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AtomicForceMicroscopyPeterEatonandPaulWest

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

AFMmodes

PeterEatonPaulWest

DOI:10.1093/acprof:oso/9780199570454.003.0003

AbstractandKeywords

ThemanydifferentimagingmodesandexperimenttypesthatmodernAFMscancarryoutexplainitspopularity.Theytransformahigh‐resolutionmicroscopeintoaversatilemeasurementstoolthatcandetermineaverywiderangeofsamplepropertieswithnanometreresolution.Thischapterdescribesthedifferencesbetweenthevariousimagingmodesavailable,suchascontact,non‐contact,andintermittent‐contactmodes.Thetheoryandpractices,aswellasthestrengthsandweaknessesofeachmodearehighlighted.Furthermore,non‐topographicalmodes,whichcanmeasuremechanical,(bio)chemical,magnetic(MFM),electrical(EFM)andthermalproperties,arediscussed.TechniquessuchasforcespectroscopyallowtheAFMtodirectlymeasuretheforceofinteractionbetweensinglemolecules.OtherAFMtechniquescanevenbeusedtomodifysamples,andthenimagetheresults.Examplesoftheuseofallmodesaregiven,tohelp

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thereadertounderstandtheirpotential.

Keywords:AFMmodes,topographica,lnon‐topographical,forcespectroscopy,contact,non‐contact,intermittentcontact,MFM,EFM

TherangeofavailableAFMmodesandexperimentsareattheheartofmodernAFM.ThewidevarietyofexperimentsthatmaybeperformedwithanAFMmakeitaversatile,powerfultool.Initiallytheonlymodeavailableforimagingwascontactmode,andthislimitedthetypesofsamplesthatcouldbeexamined,thetypesofexperimentsthatcouldbeperformed,andthetypeofdatathatcouldbeproduced.NowthereareaverylargenumberofpossiblemodesofoperationofAFM.Forexample,in1999,Friedbacheretal.attemptedtolistthenamesofalltheSPMmodesdescribed,andarrivedatmorethan50terms[94].SomeoftheseSPMmodeswereSTMorSNOM(ScanningNearfieldOpticalMicroscopy),butthereareatleast20differentmodesofAFM.SNOMisanexampleofusingtheclosecontactandpositioncontroloftheAFMtomeasurepropertiesofthesurfaceotherthantopography(inthiscase,opticalproperties).Asshowninthischapter,manyofnewermodesinAFMarealongtheselines:techniquesthatusetheincredibleresolutionprovidedbyscanningaprobeclosetothesurfacewithanAFMtomeasuredifferentpropertiesofthesamplesurfaceonthenanoscale.SNOM(alsosometimescalledNSOM,near‐fieldscanningopticalmicroscopy),isaverypowerfultechniquecombiningnear‐AFMresolutionwiththespectroscopicinformationthatisavailablebyusinglight‐basedtechniques.However,SNOMisnotcoveredinthisbookbecausealthoughsomeearlySNOMsinstrumentsweredevelopedbymodificationofAFMs,experimentsarenowgenerallycarriedoutwithspecializedSNOMinstruments,whichareratherdifferentfromanormalAFM.ForreviewsofSNOM,see[95,96].AtablecategorizingmajortechniquesinScanningProbeMicroscopyisshowninFigure3.1.

ForthepurposesofmakingthisapracticalguidetoAFM,inthischapterweconcentrateontechniqueslikelytobeaccessibleandofinteresttothereader.ThismeansthatwewillnotdescribeindetailtechniqueswhicharenotattainablewithcommercialAFMswithoutsignificantmodification,norcovermodesthathavebeendescribedbutnotwidelyadopted.Somemoreadvancedtechniquesarecoveredintheapplicationssection,Chapter7.

3.1TopographicmodesThebasisofAFMasamicroscopictechniqueisthatitmeasuresthetopographyofthesample.AsdescribedinChapter1,thedatasetsgeneratedinthiswayarenotconventionalimages,asproducedbyopticalmicroscopy,butratheramapofheightmeasurements.Thesemaybelatertransformedintoamorenaturalisticimagewithlightshading,perspective,etc.tohelpuspicturetheshapeofthesample(thisprocessiscoveredinChapter5).Inordertomaketheseheightmeasurements,avarietyofmodeshavedeveloped,whichcanbedividedintothosemodeswhichmeasurethestaticdeflection(p.50)

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Fig.3.1. SummaryofthenamesofsomeSPM‐basedtechniques.

oftheAFMcantilever,andthosethatmeasurethedynamicoscillationofthecantilever.Thedifferencesbetweenthemodesleadnotonlytodifferentexperimentalprocedures,buttodifferencesintheinformationavailable,differingsuitabilitiesforparticularsamples,andeventodifferencesintheinterpretationofthedata.

3.1.1Contactmode

ContactmodeAFMwasthefirstmodedevelopedforAFM.Itisthesimplestmodeconceptually,andwasthebasisforthedevelopmentofthelatermodes.Thereforeunderstandingcontactmodehelpstounderstandhowtheothertechniqueswork.Althoughthelimitationsofcontactmodepromptedthedevelopmentofmodesthatcouldexaminedifferentsamplesindifferentenvironmentsandgivedifferentinformation,contactmodeisstillanextremelypowerfulandusefultechnique.Contactmodeiscapableofobtainingveryhigh‐resolutionimages.Itisalsothefastestofallthetopographicmodes,asthedeflectionofthecantileverleadsdirectlytothetopographyofthesample,sonosummingofoscillationmeasurementsisrequiredwhichcanslowimaging.

InordertounderstandthewayAFMmodeswork,itisnecessarytouseso‐calledforce–distancecurves.Acartoonofasimpleforce–distancecurveisshowninFigure3.2.Asthenameimplies,thesecurvesareaplotofforce(ontheyaxis)versusdistance(onthexaxis).SuchacurveissimpletoacquirewiththeAFM.Itiscalculatedfromadeflection–distancecurvewhichiseasilymeasuredbymonitoringthedeflectionofthecantileverasthepiezoisusedtomovethetiptowardsthesample.Typically,atasetdeflectionlevel,thedirectionisreversed,andthetipwithdrawsfromthesample.Thisresultsinadeflectionversusdistancecurve,whichmaybeconvertedtoaforce–distancecurve.Measurementofforce–distancecurvesisaverysensitiveandquantifiablewayto(p.51)

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Fig.3.2. Simplifiedforce–distancecurveshowingcontact(repulsiveregion)scanningregime.Adeflection–distancecurve,whichistherawdatafromwhichaforce–distancecurveismeasured,hasasimilarshape.Right:illustrationofprobebendingineachregime.

determinetip–sampleinteractions,andisthebasisforseveralnon‐topographicAFMmodes,suchasforcespectroscopyandnanoindentation.Moreinformationabouttheuseofsuchcapabilitiesofforce–distancecurves,andhowtheyareconvertedfromdeflectiontoforceisgiveninSection3.2.1,andSection4.5,respectively.

ConsideringtheapproachcurveshowninFigure3.2,whenthetipisfarfromthesamplesurface,thecantileverisconsideredtohavezerodeflection;asthetipapproachesthesurface,itnormallyfeelsfirstanattractiveforce,anda‘snap‐in’occurs,asthetipbecomesunstableandjumpsintocontactwiththesurface.Astheinstrumentcontinuestopushthecantilevertowardsthesurface,theinteractionmovesintothe‘repulsive’regime,i.e.thetipisnowapplyingaforcetothesample,andthesampleappliesanoppositeforcetotip.Inthisregime,acombinationofcantileverbendingandsamplecompressionwillbeoccurringaccordingtotherelativecompliancesofthesamplesurfaceandAFMprobe.Ifthedirectionofmovementisreversed,theinteractionpassesagainintotheattractiveregime,andthetipstaysonthesurfaceuntilinstabilityoccursoncemore,andthetipsnapsoffthesurface.Itiswithintherepulsiveregimethatcontact‐modeimagingusuallyoccurs(forexample,atthepointlabelled‘set‐point’inFigure3.2).Inotherwords,incontact‐modeAFM,thetipoftheprobeisalwaystouchingthesample.Thishasthefollowingimportantimplicationsforcontact‐modeAFM:

1.Asaresultoftherepulsiveforcebetweenthetipandthesample,thesamplemaybedamagedorotherwisechangedbythescanningprocess.2.Conversely,thetipcouldalsobedamagedorchangedbythescanningprocess.3.Asthetipandsampleareconstantlyincontactwitheachotherasthetipmovesalongthesample,inadditiontothenormalforcetheyapplytoeachother,lateralforcesareexperiencedbybothprobeandsample.4.Thecontactbetweenthetipandthesamplemeansthatthenatureofthesamplesurfacemayaffecttheresultsobtained.Thismeansthatthetechniquecanbesensitivetothenatureofthesample.

(p.52) TheforcesappliedtothesurfacebytheprobeincontactmodearegivenbyHooke'slaw:

F = −k × D

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(3.1)whereF=force(N),k=probeforceconstant(N/m)andD=deflectiondistance(m).

Thebasisofcontact‐modeAFMisthatthemicroscopefeedbacksystemactstokeepthecantileverdeflectionatacertainvaluedeterminedbytheinstrumentoperator.Thispointisknownastheset‐point.Theset‐pointisoneoftheimportantcontrolparametersthattheoperatormustadjusttooptimizeimaging,andthereareequivalentparametersforallotherAFMimagingmodesaswell.Equation3.1showsthateitheraprobewithahighforceconstant(onewithastiffcantilever),oragreaterdeflection(i.e.ahigherset‐point),willleadtoahigherappliedforce.BecausethefeedbacksystemoftheAFMcannothaveinstantaneousresponse,theverticaldeflectionwillactuallyvarysomewhatduringimaging(indicatedbytheredregionofthecurveinFigure3.2).Theamountitvarieswilldependonthetopographyofthesample,flexibilityofthecantilever,scanningspeed,andhowwellthefeedbackcircuithasbeenoptimized.OptimizationoftheseparametersisdiscussedinSection4.2.TheAFMsoftwaremaydisplaythedeflectionsignalasalineplotasthetippassesoverthesample,orasanimage.Thedeflectionsignalincontact‐modeAFMistheerrorsignal,thatis,thesizeofthedeflectionisameasureofhowmuchthecantileverisdeflectingbeforethedeflectionis‘corrected’bythefeedbackcircuitviaheightadjustmentbythepiezo.Therefore,intheidealsituation,therewouldbenocontrastinthedeflectionimage.Themorecontrastexistsinthedeflectionsignal,themore‘errors’willbepresentintheheightimage,becauseregionsofhighcontrastinthedeflectionimagecorrespondtoregionsintheheightimage,wherethefeedbackhasnotyetcorrectedforcantileverdeflection.However,usuallyitisnotpossibletohavethefeedbacksignalrespondperfectly,andthedeflectionsignalwillshowtheslopeofthesample,becauseitisregionswherethereishighslope,ormoreprecisely,agreatrateofchangeofslopewithdistance,thatgiverisetolargecantileverdeflections.

