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AtomicForceMicroscopyPeterEatonandPaulWest

Printpublicationdate:2010PrintISBN-13:9780199570454PublishedtoOxfordScholarshipOnline:May2010DOI:10.1093/acprof:oso/9780199570454.001.0001

AFMinstrumentation

PeterEatonPaulWest

DOI:10.1093/acprof:oso/9780199570454.003.0002

AbstractandKeywords

ThischapterdescribesthedesignofmodernAFMinstrumentsindetail.Itshowsbothhowtheinstrumentsarebuilt,andhowtheywork.Therearedescriptionsofthemechanical,electronic,andsoftwaredesignoftheinstrument,aswellasasectiononthedesignofAFMprobes,oneofthemostimportantcomponentsinanyAFM.Fortheinstrumentuser,understandinghowtheinstrumentworkscangreatlyimprovetheresultsobtained,andthischapterhasalltheinformationanAFMusercouldneedabouthowAFMswork,andmoreimportantly,whytheyworkthatway.

Keywords:instrument,hardware,software,probes,cantilevers,design,electronics

IntheoryanAFMisarelativelysimpleinstrument.However,constructinganAFMwithnanometre‐scaleresolutionrequiresaconsiderableamountofsophisticatedengineering.

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ThemaincomponentsofanAFMarethemicroscopestageitself,controlelectronicsandacomputer.Themicroscopestagecontainsthescanner(themechanismformovingtheAFMtiprelativetothesample),sampleholderandaforcesensor,toholdandmonitortheAFMtip.Thestageusuallyalsoincludesanintegratedopticalmicroscopetoviewthesampleandtip.Often,thestageissupportedonavibrationisolationplatformwhichreducesnoiseandincreasestheresolutionobtainable.Thecontrolelectronicsusuallytakestheformofalargeboxinterfacedtoboththemicroscopestageandthecomputer.Theelectronicsareusedtogeneratethesignalsusedtodrivethescannerandanyothermotorizedcomponentsinthemicroscopestage.TheyalsodigitizethesignalscomingfromtheAFMsothattheycanbedisplayedandrecordedbythecomputer.ThefeedbackbetweenthesignalscomingoutandgoingbackintotheAFMstageishandledbythecontrolelectronics,accordingtoparameterssetviathecomputer.SoftwareinthecomputerisusedbytheoperatortoacquireanddisplayAFMimages.Theuseroperatesthesoftwareprogram,andtherelevantacquisitionparametersarepassedontothecontrolelectronicsbox.Thecomputerusuallyalsocontainsaseparateprogramtoprocessandanalysetheimagesobtained.AphotographofatypicalAFMillustratingthesecomponentsisshowninFigure2.1.

2.1BasicconceptsinAFMinstrumentationThethreebasicconceptsthatonemustbefamiliarwithinordertounderstandtheoperationofanAFMarepiezoelectrictransducers(inAFM,oftenknownaspiezoelectricscanners),forcetransducers(forcesensors),andfeedbackcontrol.Basically,thepiezoelectrictransducermovesthetipoverthesamplesurface,theforcetransducersensestheforcebetweenthetipandthesurface,andthefeedbackcontrolfeedsthesignalfromtheforcetransducerbackintothepiezoelectric,tomaintainafixedforcebetweenthetipandthesample.

2.1.1Piezoelectrictransducers

Piezoelectricmaterialsareelectromechanicaltransducersthatconvertelectricalpotentialintomechanicalmotion.Inotherapplications,theymayalsobeusedintheoppositesense,i.e.ifachangeiscausedinthematerial'sdimensionstheywillgenerateanelectricalpotential.Piezoelectricmaterialsarenaturallyoccurringandmaybecrystalline,amorphousorevenpolymeric,althoughthematerialsusedforAFMaregenerallysyntheticceramicmaterials.Whenapotentialisappliedacrosstwooppositesidesofthepiezoelectricdevice,itchangesgeometry.Themagnitudeofthedimensionalchangedependsonthe(p.10)

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Fig.2.1. PhotoofadesktopAFMillustratingthemajorcomponents.Theyarethemicroscopestage,computer,electroniccontroller,computermonitor,andopticalmicroscopemonitor.ThetrackballisusedformovingthesamplestageintheX‐Yaxis.Resolutioncanusuallybeimprovedbyplacingthemicroscopestageonavibrationisolationtable.

material,thegeometryofthedevice,andthemagnitudeoftheappliedvoltage.ThisisillustratedschematicallyinFigure2.2.

Typically,theexpansioncoefficientforasinglepiezoelectricdeviceisontheorderof0.1nmperappliedvolt.Thus,ifthevoltageusedtoexcitethepiezomaterialis2volts,thenthematerialwillexpandapproximately0.2nm,orapproximatelythediameterofasingleatom.ItistheabilitytoaccuratelycontrolsuchtinymovementthatmakespiezoelectricmaterialssousefulforAFM.Thus,piezoelectricmaterialsareusedforcontrollingthemotionoftheprobeasitisscannedacrossthesamplesurface.Piezoelectricsareavailableinavarietyofsizesandshapes,andaregenerallyusedinmorecomplexgeometriesthandepictedinFigure2.2,sothattheycanscanthetipinmultiple

Fig.2.2. Apiezoelectricdiskwillexpandradially(d2>d1)whenavoltagepotentialisappliedtothetopandbottomelectrodes.Thediskwillchangeshapesuchthatvolumeispreserved.

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(p.11)

Fig.2.3. Schemeofforcetransduceroperation.ThefunctionofthetransduceristomeasuretheforcebetweentheAFMprobetipandthesamplesurface.

directionsacrossthesamplesurface.Section2.2.1describesingreaterdetailhowpiezoelectricmaterialsareconfiguredtoscanaprobeinthreedimensions.

2.1.2Forcetransducers

TheforcebetweenanAFMprobeandasurfaceismeasuredwithaforcetransducer.AsillustratedinFigure2.3,whentheprobecomesintocontactwiththesurface,thevoltageoutputfromthetransducerincreases.Itisimportantthattheoutputofthetransducerbemonotonicandincreasesasagreaterforceisappliedbetweentheprobeandsurface.Forcetransducersmaybeconstructedthatmeasureforcesaslowas10piconewtonsbetweenaprobeandasurface.Typically,theforcetransducerinanAFMisacantileverwithintegratedtip(theprobe),andanopticallever;however,thereareseveraltypesofforcesensorsthatmaybeusedinanAFM(thesearedescribedinSection2.2.2).

2.1.3Feedbackcontrol

ThereasonanAFMismoresensitivethanastylusprofilerthatsimplydragsatipoverthesamplesurface,isthatfeedbackcontrolisusedtomaintainasetforcebetweentheprobeandthesample.AsillustratedinFigure2.4,thecontrolelectronicstakethesignalfromtheforcetransducers,anduseittodrivethepiezoelectricssoastomaintaintheprobe–sampledistance,andthustheinteractionforceatasetlevel.Thus,iftheproberegistersanincreaseinforce(forinstance,whilescanningthetipencountersaparticleonthesurface),thefeedbackcontrolcausesthepiezoelectricstomovetheprobeawayfromthesurface.Conversely,iftheforcetransducerregistersadecreaseinforce,theprobeismovedtowardsthesurface.Section2.3.2hasamoredetaileddiscussionoffeedbackcontrolmethodologiesinAFM.

2.1.4AFMblockdiagramandrequirements

IngeneraltermsthedesignofanAFMisasshowninFigure2.5.Theforcetransducermeasurestheforcebetweentheprobeandsurface;thefeedbackcontrollerkeepstheforceconstantbycontrollingtheexpansionofthezpiezoelectrictransducer.Maintainingthetip–sampleforceatasetvalueeffectivelyalsomaintainsthetip–sampledistancefixed.Then,thex‐ypiezoelectricelementsareusedtoscantheprobeacrossthesurfaceinaraster‐likepattern.Theamountthezpiezoelectricmovesupanddowntomaintainthe(p.12)

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Fig.2.4. Schematicoffeedbackcontrol;whentheforcesensorsensesachangeinsampleheight,thepiezoelectricmovestomaintainthesametip–sampleforce.

tip–sampledistancefixedisassumedtobeequaltothesampletopography.Inthisway,bymonitoringthevoltageappliedtothezpiezo,amapofthesurfaceshape(aheightimage)ismeasured.

Thereareseveralengineeringchallengesthatmustbemettodesignandconstructasuccessfulatomicforcemicroscope.Theyare:

•Averysharpprobemustbeconstructedsothathigh‐resolutionimagesaremeasured.•Togettheprobewithinthescanningrangeofthesurface,amacroscopictranslationmechanismmustbeconstructed.•Theforcetransducermusthaveaforceresolutionof1nNorlesssothattheprobeisnotbrokenwhilescanning.•Afeedbackcontrollerthatpermitsrapidcontrolsothattheprobecanfollowthetopographyonthesurfacemustbecreated.•AnX‐Y‐Zpiezoelectricscannerthathaslinearandcalibratedmotionmustbeused.•Astructurethatisveryrigidmustbeconstructedsothattheprobedoesnotvibraterelativetothesurface.

Fig.2.5. BlockdiagramofAFMoperation.

(p.13)

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Fig.2.6. PhotoofanAFMstage,withcomponentshighlighted.

•Ahigh‐speedcomputerthatcandisplaytheimagesinrealtimeastheyarecollectedmustbeused.•Astagethatallowsrapidexchangeoftheprobeusedforscanningmustbecreated.

Thewaysinwhichthesechallengesareovercomearediscussedinthefollowingsectionsofthischapter.

2.2TheAFMstageTheAFMstageistheheartoftheinstrument;Figure2.6showsanAFMstageandhighlightsthemajorcomponents.Theremustbeprobeandsampleholders.Thereisacoarseapproachmechanism,theZmotor,whichcanmovetheAFMscannertowardsthesample.ThereisalsoanX‐Ypositioningstagewhichisnotrequiredbutisusefulforpositioningthefeatureforimagingundertheprobe.Tohelpwiththis,thereisusuallyanopticalmicroscopeforviewingtheprobeandsurface.

AmechanicalstructureisrequiredtosupporttheAFMscannerandothercomponents.Intheconstructionofthestageitisimportantthatthemechanicalloop,whichcontainsallthemechanicalcomponentsbetweentheprobeandsurface,beveryrigid.Ifthemechanicalloopisnotrigid,thentheprobewillvibraterelativetothesampleandintroduceunwantednoiseintotheimages.

Ingeneral,ifthemicroscopestageissmaller,itwillbelesssusceptibletoexternalvibrations.Creatingarigidmechanicalloopbecomesmoredifficultthelargerthesamplesizeis.ThehighestresolutionAFMstendtobeverysmallsothatthemechanicalloopisrigid,andthemicroscopestageisnotsusceptibletoexternalenvironmentalvibrations(ornoise).

(p.14)

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Fig.2.7. Thedifferencebetweensample‐scanning(left)andprobe‐scanning(right)microscopes.InasamplescanningAFMthesampleismountedonanx‐y‐zscannerandtheforcesensorremainsfixed.IntheprobescanningAFMthesampleremainsfixedandtheprobeisscanned.TheadvantageofaprobescanningAFMisthatitcanscanlargersamples.

Inthisbook,themotioncontrolmechanismsoftheAFMstagecapableofmovingseveralmillimetresorgreater(thecoarsemovementcontrols)aredesignatedX,YandZ.Themotioncontrolmechanismsthatareusedformovingsmalldistances(thex,yandzscanners)aredesignatedx,yandz.

ThedesignofallAFMinstrumentscanbedividedintotwodifferentconfigurationsasillustratedinFigure2.7.Inthefirstconfiguration(left)thesampleisscannedandtheforcesensorisheldinoneplace.Inthesecondconfiguration,thesampleisheldfixedandtheprobeisscanned.IngeneralallAFMscanbedividedintosuchsample‐scanningorprobe‐scanningmicroscopes.Forsample‐scanningAFMs,themassofthesampleisincludedinthefeedbackloop,reducingthesizeofsamplethatmaybeprobed,aswellaspracticallimitsonthesample'sdimensions.Theadvantageoftheprobescanning(alsoknownastip‐scanning)microscopeisthatitcanbeusedonanysizeofsample.Inaddition,becausethereisnothingunderneaththescanningprobeexceptthesample,itissimpletoaddaccessoriestothistypeofmicroscope.Forexample,aliquidcelliseasiertousewithaprobescanningmicroscope,andtheyareeasiertointegratewithadditionalopticaloptions,forexampletoirradiatethesamplefromthesidewhilescanning,ortomounttheentireAFMinanopticalmicroscope.However,theconstructionofaprobescanningmicroscopeismuchmoredifficult,asthewholetip–optical‐leverassemblymustbemovedwhilescanning,andcaremustbetakennottointroducefurthervibrationsfromthescanningmechanismintotheprobe.AsamplescanningAFMdesignisrathersimpler,butsomewhatlimitssamplesize.

