,theirmajordifferenceliessolelyontheAFMside.
WherePeakForceTappingaffordseaseofuse,simultaneousquantitativeanddistinctivemechanicalproperties,TappingModeprovidesphasecontrastandresultingindataambiguity.
LittledifferenceisexpectedinKPFMperformance,andthisislargelytrue,withsomeexceptions.
Figure11showsthepotentialmapsonSn-PbacquiredwithPeakForceKPFMandKPFM-FMonthesamespotwiththesameprobe(PFQNE-AU,prototype).
ThecontrastsbetweenSn(lighter)andPb(darker)domainsmeasuredusingthetwomodesareindeedalmostidentical,240mVand235mVrespectively.
TheirabsoluteFigure10.
Height(left)andPeakForceKPFMpotential(right)mapofsingle-walledcarbonnanotubes(SWCNTs)laidonaSisubstrate.
AsinglestrandCNT(pointedtobytheupperarrow)sticksoutofaCNTbundle(pointedtobythelowerarrow),whichcanberesolvedinpotentialmap,butnolongerwithaccuracyasthedimensionistoosmalltogivedominantcontributioninFM-KPFM.
Figure11.
PeakForceKPFMandKPFM-FMPotentialMapsandcrosssectionprofiles(top)oftheSn-Pb(60:40byweight),andatbottomaretherespectiveadhesionandphaseimaging(4mscan).
6usethemaximumpossibletappingamplitudesetpoint.
Ourexperiencesuggestslighttappingisbeneficialinmostcases.
Itmaynot,however,besufficienttoeliminatepossibleartifactsforcertainsampleswhenrunningsingle-pass-basedKPFM-FM.
Phasecontrastsometimescanbesostrongthatsingle-passKPFM-FMsimplycannotremovephasecross-talk(e.
g.
,onpolymerswithstrongdipoles).
Inthiscase,onehastoturntodual-passbasedtechniques,wheresufficientlift-heightcanbeusedforthetiptoclearthesamplesurfacetoeliminatephaseshiftduetodirecttip-samplecontact.
PeakForceKPFMprovesadvantageousonthisregard,andcanalsobeusedtoidentifypossibleartifacts.
Byincrementallychangingtheliftheight,ifpotentialcontrastshowsanabruptchangeinresponsetoasmallchangeinliftheight,onecandeterminebeyonddoubtthatthepotentialcontrastobtainedbelowacertainlift-heightcontainsartifacts.
Thisisexemplifiedintheimagingofabrushpolymersampleonmicawhere,whentheliftheightischangedfrom25nmto27nm(arelativelysmallchangecomparedtothepolymerchainwidthof5nm),insteadofapossibleblurringofthepotentialcontrastonthechainsasthetipgoesup,thechainstructuredisappearedaltogether(seeFigure13).
Thechainpatternseenatsmallerliftheightscanthereforebeattributedtoartifacts.
PeakForceKPFMprovidesameanstoidentifyandeliminatepossibleartifactsfromtip-sampledirectcontact.
Figure12.
PeakForceKPFMdataincludingheight,potentialandquantitativemechanicalpropertymapssuchasYoung'smodulus,deformationandadhesiononapolymerblendconsistingofpolystyrene(PS)andlow-density-polyethylene(LDPE)(10mscan).
Figure13.
SequentialPeakForceKPFMmapsofabrushpolymersampleonmicasubstrateversusliftheight.
Anabruptchangeinpotentialcontrastisobservedwhenliftheightincreasesfrom25nmto27nm,suggestingthatthepotentialcontrastofthepolymerchainsseenataliftheightof25nmorbelowareartifacts,causedbyphaseshiftfromdirecttip-samplecontact.
Scansizeis250nm.
Theinsetattheupper-leftcorneristheheightimage.
7quantifyingKPFM,whichinturnexpandsKPFM'sutilityinevermoredemandingapplications.
Table2listssomeofthemajorsourcesresponsibleformeasurementinconsistency.
Evenwithasoundelectronicdesignthathaslittleelectroniccross-talk,operatingparametersandprobevariationcancausedatafluctuation.
Theseinclude(1)whetheracdriveisrighton,andalwayson,theresonantfrequencyofthecantilever;(2)whethertip-sampleseparationiskeptthesamefromruntorun;(3)whethertheworkfunctionofthetip,whichisessentiallythereferencepoint,remainsunchanged;and(4)whetherthesampleisundergoingoxidation,adsorptionofmolecules,oralterationduetopossibleelectrochemicalreactions(ascurrentmayflowbetweenthetipandsample).
Toovercometheseuncertainties,aScanAsystKPFMoperationmodewasimplemented,whichresemblesScanAsystinthatitprovidesautomatedimagingoptimization,butdiffersinitstechnicalimplementation.
ItisworthnotingthatKPFM-FMdoeshavesomeperceivedadvantagewhenimagingfeaturessmallerthanafewnanometers,astheaveragetip-sampleseparationcanbemaintainedsmallerthancanbepracticallyachievedwithlift-mode-basedPeakForceKPFM.
This,however,doesnotoffsetthesubstantialadvantagesthatPeakForceKPFMoffers.
InterpretingKPFMPhase:InadditiontoKPFMpotentialdata,KPFMphasedataissimultaneouslyobtainedandcanproveuseful.
Itreflectsthedielectricconstantcontrastofthesample.
Referringtoequation2above,onefindsthesecondderivativeofcapacitance,whichhasdependenceondielectricconstantofthematerialbetweenthetipandtheconductiveportionofthesample,canbeobtainedfromthe2ωterm.
ItcanalsobeobtainedfromtheDCterm,especiallywhenVCD=VCPD,whichisthecasewhenKPFMisactivelyrunning.
Thisisequivalenttoelectrostaticforcemicroscopy(EFM)phaseimaging,withtheadvantagethatworkfunctionanddielectricinformationareseparated,whilethestandardEFMphaseimagingisamixofworkfunctionanddielectricinformationRepeatabilityWhilerepeatabilityofrelativecontrastwithinoneKPFMimagehasbeenreasonablygood,evenwiththesametypeofprobe,absolutevaluescanvaryhundredsofmVfromexperimenttoexperiment.
Improvingmeasurementconsistencyisacrucialsteptowardquantitativeworkfunctionmeasurement.
Withanewprobedesignandoptimizedinstrumentation,wehavefoundwaystoreduceprobe-to-probemeasurementscattertobelowastandarddeviationof50mV.
ThisrepresentsamajoradvanceforFigure14.
PeakForceKPFMdataobtainedusingninedifferentPFQNE-AL(Bruker)probesontheBrukerKPFMstandardsample.
ThevalueonAl(greytriangle),Au(goldtriangle)andtheirdifferences(bluediamond)areplotted.
Standarddeviationofeachislistedatright,whichisontheorderof5ximprovementovertraditionalKPFMmeasurements.
SourceofUncertaintyBrukerSolutionOperatingFrequencyTightparametercontrol(ScanAsyst-KPFM):ThermaltuneforresonancefrequencyFixedoscillationamplitudeOptimalphasesettingTip-SampleSeperationTipWorkFunctionChangeDuetoTipWearProbeDesign:SingletipmaterialProprietarywaytolimitDCcurrrentflowElectrochemicalReactionUnderBiasTable2.
PossiblesourcesforKPFMmeasurementinconsistency.
8InScanAsystKPFM,thealgorithmseekstheresonantfrequencyofthecantileverusingthermaltunetoensuretheaccuracyandconsistencyoftheoperatingfrequency.
Thecantileverisalwaysdriventoafree-airoscillationamplitudeof20nmwhenperformingeitherPeakForceKPFMorKPFM-FM,andthedrivephaseisalwaysaccuratelyandautomaticallyset.
AproprietaryprobedesigneliminatespossibleDCcurrentflowbetweenthetipandsample,andtheuncoatedsilicontipensuresnosignificantworkfunctionchangewilloccurfromtipwear(asoftenhappenswithmetalcoatedprobes).
TheseenhancedcapabilitieshavegreatlyimprovedKPFMrepeatability;Figure15showcasestherepeatabilityobtainedwithninedifferentPFQNE-ALprobesontheBrukerKPFMstandardsample.
Astandarddeviationoflessthan20mVhasbeenachievedinthepotentialsmeasuredonanAlstrip,anAustrip,andintheirpotentialdifference.
Whenthetipworkfunctionisproperlycalibrated,anaccurateworkfunctionofthesamplecanbededuced.
Inaddition,theScanAsystKPFMmodebringsease-of-usetotheoperation.
SensitivityFrequencymodulationKPFMwasfirstrealizedunderultrahighvacuum(UHV)in1998,8andwasnotintroducedintoambientAFMuntilabouttenyearslater.
InadditiontotheenvironmentchangethatcanaffectKPFMmeasurementfidelity,thereisalsoadramaticdifferenceindetectionsensitivity.
ThisisimmediatelynoticeablewhenyoucompareAM-KPFMandFM-KPFMdatainanambientsetting.
Thelatterisusuallymuchnoisier,anevidenceoflackofsensitivity.
ItisthereforehelpfultounderstandwhatgovernsFM-KPFMdetectionsensitivity.
Mathematicaldeductionisnotincludedinthisapplicationnote,butaspreviouslymentioned,theelectricforcegradientcanbeviewedasanadditiontothenaturalspringconstantofthecantilever.
Forasmallerspringconstant,thesameelectricforcegradientwouldmeanalargerrelativechange,causingalargerfrequencyshiftandthusastrongersignal.
TheQsimplymakesthephaseversusfrequencyplotsteeper,furtherenhancingthesignal:KPFMSensitivity∝kItisnoteworthythatunderUHV(i.
e.