Theimagingmodedescribedsofarisknownasconstant‐forcecontact‐modeAFM.Iftheuserturnsofffeedbackaltogetherwhileimaging,thentheyareeffectivelyusingconstant‐heightcontact‐modeAFMratherthanconstant‐forcecontact‐modeAFM.Becauseconstant‐forcemodeisbyfarthemostwidelyusedmode,ingeneralanyreferencetocontact‐modeAFMwillmeanconstant‐forcemodeunlessspecifiedotherwise,andthisistheconventionwefollowinthisbook.Inconstant‐heightmode,withnofeedbackactive,theimagesignalcomesentirelyfromcantileverdeflection,ratherthanfromthevoltageappliedtothezpiezo(whichwouldbetypicallysetataconstantvalue).Heightmeasurementswillthereforerequirespecificcalibrationofthecantileverdeflection,toextractrealsampletopography.Constant‐heightmodeAFMdoeshavesomespecificapplications:itcanbeusefulinconditionswherescanningiscarriedoutsofastthatthefeedbacksystemcannotcope[9,36].However,undertheseconditions,AFMisinfactactingratherlikeastylusprofilerasthetip–sampleforceisnotfullycontrolled.Typically,tocarryoutthesemeasurements,thefeedbacksystemisinitiallyusedtodeterminethelocationofthesamplesurface,andtheapproximatetopography,beforebeingturnedoff,orjustreducedtoaverylowlevel.

F = −k × D

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However,evenusingconstant‐forceAFM,thesoftwaretypicallywillallowtheusertosavethedeflectionimage,andsomeoperatorschoosetopublishthisimage,asitisoftena(p.53)

Fig.3.3. Illustrationoftherelationbetweenheightanddeflectionimages.Lefttoright:height,right‐shadedheightanddeflectionimagesofthesurfaceofamosquitoeye.Theheightimageshowshowmuchthezscannermovestomaintaintheset‐point.Thedeflectionimageshowshowthecantileverbendsasitpassesoverthesample,andisthesignalusedforfeedbackincontact‐modeAFM.Thisimageisverysimilartotheshadedheight.

simplewaytoshowtheshapeofthesample,andmayevenshowfeaturesnotvisibleintheheightimage(whichcouldbeanindicationthatfeedbackwasnotoptimized).However,itisworthrememberingthatwherefeedbackwascorrectlyoptimized,theAFMheightimagewillalsocontainallthefeaturespresentintheerrorsignal.Onewaytoshowthisistoapplyashadingalgorithmtotheheightimage–thiseffectivelygivesthederivativeoftheheightimage;theresultingimagewillbeverysimilartothedeflectionimage.AnexampleofthisisshowninFigure3.3.NotethatinthedeflectionimageshowninFigure3.3thez‐scaleisinvolts.Thez‐scalewasincludedhereforillustrativepurposes,insuchimagesthez‐scaleisalmostcompletelymeaninglessscientifically–evenifconvertedtonanometres,thesizeofthedeflectioncouldeasilybechangedbyadjustmentofthefeedbackparameters,andsoshouldalwaysberemovedfromtheimagebeforepresentation.

Thedeflectionsignalisused,asdescribedpreviously,withthefeedbackparameterstodeterminehowthezpiezoelectricmustmovetomaintainaconstantcantileverdeflection(andhenceconstanttip–sampleforce).Theamountthezpiezomovestomaintainthedeflectionset‐pointistakentobethesampletopography;thissignal,plottedversusdistance,formstheheightortopographyimageincontact‐modeAFM.Thereisathirdsignalwhichistypicallyavailableincontact‐modeAFM.Thisderivesfromthelateraltwistingofthecantilever,andisthereforeusuallycalledlateraldeflection.Thissignalistypicallyusedduetoitsmaterialsensitivity,ratherthanasameasureofsampletopography,anditisthereforecoveredinthenon‐topographicmodespartofthischapter(Section3.2.3.1).TheoriginoftheverticalandlateraldeflectionsignalsinatypicalopticalleverAFMset‐upisshowninFigure3.4.ThephotodetectorusedinopticalleverAFMsusuallycomprisesoffoursegments.Thedifferenceinsignalbetweenthetoptwoandbottomtwosegments,i.e.(A+B)–(C–D)givestheverticaldeflection(measuredinvolts,oramps),andthedifferencebetweentherightmosttwosegmentsandtheleftmosttwosegmentsgivesthelateraldeflection,i.e.(B+D)–(A+C).

Itisworthnotingherethatincontact‐modeAFM,likemostoftheothermodes,two

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versionsofeachdatatypecanbeavailable,thesebeingthedatacollectedintheleft‐to‐rightdirection,andthereverseset,collectedintheright‐to‐leftdatadirection.By(p.54)

Fig.3.4. Illustrationofhowthephotodetectordetectsverticalandhorizontalbendingofthecantilever.

conventionAFMimagesarepresentedwiththefastscanaxisdataappearinghorizontally,nomatterinwhichdirectiontheAFMtipwasscanned.Sotherewillbeforwardandbackwardheight,verticaldeflectionandlateraldeflectionimagesavailable,meaninguptosixdatachannelsmightberecorded.Iftheinstrumentisequippedwithazaxiscalibrationsensor,bothzvoltageandzsensorchannelsmightbeavailable,raisingthetotaltoeightchannels.Typically,whiletheprobescansovereachlineinbothdirections,onlyonedirectionwillbesaved.Thisisbecausetheheightdatainthetwodirectionsshouldbeidentical.Theverticaldeflectionimagesshouldbethesameonpartsofequalslope,andgiveoppositecontrastonregionsofchangingslope,buttheinformationavailablefromthedatacollectedinthetwodirectionsiseffectivelythesame.Soformostchannels,thereisrarelyanyneedtosavethedatacollectedinbothdirections,althoughitissometimesusefultoobservebothforwardandbackwardheightdatawhileoptimizingscanningconditions,asdiscussedinSection4.2.Lateraldeflectiondatafrombothdirectionsissometimessaved,tohelpunderstandfrictionalpropertiesofthesample,whichisdiscussedinSection3.2.3.1.

Applicability

Contact‐modeAFMhasareallywiderangeofpotentialapplicationsandsomeofthesearedescribedinChapter7.However,itispossibletosummarizesomegeneralcaseswherecontactmodeislikelytobechoseninpreferencetoothertechniques.Probablythebestreasontousecontactmodeisitshighresolution.Somedynamicmodescanalsoachieveextremelyhighresolution,butcomparedto,forexample,intermittent‐contactmode,theresolutionofcontactmodeispotentiallyextremelyhigh.Whatkeepsitfrombeingusedmorewidelyisthattheappliednormalforceleadstoahighlateralforceappliedtothesampleaswell.Inthecaseofweaklyadsorbedsamples,orsoft,easilydeformedsamples,thiscanleadtoproblemsofsampledistortion,damage,orevenremovalfromthesubstrate[97,98].Becauseofthis,ithasbeensuggestedthatcontact‐modeAFMisnogoodforsoftsamples.Thisisnotthecase,astherearemanyreportsofsoftbiologicalsamples,eveninahydratedstate,beingsuccessfullyimagedbycontact‐modeAFM(forexamples,see[99–103]).Often,contactmodeischosentoimagesuchdelicatestructureswhensub‐molecularresolutionisrequired[99,100,102,104].What(p.55) istrueisthatinambientconditions,acapillarylayerofwaterwillformbetweenthetipandthesurface.Oneeffectofthisisto‘pull’theAFMtipontothesurface,oftenapplyinganevenstrongerforcethantheforceapplied(viatheset‐point)bytheoperator.Thusitiseasyto

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unwittinglyapplyaverylargeforce(>nN)tothesampleincontact‐modeAFMinambientconditions.Inwater,theseforcesdonotexist,soitiseasiertoimagewithaverygentleforce.Forthisreason,andduetosomecomplicationsofimagingindynamicmodesinliquids(seethenextsection),imaginginliquidisastrongpointofcontactmode.Asmentionedpreviously,contactmodealsoworkswellinhigh‐speedAFM,andsomehigh‐speedAFMset‐upsusethismodeexclusively[36].

3.1.2Oscillatingmodes

InthefirstpaperonAFM,BinnigandQuateacknowledgedthepotentialbenefitsofoscillatingthecantileverinanAFM,andcomparedtheresultsofusinganoscillatingprobewiththosefromcontactmode.Atthetimecontactmodegavefarbetterresults,probablyduetothenatureoftheprobeused[19].Althoughtheuseofoscillatingmodeswererevisitedshortlyafterwards[105],itwasseveralyearsbeforeoscillatingprobemodesbecamepopular,andforquiteawhilenearlyallAFMwascarriedoutincontactmode.TheprimarymotivationforusingoscillatingmodeinanAFMistotakeadvantageofthesignal‐to‐noisebenefitsassociatedwithmodulatedsignals.Thus,anAFMthathasoscillatingmodescanmeasureimageswithasmallprobe–sampleforce.

Therearenowalargenumberofdynamicmodesofoperation,andevenmorenamesforthosemodes.However,allofthesemodesarevariationsonatheme.Thecantileverisoscillated,usuallywithanadditionalpiezoelectricelement,andtypicallyatitsresonantfrequency.Whentheoscillatingprobeapproachesthesamplesurface,theoscillationchangesduetotheinteractionbetweentheprobeandtheforcefieldfromthesample.Theeffectisadampingofthecantileveroscillation,whichleadstoareductioninthefrequencyandamplitudeoftheoscillation.Theoscillationismonitoredbytheforcetransducer(i.e.bytheopticalleverinmostAFMs),andthescanneradjuststhezheightviathefeedbacklooptomaintaintheprobeatafixeddistancefromthesample,justasincontact‐modeAFM.Theonlyrealdifferencesbetweenthevariousoscillatingmodesavailableareinthesize(amplitude)oftheoscillationappliedtotheprobe,andthemethodusedtodetectthechangeinoscillation.ThegeneralprincipleofoscillatingAFMmodesisshowninFigure3.5.