2.2.1x‐y‐zscannersTypically,thescannersusedformovingtheproberelativetothesampleinanAFMareconstructedfrompiezoelectricmaterials.Thisisbecausesuchpiezoelectricmaterialsarereadilyavailable,easilyfabricatedindesirableshapes,andcosteffective.However,(p.15) scannersforAFMmaybeconstructedfromothertypesofelectromechanicaldevicessuchasflexurestages[27,28],voicecoils[29],etc.Allthatisimportantisthattheelectromechanicaldevicemusthaveveryaccuratepositioning.

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2.2.1.1PiezoelectricscannersThemostcommontypesofpiezoelectricmaterialsinuseforAFMscannersareconstructedfromamorphousleadbariumtitanate,PdBaTiO3orleadzirconatetitanate,Pb[ZrxTi1–x]O3,0<x<1(usuallyabbreviatedasPZT).Theceramicsmaybe‘hard’or‘soft’,dependingontheformulation.Thisaffectshowmuchtheycanexpand,versustheappliedvoltage,aswellasthelinearityoftherelationshipbetweenappliedvoltageandexpansion.Hardceramicshavesmallercoefficientsofexpansion,butaremorelinear.Softceramicformulationshavemorenon‐linearitiesandhavegreaterexpansioncoefficients.Afterfabrication,piezoelectricceramicsarepolarized.Polarizationmaybelostbyelevatingthepiezostoatemperatureabovetheircriticaltemperatureorbyapplyingtoohighavoltage.

Electronically,piezosactascapacitorsandstorechargesontheirsurface.Capacitancesofceramicsmaybeaslargeas100microfarads.Onceachargeisplacedonthepiezoceramic,thepiezoceramicwillstaychargeduntilitisdissipated.ElectroniccircuitsusedfordrivingthepiezoceramicsinanAFMmustbedesignedtodrivelargecapacitiveloads.

Allpiezoceramicshaveanaturalresonancefrequencythatdependsonthesizeandshapeoftheceramic.Belowtheresonancefrequency,theceramicwillfollowanoscillatingfrequency,atresonancethereisa90°phasechange,andaboveresonancethereisa180°phasechange.Toagreatextent,theresonancefrequenciesofthepiezoelectricceramicslimitthescanratesofatomicforcemicroscopes.Asaruleofthumb,thehighertheresonantfrequencyofthescanner,thefasteryoucanscan.

Piezoelectricmaterialscanbefabricatedinseveralshapessuchthattheyhavemoreorlessmotion.Asanexample,adisk,asillustratedinFigure2.2,getslongerandnarrowerwhenavoltageisapplied.Thepiezoelectricceramicchangesgeometrysuchthatthevolumeispreservedduringextension.Anotherconfigurationforapiezoelectricceramicisatube,withelectrodesontheinsideandoutside.Thisconfigurationgivesalotofmotion,andisveryrigid.Anotherconfigurationisthebimorph,constructedfromtwothinslabsofpiezomaterialthatarepolarizedinoppositedirections.Whenavoltageisappliedtheceramicexpandsinaparabolicfashion.Themotionsofthesegeometries,alongwiththeequationsofmotionareillustratedinFigure2.8.

Ideally,thepiezoelectricceramicswouldexpandandcontractindirectproportiontothedrivingvoltage.Unfortunately,thisisnotthecase,andallpiezoelectricmaterialsshownon‐linearbehaviour.Theyshowtwoprimarynon‐idealbehaviours,hysteresisandcreep[30].Hysteresis,derivedfromthewordhistory,causestheceramictotendtomaintaintheshapethatitwasinpreviously.Astheceramicisexpanding,thereisanegativeshapednon‐linearity,andasthematerialiscontracting,thereisapositiveshapednon‐linearity.Hysteresiscausesa‘bending’distortionintheimagesobtained,unlesscorrected.Creepoccurswhentheceramicissubjectedtoasuddenimpulsesuchasavoltagestepfunction.Thismeansthatwhenthepiezoisusedtomovetoadifferentpartofthescanrangebyapplyinganoffsetvoltagetoit,itwilltendtocontinuemovinginthe

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samedirectionastheoffset,evenafterthevoltagehasstoppedchanging.BoththeseeffectsareillustratedinFigure2.9.Realexamplesoftheeffectsofthesenon‐linearitiesonAFMimagescanbefoundinChapter6.Thesenon‐idealbehavioursmustbecorrectedtoavoidsuchdistortionsintheAFMimages.

(p.16)

Fig.2.8. TypicalgeometriesforpiezoelectricelementsusedinAFM.Fromtop:piezoelectricdisk,tubeandbimorphscanners.

Correctingthenon‐idealbehavioursofpiezoelectricceramicsisessentialformakingaccuratemeasurementswithanAFM.Duetothedifferentwaystheaxesareoperated–xandyinarasterpattern,zmovedbythefeedbackcontrol–thecorrectionsrequiredaredifferentforthex‐yaxesandthezaxis.Also,hysteresisandcreepmakeitdifficulttoscantheAFMveryquickly,andmaintainaccuracy.Thenon‐idealmotionsofpiezoelectricceramicsmaybecorrectedusingopen‐looporclosed‐loopmethods[31].Thefollowingsectionsdescribethetypicalmethodsusedtocorrectfornon‐linearitiesinpiezoelectricscanners.

Fig.2.9. Examplesofnon‐linearbehaviourinpiezoelectricscanners.Top:hysteresis;whenavoltagerampisappliedtothepiezo,theresponseisnon‐linear.Bottom:creep;afteranimpulseappliedtothepiezo,themovementcontinuesinthesamedirection.

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(p.17) 2.2.1.2x‐yaxiscorrectionOpen‐looptechniquesrequirecalibrationoftheAFMscannertomeasurethenon‐linearities.Thentheimageiscorrectedusingthemeasurednon‐linearities.Inpracticalterms,onemustmeasureaverywell‐knownsample,withrepetitivepatternstobeabletodeterminethenon‐linearitiesinthescanneraccurately.Calibrationspecimensmaybebought,oraresuppliedwithinstrumentsforthispurpose.SeeAppendixAforalistofusefulmaterialsthatmaybeusedincalibratinganAFM.Themostcommonlyusedcalibrationspecimenstaketheformofalithographicallyproducedsilicongrid.Suchsamplesareadequateforcalibrationinthehundredsofnmtomicrometerscale.However,asthenon‐linearitiesvarywithscansize,furthercalibrationisrequiredforatomic‐resolutionscanning.Typically,thismeansscanningasamplewithawell‐knownatomicstructure.Oncecalibrated,theAFMcontrolsoftwarewillalterthevoltageusedtoexcitetheceramicinrealtime,whilescanning,tocompensateforthenon‐idealbehaviour.Alternatively,afteranimageismeasureditmayalsobe‘corrected’byapplyingacorrectionfunctionthatwaspreviouslycreated.Again,asthecalibrationfactorsdependonthescanningconditions,caremustbetakentoreplicateallthescanningparametersexactly,ifoneistofollowthisroute.Inaddition,itisworthrememberingthatafterproduction,piezoelectricscanners‘relax’slightly,overalongperiodoftime.So,evenifanewscannerisperfectlycalibrated,afterayearorsothepersonresponsiblefortheinstrumentshouldrecheckthecalibrationtomaintainaccuracy.ProcedurestorecertifyAFMscannersaredescribedinAppendixB.Open‐looptechniquesareadequateforcorrectingnon‐linearitywhenmakingmeasurementwithpre‐determinedscanrangesandspeeds.However,open‐looptechniquescannotcorrectforproblemsassociatedwithcreep,andarenotreallysuitablewhereaccuracyisofmoreimportancethanhighresolution(i.e.metrologicalapplications).Inthesecases,itisnecessarytouseexternalcalibration.

Anexternalpositionsensorcanbeusedinanopen‐looporclosed‐loopdesign.Intheopen‐loopconfigurations,thepositionofthescannerismeasured;thentheimageiscorrectedafteritismeasured.Intheclosed‐loopconfiguration,themotionoftheprobeiscorrectedinrealtimewithafeedbackelectroniccircuit.Figure2.10showstheuseofexternalsensorsinaclosed‐loopdesign.Piezoelectricscannersoperatingwithpositionsensorsinaclosed‐loopscanningconfigurationareoftentermedlinearizedscanners,asitisonlyinthisconfigurationthattheirmovementislinear.

Fig.2.10. Blockdiagramforanx‐yclosed‐loopscannerconfiguration.

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(p.18) 2.2.1.3PiezoelectricdisplacementsensorsManytypesofpositionsensorsmaybeusedforcorrectingtheunwantedcharacteristicsinpiezoelectricmaterials.Thepositionsensormustbesmallinsize,stableoverlongtimeperiods,easilycalibrated,haveverylownoiselevels,andbeeasilyintegratedintoascanner.Severaltypesofpositionsensorsareavailableincludinglight‐basedsensors[31],straingauges,inductionsensors,andcapacitancesensors.Opticalsensorsavailableincludeasimpledesignbasedonaknifeedgeattachedtothescanneroccludingalightbeam.[32]Thesignalfromaphotodetectorisreducedastheknifeedgecutsthebeam.Othertypesoflight‐basedmotionsensorsincludeusingapinholeaboveapositionsensitivedetectorandalightlever.Eachoftheselight‐baseddesignsrequiresahigh‐gainamplifier.Theprimaryadvantageofthelight‐basedpositionsensorsisthatthepartsrequiredforconstructionarerelativelyinexpensive.Therearemanydisadvantageshowever,includingthefactthatthesensorisnotinherentlycalibrated,misalignmentsofthelightsourcecauseproblems,highnoise,andtherequirementforahigh‐gainamplifier.ThelightsourcesalsocancausethermaldriftintheAFMscanhead.Interferometersmayalsobeusedforthisfunction[28,33],buttheytendtoberatherbulkyanddifficulttointegrateintotheAFMhead.Capacitance‐basedmotionsensorsaresimpledevicesthatmeasurethecapacitancebetweentwoplateswhichdependsonthedistance,d(Figure2.11)betweentheplates,andthuscanmakeahighlysensitivepositiondetector.Capacitancesensorsarecommonprimarilybecausetheelectronicsforcapacitancesensorsareverysensitive,and

Fig.2.11. DifferentapproachestoincludesensorsinAFMscanners.Top:acapacitivesensor,middle,aninterferometer‐basedsensor;bottom:aninductivesensor.

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(p.19)

Fig.2.12. Zoomtofeatureexample.Inthiscase,withalinearizedx‐yscanner,selectingthesmallfeatureallowedanimmediatezoomtothecorrectregion.Non‐linearizedscannerscannotaccuratelyzoomtosmallregionsofthescanrange.

theyarealsocompact,andsosimpletointegrateintotheAFM.Temperature‐basedstraingaugesmaybeused.Straingaugescanbeattacheddirectlytothepiezoelectricmaterialortheymaybeattachedtoastructurewhichflexeswhenthepiezoceramicexpands.

InductionsensorsarefarmoresuitableformeasuringthedisplacementofthepiezoelectricsinSPMscannerscomparedtoopticalsensors.InductivescannersareconstructedfromacoilthroughwhichanACcurrentflowsgeneratingapulsatingelectromagneticfieldsurroundingthecoil.Placingthecoilanominaldistancefromanelectricallyconductive‘target’inducesacurrenttoflowonthetarget.Theinducedcurrentproducesasecondarymagneticfieldthatreducestheintensityoftheoriginalfield.Thestrengthoftheelectromagneticcouplingbetweenthesensorandtargetdependsuponthegapbetweenthem,sothatthesensorcanmeasurethemovementofthescanner.Incomparisontoopticalsensors,inductionsensorsaresmallandeasilyintegratedintotheAFMscanheadinallthreeaxes,havelownoise,arestable,andnotsubjecttodrift,andonlyrequirecalibrationonceatthefactory.OtherpositionsensorsforAFMpiezosbasedontheinteractionofmagneticfieldshavealsobeenused,andcangiveverylownoiselevels.Thesedifferfromtheinductionsensordescribedhereinthegeometryofthemagneticfield‐producingelements.Figure2.11illustratesthemodeofoperationofanumberofpositionsensorscommonlyusedformeasurementofpiezoelectricelementmovement.