,withoutairdamping)theQofstandardEFMprobecanbehundredsoftimeslargerthaninair,therebyaffordingamplesignalamplificationoftheFM-KPFMsignal.
Measurementsensitivityhasrarelybeenanissueandhighqualitydataisregularlyattained.
SensitivityisneitheranissueforAM-KPFMinambientconditions,asthesignalitself,convolutedfromthetipapex,tipconeandthecantilever,isoftenlargeenoughwithconventionalEFMprobes.
ThelowQinair,however,imposesapracticalchallengeforFM-KPFMdetection,wherethesignalisoftenweakasthemajorityofthesignalisonlyfromthetipapexandthelowerpartofthetipcone(thesamereasonFM-KPFMhasbetterspatialresolution).
AlargeQ/kratio,meaningsmallerspringconstantandlargerQ,isdemandedoftheprobe.
PeakForceKPFMopensuproomforimprovement,asopposedtoKPFM-FMbasedonTappingMode.
TappingModerequiresthecantilevertohaveasufficientlylargespringconstanttoovercomecapillaryforcesfromwaterlayersthatareoftenpresentonsamplesurfaces.
ItalsorequirestheQtobenotsolargeastolimitTappingModebandwidth.
PeakForceTappingremovestheselimitations,allowingtheuseofcantileverswithamuchsmallerspringconstantandlargerQ,enablingroomforprobeoptimization.
Currently,PFQNE-AUprobesaretwiceassensitiveasthecommonlyusedSCM-PITprobes.
ProbeswithhigherQ/kratiocanbedesignedtofurtherimprovePeakForceKPFMsensitivity.
PlatformsandAccessoriesAllKPFMmodesareavailableonBrukerDimensionIconandMultiMode8AFMs,andcanbeusedinconjunctionwithavarietyofaccessories.
EnvironmentalControl:Mostnotably,forsamplesthatrequirestringentenvironmentalcontrol(e.
g.
,lithiumbatteryanodeorcathodematerials,organicphotovoltaicorlightemittingdevices),aturn-key1ppm-levelofoxygenandwatercapableglovebox(customizedforbestperformance)canbeused.
Thegloveboxsolutionprovesbeneficialtomeasurementrepeatabilityofsamplessubjecttochangewhenexposedtoambientair,includingmostsemiconductormaterialsandmetals.
BacksideIllumination:ThePhotoconductiveAFMmodule,offeredontheDimensionIconsystem,iscompatiblewithindustry-standardNewportsolarsimulatorstoenableeven,backsidesampleilluminationacrossthescanarea.
ThisallowsKPFMpotentialmappingwhileilluminatingwithachievableintensitiesequivalentto300suns,enablingstudyofstaticanddynamicphotovoltaicresponsestoilluminationoforganicsolarcells/materials.
Figure16showsPeakForceKPFMdataonaMDMO(poly[2-methoxy-5-(3',7'-dimethyloctyloxyl)]-1,4-phenyleneFigure15.
Turnkeyglove-boxenablingallAFMfunctionstobeperformedina1ppmleveloxygenandwaterenvironment.
ShowninsideisaDimensionIconAFM,aversionofglove-boxfortheMultiMode8isalsoavailable.
9Therefore,theamplitudeatacbiasdrivingfrequencyωandthesecondharmonic2ωare:ACVzCφω=A2241ACVzC=AωWeobtaintheelectrostaticpotentialdifference:ωωφ241AAVac=and224ACVAzCω=dC/dzreflectsthedielectricconstantvariationsacrossthesample.
Implementation:KPFM-HVisimplementedinadual-passfashion.
Onthefirstpass,PeakForceTappingisusedtoobtaintopographyandmechanicalproperties.
Onthesecondpass(lift-mode),PeakForceTappingdriveisstopped,andanacbiaswithafrequencylowerthanhalfofthecantileverresonantfrequencyisappliedbetweenthetipandsample.
Theverticaldeflectionsignalissimultaneouslyfedtotwosynchronizedbutseparatelock-inamplifiers;onetodetecttheamplitudeandphaseatthedrivefrequency,andtheothertheamplitudeatthesecondharmonic.
CalculationiscarriedoutinthebackgroundtoobtainelectrostaticpotentialdifferenceΔφ,anddC/dz.
Thistechniqueallowsonetomeasurevoltageintherangeof±200Vwithanerrorlessthan15%.
Highervoltage(upto±1000V)canbemeasuredwithaccuracyonlylimitedbynonlinearityofphotodetectorsintheAFM.
ThistechniqueisavailableonMultiMode8AFMs(noadditionalhardwarerequired)andDimensionIconAFMs(aPeakForceHVmoduleisrequiredtominimizemeasurementdistortionfromelectronicinterference).
vinylene)-PCBM([6,6]-phenylC61-butyricacidmethylester)bulkheterojunctionsolarcell.
Workfunctiondown-shifts535mVunderilluminationsimulating300sunsintensity.
KPFM-HVModeKPFM-HVstandsforHigh-VoltageKPFMmode,whichmeasureselectrostaticpotentialbeyond±10V.
KPFM-HVisadual-passtechnique,withPeakForceTappingasthebaseAFMmode.
Questionarisesaswhyonewouldneedtomeasurehighvoltage.
KPFM,aswehavelearned,measurestheworkfunctiondifferencebetweenthesampleandtip.
Whenwelookthroughtheworkfunctiontableoftheelements,9thehighestworkfunctionis5.
93eV(Osmium)andlowest2.
14eV(Cesium),sothemaximumpossibleworkfunctiondifferencewillneverexceed3.
79V.
AlltheKPFMtechniquesdescribedabovecovertherangeupto±10V,andthereforesufficeforanyworkfunctionmeasurementtask.
Demandariseswhenitcomestomeasuringtrapped(immobilized)chargesininsulators.
Forinstance,whenonewalksonacarpetonadryday,staticchargecanaccumulateuptotens,hundreds,oreventhousandsofvolts.
TheKPFM-HVmodemeetstheneedformeasuringhighvoltageelectrostaticpotentials.
ThistechniqueisnolongerusingaKPFMfeedbackloop,norahighvoltagesourceasonemaylogicallythink.
Itdeviatesfromtheforceorforce-gradient-nullingconceptcentraltotheaforementionedKPFMtechniques.
ItisdonewithexistinghardwarecommontoanAFM,andthroughcalculation.
Weadopttheconceptthatthesampleandtipformacapacitor.
Wefurtherassumetheelectricforcefollowsthesameexpression:Term22TermTermDC22)2cos(41)sin()21(ωωωωφφtVzCtVzCVzCFACACACel+++=whereistheelectrostaticpotentialdifferenceatthetipinreferencetothesample.
Figure16.
PeakForceKPFMPotentialmap(thirdfromleft)ofMDMO-PCBMbulkheterojunctionsolarcellonanITOsubstrateindark(bottomhalf)andunderilluminationwithanintensityequivalentto300suns(tophalf).
A535mVdownshiftofworkfunctionisseenunderillumination,a3Drenderingandhistogramofpotentialdataisattheright.
SamplecourtesyofDr.
PhilippeLeclere,UniversityofMons.
10Examples:Somepolymerscanbechargedthroughcontactelectrification.
Simplycontactingandthenseparatingtwosimilarordissimilarpolymerpieces,orcontactingittoandthenseparatingitfromaconductingsurface,induceschargeonsurfacesbeingcontacted.
Figure19showsthepotentialmap(left),phase(middle),anda3DrenderingofthepotentialmapofaPDMS(polydimethylsiloxane)film.
ThesampleispreparedbycastingaPDMSfilmabout0.
5mminthicknessonasiliconwafer.
Apieceispeeledoffthesiliconsubstrateandthenitsundersideisimaged.
Thepotentialmapshowstheelectrostaticpotential,reflectingelectrostaticchargedensity(absolutevalue),andsign,whichislearnedfromthephasedata.
The3Drenderingshowsaminimumof-99Vatthecenterofanegativelychargedarea,withpositivechargeshavinganelectrostaticpotentialashighas156V.
PDMSsamplescanbeeasilyobtained,infact,aPDMSgel-padisoftenfoundinAFMprobepackaging.
Simplycutoffapieceofgel-padfromthebottomofanAFMprobebox,andusethecontactelectrificationtechniquetohaveitcharged.
Chargecanalsobeintroducedthroughtriboelectriccharging(onetypeofcontactelectrification,throughrubbing),forinstance,byrepeatedlyscanningthesameareaforsomeextendedperiodoftime.
Figure19Figure17.
KPFM-HVdiagram,inthefirstpass,surfacetopographyandmechanicalpropertiesareobtainedinPeakForceTapping;inthesecondpass,anacbiasatafrequencylowerthanhalfofthecantileverresonantfrequencyisappliedbetweentheprobeandthesample,whichcausestheprobetooscillateatfrequencyωanditssecondharmonic2ω.
Theelectricpotentialbetweenthetipandsampleiscalculatedbasedontheoscillationamplitudeatfrequencyωand2ω.
NotethatnoKPFMfeedbackisinvolved.
Figure18.
KPFM-HVimagesofPDMS(polydimethylsiloxane)filmsafterbeingchargedbypeelingofffromthesiliconsubstrateuponwhichitwascast.
TheHVPotentialdata(left)showstheelectrostaticpotentialandthesignofcharge;HVPhasedata(middle)denotesnegativechargewithnegativephase,andpositivechargewithpositivephase.
Attherightisa3Drenderingofthepotentialmap,thenegativechargegivesrisetoanelectrostaticpotentialof-99Vatitscenter,andsomeoftheadjacentpositivechargesgoashighas158V.
Figure19.