Irrespectiveofthemanydifferenttermsusedtodescribethetechniques,thereareactuallyonlyafewkindsofconditionsusedinoscillatingimagingmodes.Theusercandecidetoseteitherasmalloralargeappliedoscillationamplitude,andsometimescandecidehowtodetectthechangeinprobeoscillation.Someinstrumentsmayonlyhaveonedetectionschemeimplemented.Theinstrumentalset‐upschematicisshowninFigure3.5.Anoscillatingsignalisgenerated,andappliedtothecantilevermechanically,suchthattheprobeisoscillatedclosetoitsresonantfrequency.Theoscillationoftheprobeismonitoredasitisbroughtclosetothesamplesurface.Thedetectedchangeintheoscillation(whetherdetectedviaamplitude,phaseorfrequency),isusedinafeedbacklooptomaintaintheprobe–sampleinteractionconstant.Thechoiceofsmallorlargeamplitudehasaconsiderablepracticaleffect,asisillustratedinFigure3.6.Usingasmalloscillationamplitude(DenotedbythearrowA),itispossibletomaintain(p.56)

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Fig.3.5. SchematicofgeneralizedoperationofoscillatingAFMmodes,showinginstrumentalset‐up.Anoscillatinginputsignalisappliedtothecantilevertomaketheprobevibrateupanddown.Theactualmovementoftheprobewilldependonitsinteractionwiththesamplesurface.Theresultingoscillationinthecantileverdeflectionismeasuredandcomparedtotheinputoscillationtodeterminetheforcesactingontheprobe.

thecantileverintheattractiveregimeonly.Thistechniqueissometimesknownasnon‐contactAFM,oralternatively,andperhapsmoreaccurately,asclose‐contactAFM(seeTable3.1).Thistechniquehassomeadvantagesduetothelowprobetip–sampleforcesinvolved,andisdiscussedbelowinSection3.1.2.1.Ontheotherhand,itcanbeseenthatifalargeoscillationamplitudeisapplied,thentheprobewillmovefrombeingfarfromthesurfacewherethere'snotip–sampleinteraction,throughtheattractiveregime,intotherepulsiveregime,andback,ineachoscillationcycle(arrowB).Thistechniqueinvolveslargeprobetip–sampleforces,socanbemoredestructive,butiseasiertoimplement.Thistechniqueiswhatwecallintermittentcontact‐modeAFM(andisalsoknownbymanyothernames,someofwhicharegiveninTable3.1),andisdiscussedinSection3.1.2.2.

Fig.3.6. DifferentoperatingregimesforoscillatingAFMmodes.A:withasmallamplitudeofoscillation,theprobecanbekeptintheattractiveregime.B:withalargeroscillationtheprobemovesthroughnon‐interacting,attractiveandrepulsiveregimes,resultinginintermittentcontact.

(p.57)

Table3.1.NomenclatureofsomeoscillatingprobeAFMmodes.

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Detection Amplitude

Low HighAmplitude Rarelyused IntermittentContactAFM(IC‐AFM),

alsoknownasAC‐AFMorTappingPhase Non‐contactAFM(NC‐AFM),

alsoknownasclose‐contactAFMRarelyused

TypicallyanAFMdesignedforuseinairorliquidhaselectronicsthatcanmeasurechangesinvibrationalamplitudeorphaseatapreselectedfrequency.Sotheinstrumentoperatorcanchoosetouseeitheroftheseforfeedback.Incombinationwithlargeorsmallamplitudes,therearefourtypesofoscillatingexperimentavailabletomostAFMusers,whichareshowninTable3.1.

Itshouldbestressedthatthetwopossibleconditionsdescribedas‘rarelyused’inTable3.1arenotunusable,justthattheyarenotcommonlyapplied.Phasedetectionisusuallyusedwithsmallamplitudes(close‐contactAFM),duetosomewhathighersensitivity,andamplitudedetectionisusuallyusedwithlargeamplitudes(intermittent‐contactAFM),butthesearenottheonlypossibleimagingmethods.Optimalimagingconditionsaresometimesdifficulttoestablish,anditmaybenecessarytotrydifferentamplitudesanddetectionschemestofindtheidealconditions.

Analternativetoamplitudeorphasedetectionisfrequency‐modulationdetection(FM‐AFM),typicallyusedinultra‐highvacuumconditions(UHV‐AFM).FM‐AFMistypicallyappliedwithsmalloscillationamplitudesinthenon‐contactregime.TypicallyFM‐AFMiscarriedoutwithaphase‐lockedloopdevice.ThistechniqueisunavailabletomostAFMusersduetotheneedforadditionalequipment,soitisnotcoveredindetailinthisbook.However,ithasbeendescribedindetail[106,107],andcomparedwiththeamplitudemodulation(AM‐AFM)techniqueswediscusshereelsewhere[108].

3.1.2.1Non‐contactmode/close‐contactmodeOneofthegreatadvantagesofoscillatingmodesinAFMisthattheycandecreasethesizeoftip–sampleforces,whilemaintaininghighsensitivitytothesampletopography.Toachievenon‐contactAFM,thetipmustbecloseenoughtothesamplesurfacetoachievethishighsensitivity,withoutpassingintotherepulsiveregimeusedforcontact‐modeAFM.Non‐contactAFMisthereforecarriedoutintheattractiveregime,asshowninFigure3.7.

Byusingahighlystiffcantileverandmonitoringthedynamiceffectsoftheattractiveforce(i.e.thechangeintheoscillation)inthisregime,itispossibletomaintainthecantileververyclosetothesurfacewithoutjumpingtotherepulsiveregime.Itispossibletoobservechangesintheoscillationamplitudeandphaseinthisregime.Theseeffectsarecausedbyachangeinthecantileverresonantfrequencywhichisinturncausedbyforcesfromthesurface(normallyattractivevanderWaalsforces)actingonthetip.The

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resonantfrequencyfarfromthesurface,ω0isgivenbyω0=c√kwherecisafunctionofthe(p.58)

Fig.3.7. Operatingregimefornon‐contactAFM.Withasmallamplitudeandstiffcantilever,theprobecanoscillatewithintheattractiveregimeonly.

cantilevermass,andkisthespringconstant.Butanadditionalforceffromthesurfacemeansthatthenewresonantfrequencyω′Oisgivenby:

(3.2)wheref′isthederivativeoftheforcenormaltothesurface[109].

Theimportantpointhereisthateitherthechangeinamplitudeorthechangeinphase(whichactuallyderivesfromthechangeinfrequency)maybeusedinthefeedbackcircuittomaintainthetipatafixeddistancefromthesamplesurface.Thenamenon‐contactAFMisactuallyquitemisleading.AllAFMmodesinvolvetheprobemovingintotheforcefieldofthesamplesurface,including‘non‐contact’AFM.Atthesortofdistancesinvolved,itisimpossibletosayatwhichpointcontactoccurs.FurthermisunderstandingiscausedbythefactthatanumberofothernameshavebeenusedfordynamicAFMmodes,andthereisnoclearconsensusonthecorrecttermstouse,sothereisgreatscopeforconfusion.Hereweusethetermnon‐contact‐modeAFMtomeanAFMcarriedoutintheattractiveregime,typicallyusingsmallamplitudesofoscillation.Section3.1.2.2dealswithdynamicmodesthatpassintotherepulsiveregime,whichwechoosetocallintermittent‐contactmode.

Non‐contact‐modeprinciplesofoperation

Typically,non‐contactmodeiscarriedoutinamplitudemodulationmode,andtheerrorsignalmaybeeithertheamplitudeorphaseofoscillationofthetip.Toavoidthepossibilityofslippingintotherepulsiveregimewhichislikelytodamageorcontaminatethetip[110],ahigh‐frequencycantileveristypicallyusedwithω0intherangeof300–400kHz.Inaddition,smalloscillationamplitudesareused,oftenoftheorderof10nm[111].Aswithalldynamicmodesofoperation,scanningspeedisusuallylowerthanincontactmode,althoughthehighfrequenciesandsmallamplitudesmeanscanningspeedcanoftenbegreaterthaninIC‐AFM.WhenusedinUHVconditions,frequencymodulationisusually

= cw′0 k − f ′

− −−−−√

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used[108].

Applicability

Non‐contact,orclose‐contactAFMisaverywidelyappliedtechnique,andcanbeusedforimagingofalmostanysampleinAFM.Itiscurrentlyusedlessoftenthanintermittent(p.59)

Fig.3.8. Possiblenon‐contactimagingconditionsunderambientconditions,withasamplecoveredinacontaminationlayer.Suchalayerexistsonmostsamplesinair.Inthefirstcaseontheleft,theprobeoscillatesabovethecontaminationlayer.Inthesecondcase;right,theprobeoscillateswithinthecontaminationlayer.

contactinambientconditions.However,withcare,itcanreplaceintermittentcontactinnearlyallapplications,andoftengivesbetter,andmoreconsistentresultsduetolowertipwear.Oneofthelimitingfactorsfornon‐contactmodeinairisthecontaminationlayerpresentonmostsurfacesunderambientconditions.Ingeneral,thepresenceofthislayermeansthattheprobe–surfaceinteractionforcesaregovernedbythecapillaryforcesbetweentheprobeandthecontaminationlayer.Fornon‐contactAFM,Theprobemaybevibratedintwodifferentdistinctregimesasitisscannedacrossthesurface,seeFigure3.8.Inthefirstregime,theprobeisoscillatedabovethesurfaceofthecontaminationlayer.Thevibrationamplitudemustbeverysmallandaverystiffprobemustbeused.Theimagesofthesurfacecontaminationlayeraretypicallyunrepresentativeofthesubstratetopographyandappeartohavelowresolution.Thisisbecausethecontaminationfillsinthenanostructuresatthesurface.However,insomecasesthistechniqueallowsthedeterminationofthelocationorshapeofliquiddropletsonthesamples'surface,whichmaybedesirable[112,113].Inthesecondregimetheprobeisscannedinsidethecontaminationlayer[110].Thistechnique,sometimescalled‘nearcontact’,requiresgreatcaretoachieve.Again,thecantilevermustbestiffsothatthetipdoesnotjumptothesurfacefromthecapillaryforcescausedbythecontaminationlayer,andverysmallvibrationamplitudesmustbeused.However,high‐resolutionimagesmaybemeasuredinthisregime.Non‐contactAFMfullyimmersedinliquidisalsopossible[114],anddelicatesamplessuchasDNAmoleculesorotherbiologicalsampleshavebeenimagedbyinthisway,andsuchmoleculesmaysufferlessdistortionwhenimagedlikethisthanwhenimagedbyintermittent‐contactmode[114–116].

