Visualizing Subsurface Deformation in Three Dimensions via Representative Transmission Electron Microscope Tomography

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Visualizing Subsurface Deformation in Three Dimensions via Representative Transmission Electron Microscope Tomography
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1 online resource (130 p.)
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english
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Mccumiskey, Edward J
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University of Florida
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Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Mechanical Engineering, Mechanical and Aerospace Engineering
Committee Chair:
Taylor, Curtis
Committee Members:
Chen, Youping
Sawyer, Wallace Gregory
Perry, Scott S
Eyink, Kurt

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Subjects / Keywords:
fib -- nanoindentation -- nanolaminate -- nanomechanics -- tem -- tomography
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
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Mechanical Engineering thesis, Ph.D.
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theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
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Electronic Thesis or Dissertation

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Abstract:
Cross-sectional transmission electron microscopy (XTEM) provides essential atomic-scale imaging for characterizing nanoscale structures, interfaces, alloy phases, subsurface damage, and more. Site-specific sample preparation has become routine with the advent of the dual-beam focused ion beam/scanning electron microscope (FIB/SEM). Using this instrument, a surface is milled away with an ion beam in order to produce a thin (< 300 nm), electron-transparent membrane, which is subsequently lifted out and attached to a TEM grid. However, even with the ability to image and mill with a resolution of < 15 nm, it can be a great challenge to align a TEM cross section with a specific feature or row of features with an accuracy of < 100 nm. Thus for studying nanofeatures such as plastic zones of nanoindentations on the order of a few hundred nm in size, researchers must either sacrifice TEM image quality by making thick cross sections, or risk missing the target region. Furthermore, even if the alignment is perfect, the two-dimensional (2D) TEM cross section provides limited information regarding the three-dimensional (3D) shape of the nanofeature. In this dissertation, a simple method for TEM-specimen preparation and 3D visualization of nanofeatures is introduced, in which nanoindentation arrays on GaAs (001), InAs films on GaAs (001), and superhard ZrC films on Si (001) are rotated at a slight angle with respect to the lifted-out cross section. With the optimal rotation angle, a more complete picture of the dislocation network beneath an indent is obtained in a single specimen, with each adjacent feature showing a different sectional view of an indentation. The images of individual sections are then compiled to reconstruct the overall structure of an indentation plastic zone in three dimensions. This method is used to improve the understanding of anisotropic deformation in GaAs (001) and interfacial deformation. It can be extended to study virtually any type of nanofeature, so long as it is repeatable and can be patterned in an array with an accuracy of tens of nm. Moreover, the yield of lifted-out FIB cross sections is increased dramatically because it circumvents the need to position the FIB slice accurately. Hardness testing of three ZrC films is also reported.
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In the series University of Florida Digital Collections.
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Includes vita.
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by Edward J Mccumiskey.
Thesis:
Thesis (Ph.D.)--University of Florida, 2013.
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Adviser: Taylor, Curtis.
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RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2013-11-30

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VISUALIZINGSUBSURFACEDEFORMATIONINTHREEDIMENSIONSVIAREPRESENTATIVETRANSMISSIONELECTRONMICROSCOPETOMOGRAPHYByEDWARDJ.MCCUMISKEYADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2013

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2013EdwardJ.McCumiskey 2

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ToConrad,mynephew 3

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ACKNOWLEDGMENTS Iwouldliketogratefullyacknowledgemyadvisor,Dr.CurtisTaylor,forhiscontinuedsupportandguidanceoverthelastseveralyears.Hehasbeenagenerous,thoughtful,andwisementorthroughoutmygraduateexperience.IhavealsoreceivedmuchguidancefromDr.GregorySawyertowardthecompletionofmydissertation,forwhichIamtrulygrateful.IhavehadthepleasuretoworkverycloselywithDr.KurtEyinkfortwosummers,fromwhomIlearnedagreatdeal.IamalsothankfultohavereceivedguidanceandinsightfromDrs.YoupingChenandScottPerry.IamveryfortunatetohavehadtheseveexpertsonmyPh.D.supervisorycommittee.IwouldalsoliketothankDr.ThomasAngeliniforsharinghisexpertiseofpost-processingand3Dreconstructions,Dr.ValentinCraciunforcollaboratingonmultipleresearchprojects,andforprovidingtheZrClmsstudiedinthisresearch,Drs.NicholasRudawskiandMichaelKeslerforoperatingtheTEMsthatproducedverynicecross-sectionalimagesforthisproject,Dr.KrishnamurthyMahalinghamforhelpfuldiscussionsregardingTEMimaging,andDr.KurtEyink(again)andDanielEsposito,whogrewtheInAslmsusedforthisdissertation.TotheformerandcurrentmembersoftheUniversityofFloridaCenterofManufacturingInnovation(formerlyMachineToolResearchCenter),Iwouldliketothankyouforyourfrequenthelpwithday-to-daytasks,andforcreatingafriendlyenvironmentinwhichtoworkandstudy.IwouldalsoliketoacknowledgetheTribologyLaboratoryandtheAtomicandMultiscaleMechanicsLaboratory,bothattheUniversityofFlorida,foralloftheirhelp,andforopeningtheirdoorstome.Furthermore,Iamgratefultoalltheteachersandprofessorswhohaveinuencedmethroughoutthecourseofmyeducation.Iamgreatlyindebtedtoallofthem,andappreciatetheircontinuedeffortstoeducatestudents.IwouldliketoalsoacknowledgetheMajorAnalyticalInstrumentationCenteratUFforprovidingandmaintaininginstrumentswhichIhaveusedovertheyears:the 4

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FIB,nanoindenter,AFM,SEMs,TEMs,andcarboncoater.ThegreatpeopleattheUFLibrariesdeserverecognitionaswell.Theyhaveexpedientlydeliverednumerousjournalarticlestome,whichIotherwisewouldhavehadaverydifculttimetrackingdown.Iwouldparticularlyliketothanksoon-to-beDr.BijoyrajSahuandMr.JaredHann,withwhomIworkedcloselyinthelab.SpecialthanksgoestoMr.MinaHanna,whosetirelessworkethicwasagreatresourceforwhennanoindentationexperimentshadtobeperformedwithaquicklyapproachingdeadline.Iamgratefulforveryunderstandingandwonderfulfriendsandfamily,fortheyhavehelpedmethroughthisridemorethantheyknow.Myparentsandbrotherhavebeenverypatient,waitingformetograduate(again),andhavegivenmeencouragementandsupportallalongtheway. 5

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 8 LISTOFFIGURES ..................................... 9 LISTOFSYMBOLS .................................... 12 ABSTRACT ......................................... 13 CHAPTER 1INTRODUCTION ................................... 15 1.1Motivation .................................... 15 1.2Goals ...................................... 17 1.3Objectives .................................... 17 1.4Approach .................................... 18 1.5OrganizationofChapters ........................... 18 2STATEOFTHEART:METHODSFORVISUALIZINGSUBSURFACEDAMAGEANDELECTRON-MICROSCOPETOMOGRAPHY ................ 20 2.1ObservingSubsurfaceDamageviaTransmissionElectronMicroscopy .. 20 2.1.1Plan-ViewTransmissionElectronMicroscopy ............ 21 2.1.2Cross-SectionalTransmissionElectronMicroscopy ......... 23 2.23DTransmissionElectronMicroscopy .................... 26 2.3SerialSectioningandFIBTomography .................... 28 2.4InsituTEM ................................... 30 2.5Etch-PitMethod ................................ 32 2.6LimitationsoftheAboveMethodswithRegardtoVisualizingSubsurfaceDeformation ................................... 34 3PROOFOFCONCEPT:MISALIGNEDFIBLIFTOUTSANDTEMTOMOGRAPHYOFGALLIUMARSENIDE(001) .......................... 37 3.1DetailedApproach ............................... 37 3.2DeformationMechanismsofGaAs ...................... 41 3.2.1FIBLiftOuts ............................... 45 3.3MaterialsandMethods ............................. 47 3.3.1Nanoindenter-TipCharacterization .................. 48 3.3.2PreliminaryNanoindentationsandSurfaceCharacterization .... 52 3.3.3NanoindentationArrays ........................ 55 3.3.4InsituFIBLiftOuts ........................... 57 3.3.5TransmissionElectronMicroscopy .................. 64 6

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3.3.6Post-ProcessingofElectronMicrographs ............... 65 3.4ResultsandDiscussionofGaAs(001)Samples ............... 66 3.4.1PreliminaryNanoindentationsandSurfaceCharacterization .... 66 3.4.2NanoindentationArrays ........................ 70 3.4.3TEMResults .............................. 71 3.4.43DReconstructionsofGaAsIndents ................. 73 3.4.5IndentationPlasticZone ........................ 77 3.4.6RepeatabilityandLimitations ..................... 78 4APPLICATIONTOOTHERMATERIALSYSTEMS ................ 81 4.1Background ................................... 81 4.1.1DeformationofNanolaminates .................... 81 4.1.2Mechanical-PropertyDeterminationusingNanoindention ..... 83 4.2MaterialsandMethods ............................. 86 4.2.1InAs-FilmGrowthviaMolecularBeamEpitaxy ............ 86 4.2.2ZrC-FilmGrowthviaPulsed-LaserDeposition ............ 87 4.2.3NanoindentationArrayswithGuidelines ............... 87 4.2.4InsituFIBLiftOutsandTEM ..................... 89 4.2.5HardnessTestingofSuperhardThinFilms .............. 90 4.3ResultsandDiscussion ............................ 93 4.3.1InAsDeformation ............................ 95 4.3.2ZrCDeformation ............................ 97 4.3.3HardnessTestingofZrCFilms .................... 101 5SUMMARYANDFUTUREWORK ......................... 108 APPENDIX AMATLABCODEFORROTATED-ARRAYPARAMETERS ............. 113 BPOST-PROCESSINGPROCEDURESTOCREATE3DIMAGES ........ 117 REFERENCES ....................................... 120 BIOGRAPHICALSKETCH ................................ 130 7