KPFM-HVpotentialmaponPDMS,encasingfivepreviouslyscannedsitesinasquare-centerarrangement.
Sequentialimagesfromlefttorightrevealthatthenegativechargesareaccumulating,spreadingoutandmergingwitheachotherasscanninggoeson.
11ConclusionBrukeroffersasuiteofnewKPFMmodes,threeofwhicharebasedonthebreakthroughPeakForceTappingtechnologywithadual-passimplementation:PeakForceKPFM,usingFrequencyModulationdetection;PeakForceKPFM-AM,usingAmplitudeModulationdetection;PeakForceKPFM-HV,usingAmplitudeModulationandextendingtheaccessiblepotentialrangebymorethanafactoroften.
PeakForceKPFM,achievedbycombiningPeakForceTappingwithfrequency-modulationKPFMexhibitsthemostoutstandingperformance:ItretainsthehighspatialresolutionandaccuracyofFM-KPFM(probemodelingrevealsthatFM-KPFMoffersaresolutiondownto10nmwithoutcompromisingmeasurementaccuracy,instarkcontrasttothemicrometer-scaleresolutionofferedbyAM-KPFM).
ItachieveshighrepeatabilitythroughtightparametercontrolusingtheScanAsystKPFMoperationalgorithmandnovelprobedesign.
ItleveragesPeakForceQNMtoproducesimultaneousmechanicalandelectricalinformation,enhancingitsmaterialidentificationpower.
ItpromisesfurtherenhancementtoFM-KPFMsensitivity(PeakForceTappingliftstherestrictionsonprobeselectionimposedbyTappingMode,andcantileverswithlowerspringconstantandhigherQcanbeemployedforimprovedsensitivity).
Ultimately,PeakForceKPFMhasbroughtusamajorstepforwardtowardhigh-resolution,quantitativeworkfunctionmeasurements.
Itispoisedtomeetthechallengesinapplicationareasthatdemandeverhigherspatialresolutionandbetteraccuracyandrepeatability.
Withprovenapplicationsonmetal,semiconductor,organicmaterials,thesuperiorcapabilitiesofPeakForceKPFMalsopromisebenefitsforbio-materials,andotheradvancedapplicationareas.
(left)showsfivepreviouslyscannedsiteswithnegativecharges.
Sequentialimagingindicatesthenegativelychargedareasspreadingoutandmergingwitheachotherasscanningcontinues.
KPFM-HVmodeprovidesasimplemeanstomeasureelectrostaticpotentialofimmobilizedchargesashighas±200V.
ProbeSelectionGuideTable3isaprobeselectionguideforeachmode,asofthedatethisnoteispublished.
Forup-to-dateinformation,pleasefollowtheguidanceprovidedintheNanoScopesoftware.
Otherprobesnotinthelistmayalsowork,buttheirperformanceinrelationtoKPFMmeasurementsensitivity,accuracy,and/orrepeatabilitymaynotbeguaranteed.
ProbeChoicesKPFMModesPeakForceKPFMPeakForceKPFM-AMKPFM-FMKPFM-AMKPFM-HV1stPFQNE-ALPFQNE-ALPFQNE-ALPFQNE-ALTAP150A2ndSCM-PITScanAsyst-AirHRSCM-PITSCM-PITSCM-PIT3rdNoneSCM-PITNoneNoneMESP-RCTable3.
ProbeSelectionGuideforEachKPFMMode.
12AppendixI:MathematicsaboutFrequencyModulationThemodulationoftheresonantfrequency,correspondingtotheelectricforcegradientmodulationatthedrivingfrequencyoftheacbiasistherefore:)sin()sin()(2~22tFtVVVzCkmmdefinetionmACCPDDCωωωω→≈Whereω~isthemodulatedfrequencycomponent,Fmdenotesthefrequencymodulationamplitude.
Forthecantilevermechanicallydriventooscillateatitsresonantfrequency,appliedwithanacbiaswithfrequencyωm,thecantilevermotioncanbewritten:Thisequationstatesthat,inadditiontotheoscillationattheresonantfrequency,apairofsidebandswillappearatω±ωm.
Thisisveryusefulforunderstandingtheoscillationspectrum.
Figure4isthespectrumwhenanMESP-RCprobeismechanicallydrivenat133kHz,whileanacbiasof2kHzisapplied.
Theamplitudeofthesidebandreflectstheamplitudeofthefrequencymodulation.
Theratioofthesumoffirstside-peakpairversusthecenterpeakheightgivesthefrequencymodulationindexFm/ωm.
Forexample,0.
1wouldmeanthefrequencymodulationamplitudeis200Hz(0.
1x2kHz).
TheFM-KPFMfeedbackistoadjustDCbiassothefirstsidebandpairdisappears,atwhichpointVCPDisfound.
Inpracticalimplementation,sidebandamplitudeisrarelydirectlymeasuredatthesidebandfrequencyusingasinglelock-inamplifier.
Amorecommonmethodusestwocascadelock-inamplifiers,withthefirstonelockingattheresonancefrequency,thephaseoutputofwhichisfedtothesecondlock-in,whichlocksattheacbiasfrequency.
Thefollowingequationprovidesinsightinthisapproach:Thephaseis:ForFm/ωm<0.
5So,feedingthephaseoutputofthefirstlock-inamplifiertoasecondlock-inamplifierlockingatfrequencyωm,theamplitudeoutputofthesecondlock-inwillbeFm/ωm,exactlythefrequencymodulationindex(somescalingfactormayexist).
AppendixII:MathematicsonProbeModelingProbemodelingstartswiththecapacitormodelfortheprobeandsample,andapproximatestheprobeasconsistingofamicro-cantileverandatipconewithapointend(seeFigure7).
Asagoodconductor,thepotentialisthesameallovertheprobe,andchargesareonlypresentonthesurfaces.
Theintegratedcapacitancesofthecantileverandtipconecanbeanalyticallyexpressed.
Electricforceandelectricforcegradientcanbededucedfromthefirstandsecondderivativesofthecapacitance.
LeverContributiontoElectricForceandForceGradientForsimplicity,weassumethecantileverisparalleltothesample,ignoringthetiltofthecantilever.
Recognizingthattheelectricforceattheendofthelevercausesmoredeflectionthanthesameforceatthebaseofthecantilever,thecapacitanceisnormalizedinproportiontoitslengthfromthebase:where,WisthewidthandListhelengthofthecantilever,Histheheightofthetipcone,zisthedistancefromthetipendtothesample,andεisthedielectricconstant.
Theelectricforcefromtheleveristherefore:andtheelectricforcegradientis:32')(2zHWLVFLever+=ε13Tip-ConeContributiontoElectricForceandForceGradientThesurfaceofthetipconeistreatedasastackofrings.
Thetotalcapacitanceisthesumofthecapacitanceofeachring,whichisapproximatedbytheprojectedareaoftheringanditsverticaldistancefromthesamplesurface:Therefore,theelectricforcefromtheconeuptoheighthis:andtheelectricforcegradientfromtheconeuptoheighthis:References1.
C.
Li,S.
Minne,B.
Pittenger,A.
Mednick,M.
Guide,andT-Q.
Nguyen,"SimultaneousElectricalandMechanicalPropertyMappingattheNanoscalewithPeakForceTUNA,"BrukerapplicationnoteAN132Rev.
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Eng,"AccuracyandResolutionLimitsofKelvinProbeForceMicroscopy,"Phys.
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Erina,andCSu,"QuantitativeMechanicalPropertyMappingattheNanoscalewithPeakForceQNM,"BrukerapplicationnoteAN128,Rev.
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Zisman,"ANewMethodofMeasuringContactPotentialDifferencesinMetals",Rev.
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AuthorsChunzengLi,StephenMinne,YanHu,JiMa,JianliHe,HenryMittel,VinsonKelly,NataliaErina,SenliGuo,ThomasMueller(BrukerNanoSurfaces)14BrukerNanoSurfacesDivisonSantaBarbara,CA·USA+1.
805.
967.
1400/800.
873.
9750productinfo@bruker-nano.
com2013BrukerCorporation.
Allrightsreserved.
DimensionIcon,MultiMode,NanoScope,PeakForceKPFM,PeakForceQNM,PeakForceTapping,ScanAsyst,andTappingModearetrademarksofBrukerCorporation.
Allothertrademarksarethepropertyoftheirrespectivecompanies.
AN140,Rev.
A1www.
bruker.
com
KPFM,togetherwithconductiveAFM,havebeenrecognizedasthetwomostusednanoscaleelectricalcharacterizationtools,complementingeachother.
1However,limitedspatialresolutionandlackofmeasurementrepeatabilityandaccuracyhaslimiteditsusefulnessinsomecriticalareas,suchasintheidentificationofdonorandacceptordomainsinbulkheterojunctionorganicsolarcells,materialdifferentiationincompositematerials,andtrappedchargesoninsulators.
ThetwomajorKPFMdetectiontechniquesareamplitudemodulationKPFM(AM-KPFM)andfrequencymodulationKPFM(FM-KPFM).
2,3Thisapplicationnotepresentsanintuitive,geometricallyrealisticprobemodeltoillustratetheirdrasticdifferencesinspatialresolutionandaccuracy.
ThismodelinghasledBrukerresearcherstocombineFM-KPFMwithaninnovativenewAFMmode,PeakForceTapping,whichoffersease-of-operationandsimultaneousquantitativenanomechnicalpropertymappingcapability(viaPeakForceQNM).
4Togetherwithanovelprobedesignandauto-optimizationsoftware,thisnewapproachhasenabledadrasticincreaseinKPFMperformance.