Usingultra‐highvacuum(UHV)conditions,FMdetectionhasadvantagesoveramplitudeorphasedetection[117]andFMdetectioniswidelyusedforUHVnon‐contactAFM.Someamazingresultshavebeenshownforfrequency‐modulationbasednon‐contactAFMinultra‐highvacuum,includingtrueatomicresolution[118,119].Forinstance,theMoritagrouphaveshowntrueatomicresolutioninanumberofsystemswiththis

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technique[106,118,120–122].Thesystemmustbeverystableforoperationtobereliablewithouttheriskofjump‐to‐contact.AnexampleimageshowingtrueatomicresolutionbyNC‐AFMisshowninFigure3.9.Figure3.9alsoshowsarareexampleofusingNC‐AFMtoidentifyatomsonasurface.ForcespectroscopyisdescribedfurtherinSection3.2.1,withrespecttousingforcespectroscopyincontactmode.Butinthisexample,unusualduetothemeasurementofforcecurvesinFM‐AFMmode,forcespectroscopywasusedto(p.60)

Fig.3.9. Examplenon‐contactAFMimages.Top:examplesofnon‐contactAFMimagesinambientconditions(air)–individualDNAmolecules(left)and1nmnanoparticles(right)[123].Bottomimages:non‐contactAFMinUHVconditionsforindividualatomidentification.Left:atomicallyresolvedNC‐AFMimageofSi,SnandPbatomsonanSi(111)substrate–someatomsmaybedifferentiatedbasedonapparentsize,butidentificationisnotpossible.Middle:short‐rangechemicalforcemeasuredovereachatomisdependentonthechemicalnatureoftheatoms.Right:thesameimageasontheleft,withatomscolouredaccordingtothecolourschemeinthemiddle.Adaptedfrom[8],withpermission.(Acolourversionofthisillustrationcanbefoundintheplatesection.)

identifytheattractiveforceaboveindividualatomswhichcouldbecorrelatedtotheirchemicalidentity[8].Furtherexamplesoftheapplicationsofnon‐contact‐AFMtoobtainatomicallyresolvedinformationaregiveninSection7.1.5.

3.1.2.2Intermittent‐contactmodeAlthoughthefirstexperimentsindynamicAFMaimedtocarryoutnon‐contactAFM,itwasnotlongbeforetheadvantagesofusingadynamicmodethatallowstheprobetotouchthesample(thatis,passintotherepulsiveregime)werediscovered[97].Forintermittent‐contactAFM,feedbackisusuallybasedonamplitudemodulation[108]andthetip–sampleinteractionpassesfromthe‘zero‐force’regime,throughtheattractiveregime,andintotherepulsiveregime,asshowninFigure3.10.

Thefactthatthetip–sampleinteractionmovesthroughallthreeregimeshasseveralimportantimplications:

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(i)Thereistip–samplerepulsiveinteraction,i.e.tipandsampletoucheachother,leadingtothepossibilityofsampleortipdamage,however:(p.61)

Fig.3.10. Intermittent‐contactoperatingregime.Inthismode,theAFMprobe'soscillationislargeenoughtomovefromtherepulsiveregime,throughtheattractiveregime,andcompletelyoutofcontactineachcycle.

(ii)Duetothemovementofthetipperpendiculartothesurfaceasitscans,lateralforcesare(almost)eliminated.(iii)Thetippassesthroughthecontaminationlayer(seeFigure3.11).(iv)Tip–samplecontactalsoallowssomesensingofsampleproperties.(v)Thefeedbacksystemrequiresthecollectionofadequatedatatocharacterizethecantileveroscillationintermsofitsamplitude.

Points(ii)and(iii)aboveexplainthepopularityofIC‐AFM.Thelateralforceswhichcancausegreatproblemsincontact‐modeAFMdonotaffectIC‐AFM.Ontheotherhand,thefundamentalinstabilityofnon‐contactAFMinair(duetooperationintheattractiveregime,andthepresenceofthecapillarylayer)isovercome,makingIC‐AFMsomewhatsimplertoachieve.InIC‐AFM,therestoringforceofthecantileverwithdrawsthetipfromthecontaminationlayerineachcycle,thusreducingtheeffectofcapillaryforcesontheimage.

Fig.3.11. Intermittent‐contact‐modeimagingconditionsinair.Theprobepassesthroughthecontaminationlayertotouchthesubstratesurface,andoutagain.

(p.62) Operatingprinciplesofintermittent‐contactAFM

InIC‐AFMtheprobeisoscillatedwithalargeamplitude,typicallyintherangeof1–100nm[108],andthefeedbackisusuallybasedontheamplitudesignal.Inmostcases,theprobeisoscillatedbyanadditionalpiezoelectricelementattachedtotheprobeholder(seeChapter2),althoughitisalsopossibletoexcitethecantilevervibrationbyothermethods,e.g.byanexternalmagnet,withamagneticallycoatedcantilever[124,125],

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whichmayreducefluidvibrationwhenimaginginliquid.Infact,ratherthandrivingtheprobedirectly,themostcommonexcitationmethodforfluidimagingistoexcitetheentirefluidcellholder,whichcausestheliquidtovibrate,acousticallydrivingthecantilever[126,127].Often,inadditiontotheamplitudesignal,thedelayinthephaseoftheprobeoscillationisrecorded.OscillationamplitudeandphaseareillustratedinFigure3.12.

Theamplitudeisreducedbythecontactwiththesamplesurface,andsoanamplitudeset‐pointissetbytheuser,andtheamplitudeistheerrorsignalinIC‐AFM.Inasimilarwaytodeflectionincontactmode,theamplitudesignalinintermittentcontactmaybeusedasanillustrationoftheshapeofthesample.Again,likethedeflectionsignal,theamplitudesignalshowswherethefeedbacksystemhasnotyetcompensatedforchangesinsampleheight,soforbestheightdata,theamplitudesignalshouldbeminimized.AnexampleimageshowingtherelationbetweenheightandamplitudedataisshowninFigure3.13.Notethatlikedeflectionimagesincontactmode,thezscaleofamplitudeimagesinIC‐AFMisusuallyinvolts,unlessspecificallycalibrated.It'scommonpracticetoremovethisscaleforpublicationasithasnopracticaluse.

Inadditiontoheightandamplitudedata,thephase‐shiftmayalsobesavedasanimage.Thereasonwhysavingthisdataisusefulisnotobvious,andthisinformationwaslargelyignoredinearlyintermittent‐contactAFM.Infact,thephaseoftheoscillatingcantileverisstronglyaffectedbytheprobetip–sampleinteractions,soitcanbeausefulwayofdistinguishingmaterials.AsaNon‐topographicmode,phaseimagingiscoveredinSection3.2.3.2.

Applicability

Intermittent‐contactmodeisaverywidelyappliedtechnique,andiscurrentlythemostcommonlyappliedtechniqueforimaginginair.Inliquid,IC‐AFMmodeisalsovery

Fig.3.12. Illustrationoftheeffectofintermittentcontactonthecantilevers'oscillation.Thefreeoscillation(solid)ismodifiedwhenincontactwithasurface(dashed)byareductioninamplitudeandaphaseshift.

(p.63)

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Fig.3.13. Intermittent‐contactAFMimagesofhumanredbloodcells.Height(left)andamplitude(right)imagesshown.

widelyapplied,althoughitissubjecttoanumberofdifficultiesspecifictooperationinliquid,namelythatmechanicalexcitationofthecantilevercanleadtoexcitationofthefluidandfluidcellaswell[128],andalackofclearunderstandingofthecontrastmechanisms[108,129,130].TheoperationofIC‐AFMmodeinliquid,aswellasinair,isdiscussedinSection4.3.Intermittent‐contactAFMisnotcommonlyappliedinvacuum,duetorestrictionsinbandwidthduetoincreaseofQinvacuum[117].Anextremelywiderangeofsampleshavebeenstudiedbyintermittentcontact‐modeAFM,someoftheseareillustratedinChapter7.

Higherharmonicsimaging

ArecentdevelopmentinIntermittent‐contactAFMistheuseofmodesofresonanceotherthanthefundamentalone.Thismayeitherbebyapassivetechnique,bymeasuringthevibrationatthesehighermodes,caninvolveexcitationatmultiplefrequencies.AdditionofsuchcapabilitiestoanAFMisrelativelysimple,themainrequirementbeingthatalock‐inamplifiercapableofmonitoringtheveryhighfrequencies.Figure3.14showsillustrationsofthefirstfourmodesofabeam‐shapedcantilever.Therequirementforahigh‐frequencyamplifierisbecausehighermodesofrealcantileversarelikelytohaveextremelyhighfrequencies.Becausethemodesareanharmonic,thesecondmodeisnotnecessarilyatdoublethefrequencyofthefundamental(i.e.f2≠2f1),butmaybeashighassixtimesthefundamentalfrequency[131].Inanycase,havingtwolock‐insisusefulbecauseitisadvantageoustobeabletomonitorbothf1andf2simultaneously.

Fig.3.14. Illustrationsofthefirstfournormalresonancemodesofabeam‐shapedcantilever.

(p.64) Thereasonforinterestinmonitoringthehighermodesofoscillationisthatithasbeenshownthathighermodescanbemoresensitivetomaterialdifferences,particularlyinthephasesignal[132].Garciaandco‐workershavestudiedthetheoryofthistypeofimaginginseveralworks[131,133,134]andexplainthatwhilethephaseshiftofthefirstfundamentalfrequencyissensitivetoenergyloss,thehigherharmonicscanbesensitivetotip–sampleinteractionsthatconserveenergyaswell,explainingthecontrastimprovementinhigherharmonicphaseimaging[134].Inrecentyears,morereports

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haveemergedalsogivingfurtherexperimentalevidenceforthehighmaterialsensitivityofthephaseshiftathighharmonics[135–137].Thishighsensitivityofthetechniquehasbeenusedtoobtainhigh‐resolutionimagesinIC‐AFMevenofverysoftsamples[138,139].ThesematerialsrequireverylowforceimaginginIC‐AFMmodetoavoiddamage,whichreducedthecontrastinthefundamentalmodetothepointwherenosub‐moleculardetailswerevisible,butincreaseddetailswereavailableinthehigheroscillationmodes.Inaddition,ithasbeenreportedthatusinghigherharmonicsforfeedbackcanimproveimagingduetohigherQofthehighermodes[135].

3.2Non‐topographicmodesEversincetheearlypapersonSTM,scanningprobemicroscopeshavebeenusedtoobtainmorethanjusttopographicinformation.Inthoseearlyexperiments,thefirstreportsofascanning‐tunnellingspectroscopy(STS)experimentsweremade[140,141],whichconsistsoframpingthetunnellingvoltageandmonitoringthetunnellingcurrentwiththetipheldfixedoveraparticularpartofthesamplesurface.Theuseoftheword‘spectroscopy’hascontinuedintothefieldofAFM,where‘spectroscopic’techniquesaredifferentfrom‘microscopy’techniquesinthattheyprobepropertiesofthesampleotherthantopography.Themostwell‐knownexampleisprobablyforcespectroscopy.