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LISTOFTABLES Table page 2-1Advantagesandlimitationsofselectedmethods. ................. 34 3-1ParametersforGaAs(001)NanoindentationArrays. ............... 56 4-1ParametersforInAs/GaAsNanoindentationArrays. ................ 88 4-2ParametersforZrCNanoindentationArrays. .................... 89 4-3ParametersforNanoindentationTestingofZrCFilms. .............. 92 4-4HardnessvaluesforZrCsamplesfor20nm
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LISTOFFIGURES Figure page 1-1InteractionofacrackfrontwithmultipledislocationloopsinSi .......... 16 2-1Schematicsofplan-viewandcross-sectional-viewTEMofindentations ..... 21 2-2Examplesofplan-viewTEMofindentations .................... 23 2-33DTEMowdiagramandexampleofareconstructedimage .......... 27 2-4Serialsectioninginadual-beamFIB/SEM ..................... 29 2-5SEMsnapshotsofseriallyFIB-slicedsectionsofasubsurfacedefect ...... 30 2-6SchematicofananoindenterbuiltintoaTEM ................... 31 2-7InsituTEMnanoindentationontoaFIB-milledspecimen ............. 32 2-8Etch-pittingtechnique ................................ 33 3-1StrategiestoimproveFIB-XTEMthroughput .................... 38 3-2Conceptof3Dreconstructionusingarotatedarray ................ 39 3-3Rotatedarrayofmxnunitcells ........................... 40 3-4Dimensionsofasinglerotatedunitcell ....................... 42 3-5Zincblendestructure ................................. 42 3-6Modelsofindentation-induceddeformationofGaAs(001) ............ 43 3-7ExamplesofTEMimagesofindentationsinGaAs(001) ............. 44 3-8FrequencyresponseofanAFMcantilever ..................... 49 3-9Photographandopticalmicrographofacube-cornerindentertip ........ 50 3-10Atomicforcemicrographsofindentertips ..................... 51 3-11InvOLScalibrationcurvefornanoindentation ................... 53 3-12ScatterplotandhistogramforInvOLScalibrationpriortonanoindentation ... 54 3-13Opticalmicrographofindentationpatternsandinscribedarrowmarker ..... 55 3-14DB235FIB/SEM ................................... 58 3-15SamplemountingintheFIB ............................. 59 3-16PreparationofacrosssectionforliftoutwithintheFIB .............. 60 9

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3-17FIBlift-outprocess .................................. 63 3-18Load-displacementcurvesforGaAs(001)nanoindents ............. 66 3-19ComparisonofAFMimagesofanindenttakenwithdifferentAFMtips ..... 68 3-20ComparisonofresidualdepthsmeasuredbyAFMandnanoindentation .... 69 3-21NanoindentationarraysonGaAs .......................... 70 3-22Stitchedtransmissionelectronmicrographsof50-NindentsinGaAs(001) .. 71 3-23Transmissionelectronmicrographsof250-NindentsinGaAs(001) ...... 72 3-24Stitchedtransmissionelectronmicrographsof1-mNindentsinGaAs(001) .. 73 3-253DreconstructionofananoindentationplasticzoneproducedwithImageJ .. 74 3-26Reconstructionsofa250-Nindent'splasticzoneusingAmira ......... 75 3-273Dreconstructionsof1,000-and50-NindentationplasticzonesinGaAs(001) 76 3-28Molecular-dynamicsresultofananoindentationonGaAs(001) ......... 76 3-29Variationofplastic-zoneradiifor250-Nindents ................. 78 3-30Histogramofnaldepthsfor1-mNindents ..................... 79 3-31Demonstrationofimageaveragingfor1-mNindents ............... 80 4-1Nanoindentationschematicandtypicalload-displacementcurve ........ 84 4-2Bentlift-outspecimensofInAs/GaAs(001) .................... 90 4-3Modiedinsitulift-outprocedures ......................... 91 4-4AtomicforcemicrographsofnanoindentationarraysinInAs/GaAs(001) .... 94 4-5EffectofcleaningscribepatternwithHF ...................... 95 4-6Transmissionelectronmicrographsof125-NindentsinInAs/GaAs(001) ... 96 4-7Transmissionelectronmicrographsof500-NindentsinInAs/GaAs(001) ... 97 4-8AtomicforcemicrographsofindentarraysontheZC500sample ........ 98 4-9ScanningandtransmissionelectronmicrographsofindentsinZC500 ..... 99 4-10Schematicsofcommontypesofcracksformedduringindentation ....... 100 4-11Load-displacementcurvesforthreeZrCsamples ................. 101 4-12HardnessandreducedmodulusofZrCsamples ................. 102 10

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4-13Effectofusingtip-area-functioncalibrationsfrombeforeandaftertesting ... 105 4-14Plotofloadoverstiffnesssquared ......................... 106 A-1MATLABcodefordeterminingarray-rotationparameters(1of4) ........ 113 A-2MATLABcodefordeterminingarray-rotationparameters(2of4) ........ 114 A-3MATLABcodefordeterminingarray-rotationparameters(3of4) ........ 115 A-4MATLABcodefordeterminingarray-rotationparameters(4of4) ........ 116 A-5OutputofMATLABprogram,givingarray-rotationparameters .......... 116 B-1Post-processingofTEMimagesinImageJ .................... 118 B-2Proceduresforcreatinga3DimageinAmira ................... 119 11

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LISTOFSYMBOLS,NOMENCLATURE,ORABBREVIATIONS AFMatomicforcemicroscope/microscopyARAsylumResearchBEPbeamequivalentpressureCCcubecornerEXLOexsituliftoutFCCface-centeredcubicFIBfocusedionbeamHRTEMhigh-resolutiontransmissionelectronmicroscopyINLOinsituliftoutInvOLSinverseoptical-leversensitivityLEDlight-emittingdiodeMAICMajorAnalyticalInstrumentationCenterMBEmolecularbeamepitaxyMEMSmicroelectronic-mechanicalsystemMLmonolayerMSTMicroStarTechnologiesROIregionofinterestSEMscanningelectronmicroscope/microscopySPMscanningprobemicroscope/microscopyTEMtransmissionelectronmicroscope/microscopyXTEMcross-sectionaltransmissionelectronmicroscopy 12

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AbstractofdissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophyVISUALIZINGSUBSURFACEDEFORMATIONINTHREEDIMENSIONSVIAREPRESENTATIVETRANSMISSIONELECTRONMICROSCOPETOMOGRAPHYByEdwardJ.McCumiskeyMay2013Chair:CurtisR.TaylorMajor:MechanicalEngineeringCross-sectionaltransmissionelectronmicroscopy(XTEM)providesessentialatomic-scaleimagingforcharacterizingnanoscalestructures,interfaces,alloyphases,subsurfacedamage,andmore.Site-specicsamplepreparationhasbecomeroutinewiththeadventofthedual-beamfocusedionbeam/scanningelectronmicroscope(FIB/SEM).Usingthisinstrument,asurfaceismilledawaywithanionbeaminordertoproduceathin(<300nm),electron-transparentmembrane,whichissubsequentlyliftedoutandattachedtoaTEMgrid.However,evenwiththeabilitytoimageandmillwitharesolutionof<15nm,itcanbeagreatchallengetoalignaTEMcrosssectionwithaspecicfeatureorrowoffeatureswithanaccuracyof<100nm.Thusforstudyingnanofeaturessuchasplasticzonesofnanoindentationsontheorderofafewhundrednminsize,researchersmusteithersacriceTEMimagequalitybymakingthickcrosssections,orriskmissingthetargetregion.Furthermore,evenifthealignmentisperfect,thetwo-dimensional(2D)TEMcrosssectionprovideslimitedinformationregardingthethree-dimensional(3D)shapeofthenanofeature.Inthisdissertation,asimplemethodforTEM-specimenpreparationand3Dvisualizationofnanofeaturesisintroduced,inwhichnanoindentationarraysonGaAs(001),InAslmsonGaAs(001),andsuperhardZrClmsonSi(001)arerotatedataslightanglewithrespecttothelifted-outcrosssection.Withtheoptimalrotationangle,amorecompletepictureofthedislocationnetworkbeneathanindentisobtainedinasinglespecimen,witheachadjacentfeature 13

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showingadifferentsectionalviewofanindentation.Theimagesofindividualsectionsarethencompiledtoreconstructtheoverallstructureofanindentationplasticzoneinthreedimensions.ThismethodisusedtoimprovetheunderstandingofanisotropicdeformationinGaAs(001)andinterfacialdeformation.Itcanbeextendedtostudyvirtuallyanytypeofnanofeature,solongasitisrepeatableandcanbepatternedinanarraywithanaccuracyoftensofnm.Moreover,theyieldoflifted-outFIBcrosssectionsisincreaseddramaticallybecauseitcircumventstheneedtopositiontheFIBsliceaccurately.HardnesstestingofthreeZrClmsisalsoreported. 14

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CHAPTER1INTRODUCTION1.1Motivation Understandingthemechanicsofmaterialshasbeenofgreatimporttotheeldsofmechanicalengineeringandmaterialssciencesincetheirconception.Afundamentalcharacteristicofanyengineeringeldisthatitappliesknowledgeofsciencetodevelopnewtechnologies,ortoadvanceexistingtechnologies.Theapplicationofknowledgeofmaterialdeformation,suchasplasticityandfracturephenomena,hasplayedanimportantroleinadvancingabroadrangeoftechnologies,includingjetturbineblades 1 ,bioinspiredhierarchicalmaterials 2 ,compliantsemiconductorheterostructures 3 ,andexibleelectronics 4 .Inc.1500,LeonardodaVinciconductedanexperimenttodeterminethetensilestrengthofironwire,andfoundthattheultimatestrengthdecreasedwithincreasingwirelength.Thisndingdeesbothcommonsenseandtheclassicalunderstandingofmechanicsofmaterials.Today,duetoadvancesintheunderstandingofmaterialdeformation,aidedbyvisualizationtechniquessuchaselectronmicroscopyandcomputersimulations,itispossibletoexplainthephenomenonthatdaVinciobservedfromanatomicperspective.Theapparentdifferenceinstrengthcouldbeattributedtoheterogeneityandthedistributionofstrength-limitingdefectsinthewires 5 .Thesedefectsserveasnucleationsitesforplasticdeformation,andthereisagreaterprobabilitythatthedefectultimatelyleadingtofailureatthelowestloadresidesinalongerwirethaninashorterone.Indentationhasbeenusedforoveracenturytostudythehardnessofmaterials.However,tobeabletointerpretexperimentallyobtainedhardnessvalues,itisimportanttounderstandthedeformationmechanismsinvolved 6 .Whilethereexistseveraltechniquestoobservestructuresatthenanoscale(<100nm),inordertoresolve 15