BackgroundUsingagold-leafelectroscopein1898,SirWilliamThomson,laterknownasLordKelvin,observedthatplatesofcopperandzincmountedoninsulatingshaftscreatedchargewhentheywerebroughtintoelectricalcontactandthenmovedapart.
Hisdiscoverycannowbeexplainedintermsofworkfunctiondifferences.
Theworkfunctionistheminimumenergy(orwork,usuallymeasuredineV),neededtoremoveanelectronfromasolid,toapointimmediatelyoutsidethesolidsurface(orenergyneededtomoveanelectronfromtheFermilevelintovacuum).
ApplicationNote#140PeakForceKelvinProbeForceMicroscopyFigure1.
EnergyandchargediagramillustratingKelvinprobetechniqueprinciple.
PeakForceTappingModeHigh-ResolutionSimultaneousAdhesion&PotentialMapsFrequency-ModulationTheaboveequationstatesthattheappliedacbiasatfrequencyωiscausingtheelectricforcetomodulateatbothωand2ω,whichcanbemeasureddirectlyusingcantileverdeflection.
Figure2showstheformsprescribedbytheaboveequation.
Mostrelevantisthefactthatoscillationamplitudeatω(shownasamplitude1)dropsto0whenVCD=VCPD,theveryideaof"nulling"electricforcetofindsurfacepotentialinamplitudemodulationKPFM.
Theelectricforcegradientisassociatedwithelectricforce,Therefore,)2cos(41)sin()()21)((Term2222Term22TermDC2222'ωωωωtVzCtVVVzCVVVzCFACACCPDDCACCPDDCel+++=Similarly,VCD=VCPDwhenthemodulationamplitudeoftheelectricforcegradientatωdropsto0,thebasisfor"nulling"theelectricforcegradienttofindthesurfacepotentialinfrequencymodulationKPFM.
AM-KPFMthroughElectricForceDetectionThemodulatedelectricforce,bytheapplicationofanacbiasbetweenthetipandsample,canbeconvenientlymeasuredusingtheoscillationofthecantilever.
TheacbiasfrequencyistypicallyselectedtobetheresonantfrequencyoftheAFMcantileverforenhancedsensitivityaffordedbycantilever'squalityfactorQ.
TheKPFMfeedback,usingtheoscillationamplitudeasinput,adjustsaDCbiasuntiltheoscillationamplitudedropsto0,whenVDCequalsCPD.
Whentwodifferentconductorsarebroughtintoelectricalcontact,forexampleviaanexternalwirecontact,electronswillflowfromtheonewithlowerworkfunctiontotheonewithhigherworkfunction,equalizingtheFermienergies.
Iftheyaremadeintoaparallelplatecapacitor,equalandoppositechargeswillbeinducedonthesurfaces.
Thepotentialestablishedbetweenthesetwosurfacesiscalledthecontactpotentialdifference(CPD),contactpotential,orsurfacepotential,whichequalstheworkfunctiondifferenceofthetwomaterials.
MeasuringtheCPDisthusquitesimple.
Anexternalpotential(alsocalledthebackingpotential)isappliedtothecapacitoruntilthesurfacechargesdisappear.
Atthispoint,theexternalpotentialequalstheCPD.
ThevariousKelvinprobetechniquesdevelopedthusfardiffermainlyonlyonhowthischarge-freestateisdetected.
In1932,WilliamZismanofHarvardUniversityintroducedthevibratingelectrodetechniqueandthe"nulling"concept.
5Verticallyvibratingthetipoverasamplecausesthecapacitancetovaryasthedistancechanges.
Thisinduceschargetoflow,givingrisetoanACcurrent.
Thebackingpotential,atwhichACcurrentisataminimumorideally0,"nulled,"isfoundtoequaltheCPD.
Thistechniqueleadstodevelopmentofsystemsthatautomaticallytrackshiftsincontactpotentialduetochangesintheworkfunctionofthesample.
J.
M.
R.
WeaverandcoworkerswerethefirsttocombineKelvinmethodwithAFM.
6Theyembracedthenullingconceptinfindingthecharge-freepoint,andcapitalizedonAFM'suniquecapabilitytodetectsmallforcesandforcegradients.
Thecentralideaisthattheelectricforceandelectricforcegradientbetweenthetwoplatesofacapacitorwillbecome"0,"whenchargedisappears.
Itisfitting,forthisreason,tocallthetechniqueKelvinprobeforcemicroscopy(KPFM),asNonnenmacherdidin1991.
7KPFMopenedthedoortomeasuringCPD,thereforeworkfunction,inthenanometerregime.
AM-KPFMandFM-KPFMarebasedonelectricforceandelectricforcegradientdetectionrespectively.
ElectricForceandElectricForceGradientAconductiveprobeandaconductivesampleformacapacitor.
Theelectrostaticforcebetweenis:2)(21VzCFel=whereFelistheelectricforce,andVisthepotentialdifferencebetweentheprobeandthesample.
VisthesumoftheintrinsicCPD,anexternallyappliedDCvoltageVDCandacvoltageVAC:)sin(tVVVVACCPDDCω+=Combiningtheabovetwoequations,wearriveat:)2cos(41)sin()()21)((Term22TermTermDC22ωωωωtVzCtVVVzCVVVzCFACACCPDDCACCPDDCel+++=Figure2.
DCdeflection(top),amplitudesatfrequencyω(center)and2ω(bottom)whentheDCtipbiasissweptwhileanacbiaswithfrequencyωissuperimposed,correspondingtotheDCterm,ωtermandthe2ωtermdescribedinequation1.
2FM-KPFMthroughElectricForceGradientDetectionThedetectionofelectricforcegradientislessstraightforward.
Theforcegradientchangestheeffectivespringconstantofthecantilever.
Whenplacingaconductivecantileverinanelectricfield,itseffectivespringconstantisthesumofitsnaturalspringconstantkandtheelectricforcegradient,thesameeffectofconnectingtwospringsinparallel.
Weknowtheresonantfrequencyofacantileverdependsonthespringconstant:Thereforetheelectricforcegradientwillcausetheresonantfrequencytochange:Whentheelectricforcegradientismodulated,ascausedbyanacbias,theresonantfrequencyofthecantileverwillbemodulated.
Asimpliedintheequation,resonantfrequencywillbemodulatedatboththeacbiasfrequencyωanditssecondharmonic2ω.
Ifoneismechanicallyshakingthecantileveratitsresonantfrequencyω,andsimultaneouslyapplyinganacbiasatfrequencyωm,usuallyonlyafewkHz,themodulationoftheresonantfrequencygivesrisetotwopairsofsidebandsatω±ωm,andω±2ωm(seeFigure4).
Theamplitudeofthesidebandmeasurestheresonantfrequencymodulationamplitude;usingtheamplitudeofthesidebandatω±ωmforKPFMfeedback,andadjustingtheDCbiasuntiltheydisappearleadstothepointofVCD=VCPD.
Inpracticalimplementations,sidebandamplitudeisrarelydirectlymeasuredatthesidebandfrequencyusingasinglelock-inamplifier.
Amorecommonmethodusestwocascadedlock-inamplifiers,withthefirstonelockingattheresonantfrequency,thephaseoutputofwhichisfedintothesecondlock-in,whichlocksattheacbiasfrequency.
Theamplitudeoutputofthesecondmeasurestheamplitudesumofω±ωm,whichisthenusedforKPFMfeedback(seeFigure5).
ProbeModeling—SpatialResolutionandAccuracyofAM-KPFMandFM-KPFMProbemodelingilluminatedourunderstandingofthespatialresolutionandaccuracyprovidedbythetwoKPFMmodes.
WeutilizedarealisticyetstraightforwardapproachtomodelingtheprobeinanattempttounderstandhowmuchFigure3.
AM-KPFMdiagram.
Anacbiaswithafrequencyω,typicallytheresonantfrequencyofthecantilever,isappliedbetweentheprobeandthesample,givingrisetoanalternatingelectricforcebetweentheprobeandsamplethatcausestheprobetooscillate.
Figure5.
FM-KPFMdiagram.
AnacvoltageisappliedtothetappingpiezotooscillatetheAFMcantileveratitsresonantfrequencyω.
Anacbiasatfrequencyωm,usuallyafewkHz,isappliedbetweentheprobeandthesample,modulatingtheresonantfrequency.
Twocascadedlock-inamplifiersareusedtodetectthesumamplitudeofsidebandpairω±ωm.
Figure4.
Amplitudevs.
frequencyplotoftheverticaldeflectionsignalrecordedwithhigh-speeddatacapturewhenaMESP-RCprobeisshaken,nearasamplesurface,bythetappingpiezoatitsresonantfrequencywhileanacbiasof2kHzisapplied,illustratingtheemergenceofsidebandsduetoacbias-inducedfrequencymodulation.
3decaystoaround200nm,whichdemonstratesthesharpdependenceofspatialresolutiononprobe-sampledistance.
Whiletheabovemodelingisonlyafirstorderapproximation,itisusefulforconceptualunderstandinganditdoesreachthesameconclusionasColchero,whousedadifferentsetofassumptions.
2Ithasbeenrecognizedthattheelectricforcefromthetipconeandcantileverpredominateoverthatfromthesmalltip-apex,therefore,AM-KPFMisnotatallaquantitativenanoscalemeasuringtool.
OnlyFM-KPFM,wheredominatingelectricforcegradientsignalcomesfromthetipapex,offershighspatialresolutionandaccuratelocalCPDinformation.
Theeffectoftipgeometryonspatialresolutionisonlysecondary.
ModesOverviewandComparisonKPFM,asacombinationoftheKelvinprobetechniqueandAFM,makessurfacepotentialmeasurementsaccessibleonthenanometerscale.