3.2.1Forcespectroscopy

Forcespectroscopyinvolvesmaintainingthex‐ypositionoftheAFMprobefixed,whilerampingitinthezaxis,tomeasurethedeflectionasthetipapproachesandretractsfromthesamplesurface.Assuch,forcespectroscopyconsistsofsimplymeasuringforce–distancecurves,asshowninFigure3.15.ThegreatutilityofthistechniqueisthattheAFMdirectlymeasurestheforcebetweenthecontactingatomsormoleculesontheendoftheprobeandsamplesurface,andasthecantilevermaybehighlyflexible,anddeflectionsensitivitywithopticallever‐basedinstrumentsisveryhigh,single‐moleculeinteractionstudiesarepossible.Often,anAFMtipwillbemodifiedwithgraftedmoleculesofinterest[142–145],althoughsuchexperimentshavealsobeenreportedwithbareAFMtips[146,147],colloidalprobes[148–150](e.g.silicaspheres,whichmaybethemselveschemicallymodified),andevenmicro‐organisms[151,152].Thesurfacesprobedhavebeenofevenwidervariety.Again,formolecule–moleculeinteractionsstudies,oftenaflatsubstratewillhavethemoleculesofinterestgraftedon[153],butalsocellmembranes[154],micro‐organisms[1155,156],wholelivingcells[157]andawidevarietyofsolidsurfacesincludingpolymers[158–160],metals[161],ceramics[162]andmorehavebeenprobed.

Thereareanumberofexperimentalissueswhichmustbetakenaccountofinordertoperformforcespectroscopy.Theseinclude:(p.65)

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Fig.3.15. Amodelforce–distancecurve.AtpointA,theprobeisfarfromthesurface,atB‘snap‐in’occursasattractiveforcespulltheprobeontothesurface.Theforcebecomesrepulsiveastheprobecontinuestobedriventowardsthesample.Atsomeuser‐definedpointC,thedirectionoftravelreverses.AtpointD‘pull‐off’occursastheforceappliedtothecantileverovercomestip–sampleadhesion.Adhesiondataisusedforforcespectroscopywhileslopedataisusedfornanoindentation(Section3.2.2).

(i)Thenumberofinteractingmolecules.Dependingonthetipradius,alargenumberofmoleculesarelikelytobeabletointeractwiththesurfaceatonetime.(ii)Orientationandaccessibilityofinteractingmolecules.Typically,theinvestigatorwouldliketomakecomparisonsbetweenthemolecularinteractionsmeasuredatthesurface,andresultsfromsolutionstudies,butthegraftingofmoleculestothetipmayaffecttheresults.(iii)Thespeedofapproachandwithdrawalofthetipforthesurfacewillaffecttheresults.(iv)Experimentalenvironment.OneadvantageofAFMisthatitmaybecarriedoutinalmostanyenvironment.Formostchemicalandbiologicalworkitisusefultocarryouttheexperimentsinliquid.Itissimplethentochangethecompositionoftheliquidtoseehowitaffectstheresults.Forexample,toproveantibody/antigeninteractions,commonlyblockingantibodiesareinjectedintosolution,afterwhichforcesmaydisappeartozero[163].(v)Statisticalvariationinresultsistypicallyverylarge.Thismeansincreasedexperimentaltime,whichisnotnormallyaproblem,aseachforcecurvetypicallytakeslessthan1secondtoacquire,butinadditionaverylargedatasetistypicallygenerated,andalotofdataanalysisislikelytoberequired.

Inreality,theresultsfromforcespectroscopybetweenmoleculesrarelylookmuchlikethecartooninFigure3.15.Usually,specificforcesbetweenmoleculesleadtomuchmorecomplicatedresults.AnexampleisshowninFigure3.16.Intheblue(retract)curve,severaltypicalfeaturescanbeseen.Oneisthealmost‐flatregionlabelleda.Inthisregion,polymerchainslinkingthemoleculestotheAFMtipwereunfolding.During(p.66)

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Fig.3.16. Anexampleofrealforcespectroscopydata:curvesmeasuredonM.xanthuscells.Theredtraceistheapproach,andtheblueistheretractcurve.Reproducedwithpermissionfrom[164].Copyright2005NationalAcademyofSciences,USA.

unfolding,onlyveryweakbondsarebroken,sothereareonlysmallverticaldeviationsinthetrace.Atb,theprobeappliedsufficientforcetobreakthebonds,asthemoleculebreaksawayfromthereceptor.Notethatatthispoint,asingleverticalmovementmaybeexpected,butthestepisstaggered,indicatingthatmultiplebondsarebroken,andonlyatpointcisthetipfinallyfreeofmoleculeslinkingittothecellsurface.Inacasesuchasthis,itisnecessarytodecideiftheverticaldistance(i.e.theforceofadhesion),seenatpointb,representstheadhesionofonemolecule,thatoftwomolecules,orofanunknownnumber.Thisiswhyitisdifficulttoautomatedataanalysisinforcespectroscopy,andthiscombinedwiththetypicalrequirementtocollecthundredsofdatapoints,meansdataprocessingforsuchexperimentscanbeverytime‐consuming.Somewaystoimprovethesituationincludereducingthechanceofmultipleinteractionsinthefirstplacebyforexamplespacingthegraftedmoleculesoutonthetip,orlookingformultiplesofsingleforcesinthe‘spectrum’offorcesmeasured[144].

Itcanbeusefultoperformforcespectroscopyinagrid‐likepatternoverthesample,leadingtothepossibilitytolocatespecificchemicalgroupsonasamplesurface[146,160,165].Itisimportant,however,torememberthatevenhighlyspecificmeasurementslikeadhesion–forceinteractions,maybeaffectedbysampletopography[159].Inthismode,forcespectroscopyissometimestermedchemicalforcemicroscopy[166].Amajorapplicationofforcespectroscopyisproteinunfolding,whichusestheAFMforcesensitivitytoprobemechanicalunfoldingoflargeproteinmolecules,abiologicallyimportantprocess,whichiscoveredinSection7.3.5.1.

3.2.2Nanoindentation

IfinsteadofmeasuringthedataastheAFMwithdrawsfromthesamplesurface,werecordthedatameasuredasthetipcontactswithandpressesontothesamplesurface,wearecarryingoutadifferentexperiment,callednanoindentation.Anothertechniqueknownasnanoindentationexists[167],whichusesadedicatedmachinetomeasureload–displacementcurvesasahardindenter(forexamplediamond)pressesintoasample.Typically,suchinstrumentsaredesignedtocreateaseriesofindents(holes)inasample,andallowthemeasurementofthesizesoftheindents(by,e.g.lightmicroscopy),andaresensitivetoforcesinthemicronewtonrange.Bycarryingoutan(p.67) analogous

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experimentusingAFMwehavesomeadvantagesandsomedisadvantages.Thesearesummarizedbelow.

AdvantagesofAFM‐basednanoindentation

•Highloadsensitivity–loadsensitivitymaybeaslowaspiconewton,althoughevenforsoftmaterialstherequiredsensitivityisnotlikelytobegreaterthanananonewton.•Inbuiltabilitytomeasuretheindentscreated,athighresolutioninx,yandz(seeFigure3.17).•Highpositioningresolution–i.e.wecanchoosesmallregionsofasample,orperformtheexperimentonverysmallsamples.

DisadvantagesofAFM‐basednanoindentation

•Non‐perpendicularprobeapproach–quantitativenanoindentationrequirestheindentertoapproachthesampleperpendicularly,whichisnotthecasenormallyforAFM.Thisproblemcanbeovercome,withcare.•Non‐linearzpositioning.Unlessthesystemisequippedwithlinearizationinthez‐axisthiscancausesomeseriousproblems.•Thesystemmustbecalibratedtoextractrealforces.

Fornanoindentationonhardmaterialsitisnecessarytouseaverystiffcantileverandahardprobe.Typically,onemightuseacantilevermachinedfromsteel,withadiamondtipgluedtotheend[168].Suchleversmaybeappropriatetoperformnanoindentationandcanbecapableofimagingthesample,buttypicallygiverelativelylow‐resolutionimages;ontheotherhand,theyareabsolutelynecessarytoindenthardmaterialsuchasmetals.ManyauthorshavealsocarriedoutnanoindentationwithnormalAFMprobes[168–172],butitisnecessarytocharacterizethetipradiusandcantilevercarefullyforquantitativeresults.Oneadvantageofsuchanapproachistheabilitytoselectfromawiderangeofspringconstants;thehighlystiffnanoindentationcantileverspreviouslyreferredtoareinappropriateforsoftsamples.Onecommonapproachtosimplifytheproblemoftipradiusdetermination(seeChapter2)fornanoindentationmeasurementsistouseacolloidalprobe,i.e.touseanormalAFMcantileverwithoutatip,butwithasmallsphericalparticleinitsplace[150,173].Ifnanoindentationexperimentsarecarriedoutinagridpatternoverthesamplesurface,thenit'spossibletodeterminethespatialvariationofhardnessandsoftness[158,174,175].DataanalysisfornanoindentationisoftenmadebymodellingtheindentationviatheHertzmodel,whichrequiresknowledgeoftheshapeofthetip,andassumesonlyelasticcompressionsofthesampletakeplace[162,176].Formorediscussionofdatatreatmentfornanoindentationseereferences[168,176,177].

Applicability

DespitethequantificationissuesassociatedwithcarryingoutnanoindentationusingAFM,ithasbeenwidelyapplied.Itisparticularlyusefultolookatrelativehardnessandsoftness.Forexample,itcangiveanideaaboutdifferencesinhardnessandsoftnessin

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differentpartsofasampleWithnanoindentationmapping,themeasurementscanbemadequantitative,whereasformanyothertechniquessuchasphaseimaging(seeSection3.2.3.2),itishardtoknowifdifferencesareduetomechanicaloradhesivepropertiesofthesample.Thereforenanoindentationhasbeencommonlyusedtostudyheterogeneousmaterialssuchaspolymercomposites[158,181,182].Furthermore,thehighpositioningaccuracymeansit'spossibletolookatsmallfeaturesnotpossiblebytraditionalnanoindentation,(p.68)

Fig.3.17. ExamplesofnanoindentationmeasurementswiththeAFM.Left:force–distancecurvesmeasuredwiththeAFMonindividualbacteria.Blackcurves:typicaldatameasuredonuntreatedandtreatedBacillusvegetativebacterialcells.Redcurves:datameasuredonBacillusspores.Thedatashowedthatthetreatmentmadethecellssofter,butthesporesweremuchharderthanthevegetativecells[178].Right:AFMimageofanindentationmadebyadedicatednanoindenter.Theindentationisinamagnesiumoxidecrystal,andtheimageshowstheindentation(blacktriangle)pile‐up–materialpushedoutofhole(whitefeaturesattrianglecorners),andalsoshowslong‐rangedislocationsinthecrystalstructure(diagonaldiscontinuities)[179].Reproducedwithpermissionfrom[180]andkindpermissionfromDrC.Tromas.

forexampleindividualmicro‐organisms[169,183](seeFigure3.17),livingcells[176,184]ormicro/nanoparticles[185–187].SomemoreexamplesofapplicationsofnanoindentationaregiveninChapter7.