Oneoftheadvantagesofclosed‐loopscancorrectionisthatthescannermovementcanbefullycalibrated.Suchcalibrationscangiveverypreciseandaccuratemotioncontrol.However,thecalibrationprocedurecanbeverytime‐consuming.Someofthemotionsensors,suchastheoptical‐basedsensor,arenon‐linearandrequireregularrecalibration.Othertypes,suchastheinductiveandcapacitativesensorsarereasonablylinearandrarelyrequirecalibration.

Zoomtofeature

OneoftheproblemswithAFMscannerswithopenloopornoscancorrectionisthatitcanbedifficulttozoomfromalargescanrangetoaspecificsmallerscanrange(zoomtofeature,Figure2.12).Withoutscanlinearization,zoomingfromalargescanrangetoa

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smallerrangerequiresseveralscans,ifoneistobesurenottolosethefeatureofinterest.(p.20) However,withthescancalibrationsensorsoperatinginaclosed‐loopconfiguration,zoomingtoaspecificscanlocationrequiresnointermediatescans.

zaxismeasurement

Correctionofhysteresisandcreepinthezaxisisdifferentfromthecorrectioninthexyaxis.Thisisbecausethexyaxismotionsarepredeterminedandthezaxismotionisnon‐deterministic,anddependsonthesurfacetopographyofthesamplebeingscanned.Itisnotpossibletopredictthesurfacetopography,soclosed‐loopmethodswillnotwork.Therefore,AFMswithzcalibrationsensorsuseanopen‐loopconfigurationformeasuringheights.Inaz‐sensoredAFM,whenaccurateheightdataisrequired,thez‐sensorsignalisusedinsteadofthezvoltagetodirectlymeasuretheheightsignal.Typically,theAFMsoftwarewillallowtheusertouseeitherthezvoltagesignal(whichhaslowernoise,andisthusmoreprecise),orthezsensorsignal(whichismoreaccurate).

2.2.1.4Three‐dimensionalx‐y‐zscannerconfigurationsPiezoelectricceramicsmustbeconfiguredsothattheycanmovetheprobe,orsample,intheX,YandZaxes.ThereareafewstandardconfigurationsthatareusedinAFMinstruments.Theyarethetripod,thetube,andflexures(seeFigure2.13).Eachofthesedesignsmaybeconfiguredformoreorlessmotion,dependingontheapplicationforwhichthescannerisbeingused.Itisalsopossibletocreatescannersthatuseacombinationofanyofthethreebasicdesigns.Currently,thetubescanneristhemostwidelyused,andisthescannerconfigurationpresentin>75%ofAFMsinuse.Thistypeofscannerissowidelyusedbecauseitisverycompact,allowsveryprecisemovementsespeciallyatsmallscanranges,butmainlybecauseitissimpletofabricate.Itisalsoparticularlyconvenienttoengineeraprobe‐scanningAFMwithatubescanner,becausethereisaclearopticalpathdownthecentreofthetube.However,ithassomedisadvantages;tubescanners,duetotheirgeometryaresubjecttoalotofnon‐linearity,particularlybow(anexampleoftheeffectofscannerbowisshowninSection6.2),whenusingthefullrangeofthescanner.

2.2.1.5ScannersforfastAFMInordertodevelopanAFMthatisabletoscanmuchfasterthannormal,thescannermustbeabletoovercomethelimitationofthetraditionalscanners,whichistheirlowfirstresonantfrequency.Ascannerwithahigherresonantfrequencywillallowfasterscanningwithoutthescannergoingintoresonance.Andoetal.havemadesignificantprogressinthisdirection[3,4,34].Forexample,afastscannerhasbeenconstructedfrompiezoelectricstacks,toachieveahighresonantfrequencyof240kHzversus15kHzforatypicaltubescanner[34].Analternativetechniqueistouseresonantscanners[35,36].Thismeansaveryhighscanratecanbeused,butthescanrateisfixed.Typicallytheseareconstructedfromhighresonantfrequencyflexurescanners,orcanalsobeconstructedwithtuningforkarrangements,althoughthesearesomewhatimpracticalforlargesamples[35].

FastscanningAFMsystemshavebeenshowntoachievescanningasfastas80msper

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frameinintermittentcontactmodeinliquid[4],orevenasfastas1msincontactmode(albeitwithoutfullfeedback)[35],comparedtoca.100secondsforanormalAFM.However,inordertoscansampleswithsignificanttopography,thegreatestchallengeistocreateaz‐axispositionerwhoseresponseisfastenoughtoreacttorapidchangesinthesampleheight,duetoextremelyfastx‐yscanningoverthesample.

(p.21)

Fig.2.13. ConfigurationsofcommonAFMscanners.Top:atubescannerisconfiguredsothatitmovesinthex‐y‐zaxes.Fourelectrodesontheoutsideareusedforthex‐yaxismotion,andtheinnerelectrodeisusedforthezaxismotion.Middle:aflexurescanneroperatesbypushingonaflexurewithapiezoelectricwhichthencausesthestagetomove.ThereisagaininthemotiongivenbytheratioofL2/L1.Aone‐dimensionalflexureisshownforclarity,typicallyflexurescannersareset‐uptoscaninthex‐yaxes.Bottom:thesimplestthree‐dimensionalscanner,thetripodscanner.

2.2.2Forcesensors

TheforcesensorinanAFMmustbeabletomeasureverylowforces.Thisisbecause,foraverysharpprobetobeused,alowappliedforceisrequiredsothatthepressure(force/area)canbelowenoughsothattheprobeisnotbroken.

AnumberofdifferentforcesensorshavebeentestedanddemonstratedtoworkwithanAFM.SomeoftheseforcesensordesignsareillustratedinFigure2.14.Theuseofanopticallever(sometimesknownasalightlever),usedroutinelyformeasuringminutemotionsinscientificinstrumentation,wasfirstdemonstratedinanAFMin1988[23].WiththeadventofmicrofabricatedcantileverstheopticalleverAFMbecamethemostwidelyuseddesignfortheforcesensorinanAFM,andtoday,nearlyallAFMsemployopticalleverforcesensors.

(p.22)

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Fig.2.14. DifferentforcesensorsemployedinAFMdesigns.

TheprincipleoftheopticalleverisshowninFigure2.15.Theleverconsistsofalaserfocusedtoaspotonthebackofareflectivecantilever;thebeamisthenreflectedontoasplitphotodetector,whichmeasuresthepositionofthelaserspot.Inananalogouswaytoamechanicallever,theopticallevermagnifiesasmallmovementofthecantilever,tocreatealargemovementatthephotodiode.Thechiefadvantageofthissystemisthatitishighlysensitivetoverysmallmovementsofthecantilever,anditisquitesimpletobuild[23,24,41].

2.2.2.1OpticalleversensorsThedesignforanopticalleverAFMsensorisillustratedinFigure2.15.Alaserbeamisreflectedbythebacksideofareflectivecantileverontoafour‐segmentphotodetector.If

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aprobe,mountedonthefrontsideofthecantilever,interactswiththesurfacethereflectedlightpathwillchange.Theforceisthenmeasuredbymonitoringthechangeinlightdetectedbythefourquadrantsofthephotodetector.

(p.23)

Fig.2.15. Schematicdiagramoftheopticalleversensor.Inanopticallever,astheendofthecantileverbendsthepositionofthelaserspotonthedetectorchanges.Asthecantilever–detectordistanceDcdislarge,asmallmovementofthecantilevercausesalargechangeinthelaserspotpositionatthedetector.

ThecantileverintheopticalleverAFMistypicallyfabricatedwithaMEMSprocess.Thecantileversaresmall,generallybetween50and300micronslong,20–60micronswide,andbetween0.2and1micronthick.Section2.5hasamoredetaileddiscussionofthecantileversandprobesusedinanAFM.TheopticalleverAFMforcesensorrequiresalignmenteachtimetheprobeischanged.Typically,alignmentisaccomplishedbyfirstpositioningthelaserbeamontothecantilever,andthenconfirmingthatthelightisreflectedontothecentreofthephotodetectorbylookingatthephotodetectorsignal.Thisalignmentprocedureisrathertime‐consuming,andisnotalwaysfullyreproducible;smallchangesinthelaseralignmentcanaffecttheforce‐sensitivityofthesystem.Thealignmentprocedureisoneofthedisadvantagesoftheopticalleversystem.AprocedureforopticalalignmentisgiveninSection4.2.ThelasercanalsogiverisetoimageartefactsasshowninSection6.6.IntheidealopticalAFMdesign,theprobewouldhavea90°anglewithrespecttothesurface.Practically,however,thisisnotpossiblebecauseoftheconstraintofthemechanismthatholdstheprobeinplace.Thisrequiresthattherebeananglebetweentheprobe/cantileverandthesurface,toensurethatonlythetipoftheprobetouchesthesample.Thisangleisusuallybetween5°and15°.Suchanglescanalsocauseartefactsintheimages.Someprobesareavailablewithacounter‐anglebuiltintothegeometry,i.e.thetipismountedontothecantileveratca.12°sothatitcanapproachthesampleatanangleclosetotheperpendicular.TheopticalleversensorisbyfarthemostwidelyusedforcesensorforAFMs.Thefollowingsectionscoverthedesignand

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implementationofopticalleverforcesensors.

2.2.2.2IntegratingopticalleverforcesensorsandscannersThefirstAFMdesignsscannedthesampleandkepttheprobestationary.Thissample‐scanningdesignisoptimalforonlylimitedtypesofsample.Tocreatetip‐scanningAFMsitisnecessarytodesignAFMscannerswherethex‐y‐zscannerisintegratedwiththe(p.24)

Fig.2.16. Designsfortip‐scanningAFMSwithopticalleversensors.Left:thelaserisscannedwiththecantilever.Right:thelaserisfixedandthecantileverisscanned,alenskeepsthelaserlightfocusedonthecantilever.

opticalleverAFMforcesensor.Thesimplestapproachtointegratingthex‐y‐zscannerwouldbetomounttheopticalleversensorattheendofthescanner.Thisisnotfeasiblebecausethezpiezoisnotresponsiveenoughtomovetheentirelightleverupanddownastheprobeisscannedacrossthesurface.SuchanAFMwouldbetooslowtobepractical.TwomethodsareemployedforcreatingacombinedopticalleverAFMscannerwithanx‐y‐zscanner.

Inthefirstconfiguration,illustratedschematicallyontheleftofFigure2.16,thelaserandphotodetectorarescannedintheX‐Yaxis,andtheprobeismountedattheendoftheZpiezoelectric.Inthisdesignthezpiezoispartoftheopticalleveroptics.ThismeansthatastheprobeismovedupanddownintheZdirectionthelightpathchanges.However,itcanbeshowngeometricallythattheZmotionofthecantileverhasaminimaleffectontheoperationoftheAFMopticalleverAFMsensor.Inthisdesign,commonlythex‐yscannerwouldbeaflexurescanner,andthezscannerasimplepiezostack.AlsoillustratedinFigure2.16istheotherapproachthatiscommonlyused.Thelaserisheldfixedandalensisusedtofocusthelaserlightontothescanningcantilever.AsthelensmovesbackandforthintheX‐Yplane,thelaserlightstaysfocusedonthecantilever.Thephotodetectormustbethenmountedonthex‐ytranslator.

2.2.3CoarseZmovement–probe–sampleapproach

OneofthemajorchallengesinAFMdesignismakingamotioncontrolsystemthatpermitstheapproachoftheprobetothesurfacebeforescanning.Thismustbedonesuchthattheprobedoesnotcrashintothesurfaceandbreak.Ananalogousengineeringchallengewouldbetoflyfromtheearthtothemoonin60secondsandstop38meters

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fromthesurfacewithoutovershootingorcrashing.

(p.25)

Fig.2.17. ‘Woodpecker’probeapproachmethod.Thesurfaceisapproachedbyalternatelyexpandingthepiezoelectricelement,andsteppingthezmotor.Thisavoidsuncontrolledcontactbetweentheprobeandthesample.Assoonasthesurfaceisencountered,thefeedbacksystemisturnedon.