KPFMtraditionallyoperatesinconjunctionwithTappingMode,however,therearemanyreasonstocombineitwiththetriedandprovenPeakForceTappingmode(seeBrukerapplicationnoteAN135).
ThefourpossiblecombinationsarechartedinTable1(thenamingofeachcombinationwillbeusedthroughthisapplicationnote).
Someofthesecombinationsmaybedoneeitherinasingle-passfashion,whereAFMimagingandKPFMmeasurementrunsimultaneouslyononescanline;orinadual-pass(orlift-mode)fashion,whereAFMimagingmodeisrunonthefirstpassandKPFMonthesecondpassusinglift-mode.
PeakForceKPFM,thecombinationofPeakForceTappingmodeandFM-KPFM,integratesthebenefitsofthetipneedstobeincludedtoaccountfor(1)halfofthetotalelectricforceinAM-KPFM,or(2)halfofthetotalelectricforcegradientinFM-KPFM.
Wesetoutwiththecapacitormodelofprobeandsample,andapproximatedtheprobeasconsistingofamicro-cantileverandatipconewithapointend(seeFigure6).
Asagoodconductor,thepotentialisthesameallovertheprobe,andchargesareonlypresentonthesurfaces.
Theintegratedcapacitanceofthecantileverandtipconecanbeanalyticallyexpressed.
Electricforceandelectricforcegradientarededucedfromthefirstandsecondderivativesofcapacitance.
(SeeAppendixIforthemathematicdeductions.
)Figure7showsthesimulationresultofthewidelyusedSCM-PITprobe,whichhasthefollowingnominalgeometry:cantilever225mlong,30mwide,tip10mtall,andconehalfangleof22.
5°.
Therelativecontributionofthetipcone,integratedtoheighth,versustotalinteraction,isplottedagainsttipheight.
ToquantifythespatialresolutionofKPFM,weadoptedthesimilardefinitionusedbyCohchero,2theradiusoftheringattheheightuptowhichtheintegralcontributionofthetipconeaccountshalfthetotalelectricforceincaseAM-KPFM;orhalfthetotalelectricforcegradientforFM-KPFM.
ForAM-KPFM,whenliftheightis5nm,thecontributionofthewholetipconeremainsbelow50%,indicatingitsspatialresolutionisdominatedbythewidthofthecantilever-onthemicrometerscale,alsoimplyingtheCPDobtainedisnotlocal,butaconvolutionoverthelargeareacoveredbythecantilever.
Thiscallsitsaccuracyintoquestion,exceptonlargeuniformsamples.
Ontheotherhand,forFM-KPFM,whenthetipislifted5nmabovethesurface,halfofthesignalisgatheredfromupto15nmabovethetipend,correspondingtoadiameterof12nm.
Thissuggestsapossibleresolutionof10nmmaybeachievedwithFM-KPFM.
TheCPDinformationcollectedislocaltothearearightunderneaththetipaffordingcredibleaccuracy.
Liftingthetiphigher,forinstance,50nmabovethesurface,thespatialresolutionFigure6.
ModelofaKPFMProbewitharectangularcantilever.
Thecapacitanceofthecantileverisanintegrationofcapacitanceofeachtinyrectanglealongthecantilever.
Asthesameforcewouldcausedifferentdeflectiondependingonitsdistancetothebaseofthelever,thecapacitanceisnormalizedtorecognizethis.
Figure7.
Thecontributionofthetipconeintegrateduptoheighthovertotalelectricforce(blue)andelectricforcegradient(purple)areplottedversusheightfromtipendforaSCM-PITprobe.
Geometriesare:cantilever225mlong,30mwide,tip10mtall,andconehalfangleof22.
5°.
The"BLUE"plotsareelectricforceattip-sampleseparation5nmand50nm.
The"purple"plotsareelectricforcegradientattip-sampleseparation5nmand50nm.
4andcapabilitiesofPeakForceTapping(easeofuseandsimultaneousPeakForceQNMcapability)andthesuperiorspatialresolutionandaccuracyofFM-KPFM.
Itisbestdoneinadual-passfashion.
ItispossibletoimplementPeakForceKPFMinasingle-passfashionbutnotwithoutsacrificingperformance,asinterferencefromPeakForceTappingcansometimesbesevere.
KPFM-FMisdoneinasingle-passfashion.
Thoughitcanalsobedoneinadual-passfashion,thereisnobenefitthatisnotcoveredbyPeakForceKPFM.
Itishelpfultoclearsomeconfusionintheliterature,wheresingle-passKPFMissometimesimproperlyusedtoreferexclusivelytoKPFM-FM,albeitKPFM-AMcanalsobedoneinasingle-passfashion.
PeakForceKPFMandPeakForceKPFM-AMBrukeroffersastandardKPFMsample,whichispatternedwithAu,Si,andAlstrips.
BoththeAlandAufilmsare50nminthicknessdepositedonann-dopedsiliconsubstrate.
Intheory,whenthetipisonanyoneofthethreedifferentregions,aconstantpotentialvalue(CPD)shouldberead.
Astaircasepotentialprofileisthereforeexpectedacrossthethreedifferentmaterials.
Thereisanoticeableslope,however,presentoneachofthestairsofthepotentialprofileacquiredwithPeakForceKPFM-AM.
Thiscanbereadilyexplainedbytheprobemodelingdescribedabove.
Thepotentialdataisaconvolutionfromthetip,thetipcone,andthecantilever.
Althoughthetipisononesinglematerial,therelativelygiganticcantilevercoversothermaterialsandthuscontributesalargeportionofthetotalvalue.
Forinstance,whenthetipisonthetheAl/Siinterface,onlyhalfofthecantileverisoverAl,andwiththemajorityoftheotherhalfoverSi(andsmallerportionextendingovertheAu).
Thefinalmeasuredvalueendsupaweightedaverageoftheworkfunctionofthethreematerials.
Asthetipmovesawayfromtheedge,morecontributioncomesfromtheAl,andlessfromSiandAu,givingrisetotheslope.
Thisistrueofalloftheinterfaces,andnotonlyspeaksofthepoorlateralresolutionofAM-KPFM,butalsoitsinaccuracyasaresultofconvolution.
Incontrast,thestairsonthepotentialprofileacquiredusingPeakForceKPFMarelargelylevel,amanifestationthatthedominantcontributionisfromthetipapex.
Thus,thecantilevercontributionbecomesnegligible.
ThedataconfirmsthatFM-KPFMoffersmuchhigherlateralresolution,duetotheminimalcontributionfromthecantilever,andmuchbetteraccuracythanAM-KPFM.
DataonaSn-Pballoyfurtherillustratesthispoint.
Thetopographyrevealsdifferentdomainsinthealloy(seeFigure9,right).
TheyareclearlyresolvedonbothpotentialmapsacquiredwithPeakForceKPFM-AM(seeFigure9,left)andPeakForceKPFM(seeFigure9,middle)withlittledifferenceperceivablebyqualitativeevaluationofthepotentialmaps.
Theircrosssection,however,revealsastarkcontrast.
PeakForceKPFMgivesadifferenceof240mVbetweenthetwoselecteddomains,consistentwiththeworkfunctiondifferencebetweenSn(4.
42eV)andPb(4.
25eV),whereasKPFM-AMgivesonlyadifferenceof97mV,whichislessthanhalfoftheexpectedtheoreticaldifference,andhalfofwhatisseenfromPeakForceKPFM.
Again,thishighlightsthebetteraccuracyofFM-detectionTable1.
ChartsummarizingthefourmajorcombinationsbetweentwomajorKPFMmodes,AM-KPFMandFM-KPFM,andtwomajorAFMmodes,TappingModeandPeakForceTapping.
Allmodesareimplementedinadual-passfashion(lift-mode),exceptKPFM-FM,whichisdoneinsingle-pass.
Figure9.
PeakForceKPFMandPeakForceKPFM-AMpotentialmapsandcrosssectionprofileofaSn-Pballoy(60:40byweight,atrightisthetopography(4mscan).
Figure8.
Height(top)andpotentialprofilesusingPeakForceKPFM-AM(middle)andPeakForceKPFM(bottom)ontheBrukerKPFMstandardsample,onthesamelocationandwiththesametip(PFQNE-AL).
5values,however,differbyabout100mV,whichisnotyetfullyaccountedfor.
MechanicalPropertyMapping:TheadhesionchannelfromPeakForceKPFMshowsadistinctcontrastbetweentheSnandPbdomainsandalsohasgoodcorrelationwithpotentialdata,renderingadditionalassuranceindomainidentification.
Ontheotherhand,littlecontrastisshownonthephasemapbyTappingMode.
Thesimultaneousquantitativenanomechanicalpropertymapping(PeakForceQNM)isanoutstandingcapabilitythatonlyPeakForceTappingcanoffer.
Thisisfurtherillustratedonapolymerfilmcomprisedofpolystyrene(PS)andlow-density-polyethylene(LDPE)castonasiliconsubstrate.
Inadditiontothepotentialmap,modulus,deformation,andadhesiondatawereobtained.
ArtifactsinTappingModeKPFM-FM:Figure11showsthatthetappingphaseimagefromKPFM-FMdoesnotdisplaymuchcontrastontheSn-Pballoysample.
WhilethiscanbeinterpretedasashortcomingofTappingModeinrevealingmechanicalproperties,asmallphasecontrastprovesmandatoryforfaithfulKPFMmeasurement.
FrequencymodulationKPFMusesphaseasameansoffrequencyshiftdetectionandanysharpphasechangefromtip-sampledirectcontactcanbeasourceoferrorleadingtoartifactsinthepotentialmap.
Inlightofthis,ifthereisasharpphasecontrast,caremustbetakentoensurethatthepotentialmapisleastaffected.