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atomicdefectswithhighresolutionandcontrast,thetransmissionelectronmicroscope(TEM)istheultimatetool.ATEMcanbeusedtoproducestrikingimagesofstructuressuchasdislocations,twins,andcrystallattices.AnexampleofanimageofacrackinteractingwithmultipledislocationloopsinSiisgiveninFigure 1-1 7 .TEMcanalsobeusedtodetermineamaterial'scrystalstructure,tocreateelementalmaps,ortoprovidequantitativeinformationsuchaslatticedimensions. Figure1-1. InteractionofacrackfrontwithmultipledislocationloopsinSi.ReproducedfromRef7withpermission. DeformationmechanismsinsemiconductorssuchasSiandGaAshavebeenstudiedintensively,becauseoftheadverseeffectsofatomic-scaledefectsondeviceperformance 8 .Forexample,dislocationspresentinatransistorcanactaselectrontraps,therebyreducingtheconductivityofthetransistor 9 .Understandingdeformationmechanismscanaidindesigningmaterialstructuresinsuchawaythatpreventsdefectsfromformingorconstrainsdefectswithinaparticularregion.Effectivelyvisualizingmaterialdeformationattheatomicscalecouldalsobeusedtovalidatetheresultsofcomputationaltechniques,suchasatomisticornite-elementsimulations.Theinterestindevelopingandreningfundamentalmodelingtechniques 16

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hasacceleratedrecently,evidencedbytheU.S.government'slaunchoftheambitiousMaterialsGenomeInitiativein2011 10 .PerhapsthegreatestchallengeinobservingnanoscaledeformationusingaTEMliesintheabilitytoroutinelypreparespecimensinawaythatguaranteeshigh-qualityimages.Thiscanbeextremelychallenging,duetotheneedtoproduceaspecimenthinenoughfortheelectronbeamtotransmitthroughit(usuallylessthan200nm).Forobservingnanoscalefeatures,cuttingabulkmaterialaroundthefeatureandthinningittotherequiredgeometrywithoutdamagingitrequiresextremeprecisionandcare.Thisisusuallyaccomplishedusingafocusedionbeam(FIB)withanimagingresolutionof<10nmtoion-millathincross-sectionalTEM(XTEM)specimen.However,alignmentwithananofeaturecanstillbeverydifcult,andevenanexperiencedusermayhavealowrateofsuccess.Additionally,sinceindividualTEMimagesaretwodimensional(2D),verylittleinformationcangenerallybeinferredregardingthethree-dimensional(3D)natureofafeature.Theabilitytovisualizecomplexfeaturesin3Dcouldaddkeyinsightintotheoverallstructureofthesefeatures,suchasthesizeandshapeofaplasticzonebeneathananoindentationinananisotropicmaterial.1.2GoalsThepurposeofthisresearchistoadvancethestateoftheartofobservingandvisualizingnanomechanicsusingTEMbydevelopingandinvestigatingtheefcacyofanexperimentalmethodtoobservenanomechanicsin3D.1.3ObjectivesTheobjectivesofthisdissertationareenumeratedbelow: 1. Developanddemonstrateanewtechniqueforpreparingsite-specicXTEMspecimensforstudyingnanofeaturesthatincreasesthroughputandguaranteesinclusionofthefeatureofinterest. 2. Demonstrate3DreconstructionofindentsubsurfacedeformationfromXTEMimages. 17

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3. Applyingtheapproachtostudynanomechanicsandinterfacialdeformationinnanolamintes.1.4ApproachTheapproachusedtomeetthedescribedobjectivesinvolvescreatinganarrayofnanofeaturesthatarearrangedinsuchawaythatcuttingalinearslicethroughthemguaranteesinclusionofmultiplesegmentsofdifferentnanofeatureswithintheslice.Averysimplesolutionistocreatearectangulararraywithevenlyspacednanofeatures,whichisslightlyrotatedwithrespecttotheslicedirection.Byusinganarrayratherthanasinglerow,thealignmentofthesliceneedonlybepositionedwithinanaccuracyofmicrons,nottensofnanometers.Theexperimentaldemonstrationofthistechniqueinvolvescreatingindentfeatureswithacommercialnanoindenter.Thefeaturesthemselvesconsistofdislocation-denseplasticzonesbeneaththematerial'ssurface.Slices(crosssections)arethenextractedusingaFIB,andthesecrosssectionsareimagedinaTEM.Aftercollectingimagesofallthefeatureswithinonecrosssection,theimagesareprocessedandassembledintovirtualstacks,whicharethenusedtocreatea3Dimagewhichrepresentsasinglenanoindentationplasticzone.1.5OrganizationofChaptersInChapter2,severalexistingtechniquesofTEM-specimenpreparationand3Dvisualizationusingelectronmicroscopyarereviewed,inthecontextoftheirapplicationtostudyingnanomechanics.Attheendofthechapter,limitationsofthesetechniquesarediscussed.InChapter3,theexperimentalapproachisdescribedindetail,andtheproposedmethodisdemonstratedonGaAs(001)withacube-cornernanoindentertipforthreeindentationloads.Thismaterialischosenbecauseitsdeformationmechanismshavebeenwellcharacterized,andbecausetheplasticzoneunderananoindentationinGaAs 18

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(001)assumesacharacteristic,repeatableshape.Theconceptofreconstructingarepresentativenanoindentationplasticzonein3Disalsodemonstrated.InChapter4,themethodisextendedtoothermaterialsystems:namelyanInAsthinlmonGaAs(001),andasuperhardZrCthinlmonSi(001).InChapter5,asummaryoftheexperimentsisprovided,andfuturedirectionsoftheresearchprojectandrecommendationsarediscussed. 19

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CHAPTER2STATEOFTHEART:METHODSFORVISUALIZINGSUBSURFACEDAMAGEANDELECTRON-MICROSCOPETOMOGRAPHYSeveraltechniqueshavebeenusedforstudyingthesubsurfacedamagebeneathnanoindentations.Stillmoretechniqueshavebeendevelopedfor3Dvisualizationofnanostructuresormicrostructures,buthaveseldom,ifever,beenappliedtostudyingsubsurfacedamageandmaterialdeformation.Eachtechniquehasitsspecicadvantagesandlimitations.Thischapterbrieyreviewssomeofthesetechniques,andhighlightslimitationswithrespecttostudyingnanoindentationplasticzones.2.1ObservingSubsurfaceDamageviaTransmissionElectronMicroscopy Typically,inordertoobservematerialdeformationattheatomicscale,aTEMisrequired,duetoitscombinationofsub-nanometerresolutionandhighcontrastofatomicdefectsincrystals.Ingeneral,therearetwoviewingorientationsforTEMimagingofmaterialscutfromthebulk(incontrasttocolloidalparticles):planview(Section 2.1.1 )andcross-sectionalview(Section 2.1.2 ).ExamplesofeachareshowninFigure 2-1 11 .ForanyTEMoperation,thespecimentobeimagedmustbethinenoughfor`electrontransparency'inordertoallowtheelectronbeamtotransmitthroughitwhilebeingminimallyscatteredbythesample.TEM-imagecontrastarisesdueelectronsbeingscatteredbyatomsinthespecimen.Foracrystallinematerial,tiltingthespecimenalongacrystallographicdirectionwhichdiffractsinsuchawaythattransmittedelectronsinterfereconstructivelyincreasesthesignalstrengthofthetransmittedbeam.Inthiscase,anydeviationsfromtheregularcrystallattice,suchasdislocationsandgrainboundaries,providecontrastinTEMimages.However,evenintheabsenceofdefectsorotherdeviationsfromaperfectlattice,thescatteringprobabilityisproportionaltothesamplethickness 12 .Therefore,thickersamplesprovidepoorimagecontrast,asmorescatteringresultsinmorebackgroundnoise. 20

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Figure2-1. SchematicsdepictingTEMcrosssectionscontainingindentions,inA)planviewandB)cross-sectionalview.RepublishedfromRef11withpermission. 2.1.1Plan-ViewTransmissionElectronMicroscopyPlan-viewTEMreferstotheobservationofspecimensinwhichtheelectron-beamdirectionisparalleltotheoriginalsurfacenormal.ItishistoricallythemostcommonorientationforTEMimagingofspecimenstakenfrombulksamples.Preparationofplan-viewTEMspecimensinvolvesthinningasamplefromthebottomand/ortopsurfacesuntilitisthinenoughforelectrontransparency.Formostmaterials,thisrequiresspecimenstobeatmostapproximately50-300nmthick.Forstudyingindentation-induceddeformation,thetopsurface(onwhichtheindentismade)istypicallyleftintact,andthewaferisthinnedfromthebackside,asdepictedinFigure 2-1 A.Thiscanbeaccomplishedbymechanicaldimplingandsubsequentchemicaletching,forexample,usingabromine-methanolsolution 13 15 .Anothertechniqueinvolvesprotectingtheindentedsurfacewithatemporarylm,andusingdimplingfollowedbyionmillingonthebacksideoftheindentedsampletothinto 21

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electrontransparency 16 17 .Indentingonapre-thinnedwafer(about100-mthick),andsubsequentbacksidepolishinghasalsobeendemonstrated 18 .ItisworthytonotethatPageetal.,whouseddimplingandionmilling,reportedthata60%successratewaspleasing,duetochallengeswithspecimenpreparation 16 .ReferringtoFigure 2-1 A,andalsoFigure 2-2 A,onecanobservethattheindentdepthistypicallyontheorderofthethicknessoftheTEMspecimen.However,theplasticzonesurroundingtheindent,whichcontainstheentiredislocationnetwork,isnearlyanorderofmagnitudegreaterthantheindentdepth. 19 Thustheinformationcontainedintheplan-viewTEMspecimenislimited,andtheprimaryadvantageofplan-viewTEMforstudyingindentationplasticzonesisitsutilityinobservingdislocationsloopsandcrackswhichextendtothesurface.Anexampleofaplan-viewTEMimageinthevicinityofaVickersmicroindentationinsingle-crystalFe0.3Si0.97isshowninFigure 2-2 B.Segmentsofscrewdislocationswhichpropagatedtothetopsurface,butreportedlyinitiatedbeneaththeindenter,canbeseensurroundingtheindentfeature.InFigure 2-2 A,therectangularprismonthesurfacedepictstheregioncontainedintheTEMimageinFigure 2-2 B.Itisapparenthowlittleinformationregardingthe3DnatureoftheindentationplasticzoneiscontainedintheTEMimage.Theplan-viewimageprovidesnoindicationofwhetherthereexistsasubsurfacecrack,howdeeptheplasticzoneextends,norhowthedislocationsinteractwiththeinterfaceofanothermateriallayerbeneaththeindent(ifany).Furthermore,itispossiblefornanoindentationstobesmallenoughtoproduceplasticzonesthatdonotextendtothesurface,inwhichcasetheplan-viewTEMimagecouldbecompletelyabsentofdislocations.Forexample,whenreferringtoa69-nm-deepVickersindentinFe0.3Si0.97,Zielinskietal.note:unfortunately,theTEMfoilisthinnerthantheindenterpenetrationdepth,soitdoesnotallowonetoobservethestructurebeneaththeindentation 18 22

