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Measuring AFM images

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AtomicForceMicroscopyPeterEatonandPaulWest

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

MeasuringAFMimages

PeterEaton

PaulWest

DOI:10.1093/acprof:oso/9780199570454.003.0004

AbstractandKeywords

Thischapterprovidesadetailed,step‐by‐stepguidetomeasuringimageswithanAFM.Standardtechniquesforpreparationofawiderangeofsamplesaregiven.Instructionsandtipsoninstrumentalset‐up,opticalalignment,sampleapproachandoptimizationofscanning,makesthisaninvaluablesectionfornewusersandeducators.Forexperiencedusers,theinformationwillhelpthemtounderstandmoredeeplytheprocessofscanningAFMimages,sotheycangetbetter,morereproducibleimages.Additionalsectionscoveroptimizationforhigh‐resolutionmeasurementsandmakingforcespectroscopymeasurements.

Keywords:samplepreparation,guidelines,measurements,imaging

Likealltechniques,AFMrequiressomeskillandpracticetooperatewell,butlearningto

measureanAFMimageisquiteeasy,andusuallyjusttakesafewhoursofinstructionandpractice.Preparingthesamples,settinguptheinstrumentandscanningtwotothreeimagescantakeonlyhalfanhour.However,ifitisanunknownsamplethatwasneverscannedbyAFMbefore,itcantakesubstantiallymoretimetoacquireusefulimages.InthischapterwediscusstheproceduresthatcanmakemeasuringAFMimageseasier.ThissectiondoesnotreplacetheAFMmanufacturer'susermanual.Detailsspecifictoeachinstrumentcanbefoundinthosedocuments.Instead,hereweshowtheoverallstepsrequiredforscanningarangeofcommonsamples,undertypicalconditions,andhowtooptimizeconditionstogetthebestimages.Thischaptercoversthemostcommonimagingprocedures;itfocusesoncontactmodeandintermittentcontact‐modeAFM(IC‐AFM).Non‐contact‐modeAFMiscurrentlyusedmuchlesswidelythanIC‐AFM,soitisnotexplicitlycoveredhere,buttheimagingprocedureisquitesimilartothatofIC‐AFM.Inadditiontoimagingprocedures,somedetailsonobtainingforce–distancecurvesareincluded,asmanyuserswillalsomeasurethese.Figure4.1showsthemajorstepsinvolvedinmeasuringanimageinanopticallever‐basedAFM.

4.1SamplepreparationforAFMIngeneral,samplepreparationforAFMisverysimple.Forexample,thereisnoneedforthesampletobecoated,electricallygrounded,stained,ortobetransparent,asrequiredforsomeelectronmicroscopictechniques.Somesamples,suchasthinfilms,canrequirenosamplepreparationatall.Othersamples,suchashumancells,orverysmallnanoparticles,mayrequireconsiderablecareinpreparationforthebestresults.The‘rules’forpreparationofsamplesforcontact‐modeAFMcanbesummarizedasfollows:

•Thesamplemustbefixedtoasurface.AFMisasurfacetechnique,soallsamplesrequiresomekindofsubstrate.SomecommonsubstratesforAFMarediscussedbelow.Ifthesampleconsistsof,orincludeslooseparticles,thesemustbeadheredtothesurfacebeforescanning.Ifsomematerialonthesurfaceisnotwellfixeddown,itcanleadtotheAFMtipmovingthematerialaroundonthesamplesurface.Thiscanleadtoa‘sweeping’ofthesurface,eventuallyclearingthesubstrate,withtheparticlesbeingmovedtotheedgeofthescanrange.Thissortofbehaviourisparticularlycommonincontact‐modeAFM,asthetipneverleavesthesurface,anditcanapplyconsiderablelateralforcestothesurface.Evenifthesampleisnot‘swept’inthisway,movingmaterialonthesurfacewillleadtoinconsistentimages,and‘streaking’asthetipencountersparticlesthatarelooseonthesurface.Itisalsocommonforsuchparticlestobetransferredfromthesurfacetothetipundertheseconditions.Thiswill(p.83)

Fig.4.1. ThemajorstepsinvolvedinmeasuringAFMimages.Theoscillationfrequencyonlyneedstobeselectedfornon‐contactorintermittent‐contactAFM.

leadtofurtherinconsistencyintheimages,anditisalsopossibletopermanentlycontaminatethetip,leadingtostrangeartefactsintheimages(seeSection6.1).•Thesamplemustbeclean.Contaminationintheformofparticlesordriedsaltswillmaketheunderlyingstructureveryhardtodiscern.Saltlayersinparticulararehardtodiscernoptically,sothattotheeyesthesampleappearsclean,butthesaltlayerwillpreventimagingofthesamplebyAFMcompletely.MostsamplesimagedinairtypicallyarecoatedwithwhatinAFMisknownasthe‘contaminationlayer’.Thisliquidlayercanbeamixtureofwaterandhydrocarbons.Dependingonthemethodusedtoimagethesample,alightcontaminationlayer(afewnanometres)maynotpreventimagingoftheunderlyingsurface(seeSections3.1and3.2).Athick(>50nm)contaminationlayercancausegreatdifficultinimagingtheunderlyingsample.Anyparticulatecontaminationwillbeimagedalongwiththesample,andcomplicateanalysis.AFMtendstoimageeverythingonthesample,soitisimportanttoremoveasmuchcontaminationaspossible.•Thefeaturesonthesamplesurfacesamplemustbesmallenoughtoscan.AFMisahigh‐resolutiontechnique,andmostinstrumentsaredesignedforsmallsamples.Theverylargestscanrangesareontheorderof150μm×150μminxandy,and28μminz,butamoretypicalconfigurationisamaximumrangeof100μmby100μmorlessinxandy,andzlimitedtolessthan10μm.Thisisthesizeofthelargestscanthat(p.84) canbemade,butmostAFMinstrumentsalsolimitthesizeofthesamplethatcanfitintothesample(sample‐scanninginstrumentsareparticularlylimited).Specificinstrumentswhichallowscanningofverylargesamplesdoexist,however,theywilltypicallyincludeautomatedsample/headmovementtoallowfor

scanningofvariousareasacrossalargesample.Suchinstrumentsaretypicallyaimedatindustrialapplications,e.g.scanningofwholesemiconductorwafers.•ThesamplehastoberigidlymountedintotheAFMsamplestage.Asamplethatisnotwellfixeddownwilltendtomovewhilescanning,leadingtodistortionintheimage.Vibrationofthesamplecanalsoaddnoisetotheimage.ThemostcommonsamplemountingforAFMisusingamountingdiskmadeofmagneticstainlesssteel.Thishasthesamplegluedtoit,sometimesusingepoxyadhesive,whichishighlyrigidoncecured,althoughdouble‐sidedadhesivetabsarealsopopularforlessdemandingapplications.Themagneticdiskisplacedinthesampleholder,whichhasamagnetinthecentre.Thisarrangementkeepsthesampleverystable,andgreatlyreducessamplemovementandvibration.Alternativearrangementswhereitisundesirabletouseamagnetunderthesample(e.g.formagneticmodes,orforopticalaccesstothesamplefrombelow),usuallyinvolvesomesortofsprungclipstosecurelyholddownthesample.

Specificsamplepreparationtechniques

ThenumberofdifferenttypesofsamplesthatcanbescannedbyAFMprecludesdescribingeachonehere,butitispossibletogivesometipsonpreparingsomeofthemostcommonlyexaminedsampleshere.