3.2.3Mechanicalpropertyimaging

Nanoindentationisaveryusefultechniqueformechanicalcharacterizationbecauseofthepossibilitytocollecttrulyquantitativedataonthemechanicalresistanceofsamples.Howeverithasseveraldrawbacks,includingthecomplicateddataanalysis,anditsrelativelyslowdataacquisition.TheverylowrateofdataacquisitioncomparedtonormalimagingAFMmodesisamajordrawback.Foranimagewith512×512datapoints,afullsetofnanoindentationdatawouldrequiremanyhourstocollect,leadingtoproblemswiththermaldriftofthesample.Forthisreason‘imaging’typestudieswithnanoindentationtendtobeusedonlyatverylowresolutions(100×100datapointsorless).Onewaytoovercomethislimitationistomeasuretheinteractionoftheprobewiththesamplesurfacewhileitacquirestopographicaldata,andusethisinformationtoderivemechanicalinformationaboutthesamplesurface.Thishastwoadvantages,firstly,dataisacquiredatamuchfasterrate,andsecondly,themechanicalinformationcollectedmaybecorrelateddirectlywiththemeasuretopography.Thereareanumberofmodeswhichacquiremechanicalinformationaboutthesamplesurfaceinthisway,andtheyaredescribedinthefollowingsections.

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3.2.3.1LateralforcemicroscopyAsdescribedinSection3.1.1,incontactmode,theverticaldeflectionofthecantilever,measuredasthedifferenceinsignalbetweenthetopandthebottomofthesplitphotodiode,(p.69) isusedasthefeedbacksignal.However,ifwecomparetheleft‐andright‐handsidesofthesplitphotodetector,weobtainthelateraldeflectionsignal.Whenmeasuringthissignal,thetechniqueissometimescalledlateralforcemicroscopy,orLFM.Thereasonwhymeasuringthiscanbeusefulisthatthissignalcontainsinformationaboutthemechanicalinteractionoftheprobetipwiththesamplesurface.Thelateraltwistingofthecantileverisameasureofthefrictionencounteredbythetipasitscansoverthesample.Thus,thissignalissensitivetothenature(shapeandfrictionalproperties)ofthesurface.Forthisreason,LFMissometimesalsocalledfrictionforcemicroscopy(FFM),andthelateralsignalissometimesreferredtoasthefrictionsignal,althoughthesignalobtainedlaterallycontainsmoreinformationthanjustthefrictionfeltbythetip.Itisimportanttobearinmindthatthelateralbendingiscoupledwithverticalbendingofthetip,andcontainsinformationabouttheshapeofthesample,aswellasitsmaterial,becausefrictiondependsontheslopethetipistravellingalong[77,188].However,usingthistechniqueitispossibletogetquantitativeinformationaboutvariationinsampleproperties.SomeexamplesofthisareshowninSection7.1.4.AdiscussiononcalibrationoflateralsignalsisincludedinSection4.2.

Asmentionedpreviously,itisnotnormallynecessarytomeasureAFMheightsignalsinmorethanonefastscanningdirection.Thesituationinthecaseofthelateraldeflectiondataissomewhatdifferent.Thelateraldeflectionsignalwillnormallyalwaysbedifferentinthetwodirections,asthecantileverwilltwistbyacertainamountassumingthereissomemeasurablelateralcomponenttothetip–sampleforce(i.e.friction).Therefore,evenonperfectlyflat,homogeneoussamples,thetwoimageswillbedifferentfromeachotherinthemagnitudeandpossiblysignofthesignal.Ingeneral,changesofslopewillaffectforwardsandbackwardsscansoppositely,andchangesinfrictionduetomaterialcontrastwillgivegreaterorsmallerdifferencebetweentheforwardandreversescans.ThisisshownschematicallyinFigure3.18.

FromFigure3.18itispossibletoseethatchangesinslopeandchangesinmaterialcontrasthavedifferenteffectsuponthelateraldeflectionsignal.Iftheusersubtractstheleft‐to‐rightandright‐to‐leftsignalsfromeachother,inthecaseoftheslopechange,theresultwillbeasignalwithalmostnocontrast.However,inthecaseofthematerialfrictionchange,theresultingsignalwillbesensitivetothesamplefriction.Largerfrictionwillgiveagreaterdifferencebetweentheforwardandreversescans,whilelowerfrictionwillgiveasmallerdifference.Thus,collectingbothforwardandreversedirectionscansandsubtractingtheminLFMcangiveusefulinformation[160,189].

3.2.3.2Phaseimaging‘Phaseimaging’inAFMreferstorecordingthephaseshiftsignalinintermittent‐contactAFM.In1995forthefirsttime,thephasesignalwasdescribedasbeingsensitivetovariationsincomposition,adhesion,friction,viscoelasticityaswellasotherfactors[190].

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Thenin1996GarciaandTamayosuggestedthatthephasesignalinsoftmaterialsissensitivetoviscoelasticpropertiesandadhesionforces,withlittleparticipationbyelasticproperties[191].Ithasbeenacommonassumptioneversincethatphasecontrastwillshowadhesionorviscoelasticproperties[192,193].Infact,asshownintheexamplesofphasecontrastinFigure3.19,phasecontrastfrommaterialpropertiesisseeninawidevarietyofsamples,butalsoreflectstopometricdifferences(differencesinslope).Thisisbecausethephaseisreallyameasureoftheenergydissipationinvolvedinthecontact(p.70)

Fig.3.18. Schematicoflateralforcesignalsrecordedonasamplewithvariationsintopographyonly(top)andinmaterialfrictiononly(bottom).Darkercoloursrepresentmaterialwithhigherfriction.Notethatinthecaseoftopographychanges(upper),thedifferencebetweentheforwardandbacklateraldeflectionsignalsisconstant;formaterialcontrast(lower),thedifferencechanges.

betweenthetipandthesample[194–196],whichdependsonanumberoffactors,includingsuchfeaturesasviscoelasticity,adhesionandalsocontactarea[197].Ascontactareaisdependentontheslopeofthesample,thephaseimagealsocontainstopographiccontributions,sounambiguousinterpretationofcontrastinphaseimagesisbestlefttoflatsamples.Eveninsuchcases,understandingofthecontributionoftheindividualfactorstothephaseshiftisnottrivial.Formoredetailsonthistopic,thereaderisrecommendedtoreadtheexcellentandcomprehensivereviewsbyGarcia[108,197].Despitethecomplicationsinvolvedininterpretation,phasecontrastisoneofthemostcommonlyusedtechniquesfor‘mechanical’characterizationofsamplesurfaces,probablyduetothe(p.71)

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Fig.3.19. ExamplesofphasecontrastinIC‐AFMondifferentsamples.Top:atriblockcopolymertopography(left)barelyshowsheightdifferencesforthedifferentphases.Thephaseimage(right)showsclearcontrast.Bottom:Langmuir–Blodgettfilmonmica,thehightopographyregion(themonolayer)hasahigherphasecontrastthanthemicainthephaseimage.Thisimageshowshowtheedgesofthesephasesalsoshowdifferentcontrastinthephaseimage,duetochangesintip–samplecontactarea.

popularityofIC‐AFM,andthefactthatobtainingthedataisverysimpleanddoesnotrequirepost‐processingofthedata.

3.2.3.3OtherdynamicmodesAnumberoflesscommonlyusedoscillatingmodeshavebeenreported[198,199],thesearetypicallyvariationsonIC‐AFM,designedtomakesimultaneousacquisitionofsamplepropertiesandtopographysimplerormorequantitative.AnexampleofthisisjumpingmodeAFM[198,200–204].ThisisavariantofIC‐AFM,thedifferencebeingthatinjumpingmode,themovementalongthefastscanaxisisdiscrete,ratherthancontinuous,andtheelectronicsaresetuptorecordthecantileverdeflectionatspecificpointsalongtheforce–distancecurveduringeachoscillation.Theadvantageofsuchatechniqueisthatif,forinstance,thepointsrecordedareequivalenttopointsaandbinFigure3.2,thetip–sampleadhesionmaybeobtained,orslopedata(seeFigure3.15)couldberecordedtoqualitativesamplestiffness.Theadvantageofthisparticularmodeisthattherelativelyhigh‐speedscanningofIC‐AFMcanbecombinedwiththeacquisitionofsuchdata.Thisisalsotheaimofpulsed‐forcemode[199,205–207],whichoperatesinaverysimilarwaytojumpingmode,althoughfastscanaxismovementiscontinuous,likenormalIC‐AFM.As(p.72)

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Fig.3.20. Exampleofpulsedforcemode.Thesampleisapolystyrene‐polymethylmethacrylateblend.A:topography,B:adhesion,bothmeasuredsimultaneously.Notethebrightbordersbetweenthephasesareduetoincreasedtip–samplecontactarea,andtheadhesionimageisinagreementwiththatmeasuredbyforcespectroscopy[159].Reproducedfrom[206]withpermission.

withjumpingmodeAFM,amajoraimofpulsed‐forceAFMistoobtainadhesiondata[208],butcollectionofotherdatapointscanagainleadtosamplestiffnessdata[199].AnexampleoftheresultsfrompulsedforcemodeisshowninFigure3.20.