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Figure2-2. Examplesofplan-viewtransmissionelectronmicroscopyofindentations.InA),therelativepenetrationdepthofanindentertipintoasurfaceiscomparedwiththeTEMspecimenthickness.Inthiscase,screwdislocationshavelefttracesonthesurfacewhicharecontainedintheTEMspecimen,butthemajorityofthescrewdislocationsremainfurtherbeneaththesurface,andsoarenotvisibleinaplan-viewTEMimage.InB),anexampleofabright-eld,plan-viewTEMimageisshownforaVickersindentwithadepthof1152nminFe0.3Si0.97.FiguresrepublishedwithpermissionfromRef18. 2.1.2Cross-SectionalTransmissionElectronMicroscopyCross-sectionalTEM(XTEM)referstotheobservationofspecimensinwhichtheelectron-beamdirectionisorthogonaltotheoriginalsurfacenormal.XTEMisparticularlyusefulforobservingsubsurfacedeformationandinterfacesbetweenlayers.However,preparationofXTEMsamplescanbemuchmorechallengingthanthatofplan-viewTEMspecimens,becauseitrequiresthinningasampleinthedirectionnormaltothesurface.Furthermore,XTEMinvestigationsofindividualfeaturesrequirethattheelectron-transparentcrosssectioncontainthefeature(s)ofinterest.JustlikeotherTEMspecimens,thiscrosssectionmustgenerallybelessthan~300nmforasingle-crystalmaterialtobeobservedinaTEM.Ideally,however,aTEMcrosssectionshouldbefarlessthan100 23

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nmthick,inordertoenhanceimagecontrast,e.g.forhigh-resolutionTEM(HRTEM)imaging.Site-specicXTEMcrosssectionsaregenerallymoredifculttothintoelectrontransparencythanbulkcrosssections,astherearelimitedmethodsforthinninganXTEMcrosssection.Withtheadventoffocusedionbeam(FIB)microscopy,preparingXTEMspecimenshasbecomeroutine 20 .SpecicdetailsregardingXTEM-specimenpreparationusingadual-beamFIB/scanningelectronmicroscope(SEM)arediscussedinSection 3.3.4 .TheoverallproceduresinvolveusingeithertheFIBorinsituSEMforimaginginordertondtheregionofinterest(ROI).Then,theROIiscoveredwithaprotectivecapbydepositingamaterialsuchasplatinumorcarbonusingtheionbeamandasourcecontainingthedepositionmaterial.Acrosssectionismilledaroundeithersideoftheprotectivecapusingtheionbeam,andthecrosssectionisthinnedfurtherandreleased(orcutfree)usingtheionbeam.ThecrosssectionisthenremovedusingamicromanipulatoreitherinsideoroutsidetheFIBchamber,andattachedtoaTEM-specimenholder.Intheformercase,nalthinningwiththeionbeamisperformedafterattachingthecrosssectiontothespecimenholder.Althoughimagequalityisgreatlyimprovedwiththinnersamples,itissometimescounterproductivetomakeasite-specicTEMcrosssectiontoothin.SupposethatasubsurfacefeaturetobeobservedviaXTEMisaspherewithadiameterof500nm.Inordertoobtainahigh-qualityTEMimage,thecrosssectionmaybethinnedtoathicknessof50nm.Thusonly10%ofthesphere'sthicknessisincludedinthecrosssection,andinformationregardingtheoverallshapeislimited.Tosolvethis,perhapsasmallersphereischosen,withadiameterofonly50nm,yetthissmallsizecreatesnewproblems.First,thepositionalaccuracywhenpreparinganXTEMcrosssectionwithaFIBisatbest~100nm;evenwithanexperiencedoperator,itispossibletocompletelymissa 24

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targetbymorethan100nm,basedonexperiencefrommyselfandcolleagues.Infact,afteryearsofexperiencepreparingFIB-XTEMspecimens,Lloydetal.reportedthatthepositionoftheFIB-milledcrosssectioncouldbecontrolledtowithinapproximately200nm,evenwhenmarkerindentswereusedoneithersideofarowofindents 21 .Thesmalleratargetfeatureis,thesmallerthemarginoferrorinliftingitout.Second,forplasticityresearch,itisgenerallyimpracticaltostudyfeaturesassmallas50nm.Individualscrewdislocationsareontheorderofthislength,anddislocationnetworks(i.e.plasticzones)aregenerallymanytimeslarger.Third,evenifitwerepossibletoperfectlypositionafeatureofinterestinanXTEMcrosssectionthinenoughtobeelectrontransparent,yetthickenoughtocontaintheentirefeature,standardTEMimagesare2Dprojectionsofallofthefeaturesinsidethecrosssectionwhichdeviatefromthecrystallattice.Thusifasubsurfacefeaturewereoftheshapeofabird'snest,theresultingimagewouldbemorereminiscentoftheshadowofthenestthanitwouldbeofcollectionoftwigsthatcanbeclearlydistinguishedfromoneanother.RecentadvancesinTEMtomographyhaveallowedforthecreationof3Dvisualizationsofverysmallnanostructures,asdiscussedinthenextsection.However,duetosizeconstraints,theapplicationtostudyingnanomechanicsislimited.Perhapspartlyduetothesechallenges,itiscommonforresearchersstudyingnanoindentation-induceddeformationviaXTEMtoobserverelativelylargeindents,i.e.>1minwidth,andwithplastic-zoneradiiofseveralm 21 27 .ThisgreatlyincreasestheprobabilityofinclusionofparttheplasticzoneintheXTEMspecimen.FewXTEMinvestigationsofindentssmallerthan1minwidthhavebeenreported 28 .AnotherapproachcouldbetoleaveanXTEMspecimenrelativelythick,therebyincreasingtheprobabilityofincludingthefeature(s)ofinterestinthecrosssection,buttothedetrimentofimagecontrast. 25

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2.23DTransmissionElectronMicroscopyTransmissionelectronmicrographsare2Dprojectionsofa3Dstructure.Moreaccurately,theyare2Dsuperpositionsofpotentiallyseveralhundredsoflayersofa3Dstructure 29 .ThisinherentlylimitstheutilityofTEMimagestoprovidestructuralinformationwithdetailinallthreedimensions.However,bytiltingasamplewithintheTEMtomultipleangles,itispossibletocaptureimagesthatcanberecombinedinawaythatallowsfor3Dvisualization.3DreconstructionofTEMimages(3D-TEM)wasrstestablishedintheeldoflifesciences 29 ,buthasrelativelyonlyrecentlybeenusedbymaterialscientists 30 .Asearlyas1968,DeRosierandKlugformulatedamethodtoreconstructa3Dobjectfromasetof2Dtransmissionelectronmicroscopeprojections,basedontheobviouspremisethatmorethanoneviewisgenerallyneededtoseeanobjectinthreedimensions 29 .Later,in1982,theNobelPrizeinChemistrywasawardedtoKlugforhisdiscoveryandapplicationoftheseelectron-microscopytechniquestoelucidatethestructureofproteincomplexes 31 .DeRosierandKlugrstusedthisnewtechniquetoreconstructthetailofabacterialphage.AschematicoverviewoftheproceduresusedisreproducedinFigure 2-3 29 .ThemethodreliesondeterminingthedensitydistributionofmaterialbyperformingaFouriertransformoftheTEMdata.Interestingly,inthespecialcaseofahelicalobject,asinthebacterialphageshowninFigure 2-3 ,onlyoneangleisnecessaryforconstructinga3Dimage,becauseoneprojectedviewinfactprovidesasuperpositionofmultipleviewsofthatsamestructure,rotatedaroundacentralaxis 29 32 .Fornonhelicalstructures,morethanoneprojectionisrequiredforgeneratingthe3Dimage.Furthermore,asthestructuralasymmetryincreases,thenumberoftiltanglesmustincreaseaccordingly.Inotherwords,ahigher-resolution3Dimagecanbeachievedbyeitherincreasingthesymmetryoftheobservedstructureorthenumberoftiltangles. 26

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Figure2-3. 3DTEM:A)Schematicrepresentationofprocedurestoreconstructa3DimagebytiltingaTEMspecimentodifferentanglesandusingFouriertransformsofprojectedimagestoobtaindensity-distributioninformationfromdifferentprojections,which,inturn,areusedtoconstructthe3Dimage,showninB).FigurereproducedfromRef29withpermission. 27

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Forasymmetricalstructures,aTEMspecimenwouldoptimallybetiltedincrementallyacrossanangularrangeof180 29 ,althoughforpracticalpurposestherangeusedislimitedto150 30 .Ingeneral,themaximumresolutionisgivenbyapproximatelythreetimesthesamplethickness,dividedbythenumberoftiltangles 30 .Thusif151imagesweretakenacrossarangeof150,fora200-nm-thicksample,themaximumresolutionofthereconstructedimagewouldbeapproximately4nm.Recently,3D-TEMhasbeenusedtoreconstruct3Dimagesofnanocrystalsontheorderofafewnanometersindiameter 33 35 ,withamaximumresolutionreportedtobe2.4 35 .Ithasalsorecentlybeenappliedtocreate3DimagesofdislocationsinGaN 36 andSi 7 .Thistechniqueisthereforeextremelycapableofvisualizingsmallnanostructures,butitispresentlynotknowntohavebeenappliedtostudyingindentation-inducedplasticity,possiblyduetosizeconstraintsandotherlimitations,asdiscussedinSection 2.6 .2.3SerialSectioningandFIBTomographyAnotherelectron-microscopytechniquewhichcanyield3DreconstructionsisserialsectioningwithaFIB.ThismethodsimplyinvolvessuccessivelymillingthinsliceswithaFIB,andtakingsnapshotsofeachslice.Whileearlyexperimentsinvolvedbothsectioningandimagingwiththeionbeam,theadventofcommerciallyavailabledual-beamFIB/SEMsystemsimprovedtheresolutionandstreamlinedtheimage-acquisitionprocess 37 .Withadual-beamFIB/SEM,thestandardprocedureinvolvesorientingthesample'ssurfacenormaltotheionbeam,andusingthebuilt-inSEMforimagingfromabird's-eyeview,asdepictedinFigure 2-4 A 38 .AtrenchisrstmilledaroundtheROI,andconsecutiveslicesaremilledaway.Withtheion-beamfocuseddowntoadiameterofapproximately10nm 39 ,verythinslicesaremilledaway,oneatatime.Theslicesarethenreconstructed,asshowninFigure 2-4 B. 28