IntheAFMstagetherearetwoseparatemotiongenerationmechanismsintheZaxis.Thefirstisastepper‐motor‐drivenmechanismwithadynamicrangeofacentimetreandaresolutionofafewmicrons.Thesteppermotorisdriveneitherbyalinearbearingoran80turnperinchscrew.ThesecondmotiongenerationmechanismintheZaxisisthezpiezoelectricelementintheAFMscanner.Thezpiezotypicallyhasadynamicrangeofabout10micronsorlessandaresolutionoflessthan0.5nm.Whilesteppermotorshavetherangeandspeedtoapproachthesurfacefromagreatdistanceinashorttime,theyhaveneithertheresolutionnorfastresponsetimetoputthetipintofeedbacksafely.Ontheotherhand,thepiezodriverissensitiveenoughtosafelygointofeedback,butcanonlymoveshortdistances.

Typically,probeapproachisachievedwitha‘woodpecker’method,(showninFigure2.17).Inthismethod,thesteppermotorissteppedasmallincrement,say1micron.Thenthezpiezoelectricceramicisextended5micronstoseeifthesurfaceisdetected.Thezpiezoisthenretracted,thesteppermotorextendsonemoremicron,soonandsoon.Akeycomponenthereisthatwhentheprobeencountersthesurface,thefeedbackisturnedonimmediately.Inthisway,theAFMcanapproachthesurfacefromseveralhundredsofmicrons,withoutriskofcrashingthetip.

TherearetwoprimarymechanismsthatmaybeusedfortheZmotioncontrol,asshowninFigure2.18.Inthefirst,threeleadscrewsareusedtogetherwithakinematicmount.Allthreescrewscanbeturnedsimultaneouslyorasinglescrewmaybeturned.Ifonlyoneofthescrewsisturned,thereisareductionofmotionatthecentreofthethreescrews.Thisgeometricreductioninmotioncanbeusedtogetveryprecisemotion.Forautomatedtipapproach,oneoralloftheleadscrewsisattachedtoamotor.Inthe

Administrator

Highlight

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secondmethod,alinearbearingisusedtodrivetheAFMscannertowardsthesample.Thelinearbearingmustbeveryrigidtoavoidunwantedvibrations.

2.2.4CoarseX‐YmovementMostAFMsincludeanX‐Ypositionstageformovingthesamplerelativetotheprobe.Thestagemaybemanualorautomatedwithmotors.TheprimaryfunctionoftheX‐Ystageis(p.26)

Fig.2.18. ConfigurationsusedforcoarseZapproachmechanism.Left:onAFMsdesignedforsmallsamples,akinematicmountistypicallyused.Oneorallofthethreadedscrewsareusuallymotorizedforanautomatedprobeapproach.Right:alinearbearingcouldalsobeemployedtomovetheAFMheadintheZaxis.

forlocatingfeaturesonasurfaceforscanningwiththeAFM.TheresolutionoftheX‐Ystageisusuallylessthan1/10therangeofthex‐yscannerthatmovestheprobe.TherearetwopossibleconfigurationsfortheX‐Ystage.Inthefirst,thesamplesitsontopofanxandycrossedrollerbearing.Inthesecond,thesampleismountedtoablockthatisdirectlyonthebaseofthemicroscope.Typicallythebaseismadefromgranite.ThemetalblockisthenpushedaroundwiththeX‐Ymotors.TheadvantageoftheseconddesignisthatthereislesschanceoftheX‐YstageintroducingnoiseintotheAFMmechanicalloop.Inbothcases,themechanismsmustbehighlywear‐resistant,asanyvibrationswillcompromisethemechanicalloopoftheAFMhead.

2.2.5Opticalorinspectionmicroscope

LiketheX‐Ystage,themicroscopeopticisnotanessentialfeatureforanAFMstage.Theopticisgenerallyusedforfindingtheregionforscanning.Also,theopticalscopecanbehelpfulinpositioningthelaserlightonthecantileverintheopticalleverAFMforcesensor.TheopticalmicroscopeinanAFMcanalsobehelpfulforprobeapproach.

TherearethreeopticalmicroscopeviewingdesignsthatmaybeusedinanAFMstage,illustratedinFigure2.19.The90°topdowndesignisoptimalforapplicationswhenhigh‐resolutionopticalmicroscopeimagingismandatory.The45°designisparticularlyhelpfulforprobeapproachandisusedwhenhigh‐resolutionopticalimagingisnotrequired.The90°bottomviewdesignistypicallyusedwithaninvertedopticalmicroscopeforbiologicalapplications.Inthiscase,itisparticularlyusefultouseaprobe‐scanningdesign,usuallywithatubepiezoorotherscannerthatcanhaveaholeinthecentre.Opticalaccessisthenunimpeded,andthelackofanyAFMcomponentsbelowthesamplereducesthechanceofinstrumentdamagefrombuffersolutionleaksortemperatureeffects;AFM

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scannersaregenerallyincompatiblewithwater,orgreattemperaturevariations.Theintegrationofhighqualityinvertedoptical/fluorescence/confocalmicroscopeswithAFMisveryusefulinarangeofbiologicalapplications,seeSection7.3,andAFMshavebeendesignedforintegrationwithsuchmicroscopessincethe1990s[42,43].

(p.27)

Fig.2.19. Left:videocameraimageofthecantileverandsampleinanAFM(90°topview).Thered‘spot’isfromthelaserthatisusedintheopticalleverforcesensor.Withscanningrangesgreaterthan1μm,itispossibletoseetheAFMcantilevermoveinthevideomicroscopeimage.Middle:thethreepossibleviewingpositionsofanopticalmicroscopeinanAFM.Right:imageinanAFMwith90°bottomview;notethelaserlight(purpleinthiscase)canbeseenthroughthecantilever,whichisseenthroughthesample(cellsonaglassslide).(Acolourversionofthisillustrationcanbefoundintheplatesection.)

2.2.6Mechanicalloop

ThegreatestfactorthataffectstheverticalresolutionornoisefloorofanAFMistherigidityofthemechanicalloop.Themechanicalloopiscomprisedofallthemechanicalelementsbetweenthesamplesurfaceandtheprobe,asillustratedinFigure2.20.Ifthisloopisnotrigid,thentheprobecanvibrateinanuncontrolledmannerrelativetothesample,andnoiseisintroducedintoimages.Itistypicallyeasiertomakethemechanicalloopveryrigidbymakingthemicroscopeverysmall.Becauseofthis,inpracticethehighestresolutionAFMinstrumentsareverysmall.ItalsomeansthatitisverydifficulttomakeAFMstagesforlargersamplessuchassiliconwafersoropticaldisksthathaveveryhighverticalresolutions.

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Fig.2.20. ThemechanicalloopinanAFMincludesallofthestructuralelementsthatarerequiredtoholdtheprobeatafixeddistancefromthesample.Thisincludesthex‐y‐zscanner,X‐Ysamplestage,Zmotorandtheprobe.

2.3AFMelectronicsMostoftheelectronicsinanAFMareresidentinaseparatecabinetfromthestageandthecomputer.Thefunctionsintheelectroniccontrollermaybeconstructedwithdigitalsignal(p.28) processing(DSP)chipsoranalogueelectronics.Thissectiondoesnotdiscusstheimplementation,butdescribestheblockfunctionsinthecontroller.TheprimaryfunctionoftheelectronicsinanAFMisto:

(a)Generatescanningsignalsforthex‐ypiezoelectrics.(b)TakeaninputsignalfromtheforcesensorandthengeneratethecontrolsignalfortheZpiezo.(c)OutputcontrolsignalsforX‐Y‐Zsteppermotors.(d)Generatesignalsforoscillatingtheprobeandmeasuringphaseoramplitudewhenanoscillatingmodeisusedforscanning.(e)Collectsignalsfordisplaybythecomputer.

Asmentionedabove,thesefunctionsmaybeimplementedwitheitherdigitaloranalogueelectronics.Inthedigitalapproach,seeFigure2.21,allsignalsfromthestagearedigitized,andaDSPchiptakescareofallofthefeedbackcontrolcalculations.Also,theDSPchipgeneratesthex‐yrasterscanfunctions.Theadvantageofanalogueelectronicsisthattheyaretypicallylessnoisy.Thiswillgenerallyleadtoalowernoiseflooroftheinstrument,andthusmayenableacquisitionofhigherresolutionimages.BecausethefunctionalityofaDSPchipiscreatedbyasoftwareprogram,theDSPapproachgivesmoreflexibilityandcanbechangedveryrapidly.Instrumentswithdigitalelectronicsmight,forexample,allowsimplesoftware‘upgrades’toenablenewfeaturesoracquisitionofmoredatachannelssimultaneously.ThefollowingsectionsareadetaileddescriptionofthefunctionsshowninFigure2.21.

2.3.1x‐ysignalgenerationThex‐ysignalgeneratorcreateaseriesofvoltagerampsthatdrivethexandypiezoelectricelementsintheAFM,asillustratedinFigure2.22.Thescanrangeisestablishedbyadjustingtheminimumandmaximumvoltage.Thepositionofthescanis

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establishedbyoffsettingthevoltagestotheceramic.Finally,thescanorientationisrotatedbychangingthephasebetweenthesignals.ItcanbeseenfromFigure2.22,thattheforwardandreversescanlinesdonotcoverexactlythesametopography.However,itisusuallyassumedthattheyareequivalent,andgenerally,thereisnoappreciabledifferencebetweenthetwo.Ingeneralitisbestifthedrivesignalsdonothavesharpedgesattheturningpoint.Sharpedgescanexciteresonancesinthepiezoelectricceramics,andcausethemtovibrate.Suchvibrationscreateunwantedartefactsand‘ringing’intheimages.HigherspeedscanningwithanAFMinparticularisalmostalwaysdoneusingroundedsignalssuchassincwavestodrivethepiezoelectricceramics.Furthermore,evenwithslowspeedAFMwhenusingstraight‐edgedsignalssuchasshowninFigure2.22,theresponseofthescannerisnotlinearattheturnaroundpoints.Toovercomethissome‘overscan’istypicallyincludedinthescanning,suchthatonlythelinearresponsepartofthedataisrecorded.Forexample,toscana10μmarea,theinstrumentmightreallymove12μmintheslowscandirection,anddiscard1μmofthedatafromeitherend.Inthisway,therecordeddatadoesnotsufferfromedgeartefacts.

ThemaximumscanrangeoftheAFMscannerisestablishedbythemechanical–electricalgainofthepiezoceramicsandthemaximumvoltagetheycantoleratebeforedepolarizing.Asanexample,thepiezoceramicsmayhaveagainof1μmpervolt.If(p.29)

Fig.2.21. BlockdiagramofAFMelectronicsfunctions.Top:electronicsasimplementedwithanalogueelectronics;Bottom:asimplementedwithahigh‐speedDSPchip.

themaximumpotentialis100volts,thenthescanrangeis100microns.Themaximumachievableresolutionissetbythenoisefloorofthedrivingvoltage.Anoisefloorof1millivoltwouldgiveanX‐Yresolutionof1nanometreinthiscase.

ItisimportantthatthebitnoiseassociatedwiththeX‐Yscangeneratorsbelessthantheanaloguenoiseflooroftheelectroniccontroller.Forexample,ifthescanrangeis100μm

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andtheanaloguenoisefloorislessthan1nm,thenthenumberofbitsrequiredisatleast100,000,whichisgreaterthan2[16]bits.ThisissignificantbecausemostDACsstoresuchdataas16bitnumbers(i.e.theycanhavenomorethan65,536possiblevalues).Thus,ifthisisthecase,someresolutionwouldbelostwhenthedatawasdigitized.Toovercomethis,oneoptionistouseascaleandoffsetDACandamplifierifthescanningDACdoesnotgiveenoughbitresolution.Thisovercomestheresolutionproblembecausealthough(p.30)

Fig.2.22. Thewaythexandypiezoelectricelementsaredrivenbyvaryingpotentials.Left:illustrationofthesignalsoutputfordrivingthexandypiezoelectricsintheAFMscanner.Right:themotionoftheprobeinthexandyaxiswhenthepiezoelectricceramicsareactivated.

witha100μmscanrangewewouldliketohave1nmresolution,wedonotrequirethatresolutionoverthewholerange,butratherit'srequiredinsmallsectionofthepossiblerange(forexamplea512×512pixelregioncoveringonly1μmoftherange).Asanalternative,aDACwithamuchhighernumberofbitsmaybeused.NotetheinclusionofcircuitsforscaleandoffsetintheAFMelectronicsinFigure2.21.