3.2.4Magneticforcemicroscopy

ThepotentialofusingAFMtomeasuremagneticpropertieswasrealizedquiteearlyinthehistoryofAFM[105,209,210].Magneticfieldsdecayquicklywithdistance,soinordertomeasurelocalpropertiestheprobemustbeveryclosetothesurface,hencetheapplicabilityofAFM.Themosttypicalexperimentcarriedoutisknownasmagneticforcemicroscopy(MFM)[211].Inthismode,thepresenceanddistributionofmagneticfieldsismeasureddirectly,byusingamagneticprobe.Typically,theseconsistofstandardsiliconcantileverswithathinmagneticcoating.Typicalmaterialsusedforthecoatingincludecobalt,cobalt‐nickelandcobalt‐chromium[212].Theadditionofsuchcoatingscanhavetwodetrimentaleffectsonthecantilever:firstlythesematerialsaretypicallysofterthantheunderlyingsilicon,andthusmayincreasewearrate,andsecondly,anycoatingaddedtotheendofthetipwillincreasetheradius,andthusdecreasetheresolutionoftheexperiment.Typically,magneticforcesareordersofmagnitudelowerthanothertip–sampleforceswhenincontact,andthusitisusefultomeasurethemwiththetipatacertaindistance(oftheorderof5–50nm)fromthesurface,thusreducingtheinterferencefromshort‐rangeforces.Thiscanbecarriedoutinanumberofways[213],someofwhichareillustratedinFigure3.21.Thesetechniquesallhavesomepracticaladvantagesanddisadvantages,butarebasicallyvariationsonatheme.In‘lifting’‐typemodes,thetopographyofthesampleismeasuredfirst,followedbyraisingtheprobe,andscanningagaintocollectthemagneticdata.Onemethodistocollectanormaltopographyscan,andthenchangethezset‐pointtolifttheprobefromthesurfaceandcollecta‘magneticimage’(p.73)

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Fig.3.21. SchematicsofvariousimplementationsofMFM.A:liftingprobebetweentopographyandMFMimages.B:Bardmethodofliftingleverbetweenscanlines.C:zset‐pointoscillation.D:Hosakamethodofmovingprobeclosetosurface,andrecordingMFMsignalatvariouspointsforeachheight.

(Figure3.21A).Thisworkswellforflatsamples,butispronetoproblemsoffeaturesfromthesampletopographyappearingintheMFMimage,andalsotoproblemsfromthermaldrift.AsdescribedbyBard[214],animprovedmethodistorecordthesampletopographyfirst,thenlifttheprobe,andmeasurethelong‐rangeforceswhilefollowingtheshapeofthetopography,butatacertain‘liftheight’.ThisisapplicabletoSTM,EFM(seethefollowingsection),orMFM.Typically,thisiscarriedoutinalternatescanlines,allowingthetopographydatatobeincludedinthesecond,magneticscanline,meaningtheprobecanstayapproximatelythesamedistanceabovethesample,evenwithchangesintopography(Figure3.21B)[215].It'salsopossibletochangethezset‐pointwhilescanning,meaningtheprobewillbeconstantlymovingtowardsthesampletocheckthetopography,andthenawayagaintoregistermagneticfieldinformation(Figure3.21C).Finally,inthemethoddescribedbyHosaka[216],ateachpixeltheprobeisliftedabovethesurface,andthefieldismeasuredatseveralpointsastheprobeisloweredagain(Figure3.21D),toobtainamagneticfieldgradient.Theprobeisthenmovedtothenextlateralpoint,liftedagain,andsoon.Thismethodisprobablytheleastpronetothermaldrift,butisratherslowtoimplement.Whichevermethodisused,liftingthetipfromthesurfacereducesresolution,andresolutioninMFMistypicallynogreaterthan30nmlaterally[212].

Fortheseliftingmodestowork,ithelpsifthereislittlesampledrift,ortohavelinearizedscanners.Typically,MFMiscarriedoutinoneofthedynamicmodes,andthemagneticeffectsonthecantileveraredetectedviaphaseshift,buttheymayalsoaffecttheoscillationamplitude.Unfortunately,evenatliftheightsofseveraltensofnanometresfromthesamplesurface,shortrangeforcesotherthanmagneticinteractionmayaffectthecantileveroscillation,givingafalseindicationofmagneticcontrast[217],aneffectwhich(p.74) issometimesoverlooked.Onewaytoovercomethisproblemistocarryouttwoscanswiththecantilevermagnetizationorientationinoppositedirections,andsubtractthemfromeachother.Non‐magneticforcesshouldthencancelout,leavingtypicallyasigmoidally‐shapedcontrastinthelinesscanswheremagneticinteractiontookplace[218].AnexampleimageobtainedinMFMviatheBardmethodisshowninFigure3.22.

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AlthoughMFMisarelativelysimpletechniquetoobtainmagneticcontrastatahighresolution,quantificationofMFMsignalsiscomplicated,andwhentryingtomeasurethemagneticdomainsonasoftmagneticmaterial,thedomainsontheprobecancauseachangeinthedomainstructureonthesurface.ReadersinterestedinmoredetailontheissuesinquantificationofMFMsignalsaredirectedtotheworkofProkschetal.[218,219].ItisworthpointingoutherethatthereareavarietyofothermagneticcharacterizationtechniquesusingtheAFM,suchasMRFMthatinvolveconsiderablymoreequipmentthanacommercialAFM[220],soareoutsideofthescopeofthisbook.

Applicability

TheinitialinterestinthestandardMFMtechniquegrewlargelybecauseofthepotentialindustrialapplications.Thedatastorageindustryislargelybasedaroundcreationofmagneticnanodomainsofthesizerangeofafewhundredsofnanometres,andthereisnoothertechniquetoaccuratelymeasuresuchfeatures.ThereforeMFMhasseenmuchuseindustrially,particularlyindatastorageapplications[210,213].Morerecently,magneticnanoparticleshavebecomethefocusofintenseinterest,andtheseareanotherfieldwhereMFMcanbeofgreatuse[221].Theverysmallmagneticmomentofthesmallestparticlescanpresentachallenge,andmuchworkhasbeencarriedoutonparticlesofca.50–100nm[221]butitshouldalsobepossibletoexaminethemagneticfieldfromparticlesassmallas20nm.SomemoredetailsofindustrialapplicationsofMFMaredescribedinChapter7.

Fig.3.22. ExampleMFMimages.Left:topographyofmagnetictapesample.Right:MFMimageofthesameregion,showingmagneticfieldsaboverecordeddatabitsonthetape.Bothare10μm×10μmimages.

(p.75) 3.2.5ElectricforcemicroscopyandscanningKelvinprobemicroscopyElectricforcemicroscopy(EFM)referstoatechniqueanalogoustoMFMwhichenablesthemeasurementofelectricalfieldswiththeAFM,ratherthanmagneticfields.Essentially,thetechniquecanbeappliedbycarryingoutexperimentsinaliftingmodeasdescribedabove,butwithoutamagneticcoatingonthecantilever.AstandardsiliconorsiliconnitridecantilevermaybeusedforsimpleEFMimaging,althoughconductive(metal‐coated)tipsarerequiredforread/writeapplications,andmoresophisticatedelectricalmodes(seebelow).Theequationforelectrostaticforcesbetweenaprobeandasurfacehavingdifferentpotentialsisgivenby:

= −1/2(Velectrostatic

2

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(3.3)

ItcanbeseenthatfromEquation3.3andEquation3.2thatthechangeinresonantfrequencyisproportionaltothechangesincapacitanceasafunctionofthesecondderivativeofzspacing.Inotherwords,aslongasthereisanon‐zeropotentialbetweentheprobeandsurface,thefrequency,andthustheamplitudeandphaseofoscillationwillbesensitivetocapacityofthesurface.

EFMhasbeenshowntodetecttrappedchargeonsurfaces[222],andinsomecasesgivesclearcontrastwherenoneisvisibleinthetopographysignal.However,ithasbeenreportedthatEFMispronetotopographicartefacts[223].EFM,likeMFMhasthegreatadvantagethatitmaybecarriedoutwithastandardAFM.Asomewhatmoresophisticatedtechniquetomeasuretip–samplepotentialisscanningKelvinprobemicroscopy(SKPM)[224,225].Figure3.23illustratestheportionoftheSKPMinstrumentusedforequilibratingtheprobesurfacepotential.Theelectronicsusedformechanicallyvibratingthecantileverarenotshown.

TheprincipleofoperationofSKPMissimple,thatiswhentwosurfaceshavethesamepotentials,therewillbenoforcesbetweenthem,soinEquation3.3,ΔV=0.Toimplementthetechnique,aDCpotentialbias(VDC)isappliedtoaconductiveprobe,whichisfurthermodulatedbyanACsignal(VAC),sothat

Fig.3.23. Schematicillustrationofinstrumentalset‐upforscanningKelvinprobemicroscopy.

(p.76)

= −1/2(VFelectrostatic )2dC

dz

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Fig.3.24. ExampleofKelvinprobeandelectricforcemicroscopy.AFMheightimage(A,shadedimage),Kelvinprobe(B),andEFM(C)imagesofcarbonnanotubesonagoldsurface.Theimagesarenotallinexactlythesameplace;theredarrowhighlightsaconnectionbetweentwonanotubesineachimage.Reproducedfrom[227],withpermission.

(3.4)

Inotherwords,theACvoltageisoscillatingattheresonantfrequencyofthecantilever[224].Thus,theprobe'selectricpotentialisvaryingatfrequencyω.Ifthesample'spotentialisnotthesame,thedifferenceinelectricalpotentialwillcausethecantilevertomechanicallyvibrateatthefrequencyω,andwhichmeansthattheelectricalsignalfromthephotodetectorwillbemodulatedatω.Afeedbackcircuitthencomparesωwithωmod,andoutputsaDCvoltagetothesamplethatminimizestheoscillationatωmod.ThisoccurswhentheappliedpotentialVDCisequivalenttothesurfacepotentialVs.SothevoltageVDCthatisrequiretominimizeωmodisdigitizedwiththeA/DconverteranddisplayedonthePCasthepotentialimage[225,226].BySKPM,absolutevaluesofthesampleworkfunctioncanbeobtainedifthetipisfirstcalibratedagainstareferencesampleofknownworkfunction.

3.2.6ElectrochemicalAFM

Althoughnotreallyaseparatemode,itisworthmentioningthatitisrathersimpletostudyasurfaceasafunctionofappliedpotentialusingtheAFM[228].Changesinsampletopographywithappliedpotentialaretheresultsofelectrochemicalreactions,andsothistechniqueisknownaselectrochemicalforcemicroscopy.Insituimagingofsuchprocessesisachievedwithanelectrochemicalcellwhichisamodifiedliquidcellwiththeadditionofelectrodestobiasthesampleandapotentiostat.Byrampingtheappliedpotentialtotheoxidationorreductionpotentialofthesurfaceduringscanning,orbetweenscans,itispossibletodirectlyobserveoxidationorreductionprocessesonthesamplesurface.Suchprocessestendtogiverisetosmall(orslow)changesinsampletopography,hencetheusefulnessofelectrochemicalAFM.Furthermore,itispossible,usingmoremodificationsoftheinstrument,tocombineimagingwithelectrochemicalmeasurementsatthenanoscale,atechniquereferredtoasscanningelectrochemicalAFM[229].AnexampleimageshowingresultsfromelectrochemicalAFMisshowninFigure3.25.