Onemeasureistouselighttapping(adefaultsettinginBruker'simplementation),thatis,toKPFMoverAM-detectionKPFM.
Thelateralresolutionisthusdefinedasthesmallestdimensiononwhichacertainaccuracy(90%)canbeachieved,thedistinctionherebeingbetweenwhetheryoucanresolvethedifferenceandwhetheryoucanresolvethedifferenceaccurately.
Figure10isaheightandPeakForceKPFMpotentialmapofsingle-walledcarbonnanotubes(SWCNTs)laidonaSisubstrate.
The30nmpartsuggestsaCNTbundle,withasinglestrandCNT(~2nmindiameter)stickingoutatthetop,whichcanbeseenonthepotentialmap.
Notea30mVdifferencefromthesubstrateisobtainedonthesinglestrandCNT,whichisonlyathirdofthatreadontheCNTbundle(105mV).
PeakForceKPFMcanindeedresolvenanometerfeatures,butisnolongeraccurate.
Thesmallerdimensioncontributesonlyanon-dominantportiontothetotalelectricforcegradient,withtherestcomingfromthesubstrate,endingupwithamuchsmallercontrastduetosignalconvolution.
NoteanevensmallervaluewouldbereadwhenusingPeakForceKPFM-AM,asthecontributionfromthetip-apexdiminishes.
ThisexemplifiesthatPeakForceKPFMhasnanometerresolvingpower,butisonlyaccurateonfeatures10nmorlarger.
PeakForceKPFMandKPFM-FMPeakForceKPFMisacombinationofPeakForceTappingmodeAFMwithFM-KPFM,whereasKPFM-FMisacombinationofTappingModeAFMwithFM-KPFM.
Inprinciple,theirmajordifferenceliessolelyontheAFMside.
WherePeakForceTappingaffordseaseofuse,simultaneousquantitativeanddistinctivemechanicalproperties,TappingModeprovidesphasecontrastandresultingindataambiguity.
LittledifferenceisexpectedinKPFMperformance,andthisislargelytrue,withsomeexceptions.
Figure11showsthepotentialmapsonSn-PbacquiredwithPeakForceKPFMandKPFM-FMonthesamespotwiththesameprobe(PFQNE-AU,prototype).
ThecontrastsbetweenSn(lighter)andPb(darker)domainsmeasuredusingthetwomodesareindeedalmostidentical,240mVand235mVrespectively.
TheirabsoluteFigure10.
Height(left)andPeakForceKPFMpotential(right)mapofsingle-walledcarbonnanotubes(SWCNTs)laidonaSisubstrate.
AsinglestrandCNT(pointedtobytheupperarrow)sticksoutofaCNTbundle(pointedtobythelowerarrow),whichcanberesolvedinpotentialmap,butnolongerwithaccuracyasthedimensionistoosmalltogivedominantcontributioninFM-KPFM.
Figure11.
PeakForceKPFMandKPFM-FMPotentialMapsandcrosssectionprofiles(top)oftheSn-Pb(60:40byweight),andatbottomaretherespectiveadhesionandphaseimaging(4mscan).
6usethemaximumpossibletappingamplitudesetpoint.
Ourexperiencesuggestslighttappingisbeneficialinmostcases.
Itmaynot,however,besufficienttoeliminatepossibleartifactsforcertainsampleswhenrunningsingle-pass-basedKPFM-FM.
Phasecontrastsometimescanbesostrongthatsingle-passKPFM-FMsimplycannotremovephasecross-talk(e.
g.
,onpolymerswithstrongdipoles).
Inthiscase,onehastoturntodual-passbasedtechniques,wheresufficientlift-heightcanbeusedforthetiptoclearthesamplesurfacetoeliminatephaseshiftduetodirecttip-samplecontact.
PeakForceKPFMprovesadvantageousonthisregard,andcanalsobeusedtoidentifypossibleartifacts.
Byincrementallychangingtheliftheight,ifpotentialcontrastshowsanabruptchangeinresponsetoasmallchangeinliftheight,onecandeterminebeyonddoubtthatthepotentialcontrastobtainedbelowacertainlift-heightcontainsartifacts.
Thisisexemplifiedintheimagingofabrushpolymersampleonmicawhere,whentheliftheightischangedfrom25nmto27nm(arelativelysmallchangecomparedtothepolymerchainwidthof5nm),insteadofapossibleblurringofthepotentialcontrastonthechainsasthetipgoesup,thechainstructuredisappearedaltogether(seeFigure13).
Thechainpatternseenatsmallerliftheightscanthereforebeattributedtoartifacts.
PeakForceKPFMprovidesameanstoidentifyandeliminatepossibleartifactsfromtip-sampledirectcontact.
Figure12.
PeakForceKPFMdataincludingheight,potentialandquantitativemechanicalpropertymapssuchasYoung'smodulus,deformationandadhesiononapolymerblendconsistingofpolystyrene(PS)andlow-density-polyethylene(LDPE)(10mscan).
Figure13.
SequentialPeakForceKPFMmapsofabrushpolymersampleonmicasubstrateversusliftheight.
Anabruptchangeinpotentialcontrastisobservedwhenliftheightincreasesfrom25nmto27nm,suggestingthatthepotentialcontrastofthepolymerchainsseenataliftheightof25nmorbelowareartifacts,causedbyphaseshiftfromdirecttip-samplecontact.
Scansizeis250nm.
Theinsetattheupper-leftcorneristheheightimage.
7quantifyingKPFM,whichinturnexpandsKPFM'sutilityinevermoredemandingapplications.
Table2listssomeofthemajorsourcesresponsibleformeasurementinconsistency.
Evenwithasoundelectronicdesignthathaslittleelectroniccross-talk,operatingparametersandprobevariationcancausedatafluctuation.
Theseinclude(1)whetheracdriveisrighton,andalwayson,theresonantfrequencyofthecantilever;(2)whethertip-sampleseparationiskeptthesamefromruntorun;(3)whethertheworkfunctionofthetip,whichisessentiallythereferencepoint,remainsunchanged;and(4)whetherthesampleisundergoingoxidation,adsorptionofmolecules,oralterationduetopossibleelectrochemicalreactions(ascurrentmayflowbetweenthetipandsample).
Toovercometheseuncertainties,aScanAsystKPFMoperationmodewasimplemented,whichresemblesScanAsystinthatitprovidesautomatedimagingoptimization,butdiffersinitstechnicalimplementation.
ItisworthnotingthatKPFM-FMdoeshavesomeperceivedadvantagewhenimagingfeaturessmallerthanafewnanometers,astheaveragetip-sampleseparationcanbemaintainedsmallerthancanbepracticallyachievedwithlift-mode-basedPeakForceKPFM.
This,however,doesnotoffsetthesubstantialadvantagesthatPeakForceKPFMoffers.
InterpretingKPFMPhase:InadditiontoKPFMpotentialdata,KPFMphasedataissimultaneouslyobtainedandcanproveuseful.
Itreflectsthedielectricconstantcontrastofthesample.
Referringtoequation2above,onefindsthesecondderivativeofcapacitance,whichhasdependenceondielectricconstantofthematerialbetweenthetipandtheconductiveportionofthesample,canbeobtainedfromthe2ωterm.
ItcanalsobeobtainedfromtheDCterm,especiallywhenVCD=VCPD,whichisthecasewhenKPFMisactivelyrunning.
Thisisequivalenttoelectrostaticforcemicroscopy(EFM)phaseimaging,withtheadvantagethatworkfunctionanddielectricinformationareseparated,whilethestandardEFMphaseimagingisamixofworkfunctionanddielectricinformationRepeatabilityWhilerepeatabilityofrelativecontrastwithinoneKPFMimagehasbeenreasonablygood,evenwiththesametypeofprobe,absolutevaluescanvaryhundredsofmVfromexperimenttoexperiment.
Improvingmeasurementconsistencyisacrucialsteptowardquantitativeworkfunctionmeasurement.
Withanewprobedesignandoptimizedinstrumentation,wehavefoundwaystoreduceprobe-to-probemeasurementscattertobelowastandarddeviationof50mV.
ThisrepresentsamajoradvanceforFigure14.
PeakForceKPFMdataobtainedusingninedifferentPFQNE-AL(Bruker)probesontheBrukerKPFMstandardsample.
ThevalueonAl(greytriangle),Au(goldtriangle)andtheirdifferences(bluediamond)areplotted.
Standarddeviationofeachislistedatright,whichisontheorderof5ximprovementovertraditionalKPFMmeasurements.
SourceofUncertaintyBrukerSolutionOperatingFrequencyTightparametercontrol(ScanAsyst-KPFM):ThermaltuneforresonancefrequencyFixedoscillationamplitudeOptimalphasesettingTip-SampleSeperationTipWorkFunctionChangeDuetoTipWearProbeDesign:SingletipmaterialProprietarywaytolimitDCcurrrentflowElectrochemicalReactionUnderBiasTable2.
PossiblesourcesforKPFMmeasurementinconsistency.
8InScanAsystKPFM,thealgorithmseekstheresonantfrequencyofthecantileverusingthermaltunetoensuretheaccuracyandconsistencyoftheoperatingfrequency.
Thecantileverisalwaysdriventoafree-airoscillationamplitudeof20nmwhenperformingeitherPeakForceKPFMorKPFM-FM,andthedrivephaseisalwaysaccuratelyandautomaticallyset.
AproprietaryprobedesigneliminatespossibleDCcurrentflowbetweenthetipandsample,andtheuncoatedsilicontipensuresnosignificantworkfunctionchangewilloccurfromtipwear(asoftenhappenswithmetalcoatedprobes).