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Figure2-4. Serial-sectioningtechniqueinsideadual-beamFIB/SEM:A)AtrenchisrstcutaroundtheROIwiththeionbeam.Theionbeamisthenusedtosuccessivelymillawaythinslicesofmaterial,whiletheelectronbeamisusedtotakesnapshotsofeachnewlyexposedsurface.Microstructuralinformationcanbeobtainedfromreconstructedlayers,asshowninB).FiguresreproducedfromRef38withpermission. Theultimateresolutionislimitedbythethicknessoftheslicesthatarecutawaywiththeionbeam.Whereasserialsectioningviamechanicalpolishingresultsinlayersontheorderofmicrometersinthickness,theFIBiscapableofremovingindividuallayersasthinas15nm,thusgreatlyimprovingtheresolutionoftheresultingreconstructedimage. 40 Alternatively,3DelementalmappingcanbeachievediftheintermediatesnapshotsareofelementalmapsinsteadofSEMimages.Sakamotoetal.demonstratedthisasearlyas1998,whentheydevelopedtheirowndual-beamFIB/SEMwithanAuger-electrondetector 41 .Also,3Dreconstructionsarenotalwaysnecessary.Simplyarrangingconsecutiveimagescorrespondingtodifferentdepthsissufcienttoimmediatelyprovideanimprovedunderstandingofastructurein3D.AnexampleisgiveninFigure 2-5 ,inwhichSEMimagesofdifferentsectionsofasubsurfaceareaareshown 42 29

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Figure2-5. ScanningelectronmicrographsofdifferentsectionsofasubsurfacedefectafterslicingwithaFIB.Imagesare~6mwide.FigurereproducedfromRef42withpermission. 2.4InsituTEMWhiletheaforementionedmethodsofstudyingnanomechanicscanprovidemanydetailsregardingtheplasticityandfractureofmaterials,theyarelimitedtostudyingtheseaftertheindentation(orotherdamage-inducing)experimenthasalreadybeenperformed.Asaresult,thedeformedregionisrelaxedincomparisonwithitsfullyloadedstate,andanyinformationregardingthesequenceofdeformationphenomena,andtheirrelationtotheload-displacementcurve,mustbeinferredratherthandirectlyobserved.Forexample,thenanoindentationpop-ineventasuddenjumpintheload-displacementcurve,longbelievedtobeattributedtotheonsetofplasticdeformationduetoinferencesfromtheTEMresults 17 hasrecentlybeenshowntooccuraftertheformationoftherstdislocations 43 ,usinganewmethoddescribedinthissection.AnaturalprogressionintheartandscienceofstudyingnanomechanicsusingaTEMistoperformthenanoindentation(orother)experimentinsidetheTEMwhile 30

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Figure2-6. SchematicshowingananoindentationsetupbuiltintoaTEMgoniometer.FigurereproducedfromRef44withpermission. imaging,hereafterreferredtoasinsituTEM.ThiswasrstdemonstratedbyWallandDahmen,whooutttedaTEMspecimenholder(goniometer)withananoindentertip,acustomspecimenmount,andagearmotorandpiezoelectrictransformerforcoarseandnetranslations,respectively 44 .AschematicoftheirdesignisshowninFigure 2-6 .Theyusedaboron-dopeddiamondindentertipsothatthetipwouldbeelectricallyconductive,whichisfavorableforimaginginsidetheTEM.SpecimenpreparationforinsituTEMisparticularlychallenging.Thespecimenmustbethinenoughtobeelectrontransparent,yetmustberigidlyattachedtoastiffframe.WallandDahmenusedstandardmicrofabricationtechniquestocreateroundmesasofSithatprotrudedfromtheSiwafersurface,sothatwhenthespecimenwasorientedvertically,theTEMbeamwouldtransmitthroughthevariable-thicknessmesa. 44 Later,Stachetal.usedFIBmillingtomachineathincrosssectionforTEMindentation,asdepictedinFigure 2-7 45 .Onedrawbackofthetheseearlyexperimentswastheiruseofpiezoelectricdrivesforindenting,whichlimitedtheaccuracyofforcemeasurements 46 .Fortunately,asinsituTEMwasbeingdeveloped,increasinginterestinstudyingthemechanicalpropertiesofverythinlms 47 andsmallvolumes 48 haddriventhenanoindentation 31

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Figure2-7. InsituTEMnanoindentationontoaFIB-milledelectron-transparentregion:A)schematicand)BTEMimage.FigurereproducedfromRef45withpermission. markettodevelopinstrumentswithever-improvingforceanddisplacementresolution,andanaturalreductionintransducersize(i.e.thecomponentmeasuringforces)asdisplacementrangesshrunk.Infact,Hysitron,Inc.hasrecentlydevelopedamicroelectronic-mechanicalsystems(MEMS)-basedcapacitivetransducerwithanoiseoorof<1.1nNforforcemeasurements 49 .Withtheminiaturizationofnanoindentationtransducers,ithasbecomepossibletoperformaccurateload-displacementnanoindentationtestsinsideelectronmicroscopes 43 .Theabilitytosynchronizeload-displacementdataacquisitionwithvideoofdeformationtakingplaceattheatomicscalehaselucidatedphenomenasuchastherelationshipofnanoindentationpop-intotheonsetofplasticityinSi 43 .2.5Etch-PitMethodOnewayofobtaininga3Drepresentationofanindentationplasticzoneshapeisbytheetch-pitmethod 50 51 .Thisissimilartotheserial-sectioningtechniquewithaFIB,in 32

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thatitinvolvessuccessivelyremovinglayersofmaterialandimaging,butuseschemicalpolishingandetchingtoremovematerial,insteadofanionbeam.ExamplesofimagesobtainedbyRobertsetal.usingthismethodareshowninFigure 2-8 51 .Theproceduretheyusedinvolvedmakingarelativelylarge(severalmwide)indentonMgO(001),withthesquare-cross-sectionindentertipalignedwitheitherthe[100]or[110]directions.Alayer20-25mthickwasthenremovedfromthesurfacebychemicalstripping/polishing,andsubsequentetchingwasusedtopreferentiallyrevealthedislocatedregions.Thiswasrepeatedasecondtime.Thedislocationpatternswereobservedateachstepviaopticalmicroscopy. Figure2-8. OpticalmicrographsofKnoopmicroindentationsonMgO(001)atdifferentdepths,revealedusingetchpitting,withtheindenteralignedwiththe[100]directionin(A),(C),and(E),andthe[110]directionin(B),(D),and(F).ReprintedfromRef51withpermission. 33

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Table2-1. Advantagesandlimitationsofselectedmethods. MethodImageTypeAdvantagesLimitationsResolution Plan-viewTEM2DmorestraightforwardpreparationthanXTEM;viewdefectsatsurfacenear-surfacefeaturesonly~atomicXTEM2Dsitespecicity;subsurfacecrosssectionsfractionofplasticzone;difculttoalignforsmallindents~atomic3DTEM3Dhigh-resolution3Dimagesofnano-structuresmoredifcultwithasymmetry;max.size~100nm~atomicInsituTEM2Dvideosshowevolutionofplasticzone;greatforconnedvolumesfornanostructuresoracutesamples,notbulk~atomicFIB/SEMserialsectioning2Dor3Dhigh-resolution3Dimages;3Delementalmappingpoorcontrastforatomic-scaledefectssuchasdislocationsnanoscaleEtchpitting2Ddepthprolegreatforobservinganisotropyofmicro-indentslargeindentsonlymicroscale 2.6LimitationsoftheAboveMethodswithRegardtoVisualizingSubsurfaceDeformationClearly,thereissignicantinterestintheresearchcommunityinobservingmicro-andnanostructuresinbothtwoandthreedimensions,andmuchefforthasbeenputforthbyresearcherstondnewmethodstodoso.Manyofthesetechniqueshavebeenappliedtostudyingsubsurfacedamagebeneathindentationimpressions.Thechoiceofonemethodultimatelyisafactorofcost,availability,thelevelofdetailthatatechniquecanprovide,rateofsuccess,userexperience,anduserpreference.Whileeachmethodhasitsadvantages,eachonealsohassomelimitationswithregardtovisualizingsubsurfacedamage.AsummaryoftheseisprovidedinTable 2-1 .Plan-viewTEMproducesonly2Dimages,andonlyfeaturesatornearthesurfacewillbepresentintheTEMspecimen,andthusintheresultingimages.Sample 34

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preparationiswellestablishedandsomewhatroutine,butarelativelyhighrateoffailure(~40%) 16 isstilltroubling.XTEMimagingprovidesmoreinformationregardingthesubsurfacedamageandplastic-zoneshapethanplan-viewTEM,butstillonlyprovides2Dimagesonitsown.Furthermore,theplastic-zonesizeisgenerallysignicantlywiderthanthethicknessofanXTEMspecimen,soonlyafractionoftheplasticzonecanbeincludedinthenalimage.ItisthereforeimpossibletoseetheentireshapeofananoindentationplasticzonefromasingleXTEMimage,andtheshapeandsizecanonlybeinferred.ThisisfurthercomplicatedbythefacttheoffseterrorinaligningtheFIBcrosssectionwitharowofindentfeaturesisapproximately200nm 21 ,sotheexactlocationoftheXTEMimagewithrespecttothecenterofanindentisnotpreciselyknown.Sometimestheimagedoesnotevencontaintheresidualindentimpression.Therefore,bothplan-viewandcross-sectionalTEMprovideonlypartofthefullpicture.Three-dimensionalTEMprovidesimpressive3DvisualizationsinsteadofstandardTEMprojections.However,ithassimilarlimitationstoXTEMinregardstothefractionofafeaturethancanbecontainedinaTEMspecimen.Serialsectioninginadual-beamFIB/SEMallowsfor3DreconstructionsofvolumesnotlimitedtothewidthofaTEMspecimen.Italsoallowsfor3Delementalmapping.Itsmajordrawback,however,isthelackofdetailofatomicdefectsinSEMimageswhencomparedtoTEMimages.Asmentionedpreviously,TEM-imagecontrastarisesduetoscattering,suchasdeviationsfromaregularcrystallatticecausedbythepresenceofdefectstructures.Withtheproperimagingconditions,dislocationsandotherdefectscanappearwithstrikingcontrastinTEMimages.SEM-imagecontrastisattributedtohowmuchasurfaceandsubsurfacevolumeeitheremitsecondaryelectronsorscatterelectronsbackawayfromthesurface,whicharefunctionsofthematerial,itsgeometry,andtheelectronbeam.TheimagecontrastandresolutionofatomicdefectsaresignicantlyreducedcomparedtothatinaTEM. 35