2.3.2Feedbackcontrolcircuit

IntheAFM,thefeedbackcontrolelectronicstakeaninputfromtheforcesensorandcomparethesignaltoaset‐pointvalue;theerrorsignalisthensentthroughafeedbackcontroller.TheoutputofthefeedbackcontrollerthendrivestheZpiezoelectricceramic.ThetypeoffeedbackcontrolusedinAFMsiscalledaproportional‐integral‐derivativecontroller(PID).TheequationgoverningthewasthisoperatesisshowninFigure2.23.

Theproportional‐integral‐derivativecontrollertakestheerrorsignalandprocessesitasfollows:ByselectingtheappropriateP,IandDtermsinEquation2.6,theprobewill‘track’thesurfaceasitisscanned,keepingZerrminimal.TheintegraltermfacilitatestheprobemovingoverlargesurfacefeaturesandthePandDtermsallowtheprobetofollowthesmaller,high‐frequencyfeaturesonasurface.ManyAFMinstrumentsactuallyuseaPIcontroller,asthederivativetermisnotused,althoughbyconventionthecontrollerisstillreferredtoasaPIDcontroller.Here,wefollowthisconvention.ThetwosignalsfromthefeedbackloopthataretypicallydigitizedtocreateAFMimagesaretheerrorsignalandthezvoltage.Thezvoltage(convertedusingtheinstrumentcalibrationtodistance)formsthe‘height’or‘topography’image.TheuseoftheerrorsignalisdescribedmorethoroughlyinChapters3and4butmostimportantly,itisusedbytheinstrumentoperatortooptimizescanningtheparameters,includingP,IandDvalues.WhenthePIDparametersareoptimized,theerrorsignalimagewillbeminimal.Section4.2describestheprocessforoptimizingthePIDparametersinanAFM.Implementation

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ofthezfeedbackloopinanAFMcanbemadewitheitheranalogueordigitalelectronics.Theadvantageofdigital

Fig.2.23. Proportional‐Integral‐Derivative(PID)controlleroperationandequation.

(p.31) electronicsisthattheyareveryflexibleandcanbeconfiguredtodomanytypesoffunctions.Analogueelectronicstypicallyhavelessnoiseandhavealargerdynamicrange.Eitherapproachwilltypicallyprovideadequateresults.

2.3.3Outputofsignalsforsteppermotors

UsuallyAFMstageshaveseveralsteppermotorsthatmustbeelectronicallycontrolled.Thesteppermotorsaretypicallydrivenwithaseriesofvoltagepulsesthatareinaspecificphasesequence.Thefunctionsinthestagethatmaybecontrolledwithsteppermotorsinclude:

•X‐Ysampletranslation.•Zmotioncontrol(1to3motors).ThesearefortheZ‐approachmechanism,whichmustbecoordinatedwithmovementsofthezpiezoscanner(seeSection2.2.3)•Zoom/focusonvideomicroscope.•Someinstrumentsallowtheusertomanually‘step’thez‐motoralittleinordertorepositionthescanningpositionalongthezpiezo.•Someinstrumentshavefocussing/alignmentcontrolsforthelaserintheopticallever.

Typically,anAFMwillhavesubsetofthesemotorizedmechanisms.SimplerAFMswillhavefewerofthemimplemented,astheysimplymaketheAFMmoreconvenienttouse.TheexceptionistheZ‐approachmechanismwhichisrequiredforallAFMinstruments.

2.3.4Oscillatingsignals

ForoperationofcertainAFMmodes,itisnecessarytomechanicallyoscillateorvibratethecantileverandtocomparethemodulatedsignalphaseoramplitudetothedriveoscillation.Section3.1.2providesadetailedexplanationofthewaythesemodesoperate.Feedbackcontrolmaybeimplementedsuchthatthephaseoramplitudedifferencetotheinputsignaliskeptconstantduringscanning.Figure2.24illustratesthecircuitusedformechanicalmodulationandphase/amplitudedetectionintheAFM.Ifthefeedbackcontrolmaintainsaconstantphasechange,thentheamplitudemayvarywhilescanning.Viceversa,iftheamplitudeismaintainedconstant,thenthephasemayvarywhilescanning.Forthisreason,theAFMtypicallyincludesA/Dconverterstocaptureanddisplaytheamplitudeandphasesignal.

2.3.5Collectingsignals

ManyelectronicsignalsassociatedwiththeZaxisintheAFMaredigitizedandmaybe

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displayedbythecomputer.Thesesignalsinclude:

•zvoltage–Thevoltagethatgoestothezpiezoelectricceramic,afterthePIDcontroller.•zerrorsignal–Thissignalisproportionaltotheoutputofthelightleverphotodetector,alsoknownasthedeflectionsignal.•Zsensor–Thesignalfromthemotionsensor,ifpresent,measuresthedisplacementofthezpiezoelectricintheAFMscanner.•Amplitude–Thesignalfromtheamplitudedemodulator.•Phase–Thesignalfromthephasedemodulator.

(p.32)

Fig.2.24. BlockdiagramoftheelectronicsemployedforoscillatingmodeAFMscanning.Thesignalusedforfeedbackcanbeselectedbyswitcha,borc.SwitchaisforDCfeedback,bforphasefeedback,andcforamplitudefeedback.

InanAFMthereistypicallyoneormorehigh‐speedanaloguetodigitalconverters(ADC).IfthereisasingleADC,themanyanaloguesignalsarepassedthroughamultiplexerintotheADCinput(seeFigure2.21).ThespeedoftheA/Dconvertermustbehighenoughsuchthatatleastonedatapointisconvertedperpixel.

Notethatbitnoise,asdescribedinthesectionaboutx‐yscanning,isalsoimportantinthecontextoftheacquisitionofthezaxisdatai.e.thezvoltagesignal.Althoughthezpiezorangeistypicallymuchlowerthanthex‐yrange(typically,alargesampleAFMscannermighthaveazrangeof10μmandanx‐yrangeof100μm),theachievableresolutioninzisalsomuchgreaterthaninthex‐yplane.Ifweimaginethecaseabove,thenwith10μmzrangea16bitADCwouldlimitusto10,000angstroms/65,356bits=1.4angstromsperbit.ThisismuchgreaterthantheresolutionofamodernAFM,whichmightbeexpectedtoshow<0.5angstromroot‐mean‐squared(rms)noiseinzundertypicalconditions.Thisbitnoisecansignificantlydegraderesultswhenscanningsmallfeaturesonaveryflatsurface,orcarryingoutsensitiveforcespectroscopyexperiments.Typically,toovercomethis,theAFMallowsasimilar‘scaleandzoom’solution;thezbitresolutionisincreasedtemporarilybyonlyusingapartofthezpiezorange.ThissettingistypicallyappliedbytheAFMoperator,ratherthanautomatically.Thisisbecauseitshouldonlybe

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usedwithflatsamplesandsmallscans,asitisnotadvantageoustoreducethezrangewhilescanningroughsamples.

(p.33) 2.4AcquisitionsoftwareTypically,asoftwareinterfaceisusedforcontrollingtheAFMstage.FunctionscontrolledbysoftwareincludesettingallmovementoftheX‐Ystagetolocatethefeatureforscanning,probeapproachtogettheprobenear/onthesurface,selectionofscanmode,settingandcontrollingscanparameters,displayofimageswhilescanning,andacapabilityformeasuringforce–distance(F/D)curves.Sometimesimageprocessingandanalysisarealsohandledwithinthesameapplication,butthesefunctionsarecoveredinChapter5.Figure2.25isascreenshotofatypicalAFMscancontrolwindow.Thefollowingsectiondescribesthefunctionsfoundinthecontrolsoftware.

2.4.1Display

VisualizingtheAFMdatainrealtimeiscriticaltotheefficientoperationoftheAFM.Thisallowsanoperatortoensurethattheyarescanningthecorrectregionofasample,andfacilitatesoptimizingthescanparameterssuchasscanrateandPIDsettings.Typicallythereareatleasttwotypesofdisplay.

Fig.2.25. AwindowsuchisthisistypicallyusedforacquiringAFMimages.TherearesectionsforA:displayingimages;B:displaying2‐Dprofiles,C:enteringscanparameters;andD:enteringfeedbackparameters.

(p.34)(a)Atwo‐dimensionalrepresentationoftheimageshowsthetopographyofthespecimenbeingscanned.Tocorrectfortiltbetweentheprobeandsample,theheightimageistypicallylinelevelledinrealtime(seeSection5.1.1foranexplanationoflevelling).Withoutrealtimelinelevelling,theimagewillonlyshowthetiltbetweentheprobeandsample.Usuallymultiplechannelscanbeshownsimultaneously.(b)An‘oscilloscopewindow’displaysatwo‐dimensionalscanlinesuchastheZsignalversusthexaxismotion.Anoscilloscopewindowisveryhelpfulforoptimizingthescanparametersandensuringthattheprobeistrackingthe

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sample'ssurface.Typically,datacollectedintheforwardandbackwardsdirectionsdatacanbeoverlaid.(c)AsdiscussedinSection2.3,thereareanumberofdatachannelsthatmaybemonitoredintheAFMinstrument.TheyincludetheZpiezovoltage,Zerrorsignal,Zmotionsensor,andphaseandamplitudesignals.TheAFMcontrolsoftwarewillallowoneormoreofthesesignalstobedisplayedonthescreen.Theymaybeavailableaseitherimages,orscanlinedataorboth.Inadditiontotheheightdata,viewingthezerrorsignalwhileoptimizingacquisitionparameterscanbeparticularlyhelpful.

2.4.2Stagecontrol

MakinganAFMpracticaltouserequiresmotioncontrolincludingatleastonesteppermotortomovetheproberelativetothesampleintheZaxis.AdditionalmotioncontrolisusedformovingthesampleintheX‐Yaxisrelativetotheprobeaswellascontrollingthezoomandfocusofanopticalmicroscope.

(a)Zmotioncontrol:ProbeapproachisaveryimportantfunctionintheAFM(seeSection2.2.3forthehardwareimplementationofthisandSection4.2forprecautionsfortheuseronapplyingzapproach).TheZ‐approachsoftwareshouldberapid,butitshouldnotallowtheprobetotouchthesurfaceinanuncontrolledmanner.Properlyoptimized,probeapproachtakeslessthanaminute.

Theapproachsoftwaretypicallyhasseveraloptionsforcontrollingtherateatwhichtheprobemovestowardthesample'ssurface.Softwarealgorithmsarealsocriticalforsettingthethresholdsignallevelsassociatedwiththeprobeinteractingwiththesurface.Oncethethresholdismet,theapproachisstoppedandtheAFMisputintofeedback.Properlyimplemented,afullyautomaticapproachsystempreventstheuseraccidentallyinputtingathresholdvaluethatwouldcrashthetipintothesurface.Ifthereisanautomatedvideomicroscope,thesoftwarealgorithmfortipapproachcanbeaugmentedtoshortenthetimerequiredforprobeapproach.Thisisachievedbyfocusingthemicroscopeontheprobe,thenthesample.Therelativepositionsoftheprobeandsamplearecompared.ThentheZmotorsaredrivenrapidlyuntiltheprobeislessthan100micronsfromthesurface.

(b)X‐Ymotioncontrol:Becausethex‐ymotionusingthescannerintheAFMusuallyhasarangeoflessthan100microns,anX‐Ymotioncontrolsystemisrequiredthatisabletomovetheprobetowithinafewmicronsofthefeaturesthataretobescanned.AnX‐Ypositioningtabledrivenwithsteppermotorsisoftenused.Softwareisthenusedtomovethetranslationstage.Thesoftwaretypicallyisactivatedbymousecontrolwithinthesoftwareorbyatrackball.

AdvancedsoftwarefunctionsmaybeaddedtomicroscopeswithautomatedX‐Ystages.Functionsincludeanabilitytomeasuremanyimagesadjacenttoeachother,andto(p.35) measureseveralimagesonpre‐setlocationsonthesample.Itispossibletodrivethestagetopre‐establishedlocationsforinspectionapplicationswithregistrationsoftware.