TheseenhancedcapabilitieshavegreatlyimprovedKPFMrepeatability;Figure15showcasestherepeatabilityobtainedwithninedifferentPFQNE-ALprobesontheBrukerKPFMstandardsample.
Astandarddeviationoflessthan20mVhasbeenachievedinthepotentialsmeasuredonanAlstrip,anAustrip,andintheirpotentialdifference.
Whenthetipworkfunctionisproperlycalibrated,anaccurateworkfunctionofthesamplecanbededuced.
Inaddition,theScanAsystKPFMmodebringsease-of-usetotheoperation.
SensitivityFrequencymodulationKPFMwasfirstrealizedunderultrahighvacuum(UHV)in1998,8andwasnotintroducedintoambientAFMuntilabouttenyearslater.
InadditiontotheenvironmentchangethatcanaffectKPFMmeasurementfidelity,thereisalsoadramaticdifferenceindetectionsensitivity.
ThisisimmediatelynoticeablewhenyoucompareAM-KPFMandFM-KPFMdatainanambientsetting.
Thelatterisusuallymuchnoisier,anevidenceoflackofsensitivity.
ItisthereforehelpfultounderstandwhatgovernsFM-KPFMdetectionsensitivity.
Mathematicaldeductionisnotincludedinthisapplicationnote,butaspreviouslymentioned,theelectricforcegradientcanbeviewedasanadditiontothenaturalspringconstantofthecantilever.
Forasmallerspringconstant,thesameelectricforcegradientwouldmeanalargerrelativechange,causingalargerfrequencyshiftandthusastrongersignal.
TheQsimplymakesthephaseversusfrequencyplotsteeper,furtherenhancingthesignal:KPFMSensitivity∝kItisnoteworthythatunderUHV(i.
e.
,withoutairdamping)theQofstandardEFMprobecanbehundredsoftimeslargerthaninair,therebyaffordingamplesignalamplificationoftheFM-KPFMsignal.
Measurementsensitivityhasrarelybeenanissueandhighqualitydataisregularlyattained.
SensitivityisneitheranissueforAM-KPFMinambientconditions,asthesignalitself,convolutedfromthetipapex,tipconeandthecantilever,isoftenlargeenoughwithconventionalEFMprobes.
ThelowQinair,however,imposesapracticalchallengeforFM-KPFMdetection,wherethesignalisoftenweakasthemajorityofthesignalisonlyfromthetipapexandthelowerpartofthetipcone(thesamereasonFM-KPFMhasbetterspatialresolution).
AlargeQ/kratio,meaningsmallerspringconstantandlargerQ,isdemandedoftheprobe.
PeakForceKPFMopensuproomforimprovement,asopposedtoKPFM-FMbasedonTappingMode.
TappingModerequiresthecantilevertohaveasufficientlylargespringconstanttoovercomecapillaryforcesfromwaterlayersthatareoftenpresentonsamplesurfaces.
ItalsorequirestheQtobenotsolargeastolimitTappingModebandwidth.
PeakForceTappingremovestheselimitations,allowingtheuseofcantileverswithamuchsmallerspringconstantandlargerQ,enablingroomforprobeoptimization.
Currently,PFQNE-AUprobesaretwiceassensitiveasthecommonlyusedSCM-PITprobes.
ProbeswithhigherQ/kratiocanbedesignedtofurtherimprovePeakForceKPFMsensitivity.
PlatformsandAccessoriesAllKPFMmodesareavailableonBrukerDimensionIconandMultiMode8AFMs,andcanbeusedinconjunctionwithavarietyofaccessories.
EnvironmentalControl:Mostnotably,forsamplesthatrequirestringentenvironmentalcontrol(e.
g.
,lithiumbatteryanodeorcathodematerials,organicphotovoltaicorlightemittingdevices),aturn-key1ppm-levelofoxygenandwatercapableglovebox(customizedforbestperformance)canbeused.
Thegloveboxsolutionprovesbeneficialtomeasurementrepeatabilityofsamplessubjecttochangewhenexposedtoambientair,includingmostsemiconductormaterialsandmetals.
BacksideIllumination:ThePhotoconductiveAFMmodule,offeredontheDimensionIconsystem,iscompatiblewithindustry-standardNewportsolarsimulatorstoenableeven,backsidesampleilluminationacrossthescanarea.
ThisallowsKPFMpotentialmappingwhileilluminatingwithachievableintensitiesequivalentto300suns,enablingstudyofstaticanddynamicphotovoltaicresponsestoilluminationoforganicsolarcells/materials.
Figure16showsPeakForceKPFMdataonaMDMO(poly[2-methoxy-5-(3',7'-dimethyloctyloxyl)]-1,4-phenyleneFigure15.
Turnkeyglove-boxenablingallAFMfunctionstobeperformedina1ppmleveloxygenandwaterenvironment.
ShowninsideisaDimensionIconAFM,aversionofglove-boxfortheMultiMode8isalsoavailable.
9Therefore,theamplitudeatacbiasdrivingfrequencyωandthesecondharmonic2ωare:ACVzCφω=A2241ACVzC=AωWeobtaintheelectrostaticpotentialdifference:ωωφ241AAVac=and224ACVAzCω=dC/dzreflectsthedielectricconstantvariationsacrossthesample.
Implementation:KPFM-HVisimplementedinadual-passfashion.
Onthefirstpass,PeakForceTappingisusedtoobtaintopographyandmechanicalproperties.
Onthesecondpass(lift-mode),PeakForceTappingdriveisstopped,andanacbiaswithafrequencylowerthanhalfofthecantileverresonantfrequencyisappliedbetweenthetipandsample.
Theverticaldeflectionsignalissimultaneouslyfedtotwosynchronizedbutseparatelock-inamplifiers;onetodetecttheamplitudeandphaseatthedrivefrequency,andtheothertheamplitudeatthesecondharmonic.
CalculationiscarriedoutinthebackgroundtoobtainelectrostaticpotentialdifferenceΔφ,anddC/dz.
Thistechniqueallowsonetomeasurevoltageintherangeof±200Vwithanerrorlessthan15%.
Highervoltage(upto±1000V)canbemeasuredwithaccuracyonlylimitedbynonlinearityofphotodetectorsintheAFM.
ThistechniqueisavailableonMultiMode8AFMs(noadditionalhardwarerequired)andDimensionIconAFMs(aPeakForceHVmoduleisrequiredtominimizemeasurementdistortionfromelectronicinterference).
vinylene)-PCBM([6,6]-phenylC61-butyricacidmethylester)bulkheterojunctionsolarcell.
Workfunctiondown-shifts535mVunderilluminationsimulating300sunsintensity.
KPFM-HVModeKPFM-HVstandsforHigh-VoltageKPFMmode,whichmeasureselectrostaticpotentialbeyond±10V.
KPFM-HVisadual-passtechnique,withPeakForceTappingasthebaseAFMmode.
Questionarisesaswhyonewouldneedtomeasurehighvoltage.
KPFM,aswehavelearned,measurestheworkfunctiondifferencebetweenthesampleandtip.
Whenwelookthroughtheworkfunctiontableoftheelements,9thehighestworkfunctionis5.
93eV(Osmium)andlowest2.
14eV(Cesium),sothemaximumpossibleworkfunctiondifferencewillneverexceed3.
79V.
AlltheKPFMtechniquesdescribedabovecovertherangeupto±10V,andthereforesufficeforanyworkfunctionmeasurementtask.
Demandariseswhenitcomestomeasuringtrapped(immobilized)chargesininsulators.
Forinstance,whenonewalksonacarpetonadryday,staticchargecanaccumulateuptotens,hundreds,oreventhousandsofvolts.
TheKPFM-HVmodemeetstheneedformeasuringhighvoltageelectrostaticpotentials.
ThistechniqueisnolongerusingaKPFMfeedbackloop,norahighvoltagesourceasonemaylogicallythink.
Itdeviatesfromtheforceorforce-gradient-nullingconceptcentraltotheaforementionedKPFMtechniques.
ItisdonewithexistinghardwarecommontoanAFM,andthroughcalculation.
Weadopttheconceptthatthesampleandtipformacapacitor.
Wefurtherassumetheelectricforcefollowsthesameexpression:Term22TermTermDC22)2cos(41)sin()21(ωωωωφφtVzCtVzCVzCFACACACel+++=whereistheelectrostaticpotentialdifferenceatthetipinreferencetothesample.
Figure16.
PeakForceKPFMPotentialmap(thirdfromleft)ofMDMO-PCBMbulkheterojunctionsolarcellonanITOsubstrateindark(bottomhalf)andunderilluminationwithanintensityequivalentto300suns(tophalf).
A535mVdownshiftofworkfunctionisseenunderillumination,a3Drenderingandhistogramofpotentialdataisattheright.
SamplecourtesyofDr.
PhilippeLeclere,UniversityofMons.
10Examples:Somepolymerscanbechargedthroughcontactelectrification.
Simplycontactingandthenseparatingtwosimilarordissimilarpolymerpieces,orcontactingittoandthenseparatingitfromaconductingsurface,induceschargeonsurfacesbeingcontacted.
Figure19showsthepotentialmap(left),phase(middle),anda3DrenderingofthepotentialmapofaPDMS(polydimethylsiloxane)film.
ThesampleispreparedbycastingaPDMSfilmabout0.
5mminthicknessonasiliconwafer.
Apieceispeeledoffthesiliconsubstrateandthenitsundersideisimaged.
Thepotentialmapshowstheelectrostaticpotential,reflectingelectrostaticchargedensity(absolutevalue),andsign,whichislearnedfromthephasedata.
The3Drenderingshowsaminimumof-99Vatthecenterofanegativelychargedarea,withpositivechargeshavinganelectrostaticpotentialashighas156V.