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AlthoughinsituTEMnanoindentationisapromisingtechniquewhichallowsunparalleledreal-timeobservationofdeformationattheatomicscale,samplepreparationisnotonlychallengingandtedious,butspecimengeometryislimited,asspecimenshavetobeelectrontransparent.Itiswellknownthatmaterialdeformationinconnedvolumesisdifferentfromthatinbulkmaterials 48 .Infact,Minoretal.notedthattheirrst-everobservationofroom-temperaturedislocationplasticityinSicouldsimplybeattributedtothehighavailabilityoffreesurfaces,asaresultofspecimengeometry 52 .Furthermore,specimenbendingisoftenaproblemininsituTEM 53 ,whichgreatlyaffectstherepeatabilityandreliabilityofindentationdata.Itisworthytonotethatcontact-mechanicstheoryreliesontheassumptionofindentingonasemi-innitehalfspace 54 55 .Thisimpliesthatthespecimenmaterialshouldbehaveasifitwereinniteindepthandinthetransversedirections,andthatthesurfaceshouldbesmoothandat.Thinspecimensthatbendorotherwisebehavedifferentlythanbulkmaterialscanleadtoerroneousorconfusingdata,sohardnessandelastic-modulusmeasurementsshouldbeinterpretedwithextremecareforinsituTEMstudies.Thismakesitdifculttoquantitativelycorrelateobserveddeformationwithnanoindentationdata,whichmeansthatpredictiveaspectsofsuchexperimentswouldbelimited.Theetch-pitmethodisastraightforwardtechniquewhichinvolvesconsecutivelypolishingasampletoremoveathinlayerofmaterial,andthenetchingthenewsurfacetorevealdislocationstructures.Theamountofmaterialthatisremovedisontheorderofseveralm,andsoifthistechniquewereusedtoproducea3Dimage,theultimateresolutionwouldbeonthatorder.Furthermore,TEMcannotbeusedinconjunctionwiththismethodtoprovideatomic-scalelateralresolution. 36

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CHAPTER3PROOFOFCONCEPT:MISALIGNEDFIBLIFTOUTSANDTEMTOMOGRAPHYOFGALLIUMARSENIDE(001)ThischapterintroducesanewmethodofpreparingFIB-XTEMspecimensinawaythatbothincreasesthroughputandresultsinagreateramountofinformationintheresultingimages,whencomparedtoprevioustechniques.Inanefforttodemonstratethefeasibilityoftheproposedtechnique,thematerialgalliumarsenide(GaAs)waschosen.GaAsdeformsanisotropicallyviadislocationnucleationandmovementundernanoindentationloading,andthedeformationassumesacharacteristicshapealongparticularcrystallographicdirections.Thisrepeatabledeformationstructureisexploitedinthisresearchtoreconstructdifferentsectionsofsimilarindentationplasticzonestoforma3Dimage.GaAsiscommonlyusedinthesemiconductorindustry,sohigh-qualitywaferscanbepurchasedcommercially.Furthermore,establishingtheproposedmethodrstusingGaAsisaseguetostudyingthethin-lmInAs/GaAssysteminChapter4.3.1DetailedApproach Previouswork(unpublished)involvingFIBliftoutsandXTEMinvestigationsofultra-low-loadnanoindentationsshowedthatevenwithahighlyexperiencedFIBoperator,itwaspossibletoliftoutacrosssectionthatentirelymissesarowofindents.Thisisbecausethesizeoftheindent'splastic-zoneradiuswasonthesameorderoftheoffseterrorforasite-specicFIBliftout.EarlyconsiderationstoincreasethelikelihoodofinclusionofthenanoindentationfeaturesweretoFIB-millacrosssectionataslightanglerelativetoarowofindents,ortostaggerindentsby100-200nm,sothataslightlymisplacedcrosssectionwouldstillintersectatleastonerow.TheseconceptsareillustratedinFigure 3-1 AandB,respectively.Anotherapproachwastoplacemarkerindentsoneithersideoftherowofindentstobeliftedout(Figure 3-1 C).Then,afterdepositingthePtstripthatcompletelyhidestherowofindentfeatures,theFIBwouldbeusedtomillalineontheedgeofthePt,coincidentwiththelineconnectingthemarkers. 37

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Figure3-1. EarlystrategiestoimproveFIB-XTEMthroughput:A)staggeringfeatures,B)millingataslightanglerelativetoarowoffeatures,andC)placingalignmentmarkersoneithersideoftherow,whichwouldstillbevisibleaftercoveringtherowwithalayerofPt.ExamplesofrealimagesfromtheFIBareshownforstaggeredindentsD)before,andE)afterFIB-millingacrosssection. Somesuccesswasobtainedbystaggeringrows(Figure 3-1 DandE),butthentheideaevolvedtobecomeacombinationofalloftheabovestrategies.Amethodwassoughttodesignanarrayofindentsarrangedinsuchawaythatwouldmathematicallyguaranteetheinclusionofthecenterofoneindentfeatureinathin(<~100nm)XTEMcrosssection.Thiscouldbeperformedbycreatinganarrayofregularlyspacedindents,andFIB-millingacrosssectionthroughthearray,ataslightanglewithrespecttothearrayedge.Thiswouldimmediately(1)increasethethroughputofsite-specicFIBliftoutsfornanoindentations,and(2)provide`snapshots'ofmultiplesegmentsofanindentationplasticzoneinasingleXTEMcrosssection,witheachsegmentoffsetfromanindent'scenterbyapredeterminedamount.Furthermore,iftheconsecutivesegmentswerestackedinsuchawaythattherstsegmentcorrespondstooneendoftheindentationplasticzone,andthelastsegmentcorrespondstotheoppositeend,thenthesegmentscouldbegivenappropriatethicknessvaluesandreconstructedintoarepresentativenanoindentationplasticzone. 38

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Figure3-2. Conceptof3Dreconstructionbyslicingthrougharotatedarrayoffeatures.TheoriginalfeatureinA)ispatternedintoaslightlyrotatedarrayinB),andasliceofitisremoved.ThesegmentsintheslicecanbeseeninfrontviewinC),andthesegmentsarethenrearrangedsothattherst-through-lastsegmentsareinorderfromlefttoright.Thesegmentsarethenreconstructedintoa3Dimage,andviewedfromdifferentperspectivesinD). Figure 3-2 illustratestheconceptofcreatinga3Dimagebyreconstructingcrosssectionsfromasingleslicethrougharotatedarrayoffeatures.TheshapeinFigure 3-2 ArepresentstheplasticzonebeneathanindentationinGaAs(001),withdislocationloopsextendingalongthefourh110idirections.AnarrayofthesefeaturesiscreatedinFigure 3-2 B,withthearrayrotatedbyananglecorrespondingtotheFIBcrosssectioncrossingexactlyonerow,regardlessofwheretherowisplacedwithinthearray.AsinglesliceisremovedfromFigure 3-2 BandviewedfromthefrontinFigure 3-2 C.Thesegmentsintheslicearethenrearrangedsothattherst-through-lastsegmentsareinorderfromlefttoright.Finally,thesegmentsarereconstructedtomographicallyintoa3Dimage,whichresemblestheoriginalfeature,asshownfromdifferentviewinganglesinFigure 3-2 D.Itisconvenienttoconsiderrotatingthearray,ratherthanthesliceitself,becausethesliceshouldbemadenormaltothepropercrystallographicorientationforXTEM 39

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imaging.ThusforGaAs,theintentionistorotatethearraywithrespecttotheh110idirections,andtomaketheFIBslice(throughthearray)paralleltoah110idirection.Inordertodeterminetheidealangleofrotationandarraydimensions,anequationisderivedasafunctionoffeaturespacingandthenumberofrowscrossedbytheFIBslice.ThegeometricrelationsofarotatedarrayofcircularfeaturesinarectangularlatticeareshownschematicallyinFigure 3-3 Figure3-3. SchematicofaFIBslicethroughanarrayofmxnfeatures,rotatedbyangle,inA).IndividualsectionsfromthesliceinA)aremagniedandassembledinB).Thearrayconsistsofcircularfeaturescenteredinrectangular`unitcells.'Inthisschematic,thethicknessofeachsegment,t,isslightlylessthanthecriticalthicknessthatwouldcorrespondtoperfectoverlapofthecompiledsegments. InFigure 3-3 ,thefeaturecenter-to-centerarraylengthandwidtharegivenbylandw,respectively,withfeaturespacingsaandbalongtheserespectivedirections.Thenumberoffeaturesalongthearraylength,m,isrelatedtothelength(l)andfeaturespacing(a)byl=a(m)]TJ /F11 11.955 Tf 11.96 0 Td[(1).(3)Forexample,anarraywithm=11indentsseparatedbya=1mwouldhavealengthofl=10m. 40

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Theunitcellheightisequaltospacingalongthewidth,b.ThetotaldistancecoveredbytheFIBslice,alongthearraywidth,isgivenbyltan().Thusthenumberofunit-cellheightscoveredbytheslice,nh,isnh=totalheightcoveredbyslice heightofunitcell=ltan() b.(3)SubstitutingEquation 3 givesnh=a(m)]TJ /F11 11.955 Tf 11.95 0 Td[(1)tan() b=a b(m)]TJ /F11 11.955 Tf 11.96 0 Td[(1)tan().(3)Rearranging,anexpressionfortherotationangleisfound:=arctanb anh m)]TJ /F11 11.955 Tf 11.96 0 Td[(1.(3)Ifthefeaturespacingisthesamealongthelengthandwidth(i.e.a=b),1thenEquation 3 isreducedto=arctannh m)]TJ /F11 11.955 Tf 11.95 0 Td[(1.(3)Forconsecutivesegmentsoftherecompiledslicestooverlapperfectly,i.e.theshiftfromoneunitcelltothenextequalstheslicethickness,thecriticalslicethicknessissimply(seeFigure 3-4 )tc=asin()(3)3.2DeformationMechanismsofGaAsAlongwithsilicon,GaAsisanextremelycommonmaterialusedinsemiconductordevices,particularlyoptoelectronicdevicessuchashigh-efciencysolarcells.UnlikeSi,GaAsisadirect-band-gapsemiconductor.Thismeansthatanimpingingphotoncanmoreefcientlyexciteelectronsintotheconductionband,withouttheneedof 41