Particulatesamples

Micro‐andnanoparticlesofallimaginablegeometriesandmaterialsareverycommonsamplesforAFM,andimagingofaverywiderangeofdifferentparticleshasbeenwidelydescribed[217,278–284].Oftensuchsamplescomeasanaqueousdispersion.Thefirststepistoensurethesampleisascleanaspossible,especiallyiftheparticlesareverysmall(wheretheeffectofcontaminantsisgreaterinrelativeterms).Wherethedispersionisknowntobeveryconcentrateditshouldbethendiluted.Oftentheidealimagewillfeaturedispersedparticles,sothatthedimensionsoftheindividualcolloidscanbemeasured.Ifthesampleistobeimagedinair,thenthesampleissimplydepositedbydroppingaknownvolumeontoaflatsubstrateandallowedtodry.AlthoughAFMcanoperateeitherinairorliquidenvironments,imagingasamplethatstillretainssignificantamountsofwaterinaircanbeproblematic,thereforeimprovedimagingafterdryingsamplesthoroughlyiscommon[285].Oftendryingsmall(<100nm)particlesontoaflatsurfaceisenoughto‘fix’thenadequatelyforAFManalysis,especiallyforexaminationbyeitherIC‐AFMorNC‐AFM.Forcontactmode,especiallyforlargerparticles,suchaproceduremightnotadheretheparticleswellenoughtothesurface.Inthiscase,itmightbenecessarytohavesomechemicalfixingtothesurface,oruseaspecialsubstrate(seebelow)[286].

Twofactorsinthesamplepreparationmethodthatcanhavedramaticeffectsonthequalityofresultsobtainedarethesolventusedtodispersetheparticles,andthesubstrateused.Waterisgenerallythesolventofchoiceforsuchapplications,asitis

convenient,(p.85) non‐toxicandthereareawiderangeofmethodsavailabletoproducehighlypurewater.Itisalwaysworthrememberingthatnotallwateristhesame,however,soforsampleswithverysmallz‐heights(e.g.nanoparticles<20nm,proteins,nucleicacids),verypurewaterisrequired,inorderthatthecontaminantsdonotmaskthesample.ExamplesoftheeffectsofdifferingwatergradesareshowninFigure4.2.Ifverycleansolutioncannotbefound,itmaybeadvantageoustofindawaytoadheretheparticlestothesurface,whichcouldbeviasilaneorpolycationmodification[287–289],followedbywashing,althoughthishasthedisadvantageofincreasingsubstrateroughness[290].SubstratesforAFMarediscussedinSection4.1.1.

Ifitisdesiredtoimageadrypowderwithoutdissolvinginaliquid,anumberoftechniqueshavebeendescribedtoimmobilizeparticles.Onetechniqueistoimmobilizelargeparticlesinafilterorsimilarporoussubstrate[291].Thiscanleadtotheparticlesbeingsufficientlyfixedtobeabletoscanthem,andthetopoftheparticlewillbeavailabletoscan,butthefullheightoftheparticleswillnotbemeasurable.Analternativeistoscatterthepowderonanadhesivesurface,suchasaflatsubstratewithathinlayerofglue.Ideallythegluewillbecross‐linked/driedafterthepowderisapplied,toavoidcontaminationoftheAFMtip.Othersystemsthatcanworkwellwithsuchsamplesincludepoly‐l‐lysinecoatedglass,andthinlayersofwax,towhichthesampleisappliedwhilethewaxissoft(atelevatedtemperatures),andwhichsolidifiesoncooling[286].Forverysmallparticles(<20nm),manychemicalmodificationsofthesubstratesurfaceproduceasurfacethatistooroughforquantitativemeasurements.Insuchcases,depositionfromultra‐purewaterontomicaorHOPGisthebesttechnique.Alternatively,somemicatreatmentshavebeendescribedthatincreasetheroughnessonlyslightly[290].

Polymers

Polymersamplescomeinawidevarietyofforms.Solidsamplesmayrequirenopreparationotherthancuttingtosizeandcleaning.PreparationofpolymerfilmsforAFMisalsosimple,andmaybedonebycasting,spincoating,spreading,self‐assembly,dipcoatingetc[146,292,293].Typicallysuchfilmsaredepositedonglassslides,asthereisnorequirementforveryflatsubstrates.

Fig.4.2. Exampleoftheimportanceofcleansolvent:imagesofaveryflatsubstrate(mica)afterdepositionofdropsof‘pure’water,followedbydrying.Left:tapwater.Middle:deionized,filteredwater.Right:commercialultra‐purewater.Allimagesare2μm×2μm,z‐scale4nm.

(p.86) Biomolecules–DNAandproteins

Oligonucleotides,especiallyDNAareverypopularsamplesforbiologicalAFMstudies.DNAisusuallydepositedonmica[294],althoughHOPGhasalsobeenused[295,296].Thenegativechargeofas‐cleavedmicaisadisadvantageforthisapplication,asDNAIsalsousuallynegativelycharged.Typicallythisisovercomebytreatmentofthemicawithasolutioncontainingdivalentcations,ordepositionorimagingoftheDNAinasolutioncontainingsuchcations(typicallyMgCl2orNiCl2containingbuffers)[297–299].Alternatively,aproceduretobindoligonucleotidestomicawiththeaminosilaneAPTEShasbeenthoroughlydescribed[300].Theprocedureshouldbefollowedcarefullysothatthisdoesnotincreasetheroughnessofthesurface.Aswitholigonucleotides,micaisthemostcommonlyusedsubstrateforproteinabsorption[294,301,302],butHOPGcanalsobeused[303].Again,divalentcationsarecommonlyusedtoencourageproteinbindingtomica,iftheproteinsarenegativelycharged[301,304].Thepresenceofmonovalentcationsinthebuffersolutioncancompetewiththedivalentcations,andpreventtheadhesionofanumberofproteinstomica[305].Othermethodstofixproteinsontomicaincludecovalentbinding,althoughthismaychangetheproteinstructuresomewhat[306],andformembraneproteins,insertionintoalipidlayerisaverysuitablestrategy[307,308].

Cellcultures

CulturedcellsaretypicallygrownonsomesortofsupportsuchasaPetridishorglassmicroscopeslide[309],tobedirectlymountedintotheAFM.Wheretheinstrumentdoesnotsupportsuchlargesubstrates,microscopeslidesmaybesimplycuttosize,orsmallcoverslipsused[310].Cellsmaybefixedanddriedbeforeanalysisorimagedinsitueitherincellculturemedium,orinafilteredbuffersolution.Incombinationwithtemperaturecontrol,suchapreparationcanleadtotheabilitytoimagelivecells[309–311].

Bacteria

BacterialcellsarecommonsamplesforAFM,seeSection7.3.2.Typicallyforimaginginair,bacteriaaretransferredtoacleanbuffer,driedontoasurfaceandextensivelywashed[169,312].Forimaginginliquid,severalprocedurestoadherethecellstothesubstratehavebeendescribed[302,313].Withoutthesetreatments,thecellswillnormallyberemovedbytheprobewhilescanninginliquid.Immobilizationstrategiesincludetheuseofgelatincoatedmicatomechanicallytrapbacteriaonthesurface[6].Thishastheadvantageofnotinducingchemicalchangesinthecells,ascouldbethecaseforbindingthecellstothesubstratewithpoly‐l‐lysineorotherchemicaltreatments[184,314,315].Anothertechniquethatmightreducethechangescausedtothebacteriaisallowingtheformationofabiofilmonthesubstratesurface[184,316].Forthosebacteriawhichdoformbiofilms,thisisthebestwaytoadherethemtoasurfaceforimaginginliquid.Forsphericalcells,physicalimmobilizationinasolidsubstratewithholes(suchasamembraneorlithographicallypatternedsurface)hasbeenreportedtobeverysuccessful,althoughthisisnotappropriateforrod‐shapedbacteria[317].