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2.4.3x‐yscancontrolTheexactscancontrolparametersthatareusedforscanningasampledependontheparticularapplication.Thereareafewvariablesthatmustbeselectedtoscanasample.Theyare:

(a)Imagesize:Thisisthewindowthatisselectedforviewingthefeaturesonasurface.Theimagesizeshouldbeatleastaslargeasthefeaturesthataretobevisualized.Oftenalargescanismeasuredandthentheoperator‘zooms’inonafeatureofinterest.(b)Numberoflinesintheimage:Thedigitalresolutionoftheimageisestablishedwiththenumberoflinesselectedfortheimage.Forexample,ifthescansizeis10×10micronsandthenumberoflinesselectedis256thenthedigitalresolutionis39nanometres.Thenumberoflinesintheimagemayrangefromlessthanonehundredtoseveralthousand.MostAFMsoftwarelimitstheimagestosquareorrectangulardimensions.(c)Imagerotationangle:Theimagescananglemaybechangedwithsoftware.Rotationanglesbetween0°and360°canusuallybeselected.Rotatingtheimagescanaxisusuallymeansthatthelargestscanrangecannotbeachieved.(d)Scanningspeed:Thisistypicallyspecifiedinhertz(i.e.linesscannedpersecond),andinnormalcircumstancesvariesfromaround0.5Hzto4Hz.Combiningthisparameterwiththenumberoflinesintheimage,givesthetimerequiredtocollectanimage.Alongwiththefeedbackparametersdiscussedinthenextsection,scanningspeedcanaffectimagequality.ThisisdiscussedfurtherinChapter4.Realistically,theimportantparameterintermsofimagingqualityisdistancecoveredovertimeratherthanfrequencyoflinecollection,soscanningspeedcanalsobeexpressedinmicrometres/nanometrespersecond.

2.4.4zcontrolSoftwareisrequiredforcontrollingthefeedbackcontrolelectronics,seeSection2.3.Therearetwofunctionsthatarecontrolled;theset‐pointvoltageandthePIDparameters.

(a)Set‐pointvoltage:Thisisthevoltagethatgoesintothedifferentialamplifier,sothisvoltageiscomparedwiththeforcesensoroutputvoltageandanerrorsignalisgenerated.Theset‐pointvoltagecontrolsthe‘relative’force.Acalibrationofthespecificcantileverisrequiredtoconverttheset‐pointvoltagetoaforce(seeSection2.5).(b)PIDparameters:Theseparameterscontrolthe‘responsiveness’ofthefeedbackcontrolelectronics.Theseparametersmustbeadjustedsuchthattheprobetracksthesurfacewhilescanning.Sections4.2–4.3provideadescriptionofoptimizationofthefeedbackcontrolparameters.

2.4.5Force–distancecurves

Force–distance(F‐D)curvesareusedtomeasuretheforcesexperiencedbytheprobe

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asafunctionofdistancefromthesurface.InF‐Dmeasurements,theprobeismovedtowardthesamplesurfacetoapre‐selectedposition,andthenretracted.TheextentofcantileverdeflectionoverthecourseofthismovementisexpressedbytheZ(deflection)signalwhich(p.36)

Fig.2.26. Softwarewindowsusedformeasuringforce/distancecurveswiththeAFM.Themainwindowshowsthecurvesacquired(A),thewindowbelowitallowstheentryofacquisitionparameters(B),andtotherightofthiswindowaresettingsforextractingdatafromthecurves(C).

isusedtogenerateaforce–distancecurve.Theendpointoftheforcecurvemightbedefinedbytheuserasacertaindistancefromthestartpoint,orasacertainvalueofcantileverdeflection.Thelatteroptionallowstheusertoeffectivelydefinethemaximumforceapplied.SoftwareformakingF‐Dcurves,illustratedinFigure2.26,hasseveralvariableparametersincluding:

(a)startandendpositionforprobe;(b)rateofprobeapproachmotion;(c)numberofF/Dcurvestosignalaverage;(d)locationonimageforF/Dcurve.

Typically,theAFMsoftwarewillalsoallowtheusertocollectaseriesofF/Dcurvesinagridpatternoverauserdefinedareaofthesamplesurface,thusenablingmeasurementofthetip–sampleinteractionacrossthesamplesurface.Thisfacilitymaybetermedlayeredimaging,volumespectroscopyorforcevolumeimaging.

2.5AFMcantileversandprobesAnopticallever‐basedAFMforcesensorrequiresacantileverwithaprobeatitsendforoperation.TypicallythesearefabricatedusingMEMStechnologyandareconsidereda(p.37)

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Fig.2.27. IllustrationofanAFMcantilever/probe/substratecreatedbymicromachiningofSiorSi3N4.Allcommerciallyavailableprobeshavesubstrateswiththesamedimension,foreaseofuseindifferentinstruments.Theprobeissometimesreferredtoasthetip,andthesubstrateasthechip.Nottoscale.

disposablecomponentoftheAFM.Inprinciple,anAFMprobeshouldlastforever;however,inpracticetheprobetipisoftenbluntedwhenittouchesasurface.Changingtheprobetypicallytakesonlyafewminutes.Inordertomakehandlingsimple,thecantileversareattachedtoacantileversubstrateorchip.Byindustryconvention,thesearenormallyca.3.5×1.6mminsize,andabout0.5mmthink,sothatprobesfromdifferentmanufacturerscanbeusedinmostprobeholdersbuiltintoAFMs.Figure2.27showsacartoonofthedesignofatypicalprobe/cantilever/substrate.

ThegeometryoftheprobeiscriticaltothequalityofimagesmeasuredwithanAFM.AllAFMimagesareaconvolutionofprobegeometryandsurface.Asanexample,inFigure2.28,iftheprobecannotreachthebottomofasurfacepit,ortrackthesidesofaparticle,theimagewillnotindicatethecorrectgeometryofthesample.FurtherdetailsontheproblemsassociatedwithblunttipsareshowninSection6.1.

2.5.1Probematerials

Inprinciple,AFMcantileverscanbefabricatedfromanymaterialthatcanbefabricatedintoaspring‐likecantilever.ThefirstAFMcantileverswerefabricatedfromtungstenwireand

Fig.2.28. Comparisonofimageprofilesobtainedwithadull(left)orasharp(right)probeonaconcavefeature(apit,top)oraconvexfeature(astepfeature,bottom).

(p.38)

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Fig.2.29. Examplesofcontactandnon‐contactprobes.Left:atypicalv‐shapedcontact‐modecantilever.Thewholeprobeismadefromsiliconnitride(Si3N4),andhasanintegratedsquarepyramidalprobetip.Right:aprobedesignedforoscillatingmodessuchasnon‐contactAFM.Thecantileverisusuallyrectangular(oramodifiedrectangleshapelikethisone).Thewholeprobeismadefromsilicon,andismuchstifferandmorepronetobreakingthanthecontactprobe;howeverithasasharpertip.

hadaprobeetchedinthesiliconattheend.EarlyintheevolutionofAFMitwasdiscoveredthatthebestAFMprobescouldbeconstructedfromMEMstechnology.TherearetwomaterialscommonlyusedforAFMcantilevers:siliconnitride(Si3N4)andsilicon(Si).

Si3N4isusedforcreatingprobesthathaveverylowforceconstants.ThethinfilmsusedforcreatingSi3N4probesmusthaveverylowstresssothecantileversdon'tbendnaturallyfromthestress.Practically,mostSi3N4filmshavesomeresidualstressandinfact,cantileversmadewithSi3N4tendtohavecurvaturealongtheirprimaryaxis.

CantileversfabricatedfromsilicontendtohavelessresidualstressthanSi3N4andsotendnottosufferfrombending.However,theSiprobesthatarefabricatedattheendofthecantilevercanbebrittleandcanbemorelikelytochipwhentheycontactasurface.Mostoftheprobesusedinopticallever‐basedAFMforcesensorsareconstructedfromSi.

2.5.2Contactversusoscillatingmodeprobes

Cantileversforopticallever‐basedAFMcanbeoperatedintwobasictopographymodes;contact(static)modeandoscillatingmodes,seeSection3.1.Thecantileversusedforcontactmodehaveforceconstantsthataretypicallymuchlessthan1N/mandarefabricatedfromeithersiliconorsiliconnitride.Ontheotherhand,oscillatingmodecantileversareusuallyfabricatedfromsiliconandhaveforceconstantsthataregreaterthan10N/m.ExamplesaregiveninFigure2.29.Therearealsoalargenumberofotherprobesavailabledifferentiatedbydifferingtipgeometries(forexamplemanyexamplesofprobeswith‘sharpened’andhigh‐aspect‐ratiotipsareavailable),cantileverforceconstants,andcoatings.Non‐topographicmodesarecommonlycarriedoutwiththesespecialitycantilevers,seebelowformoreaboutsuchcantileversandSection3.2fordetailsoftheirapplications.

TherectangularcantileversusedasAFMforcesensorshavethesamemechanicalpropertiesasallcantileveredbeams.Theyhaveaverticalforceconstantandresonant

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frequencygivenbyEquation2.5.AdditionallyacantileverhastorsionalandlateralbendingforceconstantsgivenbyEquations2.6and2.7.Thecalculationsofthecorrespondingequationsforv–shapedleversisconsiderablymorecomplex,see[44].

(p.39)

(2.7)

(2.8)

(2.9)

where:Kver=verticalforceconstant

Ktor=torsionalforceconstant

Klat=lateralforceconstant

E=Young'smodulus

G=modulusofrigidity

w=cantileverwidth

l=cantileverlength

t=cantileverthickness

2.5.3Controloftipshape

HorizontalresolutionwithanAFMcanoftenbeimprovedwithsharperprobes.TherearemanytechniquesavailableforsharpeningAFMprobes.BecausethesharpnessandreproducibilityofmanufacturedprobesisoneofthelimitingfactorsonthequalityofAFMresults,newtypesofprobesareunderconstantdevelopment.Examplesofthisincludecompositeprobessuchasmixedsilicon/siliconnitrideprobes,andprobesterminatingincarbonnanotubes.However,itremainsamajorchallengetoproduceprobeswithareproducibletipradiusbelow10nmatareasonablecost.

•Si3N4probesaresharpenedbyaddinganextraprocessstepthatchangestheshapeofthepitthattheSi3N4filmisdepositedon.However,this

= w × ×kver

E

4( )t

l

3

= t × ×klat

E

4( )w

l

3

= w × × ×ktor

G

3t3

l

1

(H + t

2)2

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techniqueoftengivesdoubletipswhichcancausesubstantialartefactsinimages.Anotheroptionisanadditionaloxidation/etchingprocessaftertheprobeismanufactured.•Siprobescanbesharpenedbychemicaletching,ionmillingorbyaddingacarbonnanotube(seeFigure2.30).Eachofthesetechniquescancreateasharperprobe,butalsoaddtothepriceoffabricatingtheprobe.

OnemethodforcontrollingthegeometryoftheprobeonanAFMcantileveristomountasphereattheendofthecantilever.Thespherecanbemounteddirectlyonacantileverthatdoesnothaveaprobe.Thespheremayalsobemountedattheendofa‘plateauprobe’,oraprobethatdoesnothavesharptip,butinsteadhasaflatplateauattheendofthetip.

Probedamage

ThequalityofanAFMimageiscriticallydependentontheshapeoftheprobeusedformeasuringanimage.TheAFMprobecanbeseverelydamagedbytipapproach.Handling

Fig.2.30. SEMimagesofdifferenttypesofsharpenedsiliconprobes.A:astandardsiliconoscillatingmodeprobe.B:‘super‐sharpsilicon’probesharpenedwithanelectrochemicaletch.C:‘high‐aspect‐ratio’probesharpenedwithionmilling.Right:probemodifiedwithcarbonnanotube.ImagesA–CreproducedwithkindpermissionfromNanoWorldAG.

(p.40)

Fig.2.31. Simplifiedviewofprobedeconvolution.Ifthecross‐sectionoftheprobegeometryisdescribedasanupsidedowntriangle,itissimpletoremovetheeffectoftheprobefromanimageofananoparticle.Theactualdiameterofthenanoparticleiscalculatedusingtheequationattheright.However,realprobesdonothavetheshapeofanupsidedowntriangle.

theprobeincorrectlybeforeitisplacedinthemicroscopecanalsocauseprobedamage.Forexample,iftheprobeisexposedtohighelectricfields,theprobetipcanbeblownoffbyelectrostaticdischarge.Finally,theprobetipcangetdirtyfromthepackingmaterialsusedtoholdtheprobewhileshipping.