(p.77)

= + sin tVbias VDC VAC

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Fig.3.25. ElectrochemicalAFMexample.ImagesshowingthemorphologyofaCdTefilmduringelectrochemicaldepositionofAu,atvarioustimes(asshowninfigure)atapotentialof−0.35V.Reproducedwithpermissionfrom[230].

3.2.7Thermalmodes

ItispossibletousederivativesofAFMtomeasurethermalpropertiesofthesample[231].Typically,thisisdonebyusingaresistiveprobe,whichcanlocallyheatthesampleormeasurethetemperaturelocally,i.e.actasathermometer.Thefirstsuchprobesweretheso‐calledWollastonwireprobes,whichconsistofaveryfineplatinumwirebentintoav‐shape.Theapexofthevformedthetipoftheprobe.Later,micromachinedprobes,developedfromsiliconnitridecantilevers,withapalladiumlayerwhichthinsgreatlyatthetipapex,toactastheresistor,weredeveloped.Onecommonexperimentinvolvesapplyingapotentialtotheprobe,whichheatstheresistance.Asthesampleisscanned(incontactmode),heatfromtheprobewillflowintothesample,theamountdependingonthethermalpropertiesofthesample,andafeedbackcircuitadjuststhecurrentflowingthroughtheresistor,tokeeptheresistance,andthusthetemperature,constant.Plottingthecurrentappliedtotheprobegivesthethermalimage,andatopographicalimageiscollectedsimultaneously.AnexampleofthesortofdatathatmaybecollectedwiththistechniqueisshowninFigure3.26.Thismethodiscommonlytermedscanningthermalmicroscopy(SThM).ThethermalimageinSThMisthereforeamapofthermalconductivity,althoughitmightbenecessarytodeconvolvetopographiccontributions[231].Byusingtemperaturemodulation(i.e.bysupplyinganACcurrenttotheresistorratherthanaDCcurrent),thedepthsensitivitymaybechanged,allowingfor(p.78)

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Fig.3.26. Exampleofscanningthermalmicroscopy.Thermalconductivityimageofasectionfromaglassfilament/cyanateresincomposite.Theglassfibresclearlyshowgreaterthermalconductivitythanthepolymermatrix.Reproducedfrom[238]withpermission.

discriminationofburiedfeatures[232].Thismodealsoallowsfortheimagingofheatcapacity[231].Inadditiontotheimaging‐typeexperiments,itispossibletoperformmanytypicalthermalanalysisexperimentsusingasimilarset‐upsuchaslocalizedcalorimetryorthermo‐mechanicalanalysis[233–236].Theaimofallthesetechniquesistocharacterizematerialsthermallyonthenanoscale.Assuchmostoftheseexperimentscouldbeperformedmacroscopicallyonwholesamplesmuchmoreeasily,sothemainapplicationisinheterogeneousmaterials.Aswellasspecializedprobes,SThMrequiressomesimpleexternalcircuitry,andsoitsadoptionasastandardAFMtechniquehasnotbeenwidespread.However,suchprobesarecommerciallyavailable,andthetechniquegivesinformationnotavailablebyothermeans,soalargenumberofstudieshavebeenappliedtopolymercomposites[237–239];inaddition,micro‐organisms[231],pharmaceuticals[232,236,240],automotivecoatings[241],metalalloys[242]andelectronicdevices[243]havebeenstudiedwithSThM.Theinterestedreaderisdirectedtoanexcellentreviewformoreinformationonthistechnique[231].

3.3SurfacemodificationAswellasmeasuringsamplesurfaces,anAFMmaybeusedtomanipulateortomodifythesurfaces.ThefinecontroloftheprobemotionoverthesurfacemakesevenastandardAFMaversatiletoolformanipulationsurfacesatthenanoscale.Therearearangeoftechniquesthathavebeenusedtomodifysurfaces,notablyincludinglocaloxidation[244],scratching[245]anddip‐pennanolithography[246].

(p.79) UncontrolledsurfacemodificationisusuallyanundesiredfeatureofAFM,butitwasrealizedearlyinthehistoryofSPMthatwithcarethistechniquehadthepotentialtofabricatenanoscaledevices[247].Oneoftheearliestofthenanolithographictechniquestobedemonstratedwaslocaloxidation[248].Inthistechnique,abiasisappliedtothetiptocausecontactpotentialdifferencewhilescanningthesurface,resultingtypicallyinanoxidationofthematerialatthesamplesurface.Theseexperimentsarecommonlycarried

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outonsiliconandresultinfeaturesofsiliconoxideatthesurface[244],althoughotheroxidation‐initiatedreactionsarepossible[249,250].Asnotedpreviously,whenscanningincontactmode,aliquidmeniscuswillbepresentbetweenthetipandsamplesurface.Innano‐oxidationthismeniscusisvitalbecauseitprovidestheelectrolyteforoxidation.Becauseoftheimportanceoftheliquidbridgeforthereaction,theprocessisverysensitivetohumidity,andthesizeofthemeniscushasbeenreportedasthefactorcontrollingthesmallestfeaturethatit'spossibletomanufacture[244].Localoxidationhasbeenperformedincontact[251–253],intermittent‐contact[253],andnon‐contactmode[254].Ifthetipisinthenon‐contactregimewhenthebiasisapplied,acapillarylayercanspontaneouslyform,andithasbeensuggestedthatthewaterbridgeunderthesecircumstancesissmallerthanincontactmode,leadingtosmallerwrittenfeatures[254].

Thistechniquehasalsobeenshowntobeapplicabletoparallelfabrication[255–257],whichisofgreatimportance,becausethemaindrawbackofAFM‐basednanolithographyforfabricationisitsslowspeed[252].Still,whilelocaloxidationhasbeenusedtocreatenanoscopicfunctioningelectronicdevices[258,259],fabricationofindustriallyusefulstructuresonalargescalebythistechniquehasyettobedemonstrated,evenusingparallelwritingtechniques.

Tocarryoutsurfacemodificationwithscratchingtechniquesisaverysimpletechnique,andisoftenusedasaproofofprincipleexperimentforlithographyapplications,becauseitissimpletoapplytoarangeofmaterials.Structureshavebeenbuiltinpolymers,silicon,metalsandmorebyscratching[245,249].Inprinciple,allthatisrequiredistoapplyahighnormalforcetothesample,andusethelithographiccontrolsintheAFMcontrolsoftwaretodirectthetipinthedesiredpattern.Inthisway,highlyintricatepatternscanbeformedwiththistechnique.Unfortunately,unlikeoxidationorDPN,itisrarelyappliedtobuildstructureswithchemicallydifferentfeatures,sothenumberofusefulapplicationsisrelativelylow.

Dip‐pennanolithographywasinventedin1999byMirkinandcoworkers[260],andhasbeenshowntobeahighlyversatiletechnique.Thegreatadvantageofthistechniqueisthatalmostanymaterialthatcanbedepositedonasurfacecanbeusedandformedintonanometre‐scalepatterns,althoughtypicallywater‐solublemoleculesorverysmallparticlesareapplied[246].Theideaisanalogoustothatofamacroscopicpen.TheAFMtipisimmersed,ordippedintoasolutionofthemoleculetobegrafted.Withahydrophilictip,andaqueoussolution,theAFMprobewillbecomecoatedinathinlayerofthewritingsolution.Then,whenthetipisincontactwiththesubstrate,thegraftingmoleculesareappliedtothesurfaceviathewatercapillarylayer[260].AschematicillustratingthisisshowninFigure3.27.

Likenano‐oxidation,thesizeofthewaterbridgeisacontrollingfactorinthedimensionofthewrittenfeatures,aswellassuchfactorsasset‐point,scanningspeed,diffusionofthemoleculesonthesurface,andtipradius[249,261].ExamplesofthesortoffeaturesthatmaybeproducedareshowninFigure3.28.Agreatvarietyof‘inks’havebeenused,and(p.80)

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Fig.3.27. Schematicofdip‐pennanolithography,showinghowthewatermeniscusisusedtotransportmoleculestothesurface.Adaptedfrom[260].

patternshavebeencreatedfromorganicmolecules[260],proteins[262,263],syntheticpeptides[264],DNA[246],polymers[263],inorganicnanoparticles[265]andmore[246,249].Amajorapplicationofthissortoftechnologyisincreationofarraysofreceptorsforparalleltesting,e.g.proteomics,genomics,etc.Forlargescaleparallelarraysofdifferingfeatures,specializedDPNinstruments,ratherthancommercialAFMSaretypicallyused.

Anumberofother,lesscommonlyusedmethodsexisttomodifysurfaceswithAFM[249,266].Theseincludethermomechanicalwriting,whichlikeSThMusesaresistanceintheprobetocontrolthetemperatureatthetip[267].However,thetemperatureisusedtomodifythesamplesurface,ratherthantoprobeit,andthehightemperatureistypicallyusedtomakeholesinpolymersurfaceswithoutriskofdamagingthetip.Thishasbeeninvestigatedasahigh‐densitydatastoragetechnique,andviatheuseofparallelprobes(theso‐called‘millipede’device[268]),hasbeenshowntobecapableofextremelyhighstoragedensity[269].SeveralauthorshavereportedtheuseoftheAFMtodirectlymanipulateindividualparticles[270],molecules[271]andevenatoms[272,273]onasurfacebyforexample,pushing,liftinganddroppingorcutting[249].Theseproceduresareinterestingforfundamentalstudiesbutaretooslowtobeofvalueasmanufacturingtechniques.SomeexamplesofassemblyusingAFMareshowninSection7.2.3.Finally,a

Fig.3.28. ExamplesofAFM‐basedlithography.Left:polymericpatternsonsiliconformedbyanodicoxidation,showinglinewidthsofapproximately2nm.Reproducedwithpermissionfrom[250].Centre:abit‐mapimageusedastheinputforadip‐pennanolithography(DPN)routine.Right:AFM(lateralforce)imageoftheresultingsurfacepatterns.

(p.81) techniquecallednanograftingisavariantofdip‐pennanolithography[274,275].Ithasthesameadvantageofflexibility–awidevarietyofmoleculesmaybeappliedtothe

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surface[274,276].ThedifferenceisthatitinvolvesusingtheAFMtiptoremovemoleculesfromapreviouslymodifiedsurface,sothatthemoleculesofinterest,whichareinsolution,canformpatcheswithinthepreviouslayer[277].Thishastheadvantageofleavingthemoleculesofinterestsurroundedwithapotentiallyinertpassivatinglayercoveringthe(typically)metallicsubstrate,makingitusefulforexamplefabricationofdevicesforbindingstudies[262].

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