Nanotubes

Carbonnanotubes,nanowiresandwhiskersareasubsetofnanoparticles.Theseparticlesarenormallyproducedinlargequantitiesaspowdersoraregrowndirectlyonasubstrate.(p.87) TypicallyoneoftwomethodsisusedforpreparingnanotubesamplesforAFMimaging:catalystgrowthordeposition.Catalystgrowthisthebestmethodforcreatingacleansampleforstudyingtheuniquepropertiesofsingle‐wallnanotubes.WhenpreparingcarbonnanotubesamplesforAFMimagingwithdeposition,itisimportanttouseadispersant.Verydiluteddispersantsuspensionsofcarbonnanotubesarespincoatedonasiliconwaferorotherflatsubstrate,rinsedthoroughlywithwater,andthendriedinair.Anycommercialspin‐coatermaybeused.

Othersolidsamples

Metalsorothersolidsamplesmaybeimagedwithlittleornosamplepreparation.Cleaning(especiallydegreasing)canberequiredforsomesamples,andlargesamplesmayneedtobecuttosize.ThelackofsamplepreparationformostsolidsamplesisagreatadvantageofAFM,andmeansoverallimagingspeedwithsuchsamplescanbehigherthanforelectronmicroscopy.Aswithothermicroscopytechniques,polishingisrequiredinordertoobservemetalgrains[318].

4.1.1SubstratesforAFM

WhenpreparingsamplesforAFM,especiallyparticulatesamples,asubstratemustbechosenonwhichtomountthesamples.Inthecaseofverylargesamples,orveryconcentratedpreparations,thenatureofthesubstratecanbeunimportant,butformanycases,itiscrucialforcorrectsamplepreparationandgoodresults.Thisisparticularlyimportantforhigh‐resolutionwork,andlookingatindividualmoleculesinparticular,forwhichanatomicallyflatsubstrateisusuallyrequired.Forimagingoflargerfeatures,asubstratewithahigherroughnesscanbeadequate.Aswellastheroughness,thechemicalnatureofthesubstratecanbeimportant.Theintrinsicnatureofthesubstrateisimportantindeterminingwhetherparticularsamplesadherewell,andinaddition,ifsubstratetreatmentisrequiredsomesubstratesareeasiertomodifythanothers.Forexample,highlyorientedpyroliticgraphite(HOPG)isacommonlyusedsubstratethatisverysimpletoobtaininatomicflatness.Thisisbecause,alongwithmica,itisalayeredmaterialthatiseasilycleaved.Cleavingsuchmaterialsexposesatomicallyflatfaces,completelyfreeofcontamination.However,chemicalmodificationofHOPGisnotsimple.Ontheotherhand,goldisahighlystablematerialthatisextremelysimpletomodifychemically,butwhileitispossibletoproduceextremelyflatsurfaceswithit,itisconsiderablymoredifficultthanforHOPGormica.Table4.1summarizessomepropertiesofcommonlyusedsubstratesforAFM.

4.2MeasuringAFMimagesincontactmodeAsshowninFigure4.1,aftersamplepreparationandplacingthesampleintheinstrument,thenextstepistoinsertaprobeintotheAFM.Itispossiblethataprobewillalreadybeinserted,butwhenbeginningwithanewsetofexperiments,anewprobeisusuallyinserted.Greatcaremustbetakenwhenhandlingthecantileverchipsastheyareverysmallandverydelicate.Acleanpairoftweezerswithflattipshelps.Usuallytheprobeholderwillhaveaslotforthechipandhavesomesortofsmallspringorcliptohold

itin(p.88)

Table4.1.PropertiesofsomecommonlyusedsubstratesforAFM.Material Preparation Roughness Commonsamples Notes†

Mica cleaving <Å(atomicallyflat)

All,especiallysinglemolecules[319,320]

Cleavedmaterial,soverystableinstorage.Hydrophilic[294,305]

HOPG cleaving <Å(atomicallyflat)

All,especiallysinglemolecules[295]

Cleavedmaterial,soverystableinstorage.Conductive.Hydrophobic[321]

Silicon None*oronlyoxideremoval

<Åtoafewnm[322]

Lithography,electronicapplications

Oftenthebestchoiceforconductingapplications[251,256,323]

QuartzorGlassslides

None* 1–10nm Largersamplesorfilms,commonlyusedforcells[302]

Notespeciallyflatbuteasytoworkwithandcheap[324]

Gold Flameannealingor

<Åtoafewnm

Chemicallymodifiedsurfaces

Easytochemicallymodify;largeatomicallyflatterraces[325–327]

templatestripping

<Åtoafewnm

Chemicallymodifiedsurfaces

Easytochemicallymodify;likecleavedmaterialshighlystableinstorage[328–330]

(*)Usuallyonlycleaningisrequired.

(†)Useofeachofthesesubstrateshasbeendescribedmanytimes;representativereferencesaregivenhere.

(p.89) place.Toallowformanufacturingdifferencesandtheuseofdifferentlengthcantilevers,thereisusuallysomeroomformanoeuvreinwhereyouplacethechip,usuallyjustafewhundredmicrometres.Itisnotpossibletoputthechipinthesameplaceeachtimebyhand,andevenafewtensofmicrometreswillcompletelychangetheopticalalignmentrequired.Itissensiblethereforetofindapositionthatworksandstickwithit,inthiswaytherealignmentonchangingtheprobewillbeminimal.Someusersfindthatplacingthechipagainsttheedgesoftheslotcangiveincreasedstabilityandmorereproducibilityofthechipposition.Somealternativeinstrumentdesignsuseeitherpre‐mountedcantileversonlarger‘cartridges’,oralignmentgrovesmachinedintothecantileverchipstohelpinplacingthechip,butmostrelyonthemanualinsertionapproachdescribedabove.

4.2.1Opticalalignment

Afterplacingtheprobeintheinstrument,thealignmentoftheopticalleveriscarriedout.Thisisdoneintwostages.Firstly,thelaserspotisadjustedontotheendofthecantilever.Therewillusuallybetwoscrewstoadjustforthis,onetomovethelaserparalleltothecantileveraxis,andtheotherperpendicular.Theexactprocedureforthealignmentcandiffersomewhatfrominstrumenttoinstrument,dependingontheviewthe

userhasofthecantileverandlaserspotontheopticalinspectionscope.Theusermusttakecarenottolookdirectlyintothelaserbeam,asitcaneasilydamagetheeyes.Visualizationofthelaserspotcanbedonebyplacingapieceofwhitecardorpaperinthepathofthelaser.AgeneralprocedureforalignmentofthelaserbeamisshowninFigure4.3.Figure4.3showstheprocedureforbeam‐shapedcantilever.Forv‐shapedcantilevers,theprocedureisverysimilarbutatsteps4–5thelaserspotispositionedbetweenthecantileverlegs.

Fig.4.3. Laseralignmentprocedure.