2.5.4Probeshapedeconvolution

Iftheprobegeometryisanalyticallyknown,itispossibletoremovetheprobegeometry'seffectonanAFMimagebyaprocesscalleddeconvolution(seeFigure2.31

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foratwo‐dimensionalrepresentationoftheproblem).UnfortunatelythegeometryofAFMprobesisnotwellknownfromfirstprinciples,astheydonotnormallyhavesimplegeometricalshapes.Furthermore,becausethemethodofmanufacturingsuchprobesisnotperfectlyreproducible,therewillbevariabilityfrombatchtobatchandevenconsiderablevariationinprobecharacteristicsproducedonthesamesiliconwafer.Thus,inordertocorrectlydeconvolvethetipcontributionsfromanimage,itisnecessarytocharacterizeeachtiponacasebycasebasis.

Unfortunately,itisdifficulttofindatechniquetoaccuratelyandnon‐destructivelymeasurethetipgeometry.BothTEMandSEMhavebeentried[45–47],butalthougheithertechniquecouldhaveinprinciplesufficientresolutionforthetask,thereareanumberofdifficulties.Neithertechniquegivesrealthree‐dimensionalinformation,sosuperpositionofvariousrotatedimagesisnecessarytofullycharacterizetheprobe.Theresolutionrequiredmustbesimilartothatofthedetailsintheimage,i.e.thesameastheresolutionofAFM.Toachievesuchresolutions,electronmicroscopesmustbeoperatedathighdrivingvoltages,andwithsuchhighvoltagessharpfeaturessuchastheprobeareeasilydamagedbyover‐charging,especiallywithoutmetalcoating,whichcanaltertheprofileofthetip.Suchdifficultiesmeanthatthesetechniquesarequiteimpractical.Theidealinstrumenttogetthree‐dimensional,high‐resolutionmeasurementsoftheprobeistheAFMitself.Thiscanbeusedbytipself‐imagingwhichisdonebyusingtheAFMtoimageaspike‐likefeature(seeforexamplethetip‐characterizationsamplesdescribedinAppendixA).Thisresultsinthespikeimagingthetip,i.e.theresultingimageisanimageofthetip,onlysomewhatdilatedbythesample,assumingthattheradiusofthespikeismuchlessthanthatofthetip.Arelatedtechniqueistoimageaverywell‐knownsamplesuchaswell‐characterizednanoparticles[48,49].Knowingthecorrectsamplegeometrythedilationbythetipiseasytoextract.Thesetechniquesaresomewhatmoreconvenient(p.41)

Fig.2.32. Exampleofblindreconstructionandsubsequentdeconvolutionofprobegeometry.Byusingtheblindreconstructiontechnique,itispossibletocalculatetheprobegeometryfromtheimageofthenanoparticles(top).Thentheprobegeometrycanberemovedfromtheentireimage,givingthesharperimageshownbelow.

thanelectronmicroscopy,butbothinvolveimaginganexternalsample,andcouldalterthenatureofthetopbycontamination(e.g.bythenanospheres)orwearing(bythespike),andthestabilityofaverysharpfeaturetorepeatedimagingbytheAFMisuncertain[50].

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However,usingatechniquecalledblindreconstruction,thegeometryofaprobecanbecalculatedbycarefullyanalysinganimageofthesampleofinterest[50–53].BlindreconstructionworksbyassumingthattheAFMimageisformedbyadilationprocess[54].Thismeansthatnotonlydoesthetipprobethesample,butthesamplealsoprobesthetip.Inprinciple,eachpixelintheimageobtainedcontainsinformationabouttheshapeoftheAFMprobetip,aswellastheinformationabouttherealsampletopography.Theideaofblindreconstructionistoextracttheinformationaboutthetipfromeachpixel.Inordertobuildupapictureofthetipfromtheinformationintheimage,thecorrelationbetweentheneighbourhoodofeachpixeliscomparedtotheneighbourhoodofeachotherpixelintheimage.Essentially,theroutinelooksforanyrepeatingpatternsintheimage,andassumesthatanysuchpatternsderivefromtheshapeofthetip.Suchmethodsareverycomputerintensiveanditcantakealongtimetoanalyseasingleimage.Forexample,todotheblindreconstructiononasingle512×512pixelimagewithaCore2processorcantake5minutes.Havingobtainedthegeometryofthetipfromtheimage,itisthenpossibletomathematicallyremovetheprobebroadeningartefactsfromtheimage.Asanexample,Figure2.32showsanAFMimageof100nmdiameternanospheres,andtheeffectsofblindtip‐shapereconstructionandsubsequentimagedeconvolutionontheimage.

Thistechniquehasbeenshowntobehighlyeffectiveundercertaincircumstances[45,55],butitdoeshavesomelimitations[54].Thetipprofileextractedisnottherealprofile,butanestimateoftheprofileofthebluntesttipthatcouldhavemadetheimage.Inaddition,imagingsomesampleswillgiveatipprofileestimatethatisclosertotherealshapethanothers.Specifically,sampleswithhighroughnessandsteepfeatureswillleadtoatipprofileclosetotherealone.Ifthesamplemeasureddoesnothavethese,itmaybenecessarytoimageanexternalsampleafterimagingthesampleofinteresttogetadequate(p.42) dataforblindreconstruction.Also,theaccuracyoftheestimatewasshowntodependstronglyontheimagesizeused.Specifically,smallimageswilltendtooverestimatethesharpnessofthetip,duetolowersignal‐to‐noiseratioatsmallscansizesandthisnoiseathighresolutionscanalsointroducedistortionsintheestimatedtipshapeversustherealshape[56].Ontheotherhand,largeimagesorimageswithalowpixeldensitywilltendtogiveresultssuggestingamuch‘blunter’profileofthetipduetoundersamplingofthesurfacetopography[57].Overall,blindreconstructionisatechniquewhichisrelativelysimpletoapply,andcanconsiderablyimprovethequalityofAFMdata,byremovinglargepartofthedilationeffectofthetip,aslongascareistakenintheapplicationofthetechnique.Itisalwaysworthremembering,however,thatinthecaseofablunttiporsharpsamplefeatures,therewillexistsomepartsofthesamplethatareneverprobedbythetip[58](seeforexample,Figure2.28,wherethecornersofthedepressions,orcornersoftheprotrusionscouldnotbeimaged),anddeconvolutioncannothelphere.

2.5.5Cantileverforceconstants

CantileveredAFMprobesfabricatedwithMEMSprocessingtechnologiesaresubjecttofairlydramaticdistributionsofspecifications.Forexample,awaferofprobescouldhaveonly85%oftheprobeslessthan10nmindiameter.Theother15%couldhaveany

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diameter.ThisdistributioncandramaticallyaffectthequalityandresolutionofAFMimages.Besidestheprobegeometry,thecantileverscanhaveasubstantialvariationinspecifications,especiallythethicknessofthecantilevers.Becausetheforceconstantofthecantilevervariesastheinversecubeofthethickness,theforceconstantsofMEMSfabricatedcantileverscanvarydramatically.Table2.1showsanexampleofthevariabilityofcantilevergeometriesandthecalculatedimpactoncriticalspecifications.Itcanbeseenthatinrelativeterms,thethicknesshasaveryhighvariabilitycomparedtothewidthorlength,andthatthisgreatlyaffectstheforceconstantvariability.

Calibrationofcantileverforceconstants

AsillustratedinTable2.1,thereisconsiderablevariabilityintheforceconstantofanAFMcantilever,mainlybecauseofvariationsinthethicknessofthecantilevers.Thus,whenknowledgeoftheexactforceappliedisrequired,theforceconstantofthecantileverusedforthetestsmustbecalculated[59].Thisisparticularlyimportantforforcespectroscopyapplications(discussedfurtherinChapter3),butknowledgeoftheappliedforceisalsoveryimportantforreproducibilityinimagingstudies.AlargeamountofworkhasbeendonetodetermineoptimumtechniquestomeasuretheforceconstantsofAFM

Table2.1.ExampleofthevariabilityinmanufacturedAFMcantileverproperties.CantileverData Value RangeThickness 2μm 1.5–2.5Meanwidth 50μm 45–55Length 450μm 445–455Forceconstant 0.2N/m 0.07–0.4Resonancefrequency 13kHz 9–17

(p.43)

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Fig.2.33. EquationsforcalculatingforceconstantsofrectangularandtriangularcantileverswiththeSadermethod[66].

cantilevers(see,forexamplereferences[60–65]).ThemostcommonlyusedmethodusedfortocalculatethenormalforceconstantistheknownastheSadermethod[66–68].Inthismethod,thephysicalgeometryofthecantileverismeasured,typicallywithanopticalmicroscopeandthequalityfactor,Q,ismeasured.Thequalityfactorisofthecantileverisessentiallyameasureofthebandwidthoftheoscillationcomparedtotheexcitingfrequency),andissimpletomeasurewiththeAFM.Withthephysicalmeasurements,andtheQofthecantilever,Equations2.11and2.12canbeusedtocalculatethespringconstant,seeFigure2.33.Thismethodhasbeenlaterextendedtothecalculationofktor,thetorsionalconstant[61],aswellastocantileversofarbitrarygeometry[69].

Severalothermethodsforcantilevercalibrationarealsowidelyused.Theaddedmassmethod,firstdescribedbyCleveland[70],takesadvantageofthechangeinfrequencyofaleverwhenamassisaddedtotheend.Essentially,themethodconsistsofphysicallyaddingasmallwellcharacterizedparticletoaprobetip,forexampleatungstenorpolymermicrosphere.ThismethodisatleastasaccurateastheSadermethod[63,71],anddoesnotrequiremeasurementofcantileverdimensions,butalthoughdescribedasnon‐destructive,(p.44) ishardtoperformwithoutthedangerofdamagingthetip,andreliesonhavingwell‐characterizedmassesreadilyavailable.

Thethirdmethodcommonlyappliedtoobtainthenormalspringconstantisknownasthethermalnoisemethod,firstpresentedbyHutteretal.[72,73].Thismethodrequiresmeasuringthethermalnoisespectrumwhenthecantileverisincontactwithasurface.Thethermalnoisespectrumcanbeveryweak,anditisnecessarytouseahighperformancespectrumanalysertocollectthedata,pressingthecantileveragainstthesurfacemeansitcanpotentiallychangethetipshape.However,thetechniquehasbeenshowntobebothpreciseandaccurate[62].

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Finally,thereferencecantilevermethod[74,75]consistsofpressingthecantileveragainstapre‐calibratedspring,orreferencecantilever.Thisisrelativelyeasytoperform,butreliesontheavailabilityofawell‐characterizedcantilever,andagain,couldbeconsideredtoalterthetipshape.

Allthemethodsmentionedabovehavefocussedonthenormalforceconstantsofcantilevers.However,forcertainapplicationstorsionalorlateralforceconstantsmustbecalibrated[76,77].ThisisdiscussedfurtherinChapter3,inthesectionsonlateral‐andtorsional‐bendingbasedmodes.

2.5.6Improvedprobingsystems

ThescanrateofanAFMlimitsthesizesofareasthatcanbeanalysedtoafewhundredmicronsatbest.ItwouldbehighlydesirabletocreateanAFMwithmultipleprobesthatcouldscanmanyareassimultaneously.Severaleffortstocreate‘multipleprobe’atomicforcemicroscopesdemonstratedthatitispossible.Inthefirstapproach,severalAFMscannerswerepositionedaboveasiliconwafersampleandscannedindependently.Inthesecondapproach,severalprobesononesiliconwaferwereusedtoscanasamplesimultaneously[7].ThegreatestchallengeforcreatingmultipleprobeAFMinstrumentationistogetalloftheprobestobeassharpasisrequiredforhigh‐resolutionscanning.InmostmultipleprobeAFMdesigns,asimplifiedcantileveractuation/sensingsystemisused,toavoidthecomplicationoffittingmultipleopticalleverset‐upsaroundclosely‐spacedcantilevers[78].Theseset‐upsalsosimplifytheoperationoftheinstrumentsgreatly,althoughtheytypicallymeanthatstandardcost‐effectivecantileverscannotbeused.