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Figure3-4. Thedimensionsofasingle,rotatedunitcellfromFigure 3-3 ,measuredalongtheX-andY-directions.Theincrementaloffsetfromoneunitcelltothenext,alongthey-direction,asin(),isequaltothecriticalslicethicknesscorrespondingtoperfectoverlapintherecompiledimage. amomentumshiftviatheassistanceofaphonon(latticevibration).GaAsisalsocommonlyusedformakingnear-infraredlight-emittingdiodes(LEDs)andlasers.GaAsisaIII-Vcompoundsemiconductorwhichassumesthezincblendestructureinthesolidform,asshowninFigure 3-5 .Thestructureisequivalenttotwointerpenetratingface-centeredcubic(FCC)unitcells,onewithGaatoms,andtheotherwithAsatomsoffsetat1=41=41=4positions.Thisissimilartothediamondstructure,buttwoelementsareinvolvedinsteadofonlyone.GaAswafersarecommonlyorientedwiththe(001)axisnormaltothesurface. Figure3-5. ZincblendeunitcellwithGaatomsattheFCCpositions,andAsatomsoffsetfromtheGaAsatomsat1=41=41=4positions. DeformationmechanismsofGaAs(001)andsimilarmaterialshavebeenstudiedintensely 13 17 19 21 25 50 51 56 60 ,becauseofthedeleteriouseffectsofatomic-scale 42

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defects 8 61 andstrain 62 ondeviceperformance.Forexample,dislocationspresentinanLEDorlasercanquenchtheluminescenceofthedevice,asdislocationsactascarriertraps,therebyincreasingtheprobabilityofrecombinationofanelectron-holepair 61 .Understandingthenatureofdislocationsources,howtoestimatedefectdistributioninamaterial,andhowtodesignamaterialinsuchawaythatimpedesdislocationcreationand/ormigrationareongoingresearchinterests 11 ,particularlyasnewdevicesbasedonnanowiresandothernanomaterialsarecommercialized 59 ,Understandingthedeformationmechanismsofamaterialcanalsoaidinvalidatingnumericalmodels,suchasatomisticornite-elementsimulationsofmaterialdeformation. Figure3-6. ModelsfordislocationactivityinindentedGaAs(001)A)causedbyindentationwithafour-sidedVickerstip,andB)thesame,butviewedfromthecrosssection.FiguresA)andB)reproducedwithpermissionfromRefs50and58,respectively. Indentation-induceddeformationinGaAs(001)istypicallymediatedbynucleationofdislocations 14 17 50 51 58 andtwins 23 25 .Nanoindentationsatroomtemperaturegenerallydonotproducehighenoughpressuresforphasetransformations 22 ,andcrackshaveonlybeenobservedforindentationsatveryhighindentationloads(e.g.severaltensofmN) 22 43

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GaAsdislocationspredominatelyslipalongf111gplanesinh110idirections,withaBurgersvectorb=a=2h110i,whereaisthelatticeconstant 56 .Schematicsofindentation-induceddislocationpatternsareshowninFigure 3-6 .InA,afour-sidedVickersindentertipisalignedwiththe[110]and110directions.Dislocationsarepreferentiallygeneratedalongthesedirections,andglidealongthe60slipplanes(whichappearastrenchesinthegure).ItshouldbenotedthatFigure 3-6 Awasmadeinthecontextoftop-viewimagingoflargedislocationnetworksobservedwiththeetch-pittechnique 50 ,whileBwasinthecontextofsubsurfacedeformation 58 ,andshowsanapproximatecrosssectionofatypicalindentationplasticzone.Plan-viewandcross-sectionalTEMimagesofnanoindentationplasticzonesinGaAs(001)areshowninFigure 3-7 ,respectively.ThefourgroupsofdislocationnetworksinAarecommonlyreferredtoasdislocationrosettes,andweremadewithabluntVickersindenteratmaximumloadsof550N 17 .TheserosettestructuresareanalogoustothepatternsinFigure 3-6 A.Figure 3-7 Bshowsthestructureofdislocationloopsbeneaththesurfacefora100-Nindentmadewithacube-cornertip 63 Figure3-7. Bright-eldtransmissionelectronmicrographsshowingcharacteristicdislocationrosettesfromnanoindentationinGaAs(001),inA)planview,fromRef17,andB)cross-sectionalview,fromRef63.Figuresrepublishedwithpermission. 44

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3.2.1FIBLiftOutsTherearetwogeneralmethodsforpreparingsite-specicXTEMsampleswithaFIB:theexsituandinsitulift-outtechniques.BothtechniquesemployaFIB,preferablyadual-beamFIB/SEM,toion-millathincrosssection(sometimesreferredtoasa`foil'or`lamella')toelectrontransparency.Usingtheexsitulift-out(EXLO)technique 64 68 ,thecrosssectioniscompletelythinnedandreleased,orseparated,fromthesampleinsidetheFIBchamber,anditisextracted(liftedout)usingamicropanipulatorandalong-depth-of-focusmicroscopeoutsidetheFIBchamber.ItisthentransferredtoastandardTEMgridwithathin(<<100nm),amorphoussupportlm.Themicromanipulatorinthiscasehasareplaceablesharpglassrodattheendofit,whichwhencomingincontactwiththeTEMspecimen,isattractedtoitthroughelectrostaticforces.Theseforcesaremorethansufcienttoovercomegravitationalforcesandattractiveforcesbetweenthespecimenandthetrenchitissittingit,andthusthespecimenistemporarilyattachedtotheglassroduponcontact.Atthispoint,thespecimenistransferredtotheTEMgrid'ssupportlmbybrushingthespecimenagainstthelm,takingcarenottopuncturetheultrathinlm,whichcanresultinacatastrophicenergyexchangeandlossofthelifted-outspecimen.UsingthisEXLOtechniqueforpreliminaryinvestigationsinthisresearch(Figure 3-1 D),onlyoneofthreeliftoutsweresuccessful.Althoughthreetrialsarenotenoughforastatisticallysignicantsampling,twofailuresweresufcienttorealizethata`high'successratecomeswithagreatamountofoperatorexperience,andthisexperienceisonlyobtainedaftermanyfailuresandmanyhundreds(orthousands)ofdollarsspentusingtheFIB.ForveryexperiencedEXLOtechnicians,thesuccessrateisapproximately50-90% 69 .Furthermore,thereareotherdisadvantagestousingtheEXLOtechniquewhencomparedtotheinsitutechnique,discussedbelow.Theinsitulift-out(INLO)technique 20 70 71 beginsthesamewayastheEXLOtechnique,butitusesamicromanipulatorinsidetheFIBchambertoliftouttheTEM 45

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specimen,andthentransfersthespecimentoaTEMgrid,alsoinsidetheFIBchamber.WhereaselectrostaticattractionisusedintheEXLOtechniquetoattractthespecimentoaglassrod,theINLOtechniqueusesanionbeamandaPtsourceinsidetheFIBtoweldthespecimentoametalprobe.Afterwelding,thespecimenisreleasedfromthesamplewithnalion-beamcuts,anditistransferredandweldedtoaTEMgridinsidetheFIBchamber.Finalthinningtoelectrontransparencyisachievedaftertheliftoutiscomplete.ThesuccessrateforahighlyexperiencedoperatorfortheINLOtechniqueisreportedtobeashighas90-100% 69 .Thereareseveraladvantagesanddisadvantagesforeithertechnique.BecausetheliftoutisperformedoutsidetheFIBchamberusingtheEXLOtechnique,itrequiresconsiderablylessinstrumenttimeaminimumof1-2hours.TheINLOtechniquetakesapproximately3-4hoursminimum.Thisisduetotheaddedtimerequiredforwelding,release,andalignmentofthebeams(whichisrequiredwheneverthestageismoved).IntheUFMAICfacility,thecostforusingtheFIBis$65perhourforUF-afliatedresearch(withouttheassistanceofatechnician),and$200perhourforoutsideresearch.ThusthenumberofhoursspentusingtheinstrumentcanbecomeamajorfactorinchoosingbetweenusingtheINLOorEXLOtechnique.Ontheotherhand,asnotedabove,thesuccessrateoftheINLOtechniqueishigher,sopayingforfailedliftoutsislesscommonwiththistechnique.Furthermore,thetechniqueallowsforintermediatethinningofacrosssection;ifitisdeterminedviaTEMthataspecimenistoothicktoprovidehigh-qualityimages,itcanbeinsertedbackintotheFIBchamberforfurtherthinning,providedthatthereremainsasufcientlythickprotectivecap(moredetailsonthecapareprovidedinthefollowingparagraphs).WiththeEXLOtechnique,itisimpossiblewithmodernequipmenttomodifyasamplewiththeFIBoranotherionmillaftertheliftoutandsubsequentTEManalysis.Forgeneralbulkoruniform-layeredsamples,thechoiceofthesetwotechniquesmaybedecidedbypreferenceofoperatorexperience.However,forthesite-specic 46

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samplesinquestion,therateofsuccesswasdeemedaveryimportantfactor.Inthisresearch,eachnanoindentationpatternismadeoneatatime,andalthoughfourfoldredundancywasused(fournominallyidenticalpatternspersample),therewasconcernthatmultiplefailuresusingtheEXLOtechniquecouldresultintheneedtostartoverwithpatterningandcharacterizinganewsample.Afailureisnotlimitedtoanunsuccessfulliftout,butalsoincludesthecaseswhereapatternedregioniscoveredwithdebris,apatternisinadvertentlymadeonaroughareaofthesurface,oranerrorismadeduringFIBmillingwhichmakesthepatternunusable.Consideringthesefactors,theEXLOtechniquehasalowerrateofsuccessthanthereported50-90% 69 ,soitwaslikelythatnewsampleswouldhavetobemadeifusingthislower-success-ratetechnique.Additionally,therewasconcernthatsignicantsamplebendingduetoresidualstressesintheindentedsampleswouldlimittheminimumthicknessofspecimensifusingtheEXLOtechnique.ThisislessofaconcernwiththeINLOtechnique,becausenalthinningoccursaftertheliftout;furthermore,itispossibletopreventbendingduringnalthinning,whichisdemonstratedinChapter4.Consideringtheabovearguments,theINLOtechniquewasdeemedsuperiorandmorecosteffective.3.3MaterialsandMethodsAnoverviewoftheexperimentalproceduresisasfollows;asharp,diamondnanoindentertipwasselectedandcharacterized;thenanoindenterusedhereinwascalibrated;initialindentationtestswereperformedonGaAs(001),andcharacterizedviaatomicforcemicroscopy(AFM);rotatedindentarraysweremadeatthreedifferentloadsonGaAs(001),andcharacterizedviaAFM;thesamplewascarboncoated;insituliftoutswereperformedonthedifferentarrays;XTEMimageswereobtained;nally,imageswereprocessedandreconstructedtocreate3Dvisualizationsofnanoindentationplasticzones. 47