(p.90) ProperalignmentofthelaserisveryimportantinordertoobtainbestresultsfromtheAFM.Pooralignmentmayreducethesensitivityoftheopticallever,couldintroduceimagingartefactsorpreventimagingaltogether.Forexample,laserlightspillingovertheedgeofthecantilevermayreflectoffthesample,andinterferewiththelaserlightreflectingoffthecantilever,seeSection6.6.2.Thehighestsensitivityisgenerallyobtainedwiththelaserspotcentredoverthepositionofthetip,thatis,veryclosetotheendofthecantilever,andinthecentre(asshowninFigure4.3bypoint7).Onetricktocheckthelaserisnotontheedgeofthecantileveristoobservethebeamprofilewithwhitepaperasdescribedabove;theedgeofthecantileverwillchangetheshapeofthelaserbeamspotonthepaper.

Havingalignedthelaserontothecantilevercorrectly,itmustthenbecorrectlyalignedwiththephotodetector.Todothisthephotodetectoristranslateduntilthelaserspotiscentrallylocatedonthefoursegments,asshowninFigure3.4.SometimesthereisavisualdisplayofthephotodetectorintheAFMsoftware,andsometimesjustanumericdisplayofthesignalsfromthephotodetectorsegments.Inbothcases,theaimisthesame,togetthelaserspottothecentreofthedetector,i.e.toequalizethesignalsfromallfoursegments.Thisisarathersimilarprocesstothelaseralignment,andtheonlycomplicationcomeswhenthespotiscompletelyoffthedetector,inwhichcasetheusermightnotknowwhichwaytoturnthescrews.Ifthisisthecase,theusersimplyturnsthedetectortranslationscrewallthewayinonedirection,andthenallthewayintheotheruntilthealignmentisfound,beingcarefulnottoapplytoomuchpressuretothescrewswhentheendofthemovementisreached.Inaddition,oftenathirdcontrolisinsertedintheopticalpath,whichcontrolsamirrorbetweenthecantileverandthephotodetector.Thiscontroldirectlyrotatesthemirror,andservesasacoarse

adjustmentforthephotodetectoralignment.ThiscontrolisshowninFigure4.4.Innormalday‐to‐dayoperationoftheAFMinair–forinstance,whenexchangingoneprobewithasimilarone–theadjustmentofthiscontrolisnotrequiredduringtheopticalalignmentprocedure.Therearetwocommonreasonswhythecontrolmightneedtobeadjusted.Themostcommonreasonforneedingtoadjustitisthatwhenchangingfromairtoliquidoperation,therefractionofthelaserattheliquid

Fig.4.4. FullopticalsystemforopticalleverAFMs,showingthevariousadjustmentsrequiredforopticalalignment(indicatedbyarrows).

(p.91) cell'sglasswindow/liquidinterfaceconsiderablyaffectsthealignmentontothephotodetector.Typically,theeffectofthisisthatinoneoftheopticalaxes,thelaserspotwillmovesofarthatthephotodetectortranslationscrewscannotmovethedetectorfarenoughtoaccountforthiseffect.Inthiscase,asmalladjustmentofthemirrorcancorrectfortherefraction,andallowsimplealignment.Becausethemisalignmentbytherefractionaffectstheopticalalignmentofthephotodetectorinonlyoneaxis,itisoftenusefultocarryouttheopticalalignmentinairfirst,andthenaddtheliquid,followedbyadjustmentofthecoarsecontrol,particularlyifviewingthecantileverwhenliquidfillsthecellismoredifficult.Thismakesadjustmentofthecoarsecontrolfarsimpler,asasmallchangetothiscontrolchangesthealignmentdrastically,andsoitcanbetrickytoadjustwithoutaprioralignment.Thesecondsituationinwhichthecoarseadjustmirrormightneedtobeadjustediswhenaverylargerealignmentofthephotodetectorisrequiredbecausethelaserspotisinadramaticallydifferentposition.Thiscanbethecasewhenchangingfromashortprobetoaverylongoneorviceversa.

4.2.2Selectinitialsettingsandprobeapproach

Oncetheprobeandopticalalignmentaredone,thenextstepistoinitiateaprobeapproach.AsdescribedinSection2.2.4thewoodpeckermethodisusuallyusedforasafeapproachtothesample,andtomoveintofeedback.Dependingontheinstrument,theautomatedprobeapproachmaybequitefastorquiteslow.Therelevanceofthisisthataninstrumentthatapproachesveryquicklycanbesettoapproachfromagreatdistance,e.g.1millimetre,withouttakingtoomuchtime.Someinstrumentsapproachextremelyslowly,andwilltakeseveralminutestoapproachadistanceofonly100micrometres.Inthiscase,theprobemustbemovedclosetothesamplemanuallyinordernottowastetoomuchtimewaittngfortheautomaticapproach.Thismustbedonecarefullyinordertoavoiduncontrolledtip–samplecontact.Themethodtodothisvaries,butgenerally

involvesusingtheinspectionmicroscopetoalternatelyfocusontheprobeandsamplesurfaceinordertojudgetheirdistancefromoneanother.Moreautomatedinstrumentscanperformeventhiscoarseapproachprocedureautomatically.Beforetheautomaticapproach,theinitialscanningparametersshouldbechosen,includingscansize,scanningspeed,gains,andset‐point.Forcontactmode,theset‐pointisameasureofthedeflectionofthecantilever,andthusameasurementofthetip–sampleforce.However,theAFMinstrumentwilltypicallyshowneitherthetruedeflection(innm)northeforce(nN),buttherawsignalfromthephotodetector(inVorA).Thus,itcanbesomewhatdifficulttoknowwhatinitialset‐pointtouse.Itisbesttousethesmallestpossiblevalueasaninitialstep.However,duringapproachtheactualdeflectionmightvarysomewhatduetothermaldrift,long‐rangetip–sampleinteractionforcesorothereffects.Iftheset‐pointistoolow,suchvariationswillgiverisetoa‘falseengage’wheretheinstrumentthinksthecantileverisonthesurface,andthefeedbackisengaged,buttheprobehasnotyetreachedthesurface.Ifsuspected,falseengagecanbecheckedforbyacquiringaforcecurve–ifthecurveisnothinglikeFigure3.2,falseengageislikely.Anotherwaytocheckforafalseengageistowatchtheerrorsignal(deflectionsignal)astheprobeapproachesthesample.A‘true’engageshouldshowa‘jump’totheset‐pointtheuserchose.Slow,gradualmovementtowardstheset‐pointismorelikelytocomefromthermallyinducedbendingofthecantilever.Thus,it'sbesttoselectaset‐pointsomewhatgreaterthanthecantilever(p.92) deflectionvalue,withsomeroomforfurtherdeflectionbeforethecantileverreachesthesurface.Theset‐pointmaybefurtherreducedifnecessaryonceonthesurface.Onceinitialparametersarechosen,andtheprobeisrelativelyclosetothesurface,anautomatedapproachiscarriedout.Notethatincorrectapproachcaneasilydamageatip,anexampleofwhichisgiveninFigure4.5.Someinstrumentsallowadjustmentoftheautomaticapproachparameters,suchasfeedbackvaluesduringapproach,orapproachspeed.Theseshouldbechangedonlywithcaution,asthekindofdamageshowninFigure4.5caneasilyresultfromusingthewrongparameters.