AnotherapproachtoimprovetheoverallproductivityofAFMistomaintainasingleprobe,buttodriveitatmuchhigherspeedsthanareavailablebynormalAFM.AsshowninFigure2.29,standardAFMcantilevershavelengthsoftheorderofseveralhundredmicrometers,typically200–400μm,andwidthsoftheorderof40μm.However,thereareadvantagestobegainedinspecificapplicationsinusingmuchshorterandsmallercantilevers[3,79–81].FastscanningAFMbenefitsfromtheuseofsmallcantilevers,specificallybecausetheycanhavemuchhigherresonantfrequenciesthanlargercantilevers,withouthavingveryhighspringconstants,andcancauselesssampledamagewhenscanningathigherspeeds[3,34,81].Smallcantileversalsohaveadvantagesforforcespectroscopy,becausethenoiseflooristypicallycontrolledbyperturbationsofthecantileverbythesurroundingmedium(airorliquid),whichhasasmallereffectforsmallercantilevers,leadingtohighersignal‐to‐noiseratio[82].SmallcantileversforfastscanningAFMwerefirstproposedin1996[83],buttheiruseisfarfromwidespread.ThemainproblemisthatuseofsuchcantileversinanormalopticalleverAFMheadneeds(p.45) modificationstotheopticsofthelightlever[3,84].Nevertheless,theuseofsmallleversforbothspectroscopicandfastscanningapplicationsisgrowing,andrecentlyacommercialsourceofsuchleversbecameavailable,andcommercialAFMinstrumentscapableofusinglaserspotssizessuitabletousesmallleversarenowalsoavailable.

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2.6AFMinstrumentenvironmentVariousenvironmentalfactorscandrasticallyaffecttheresultsobtainedwithAFM.Theseincludetheenvironmenttheinstrumentismaintainedin,forexamplethepresenceofvibrationsinthebuildinginwhichtheAFMishoused.AnAFMisaverysensitivedevice,andishighlysusceptibletointerferencefromvibration.ThetwomaintypesofvibrationpickedupbytheAFMareacousticandmechanicalvibrations.Acousticvibrationsaretransmittedthroughtheair,andaresometimes,butnotalways,alsoaudibletohumans.IndecidingwheretoplaceanAFMinyourorganization,itisalwaysworthlookingforthequietestroomyoucanfind;evenpeopletalkingquietlycanshowupintheAFMwhenscanningatveryhighresolution,soitisideallylocatedinaplacewithfewotheractivitiestakingplace.Section6.4.2showsanexampleofacousticnoiseinanAFMimage.Ingeneral,locatingtheAFMinaroomwithlittletrafficandaudiblenoisereducesthesesortsofinterferingvibrationstoareasonablelevel.Someacousticnoisehowever,suchasthefansusedtocooltheAFMorcomputersystem,orfromairconditioningunitsarehardtoavoid.Inaddition,increasingly,AFMinstrumentsarebeinginstalledinlocationswithunfavourablecharacteristicsfortheoperationofanAFM.Inthesecases,someformofisolationfromacousticandfloorvibrationsisnecessary.Typically,theAFMiseasilyisolatedfromacousticnoisebyplacingitinasealedcabinetconstructedfromacousticdampingmaterials.Onedrawbackofthesecabinetsisthatsuchmaterialsarecommonlymadeofpolymerfoam,andtheytendtobegoodthermalinsulatorsaswell,sothatasmallacousticcabinetcanoftenmeanitismoredifficulttodispersetheheatgeneratedbytheAFM,leadingtopoorthermalstability.Analternativetosuchcabinetsistocladthewallsoftheroomwithsound‐absorbingpanels;thesegreatlydecreasethetransmissionofacousticnoisetotheinstrumentwithoutreducingthecoolingpotential.

MechanicalvibrationsaretransmittedtotheAFMstagefrommechanicalcontact.Therearemanypossiblesourcesofsuchmechanicalnoise.Typically,however,thenoisereachestheAFMviafloorcontact.ThereforeisolationoftheAFMstagefromthefloorisnecessary.ThemostsimplemethodtodothisisbysimplymountingtheAFMonagranitestage(oftenincludedaspartoftheAFM),andfurtherisolatingwithametallicplate/rubberballsstack.Suchsystemsworkadequatelyforlow‐resolutionworkorworkwithquiteroughsamples,butaregenerallyinadequateformoredemandingapplications.Forbettervibrationisolationstwotypesofsolutionexist;activeandpassivevibrationisolation.

ActivevibrationsolutionsgenerallytaketheformofaplatformfortheAFM,whichmaybesuspended,devicesthatmeasurethevibrationtransmittedfromthebaseoftheplatform(accelerometers),andactiveelements(transducers)thatcountermeasuredvibrations,viaafeedbackloopincludingthesignalfromtheaccelerometers.SuchdevicesworkextremelywellinisolatingAFMinstruments,andaregenerallyverycompact.

(p.46)

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Fig.2.34. Examplesofdifferenttypesofvibrationisolation.Left:anactivevibrationisolationplatform(reproducedwithpermissionfromHerzan).Centre:acompressedair‐basedisolationtable.Thistypeofpassivevibrationisolationisparticularlyappropriateforlargeinstruments.ReproducedwithpermissionfromKineticSystems,Inc.Right:animageofanAFMmountedonabungeecordsuspendedplatform.ThesuspendedplatformisenclosedinacabinetdesignedtofurthershieldtheAFMfromacousticnoise.ImageusedwithpermissionfromAgilent.Metallicspringsarealsosuitableforsuspensionofplatforms.

Passivevibrationsolutionsbasicallyconsistofsomesortofspring,aweight,andadampingdevice.Usually,thesewilltaketheformofanairtableorasuspendedplatform.Thesuspendedplatformisaverysimpledevice,andconsistsofplacingtheAFMonaheavystage(whichformstheweight)thatissuspendedbysprings(eitherstrongelasticbungeecords,ormetalsprings).Withlongspringsandalargeweight,thesedeviceshaveexcellentisolationcharacteristics,butusealotofspace.Theairtableismarginallymorecompactandconsistsofasuspendedplatform,whichiscushionedbyair.Ingeneral,anyofthesolutionsmentionedhereworkextremelywell,andattenuatefloorvibrationsfrommostlocationstoanacceptablelevelforhigh‐resolutionAFMwork.SometypicaldevicesareshowninFigure2.34.

2.7ScanningenvironmentTypicallyAFMiscarriedoutunderambientconditions,butamajoradvantageofAFMistheabilitytoimagethesampleinalmostanyenvironment,fromvacuum,togas,toliquid.Themostcommonapplicationistoscaninliquid,whichisparticularlyimportantinbiologicalapplicationsinordertomeasurethesamplesintheirnativestate,orforelectrochemicalmeasurementsofmetallicsurfaces.FormoreexamplesofliquidscanningapplicationsseeChapter7.Inaddition,scanninginliquidhassomeadvantagesoverscanninginair,suchasreproducibilityofthescanningenvironment,andnotably,thetip–sampleinteractionsinliquidaremuchweaker.Oneofthemajorproblemsofscanninginambientairisthattypicallyameniscuslayerofwaterwillcoatthesampleand/ortip.InteractionoftheAFMwiththislayerofwaterwilldominatethebehaviourofthetip–sampleinteraction[85],makingitdifficulttoapplyasmallforcetothesamplewhenscanning(especiallyincontactmode)[86].Scanninginwaterremovestheseforcesaltogether.

Practically,mostAFMsrequiretheuseofaspecificliquidcellinordertoscaninfluid.TheleakingofwaterinanAFMexperimentcancauseproblemsfortheinstrument.Apartfromthenormalincompatibilitiesbetweenelectronicsandwater,piezoelectricscanners

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arehighlysensitivetomoistureandmustbewellsealedtoprevent(p.47)

Fig.2.35. TwoapproachestoAFMscanninginliquidwithaprobe‐scanningmicroscope.Scanninginadropletofwater(left)issimpler,butallowslesscontrolofthesolution.ScanninginanAFMfluidcell(right)allowsexchangeoffluids,andcontroloffluidtemperature,ionicstrength,etc.

damagefromwaterfromtheliquidcell.Duetothespecificdangerofpiezodamage,AFMsdesignedforliquidworkareusuallybasedonthetip‐scanningdesign,tominimizethechanceofliquidreachingthescanner.AFMliquidcellswilltypicallyhaveportstoexchangefluidsduringscanning,andcanbeofasemi‐closedorcompletelysealeddesign.Withsealedcells,someflexibility(arubbermembraneoro‐ring)mustbeincludedtopermitthemovementofthepiezo,orofthesample.Othertypicaladditionstoliquidcellsareelectricalconnections(forelectrochemicalAFM),orheating/coolingcircuits(seenextsection).Analternativetoaliquidcellforscanninginfluidistosimplyscanwithinadropletofwater.AnillustrationofthistechniqueandofaclosedliquidcellisgiveninFigure2.35.Inthismethod,typicallyappliedwithprobescanningmicroscopes,thebottomofthescannerassemblyiscoveredbyaglasswindow,toallowthelasertofocusonthecantilever,whichismountedbelowtheglasswindow.Adropletofliquidsitsonthesamplesurface,andwhenthescanningheadisloweredintoit,theliquidformsacontinuousbridgebetweentheglassofthescanninghead,andthesamplesurface.Thistechniqueonlyworkswithaqueoussamples,andhydrophilicsamples,asthesurfacetensionofthewaterisrequiredtokeepthedropletinplaceastheAFMheadislowered.Furthermore,thedropletispronetoevaporateoveraperiodoftime.Withthesecaveats,however,thetechniqueissurprisinglyeffective,andgreatlyreducesthechancesofbubblesenteringtheopticalpath,whichcancauseproblemsinclosedcells.Non‐aqueoussolventsmustbescannedintheclosedliquidcell.MoredetailsaboutproceduresforscanninginliquidsaregiveninsectionsChapter4.

Temperaturecontrol

TemperaturecontrolofscanningishighlydesirableforawiderangeofapplicationsinAFM.Infact,AFMhasbeenperformedataverywiderangeoftemperatures;imagingattemperaturesaslowas5K[1,87]andashighas750°C[88].However,forpracticalpurposes,withcommercialAFMs,inair,amorelimitedrangeoftemperaturesisavailable,duetotwomaineffects:

•atlowtemperatures–condensationonthesampleormicroscope;•athightemperatures–destructionoftheAFMscanner.

(p.48)

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Fig.2.36. Exampledatashowingtheeffectoftemperaturevariationsonpositioningaccuracy.Left:whileheating,thepositionoftheprobeonthesamplewilldriftconsiderably:Right:atelevatedtemperatures,oncestabilized,theprobewillnotdrift.

Whenheatingthesample,toavoiddamagetothescannerthemostimportantthingistothermallyisolatethescannerfromthehotsample,thisistypicallydonebyuseofaspacingmaterialwithveryhighthermalinsulation,andhighstiffness(i.e.aceramicsuchasMACOR®–aceramicwithverylowthermalconductivityandalowthermalexpansioncoefficient).

Asasampleisheatedorcooled,therewillbeconsiderablethermaldriftintheAFMstageintheX‐YandZdirections.Thethermaldriftcanonlybeminimizedbymakingthestageassymmetricalaspossibleandusinglowdriftmaterials.Usuallythereisdriftasthestagetemperatureisraised,andthedriftstopswhenthedesiredtemperatureisreachedandthestagetemperatureisstabilized.DataillustratingthisisshowninFigure2.36.

CoolingsamplesinanAFMstagehasanotherpotentialproblem.Condensationoccursonthecomponentsthatarebeingcooled.WhencoolingasampleinanAFMstage,itisrecommendedthattheentirestagebemaintainedinadryenvironmentsuchasinaglovebox.Ifgoingtoverylowtemperatures,theidealsituationistoscaninavacuum.Assuchtemperaturesaregenerallyusedinphysicsapplicationsthisisrathercommon.Anotherapproachistoimageinliquidnitrogenvapouratambientpressure[89].Atcryogenictemperatures,AFMbecomesverysensitive,duetothelackofthermalexcitationfromairmoleculesonthecantilever,andalsoreducedsamplemovement,andsomeuniqueexperimentsmaybecarriedout.Examplesincludebiologicalmoleculestoodelicatetomeasureinambientconditions[90,91],measurementoffrozenliquids[92]andevensingleatomhoppingfromsampletotip[1].WhilethedesignanduseofAFMstobeinsertedinvacuumandoperatedatcryogenictemperaturesisoutsidethescopeofthisbook,theinterestedreaderisdirectedtothereferences[90,93].

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