PDMSsamplescanbeeasilyobtained,infact,aPDMSgel-padisoftenfoundinAFMprobepackaging.
Simplycutoffapieceofgel-padfromthebottomofanAFMprobebox,andusethecontactelectrificationtechniquetohaveitcharged.
Chargecanalsobeintroducedthroughtriboelectriccharging(onetypeofcontactelectrification,throughrubbing),forinstance,byrepeatedlyscanningthesameareaforsomeextendedperiodoftime.
Figure19Figure17.
KPFM-HVdiagram,inthefirstpass,surfacetopographyandmechanicalpropertiesareobtainedinPeakForceTapping;inthesecondpass,anacbiasatafrequencylowerthanhalfofthecantileverresonantfrequencyisappliedbetweentheprobeandthesample,whichcausestheprobetooscillateatfrequencyωanditssecondharmonic2ω.
Theelectricpotentialbetweenthetipandsampleiscalculatedbasedontheoscillationamplitudeatfrequencyωand2ω.
NotethatnoKPFMfeedbackisinvolved.
Figure18.
KPFM-HVimagesofPDMS(polydimethylsiloxane)filmsafterbeingchargedbypeelingofffromthesiliconsubstrateuponwhichitwascast.
TheHVPotentialdata(left)showstheelectrostaticpotentialandthesignofcharge;HVPhasedata(middle)denotesnegativechargewithnegativephase,andpositivechargewithpositivephase.
Attherightisa3Drenderingofthepotentialmap,thenegativechargegivesrisetoanelectrostaticpotentialof-99Vatitscenter,andsomeoftheadjacentpositivechargesgoashighas158V.
Figure19.
KPFM-HVpotentialmaponPDMS,encasingfivepreviouslyscannedsitesinasquare-centerarrangement.
Sequentialimagesfromlefttorightrevealthatthenegativechargesareaccumulating,spreadingoutandmergingwitheachotherasscanninggoeson.
11ConclusionBrukeroffersasuiteofnewKPFMmodes,threeofwhicharebasedonthebreakthroughPeakForceTappingtechnologywithadual-passimplementation:PeakForceKPFM,usingFrequencyModulationdetection;PeakForceKPFM-AM,usingAmplitudeModulationdetection;PeakForceKPFM-HV,usingAmplitudeModulationandextendingtheaccessiblepotentialrangebymorethanafactoroften.
PeakForceKPFM,achievedbycombiningPeakForceTappingwithfrequency-modulationKPFMexhibitsthemostoutstandingperformance:ItretainsthehighspatialresolutionandaccuracyofFM-KPFM(probemodelingrevealsthatFM-KPFMoffersaresolutiondownto10nmwithoutcompromisingmeasurementaccuracy,instarkcontrasttothemicrometer-scaleresolutionofferedbyAM-KPFM).
ItachieveshighrepeatabilitythroughtightparametercontrolusingtheScanAsystKPFMoperationalgorithmandnovelprobedesign.
ItleveragesPeakForceQNMtoproducesimultaneousmechanicalandelectricalinformation,enhancingitsmaterialidentificationpower.
ItpromisesfurtherenhancementtoFM-KPFMsensitivity(PeakForceTappingliftstherestrictionsonprobeselectionimposedbyTappingMode,andcantileverswithlowerspringconstantandhigherQcanbeemployedforimprovedsensitivity).
Ultimately,PeakForceKPFMhasbroughtusamajorstepforwardtowardhigh-resolution,quantitativeworkfunctionmeasurements.
Itispoisedtomeetthechallengesinapplicationareasthatdemandeverhigherspatialresolutionandbetteraccuracyandrepeatability.
Withprovenapplicationsonmetal,semiconductor,organicmaterials,thesuperiorcapabilitiesofPeakForceKPFMalsopromisebenefitsforbio-materials,andotheradvancedapplicationareas.
(left)showsfivepreviouslyscannedsiteswithnegativecharges.
Sequentialimagingindicatesthenegativelychargedareasspreadingoutandmergingwitheachotherasscanningcontinues.
KPFM-HVmodeprovidesasimplemeanstomeasureelectrostaticpotentialofimmobilizedchargesashighas±200V.
ProbeSelectionGuideTable3isaprobeselectionguideforeachmode,asofthedatethisnoteispublished.
Forup-to-dateinformation,pleasefollowtheguidanceprovidedintheNanoScopesoftware.
Otherprobesnotinthelistmayalsowork,buttheirperformanceinrelationtoKPFMmeasurementsensitivity,accuracy,and/orrepeatabilitymaynotbeguaranteed.
ProbeChoicesKPFMModesPeakForceKPFMPeakForceKPFM-AMKPFM-FMKPFM-AMKPFM-HV1stPFQNE-ALPFQNE-ALPFQNE-ALPFQNE-ALTAP150A2ndSCM-PITScanAsyst-AirHRSCM-PITSCM-PITSCM-PIT3rdNoneSCM-PITNoneNoneMESP-RCTable3.
ProbeSelectionGuideforEachKPFMMode.
12AppendixI:MathematicsaboutFrequencyModulationThemodulationoftheresonantfrequency,correspondingtotheelectricforcegradientmodulationatthedrivingfrequencyoftheacbiasistherefore:)sin()sin()(2~22tFtVVVzCkmmdefinetionmACCPDDCωωωω→≈Whereω~isthemodulatedfrequencycomponent,Fmdenotesthefrequencymodulationamplitude.
Forthecantilevermechanicallydriventooscillateatitsresonantfrequency,appliedwithanacbiaswithfrequencyωm,thecantilevermotioncanbewritten:Thisequationstatesthat,inadditiontotheoscillationattheresonantfrequency,apairofsidebandswillappearatω±ωm.
Thisisveryusefulforunderstandingtheoscillationspectrum.
Figure4isthespectrumwhenanMESP-RCprobeismechanicallydrivenat133kHz,whileanacbiasof2kHzisapplied.
Theamplitudeofthesidebandreflectstheamplitudeofthefrequencymodulation.
Theratioofthesumoffirstside-peakpairversusthecenterpeakheightgivesthefrequencymodulationindexFm/ωm.
Forexample,0.
1wouldmeanthefrequencymodulationamplitudeis200Hz(0.
1x2kHz).
TheFM-KPFMfeedbackistoadjustDCbiassothefirstsidebandpairdisappears,atwhichpointVCPDisfound.
Inpracticalimplementation,sidebandamplitudeisrarelydirectlymeasuredatthesidebandfrequencyusingasinglelock-inamplifier.
Amorecommonmethodusestwocascadelock-inamplifiers,withthefirstonelockingattheresonancefrequency,thephaseoutputofwhichisfedtothesecondlock-in,whichlocksattheacbiasfrequency.
Thefollowingequationprovidesinsightinthisapproach:Thephaseis:ForFm/ωm<0.
5So,feedingthephaseoutputofthefirstlock-inamplifiertoasecondlock-inamplifierlockingatfrequencyωm,theamplitudeoutputofthesecondlock-inwillbeFm/ωm,exactlythefrequencymodulationindex(somescalingfactormayexist).
AppendixII:MathematicsonProbeModelingProbemodelingstartswiththecapacitormodelfortheprobeandsample,andapproximatestheprobeasconsistingofamicro-cantileverandatipconewithapointend(seeFigure7).
Asagoodconductor,thepotentialisthesameallovertheprobe,andchargesareonlypresentonthesurfaces.
Theintegratedcapacitancesofthecantileverandtipconecanbeanalyticallyexpressed.
Electricforceandelectricforcegradientcanbededucedfromthefirstandsecondderivativesofthecapacitance.
LeverContributiontoElectricForceandForceGradientForsimplicity,weassumethecantileverisparalleltothesample,ignoringthetiltofthecantilever.
Recognizingthattheelectricforceattheendofthelevercausesmoredeflectionthanthesameforceatthebaseofthecantilever,thecapacitanceisnormalizedinproportiontoitslengthfromthebase:where,WisthewidthandListhelengthofthecantilever,Histheheightofthetipcone,zisthedistancefromthetipendtothesample,andεisthedielectricconstant.
Theelectricforcefromtheleveristherefore:andtheelectricforcegradientis:32')(2zHWLVFLever+=ε13Tip-ConeContributiontoElectricForceandForceGradientThesurfaceofthetipconeistreatedasastackofrings.
Thetotalcapacitanceisthesumofthecapacitanceofeachring,whichisapproximatedbytheprojectedareaoftheringanditsverticaldistancefromthesamplesurface:Therefore,theelectricforcefromtheconeuptoheighthis:andtheelectricforcegradientfromtheconeuptoheighthis:References1.
C.
Li,S.
Minne,B.
Pittenger,A.
Mednick,M.
Guide,andT-Q.
Nguyen,"SimultaneousElectricalandMechanicalPropertyMappingattheNanoscalewithPeakForceTUNA,"BrukerapplicationnoteAN132Rev.
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Gil,andA.
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AuthorsChunzengLi,StephenMinne,YanHu,JiMa,JianliHe,HenryMittel,VinsonKelly,NataliaErina,SenliGuo,ThomasMueller(BrukerNanoSurfaces)14BrukerNanoSurfacesDivisonSantaBarbara,CA·USA+1.
805.
967.
1400/800.
873.
9750productinfo@bruker-nano.
com2013BrukerCorporation.
Allrightsreserved.
DimensionIcon,MultiMode,NanoScope,PeakForceKPFM,PeakForceQNM,PeakForceTapping,ScanAsyst,andTappingModearetrademarksofBrukerCorporation.
Allothertrademarksarethepropertyoftheirrespectivecompanies.
AN140,Rev.
A1www.
bruker.
com
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