4.2.3Optimizingscanconditions

OptimizingthescanningparametersforthebestpossibleimagequalityandmostaccurateimagesisprobablythemostimportantstepinAFMdataacquisition.Often‘standard’parametersareusedinitiallyfortheapproach,andsuchnumbersmightbeprovidedbytheinstrument'smanufacturer.However,thesevalueswillrarely,ifever,besuitabletoobtainedgoodimages.Thewiderangeofpossiblesamples,scanningenvironments,andevenprobemanufacturingdifferencesmeansthatdifferentparametersareusedfornearlyeveryscanningsession.Themethodtooptimizetheparametersisaniterativeone.Theparametersarechangedinsteps,oneatatime,untilthetipisproperlyfollowingthesurface,andisgivingatrueimageofthesample.Oncetheoptimalparametersaredetermined,ifthesampleishomogeneous,andtheinstrumentstable,theoptimizedparametersmightbesuitableforvariousimagesonthesamesample.Changingtoasimilarsamplewiththesameprobeusuallymeanssmalladjustmentsarenecessary,againreachedviaaniterativeprocedure.Althoughittakesawhiletofullymasterthisprocedure,followingthemethodoutlinedinthischapterwillallowoptimizationofscanningparametersinafewminutes.

Fig.4.5. Examplesofprobedamageonapproach.Left:SEMimageofsharpprobeandanAFMimagemeasuredwiththesharpprobe.Right:SEMimageofdamagedprobeandanAFMimagemeasuredwiththedamagedprobeonthesamesample.

(p.93) Whenscanningthesamplebegins,itisusefultoseealine‐scan(atwo‐dimensionalplotofthesignaltheinstrumentisrecording).Often,theheightdata,aswellasthez‐errorsignal(incontactmode,thecantileverdeflection)canbeshown,andsometimesbothforwardandreversesignalsareshown.ThefunctionoftheAFMsoftwarethatdisplaysthesesignalsissimilartoanoscilloscope,soitissometimesreferredtoastheoscilloscopewindow.Thiscanbeextremelyusefulforoptimizationofscanning.Asforwardsandbackwardsscanninglinesmeasure(almost)thesamepartsofthesample,evenwhentheslowscanaxisisenabled,thetwoheighttracesshouldcoincide.Largedifferencesbetweenforwardsandbackwardstracesareanimmediateindicationthatsomethingisnotrightwiththescanning.Thereareanumberofpossiblereasonsforforwardsandbackwardstracesnotmatchingbutthemostcommonreasonisthatimagingparameters(gains,set‐point,andscanningspeed)arenotyetoptimized.AnexampleofthesignalsshownbytheoscilloscopewindowisshowninFigure4.6,illustratingtheeffectofdifferentfeedbacksettingsontheresultsobtainedonasimplesample.Forclarity,onlyresultsfromonedirectionareshown.

IftheAFMprobeisscanningoverthesampleinthenormalrastermotion(asshowninFigure2.22),thefeaturesintheoscilloscopewindowwillofcoursekeepchanging.Itcanbeextremelyhelpfultohavetheprobescaninalineoverthesample,withoutmovingintheslowscanaxis.Usually,thesoftwarewillhaveanoptiontodothis,anditisoftenthebestwaytoadjustthescanningparametersastheireffectonthescanningcanbeseendirectlywithoutinterferencefromchangesinsampletopography.Itishighlyrecommendedthattheline‐scanoptionisusedifdifficultyarisesinsettingthegains,etc.Afteroptimization,thentheslowscanaxismovementcanbere‐enabledandtheimagequalitychecked.WhenfirstlearningtooperateanAFM,itishelpfultoscanatestsampleandseetheeffectofthefeedbackparametersontheheight(zvoltage)anddeflectionsignals.Suchasamplehasaverysimple,reproducibletopography(usuallyaseriesofsquarepitsorposts),soitiseasytoseewhenthescanningparametersareperfect.Animageofsuchasample,withtheeffectofvaryingthefeedbackparametersisshownin

Figure4.7.SomeusefulteststructuresarediscussedinAppendixA.

Thegeneralproceduretousetoadjustscanningparametersisasfollows.

1.Increasefeedbackgains(PIDvalues)stepbystep,observingforthestartoffeedbackoscillation(thefine‐structurednoiseseentowardsthebottomofFigure4.7).Typically,theintegralgainisincreasedfirst,andthentheproportionalgainadjustedinapproximatelythesameproportion.2.Whenfeedbackoscillationoccurs,reducethegainsagain,untilitdisappears.Theoptimalvalueisthehighestgainsettingyoucanusewithoutaddingfeedbacknoisetotheimage.3.Whengainsareoptimized,adjusttheset‐point.Ideallywewouldusetheminimumvaluetokeeptheprobeonthesurface,inordertoreduceprobewear.However,sometimesagreaterforceisrequired.4.Thegainsmayneedtobeoptimizedagaintoaccountforchangeinset‐point.5.Adjustscanspeedifdesired.6.Gainsandset‐pointmayneedadjustingoncemoretotakeaccountofchangeinscanningspeed.

(p.94)

Fig.4.6. Theeffectofdifferentfeedbacksettings.Themotionoftheprobeoverasimplesample,resemblingacalibration/testgrid(left),andtheoscilloscopewindowshowingdeflection(z‐error)andheightinformation(right).NotethatfeedbackinAFMisneverinstantaneous,sothebottomexamplestillshowssomeimperfections.

Notethatgain,speed,andset‐pointareallrelated.Atlowscanspeeds,lowgains,andlowset‐point(lowappliedforce)maybeadequate,butfasterspeedstypicallyrequirehighergains,andmightrequirehigherset‐point.

4.2.4Choosingscansizeandzooming

Ifthesampleisheterogeneous,andcertainfeaturesmustbescanned,normallyithelpstostartwithalargescanofthearea,andthenzoomtothefeatureofinterest(seeFigure4.8).ZoomingdirectlyintofeatureswithAFMworkswellforinstrumentswithscanlinearization(seeChapter2).Withnon‐linearizedscanners,itisbesttozoomin‘gradually’,byzoomingtonothanlessthan50%ofthecurrentimagesizeatatime.Thus,severalzoomsmayberequiredtofindtheregionofinterest.

(p.95)

Fig.4.7. Imageofatest/calibrationsampleshowingtheeffectofchangingthegainsettingsduringscanning.Theheightimageisshownontheleft,andtheshadedheightisontheright,whichshowsthefinedetailsoftheeffectsofthegainsettingsmoreclearly.

Fig.4.8. Exampleofzoomingtofeature.Selectingafeatureofinterestintheleftimagegivestheimageatright.

4.2.5OthersignalsandmeasuringLFMimages

Whenscanningisoptimizedtheusermaychoosewhichsignalimagestosave.Theuserwillalwayswanttosaveaheightimage,whetherfromzscannervoltageorzsensordata,asitistheonlysignalwithafullycalibratedzscale,fromwhichtheusercanmakeheightmeasurements.Theerrorsignal(cantileververticaldeflectionsignal)imagecanbeusefultoappreciatequicklytheshapeofthesample,aswellastospotareaswheretheheightsignalisinvalid(areasoflargeorunchangingerrorsignal).Someresearcherspublishtheerrorsignal;oftenitisasimplewaytodisplayfeaturesatdifferentheightsinthesameimage.Thelateraldeflectionsignalmayormaynotbeuseful.Onmanysamples,thelateraldeflectionsignalwillshownomoredetailsthantheverticaldeflectionsignal.ThisisbecauselateraltwistingofAFMcantileversismuchlesssensitivethanverticalbending[77].However,ifthereisarequirementtorecordthelateraldeflection(forexample,iffrictioncontrastisexpectedinthesample),itissimplyamatterofselectingthesignalto

besaved.Unliketheotherchannels,forwhichforwardsandbackwardssignalsshouldbeequivalent,itcanbeworthwhilerecordingbothforwardandbackwardslateraldeflection(p.96) signals.Thisisbecause,asshowninSection3.1.1,comparisonofforwardandbackwardslateralforcesignalscanhelptodistinguishtopographicalfromfrictionaleffectsontheLFMsignal.Itisalwaysworthrememberingthattip–samplefrictionandthuslateraldeflectionwilldepend,amongotherfactors,onthenormalforceappliedbythetiptothesample,i.e.greaterset‐pointswillgivegreatercontrastintheLFM.SomeexamplesofLFMmeasurementsareshowninChapter7(Section7.1.4),illustratingthedifferencebetweenforwardandbackwardsLFMsignals.IftheuserwishestoobtainquantitativefrictionmeasurementsfromLFM,thereareanumberofcalibrationissueswhichmustbeaddressed[331,332].WhilecalibrationofnormalforcesisanissuewhichpotentiallyimpactsonallAFMmeasurements,calibrationoflateralforcesisonlyimportantforquantitativeLFM.Despitethis,alargeamountofworkhasbeen,andstillisbeingdoneinordertounderstandhowsuchacalibrationcanbemade[331–336].Thisisbecausethetipshapeandradius,thecantilevertwistingforceconstant,andtheopticalleversensitivitymustallbecalibratedintoordertofullyunderstandtheLFMsignal.Also,unlikenormaldeflectionthereisnosimple‘built‐in’methodtoinducealateraldeflectionofthecantileverintheinstrument,makingtheopticallevercalibrationmorecomplicated.

Oneofthefirstmethodstobeproposedforlateralforcecalibration,andprobablythemostwidelyusedwasdescribedbyOgletreeetal.in1996[77].TheOgletreemethod(alsoknownasthe‘wedge’method)hasaconsiderableadvantageoversomeothersinthatitsimultaneouslycalibratesthecantilevertwistingconstantandopticalleversensitivity.Themethodinvolvesusingcalibrationsampleswithknownslopestoinduceafixedlateralforceatthetip–sampleinterface.Bycomparinglateralforcesignalsindifferentdirectionsandatdifferentnormalforces(deflectionset‐points),alateralcalibrationfactorwhichenablesmeasuringthetip–samplefrictionforceinnewtonspervoltcanbeobtained.Thismethod,alongwithimprovedversionsusingsimplermaterialshasbeenwidelydiscussedintheliterature[331,333,337].Othermethodstocalibratethelateralfrictionconstantincludepushingthecantileveragainstapiezoelectricsensor[335],measuringstaticfriction[336],quantitativecomparisonwithasimilarleverthat'spressedagainstaside‐wallwhilethebendingmeasured[331],numericalmethods[61]andothers[338,339].

4.3MeasuringAFMimagesinoscillatingmodesMeasuringimagesinoscillatingmodesisingeneralverysimilartomeasuringimagesincontactmode,withjustafewdifferences.Firstlyanon‐contact/intermittent‐contactprobeisused,usuallywithamuchhigherspringconstant,andhigherresonantfrequency.OnepracticalconsiderationhereisthatIC‐AFMprobesareevenmorefragileandeasytobreakthancontactprobes.Acontactprobecansometimessurviveacrashintothesample,astheyareveryflexible,butintermittent‐contactprobesnearlyalwaysbreakwhenthishappenssoevenmorecaremustbetakenwiththem.

Theopticalalignmentprocedureisidenticalforthetwotechniques.However,oncetheintermittent‐contactprobeisloadedandaligned,theoperatingfrequencymustbe

selected.Thisissometimesdoneviaanautomatedroutine,butoftenitismanual.Automatedroutineswillusuallyrequirethattheuserenteranupperandlowerboundaryforthepossibleresonancefrequency,andwillthenassumethattherewillbeonepeakwithinthat(p.97) frequency.Theautomatedroutinescannotcopeundercertainconditions,soitisimportantthattheuserknowshowtomanuallyselectthefrequency.Thisisdoneviaa‘cantilevertuning’windowintheAFMsoftware.Thisprogramsweepstheoscillationfrequencyofthedrivingpiezoupanddownoverafixedfrequencyrangeanddisplaystheamplitudeofoscillationateachpoint.Theusershouldhavesomeideaofthenaturalfrequencyofthecantilever,sothestartandendoftherangetotestininputtedtothiswindow.Thisinformationissuppliedbythecantilevermanufacturer,andtypicallycoversquiteabroadrange(e.g.200–400kHz).Withinthisrange,thecantilever'soscillationshouldbevisibleasasingle,strongpeak.Thepresenceofmultipleormisshapenpeaksinthefrequencyspectrumisanindicationthatsomethingiswrong.Theprobecouldbedamagedornotfixedcorrectlyintheprobeholder.Oncethepeakislocated,typicallytheusershouldzoomintotherelevantpartofthefrequencyspectrumtovisualizethepeakmoreclearly.AnexampleoftheviewofacantilevertuningwindowisshowninFigure4.9.

Itcanbeseenthattheinstrumentoftenshowsnotonlyoscillationamplitudeversusfrequency,butalsooscillationphaseversusfrequency.Asshownhere,thephasechanges180°–being90°outofphaseattheamplitudemaximum,thegreatestslopeinthephasecurvecoincidingwiththemaximumintheamplitudecurve.ThemeaningoftheseplotsisalsoillustratedinFigure4.9.Theresonantfrequencyrepresentsthepointatwhichtheamplitudeismaximum,whilethephaseoftheoscillationofthecantilevermatchestheappliedphase(θ=0°).Theactualoperatingfrequencyisatthemaximumoftheamplitude,buttheuserusuallychoosesafrequencyalittlewayoffthemaximum(onthe

Fig.4.9. Exampleofrealamplitudeandphaseversusfrequencyplotsusedincantilevertuning.Theverticallinesrepresenttheoperatingfrequency,chosenbytheuser.Insetcartoonsshowthemeaningoftheamplitudeandphaseplots.Top:thecantilever'soscillationamplitudeismaximizedattheresonantfrequency.Bottom:belowresonantfrequency,themeasuredcantileveroscillationfollowstheappliedoscillation(phase,θ=0°),atresonanceitlagstheappliedforce(θ=90°),andaboveresonantfrequencytheappliedoscillationlagsmeasuredoscillationfurther(θ=180°).

(p.98) low‐frequencysize),totakeaccountofthefrequencyshiftasthetipapproachesthesample.Selectingthewrongfrequency(suchasoneatahigherfrequencythantheamplitudemaximum)mayallowimaging,butwillusuallygiveverypoorimagesandpossiblyimageartefacts.Havingselectedtheoperatingfrequency,theamplitudeofthedrivingpiezooscillationisadjustedtogivethedesiredoscillationamplitudeofthecantilever.Theoscillationamplitude,likethecantileverdeflection,isnormallyshownonlyintermsofthephotodetectoroutput(e.g.rmsamplitudeinvolts),sothedesiredsignalvariesfromoneinstrumenttoanother,butasdiscussedinChapter3,amplitudesinintermittent‐contactAFMcanvaryfrom1to100nm[108].InmostAFMsystems,anamplitudeset‐pointisthenchosen.ForcontactAFM,theset‐pointisadeflectionvalue,whichmeansthatincreasingtheset‐pointleadstogreaterforcesbetweenthetipandthesample.However,forintermittent‐contactmode,feedbackisbasedonadecreaseinamplitude,soalowerset‐pointmeansagreatertip–sampleinteractionforce.Forexample,ifthefreeoscillationamplitude,A0is1.0V,theusermightchoose0.9Vasaconservativeset‐point,meaningthefreeamplitudewillbeallowedtodecreaseby10%duringapproachatwhichpointthesystemwillgointofeedback.Thus,avalueoflowerthan0.9Vwouldmeanagreaterforceofinteraction,andviceversa.Now,unlikecontact‐modeprobes,IC‐AFMprobesarehighlystiff,andsotheyarelesspronetothermalnoiseandbending,andthusoscillationamplitudeishighlystable.Thisshouldmeanthatfalse‐engageislessofaproblem.However,long‐rangeforcesbetweentipandsampledousuallyaffecttheoscillationslightlywhenoperatinginair.So,theusermustonceagainbecarefultoavoidfalse‐engage,sothatitmightbenecessarytousealowerset‐pointthan90%.Itisuseful,again,toobservetheerrorsignal(theamplitude)asthetipapproachesthesample,tohelpdiagnosefalseengage.Oncetheoscillationfrequencyandamplitudeset‐pointarechosen,anapproachmaybemade.Duetothechangeinresonantfrequency

astheprobeapproachesthesample,itissometimeshelpfultowithdrawtheprobealittleafterasuccessfulapproach,andre‐optimizetheoperatingfrequency.

Havingapproachedsuccessfully,scanningandoptimizationofgainsareverysimilartocontactmode.SotheproceduredescribedinSection4.2.3canbeused.Thefirst‐timeuserisremindedthattheimagingmechanismforIC‐AFMiscompletelydifferentfromthatofcontact‐modeAFM(seeChapter3).ThismeansthatoptimalimagingparameterswillusuallybecompletelydifferentforcontactandIC‐AFM,evenonthesamesample,andusingsimilarprobes.OneaspecttobeawareofisthattheresponseoftheprobetolargetopographicchangesisratherslowinIC‐AFMcomparedtocontactmode,meaningscanningmayneedtobecarriedoutmoreslowly.Ifthetipdoesnotproperlytrackthesurface,eitherthespeedmaybedecreased,thegainsincreased,ortheamplitudeset‐pointdecreased.AnexampleoftheeffectofscanningtooquicklyisshowninChapter6.Notethatunlikeincontactmode,it'snotreallypossibletomakeforce–distancecurvesinIC‐AFMmode.Onereasonforthisisthatthecantileverissostiffthattryingtodothiswouldapplyaverylargepressuretothetipoftheprobe,anddamageit.However,oftenAFMsystemsdoallowtheusertoobtainamplitude–distancecurves.AnexampleshowingtheutilityofthisisshowninFigure4.10.Amplitude–distancecurveshavealsofounduseinmeasuringlong‐distanceforcesonthetip,forexampleinMFM[340].

AsdescribedbyGarciaetal.[341,342],thissortofcurvecanserveausefuldiagnosticpurpose.AsshowninFigure4.10,itispossibletoobservenon‐idealcurves,i.e.curveswherethereismorethanonepossibletip–sampledistanceataparticularamplitude(p.99)

Fig.4.10. Left:amplitude–distancecurveshowingjumpingfromahighamplitudestate(H)toalowamplitudestate.Right:effectofthisjumpingonanimage.Thedashedlinesintheleft‐handfigurecorrespondtotheset‐pointsusedinthethreeregionsintherightimages.Withaset‐pointnearthediscontinuityinamplitude–distance,unstableimagingwilloccur.Reproducedwithpermissionfrom341.Copyright2000bytheAmericanPhysicalSociety.

set‐point.Thissortofsituationwillleadtoinstabilityinimaging.Theoriginoftheinstabilityintheimageontherightwouldbeunclearwithouttheamplitude–distancecurve.Ifsuchafeatureisobservedbytheuser,heshouldchangetheamplitudeset‐pointtoavaluewithauniquesolution,shownbytheupperandlowersegmentsintheimageinFigure4.10.Thisexampleillustratesthatsometimesscanningparameterscanbeadjustedinoneoftwodirectionsinordertoimproveimaging.Inthecaseshownabove,thebestsolution

mightbetoincreasetheset‐point,ratherthandecreaseit,asitwillresultinlowertipwear.

Asdescribedpreviously,inIC‐AFMtherearenormallyfourtypesofsignalthatmaybesavedasimages.Therearesignalsoffourtypes–theheight(zpiezovoltagesignal,andzsensor,ifavailable),amplitude(errorsignal),andphasesignals.Inaddition,eachchannelmaybeobtainedinoneoftwodirections,orinboth.Itisuptotheuserwhichimagestorecordandsave.Theheightsignalsarethemostimportant,astheyaretheonlysignalswithameaningfulzscale,andtheonlysignalsfromwhichwecanmakeusefultopographicalmeasurements.Itisnotreallynecessarytocollectsignalsinbothdirections,soonlyoneheightsignal(typicallythezsensordata,ifit'savailable,otherwisethezpiezovoltage)isnormallycollected.Theamplitudesignalcanhelpinvisualizingtheshapeofthesample,andinspottingfeaturesforlatermeasurementintheheightimages.Thephaseimagecanserveasimilarpurpose,andinadditiongivesinformationaboutheterogeneityofthesample(seeSection3.2.3.2formorediscussiononthis).Thus,thephaseimagecanbehighlyusefuloncertainsamples.Itisrarethatbothforwardandbackwardimagesareneeded,sotypicallythreeimageswillbecollected,height,amplitudeandphase,eitherinforwardorbackwarddirections.Ifthisisthecase,itisimportanttheuserrememberstocollectallimagesinthesamedirection,asforwardandbackwardimagesmaynotbeperfectlyalignedwitheachother.Ifthephaseimageis(p.100) ofparticularuseinanapplication(e.g.fordiscriminationofphasesinapolymer),itcanbeusefultooptimizethephasesignal.Todothis,theamplitudeset‐pointisusuallyvaried,asahighset‐pointwillgenerallygivelittlecontrastinthephasesignal,whiletoolowaset‐pointcandamageorcontaminatethetip,whichwillalsonegativelyaffectthephasesignal.

4.3.1Intermittent‐contactmodeinliquidImaginginIC‐AFMinliquidisdifferentfromimagingincontactmodeinliquid.Normalacousticexcitationofthecantileverinliquidleadstoanumberofpeaksinthefrequencyspectrum,insteadofthesinglesharppeaktypicallyobservedinair.Theactualcantileverresonanceisalsoshiftedtolowerfrequencyandisbroadened(hasreducedQ),comparedtotheresponseinair[128].Finally,dampingalsoreducestheamplitudeoftheoscillation,meaningthathigherdrivingamplitudeswillberequired.Theadditionalpeaksarisefromexcitationoftheliquidintheliquidcell,whichfurtherexcitethecantilever[126,127].Theshapeofthecantilever'soscillationresponseinliquidwilldependontheleveritself,thegeometryofthefluidcell,andthedistanceoftheleverfromthesample[128,343].Inconsequencetheusercanbeconfusedaboutwhichoperatingfrequencytouse,especiallyasthecantilevermanufacturerwillonlyspecifythevalueoff0inair.However,manyofthesepeaks,notnecessarilynearcantileverresonances,canbeusedtoimagethesampleinIC‐AFM,althoughsomewillworkbetterthanothers[344].Typically,bestresultswillbeobtainedusingthe‘true’resonance,i.e.thatobtainedbydirectexcitationoftheprobe.Determiningthefrequencyofthispeakissometimesamatteroftrialanderror.Iftheuserdoesnotknowthetypicalfrequencyforaparticularcantilevertype,thenitisbesttochooseapeaktwotothreetimeslowerinfrequencyintheairpeakwhichhasarelativelysharpresponse.Trytoimageatthechosenfrequency;

ifthisdoesnotwork,tryanother,andsoon.Oncethedirectexcitationpeakfrequencyisfound,itisnormalthatapeakofsimilarfrequencywillexistforsimilarcantilevers.Asthefrequencyofthecantileverresonancesinliquidcanbehighlydependentonthedistancebetweentheleverandthesample,itisbesttoadjusttheoperatingfrequencywhentheprobeisveryclosetothesample[345].Commonlylow‐frequency(contactmode)cantileversareusedforIC‐AFMinliquid,assamplesaretypicallyverysoftwhenhydrated,andthusthere'sgreatpotentialforsampledamagebyIC‐AFMinliquid[346].TherearemanyexamplesintheliteratureofimaginginliquidusingIC‐AFMaswellasstudiesofoscillationofAFMleversinliquid,usingawidevarietyofprobes,whichcanalsohelpindeterminingthebestoscillationfrequencytouse[344,347–350].Itisworthpointingoutthat,asmentionedinpreviouschapters,alternativedrivemechanismsexistwhichdonotacousticallyexcitethecantilever,e.g.magneticdrivingofthelever[124,218].Suchdirect‐drivearrangementsavoidthedifficultiesinchoosingapeaktouse–onlythe‘true’oscillationfrequencywillresonate.However,thesearrangementsmakelittle,ifanydifferencetoimagequality[125].

4.4High‐resolutionimagingObtainingAFMimagesatrelativelylowresolution(scansizes>1μm,resolutionof>50nm)isquiteeasy,buttoobtainveryhigh‐resolutionimages(resolutiononthe(p.101)orderof5nmorless)canbeconsiderablymoredemanding.Toobtainveryhighresolutionalargenumberoffactorsmustbeoptimized.

Theprobetipmustbecleanandparticularlysharp.Evenamongstprobesratedasextrasharp,alargevariationinactualtipradiusislikelytobefoundasdiscussedinChapter2.Fordemandingapplications,severaltipscouldbetried,oratip‐checksamplecanbeused.Whenallelsefails,attemptingtoscanawell‐knownsample(especiallyoneoftheprobesharpnesscharacterizationsamples)canoftenhelptodiagnoseproblems.Typically,ifgreatresultsonsuchatip‐checkersamplecannotbeobtained,theywon'tbefoundfromthesampleofinteresteither.AlistofsamplessuitabletocharacterizeAFMprobesisincludedinAppendixA.

Thesamplemustbewellfixedtothesubstrate,whichshouldnotbemoving.Theinstrumentmustbeatthermalequilibrium,andwithoutdrift.Sampledriftisfairlyeasytospot,andanillustrativeexampleisgiveninSection6.6.4.Sometimesthemethodusedtofixthesampleitssubstratecanbeatfault,andamorerigidmounting(suchasgluingwithanepoxyadhesive)canhelp.Thermaldriftcharacteristicscansometimesbehelpedbyremovingsourcesofillumination,whichcanheatthesampleenvironment.Often,thermaldriftisreducedwithtime,soleavingtheinstrumentsetup,withthelaseraligned,thetipclosetothesample,orinfeedbackwithit,andtheoscillation(ifused)atthecorrectfrequency,for30minutestoanhour,canreducedriftconsiderably.

Sourcesofexternalnoiseandthevibrationisolationmustbeoptimized.Whenscanningveryflatsamplesatveryhighresolution,noiseintheimagethatwaspreviouslyinvisiblecanoftenbeseenintheimage.Inthiscase,theusermustsimplyremoveallpossiblesourcesofnoise,suchaslightsorelectronicequipmentthatarenotrequired,andensurethevibrationisolationisfullyfunctional,anduncompromised(e.g.byamechanical

connectionfromthestagetoanun‐isolatedsurface).

Finally,scanningparametersmustbeoptimized.Forverysmallscansitispossibletoscanveryquickly,asusuallythefeedbacksystemdoesnothavegreatchangesinz‐heighttocopewith.Inaddition,itisusuallynecessarytoscanveryquicklytoovercomeevensmallamountsofsampledriftwhenimagingverysmallareas.Forexample,toobtain‘atomiclattice’resolution,withascansizeofca.10nm,itiscommontoscanatabout60linespersecond.Forhigh‐resolutionimages,theperfectfeedbackisoftenfoundbymakingmanytinychangestothegainstoreachtheidealimagingconditions.

4.5ForcecurvesForce–distancecurvesaremeasuredbymonitoringthedeflectionofthecantileverasitapproaches,touches,andwithdrawsfromthesample.Bydefault,therefore,theyaremeasuredincontactmode.Parameterstobeselectedbytheuserwillincludethexandypositionsatwhichthecurveistoberecorded,datadensity,movementspeed(acquisitionrate),maximumalloweddeflection(force),lengthofthecurveandmore.Iftheareaofinterestislocatedinaparticularregion,itcanbeusefultoimagethesamplebeforemeasuringcurves.However,undersomecircumstances,suchaswhenthecantileverisverystiff,orhasbeenmodifiedwithalayerofmolecules,itisnotconvenienttodoimagingandforcespectroscopyatthesametime,especiallyimagingincontactmodewhichcandamageasensitivelayeronthetip.SoAFMsoftwareoftenhasaseparatemode(p.102) formeasuringforcecurves,whichmayalsoallowimagingincontactmode.SomeinstrumentsevenallowakindofhybridIC‐AFM/forcespectroscopy,whereimagingcanbeperformedinIC‐AFM,andwhentheareaofinterestislocated,theinstrumentlocatesthesurfaceusingamplitudemodulation,andonlystopsthetiposcillationduringacquisitionofacurve.Thiscanreducetipdamagebeforetipacquisition.Attemptingtomeasureforcecurvesinselectedregionsofasamplewithnanometreresolutioncanbechallenging,partlyduetosampledrift,butalsoduetopositioningdifficultiesandlinearizedscannerscanhelpgreatly.Analternativetocarryingoutforcespectroscopyinonelocationistoperformtheexperimentinagridpatternoverthesamplesurface,thusenablingagridofforcecurveswhichcanbeprocessedintoamapofadhesionforcesorsamplestiffness.It'sworthnotingthatat1Hzperforcecurveacquisitionof1Hz,a256×256pixelmapwouldtakemanyhourstoacquire,sosuchmapsareusuallyobtainedatlowresolutions.

Regardlessofthemannerinwhichsuchacurveisrecorded,theresultisaplotofdeflectionversusdistance,whichtheuserusuallywantstoconverttoforceversusdistance.Thefirststepistoconvertthedeflection(V)intotheactualdistancethetipmoved(m),thenusingthespringconstant(N/m),andthiscanbeconvertedtoforce(N).Thenormaldeflectionsensitivityiseasilyobtainedbymeasuringtheslopeofadeflectionsignalversusverticalpiezodisplacementplotonastiff,hardsurface[142].Thesurfacechosenisoftenanextremelystiffonesuchassapphireorstainlesssteel,butitisonlyimportantthatitisconsiderablystifferthanthetip;measurementswithflexiblecantileverscoulduseanyreasonablystiffsurfaceforthis.Theusermustobtainsuchadeflection‐calibrationcurvetoaccompanyeachsetofdatawithoutrealignmentofthe

laseronthecantilever;theexactalignmentoftheopticalsystemdirectlyaffectsthiscalibration[351].Oncethisisobtained,thecurvemaybeconvertedtoforce–distancewiththenormalspringconstant.SeeSection2.5forproceduresforcalibrationofnormalspringconstants.

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