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3.3.1Nanoindenter-TipCharacterization Inordertocreateawell-developedplasticzoneatshallowindentationdepths 55 ,thesharpest,mostacutenanoindentertipavailablewasusedinthisexperiment.Thegeometriesofthreenanoindentertipswererstcharacterizedviaatomicforcemicroscopy(AFM)priortoanyindentationexperiments,sothatthesharpest,mostuniformtipcouldbechosen.AFMmeasurementsofthreeindentertipswereperformedusinganMFP-3DAFMandNanoindenter(AsylumResearch,SantaBarbara,CA),withacontact-mode,nanocrystalline-diamondAFMtip(NaDiaProbesno.CTIR1-4,fromNanoscienceInstruments,Phoenix,AZ)tominimizetipwearwhilescanningonthediamondsurface.Foraccurateheightmeasurements,theinverseoptical-leversensitivity(InvOLS)oftheAFMtipwascalibratedpriortoscanning.Thiswasperformedby`indenting'theAFMtipintoaatsapphirespecimen.Theassumptionisthatthereisnegligibledisplacementofthetipintothesapphiresubstratei.e.neitherelasticnorplasticdeformationsothatonlytheAFM-cantileverdeectionisbeingmeasured.TheInvOLSvalueiscalculatedbyttingalinetothecantileverdeection(measuredusingtheAFMphotodiode)versusverticalorZ-piezodisplacementoftheAFM.Thedisplacementcorrespondstoamountthatthecantileverisexing.Thistestwasperformed50times,andaGaussianttotheInvOLSmeasurementswasappliedinordertodetermineanInvOLScalibrationconstantof205.8nm/V.ThisisthenusedbythesoftwaretoproduceheightdataforAFMimagesandforspring-constantdetermination.TheAFMtip'sspringconstantwasdeterminedusingthethermal-noisemethod 72 ,whichisbuiltintotheAsylumResearchsoftware.TheAFMcantileverisapproximatedasasimpleharmonicoscillator,vibratingevenintheabsenceofaninputsignal.TheamplitudeofoscillationismeasuredacrossarangeoffrequenciesfromHztoMHz,andthecantileverresonancesareeasilyidentiablefromaspectraldensitycurve.Fromthiscurve,theresonantfrequencyisdenedastherstresonantpeakinthiscase,8.97 48

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Figure3-8. A)Spectral-densitycurveacrossafrequencyrangefrom10Hzto1MHzforasupersharpAC-modeAFMtip,measuredover10hoursintheabsenceofaninputsignal.Theresonantpeakisidentiedasthepeakat256kHz.InB),aLorentziancurveisttothepeak,fromwhichtheresonantfrequencyisdetermined. kHz.Usingtheequipartitiontheorem,thesoftwarethencalculatesthespringconstanttobe0.0208N/m,whichisjustwithinthemanufacturer'sspeciedrangeof0.02-0.05N/m.AspectraldensitycurveforadifferentAFMtip(ahigh-frequency,supersharpAC-modetip)isshownasanexampleinFigure 3-8 .OncetheAFMtipwascalibrated,threenanoindentertipswereimagedbyAFM,withtheindentertipsscrewedintoathreadedmountprovidedbyAsylumResearch,sothatthetipsfacedupwards(seeFigure 3-9 ).Thethreediamondnanoindentertipswereacube-cornertippurchasedfromAsylumResearch,andacube-cornerandconosphericaltip,bothpurchasedfromMicroStarTechnologies(Huntsville,TX).Thetipapexeswerefoundbyreectingaashlightoffofthetips'facets(forthecube-cornertips)oroffoftheroundedapex(forthecaseoftheconosphericaltip)untilthereectedlightwascenteredbeneaththeAFMtip,asseenfromtheAFM'sbuilt-inopticalmicroscope.TheAFMtipwassubsequentlyengagedontothenanoindentertip,atwhichpointAFMimagesoftheindentertip'sfacetsweretaken.Inthecaseofthepyramidaltips,thescanareawastranslateduntilanedgewasfoundandtheedgewas 49

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Figure3-9. A)Aphotograph,andB)anoptical-micrographofacube-cornernanoindentertip,mountedsuchthatthetipfacesupwards.TheunitsinA)aremm. trackedupwarduntiltheapexwaslocated.Fortheconosphericaltip,thescanareawastranslatedupthetipuntiltheapexwaslocated.ThedefaultscanningdirectionintheAFMsoftware(0)correspondstothefast-scanaxisoftheAFMtipbeingparalleltothecantileveralongitslength.InordertopreventcrashingtheAFMtipintothenanoindentertip'ssurfacewhichcanbecausedwhentheslightly(~15)declinedAFMcantileverbombardstheinclinednanoindentertip'ssurfacethescanningdirectionwaschangedto90.Inaddition,AFMscanwindowswerenolargerthan1minsizeuntiltheapexwasreached.Theseconditionsresultedinaslow,butsafe,proceduretolocatetheapex.AtomicforcemicrographscorrespondingtothesethreetipsareshowninFigure 3-10 .Inthecaseofthecube-cornertipfromAsylumResearch,debristhathadaccumulatedonthetipsurfaceinpreviousindentationexperimentswasvisibleintheAFMimages.Thetipwastherefore`cleaned'bymanuallyloweringaatpolystyrenespecimenontothetipseveraltimes,soastocreateseverallargeindentationsthatwouldpushthedebrisawayfromtheapex.Thespecimenusedforthisapplicationwastheoutsideofastandardsamplebox,cleanedwithethanolanddriedwithclean,compressedair.ThedifferencescanbeseenbycomparingFigure 3-10 CandD. 50

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Figure3-10. Contact-modeatomicforcemicrographsofdiamondnanoindentertips:A)aconosphericaltip,B)acube-cornertipfromMicroStarTechnologies,andacube-cornertipfromAsylumResearch,C)beforeandD)aftercleaningit.Thelargerimagesareheightimages,withthesameverticalscale(right);theinsetsarethecorrespondingdeectionimages,scaleddifferently.Toaidtheeye,pyramidswithequilateral-trianglebasesaresuperimposedoverB)andD);extrafacetsarehighlightedinred. 51

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Unusualextrafacets,deviatingfromtheidealtipgeometries,wereobservedfortwooftheindentertips.Thesemaybeattributedtoerrorsingrindingnearthetipapexes.TheAFMimagesinFigure 3-10 showconstant-heightcontours,whichhelponeseethatactualcross-sectionshapeforagivendepth.TheextrafacetsinFigure 3-10 BandDareindicatedwithreddashedlines,andtheidealgeometries(equilateral-triangularcrosssections)aresuperimposedovertheseimages.Thenominalradiiofthetipsweremeasuredtobeapproximately65nm,85nm,and120nm,fortheAsylumcube-corner,MicroStarTechnologiescube-corner,andconosphericaltips,respectively.BecausetheAsylumcube-cornertipwasthesharpest,itwasultimatelychosenfortheseexperiments.3.3.2PreliminaryNanoindentationsandSurfaceCharacterizationPriortomakingnanoindentationarraysforTEManalysis,theload-depthresponsewascharacterizedonGaAs(001).Allindentsinthisstudyweremadewiththecube-cornertippurchasedfromAsylumResearch.A~1cmx~1cmsubstratewascutfromann-type,Si-doped,epi-readyGaAs(001)wafer(AXT,Fremont,CA)usingadiamondscribe.ThesurfacewascleanedwithaCO2-snowgun,whichabrasivelybombardsthesurfacewithicecrystals,andsimultaneouslywithcompressedN2topreventcondensation.AsylumResearch'sAFMmodulecansimplybereplacedwithananoindentationmodule,whichconsistsofaexureandahousingforatip.Unliketraditionalnanoindenters,itusestheopticallevertechniquetomeasureforces,similartoanAFM 73 .However,insteadofreectingthelaseroffofacantileverwhichexeswhenaforceisapplied,thelaserisreectedoffofarigidmirrorchip,whichishinged,andpivotsasthenanoindenter'sexureiselasticallydeformed.Thenanoindenterwascalibratedpriortomakinganyindentsforthisexperiment.Afterloadingasapphire-balltipwitharadiusof>1m,thenanoindenterwaslefttothermallystabilizeformorethanonehour.The`virtualdeection'ofthetipwasthen 52

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calibratedbysweepingtheZpiezo10minair,withthesapphiretiploaded,andmeasuringtheresultingchangeinthedeectionsignal.ByttingalinetotheresultingdeectionversusZ-sensorcurve,andresettingthevirtual-deectionconstantusingtheslopeofthisline,theerrorduetotheverticalpositionofthetipwascorrected. Figure3-11. RepresentativeInvOLS-calibrationcurveforasapphire-balltiponasapphiresample.Thelinearityofthedeection-displacementcurveisanindicationthatonlytheindenter'sexure(aspring)isdeformingappreciably;otherwise,Hertzian-elasticorelastoplasticcontactofaroundtiponaatsurfacewouldproduceanonlinearresponse.Adeectionchangeof4Vcorrespondstoanindentationforceofapproximately10.7mN. ThenextstepwastocalibratetheInvOLSforthenanoindentermodule.Thisisdonebyindentingwiththesapphire-balltipontoaatsapphiresubstrate.SimilartotheInvOLScalibrationforAFM,theassumptionisthatthedisplacementofthetipintothesurfaceisnegligiblewhencomparedtotheexingofthespringinthenanoindentermodule.Forthecalibration,thesapphiretipwasindentedintothesurfaceatotalof100times.Thephotodiodeknobwasadjustedpriortothissuchthatthemeasureddeectionsignalwasapproximately)]TJ /F1 11.955 Tf 9.3 0 Td[(2Vwiththetipinair,andthetipwasindentedintothesurfaceuntilamaximumdeectionvoltageofapproximately+2Vwasreached,foratotalchangeinvoltageof~4V,andacorrespondingindentationforceof~10.7mN.ArepresentativeInvOLS-calibrationcurveisshowninFigure 3-11 53

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TheInvOLSvalueswerecalculatedbyttingalinefrom)]TJ /F1 11.955 Tf 9.3 0 Td[(1.0to+1.0V(correspondingtothelinearrangeoftheZpiezo)tothedeectionsignalversusdistance.Theuctuationofthe100calculatedInvOLSvaluescanbeseeninFigure 3-12 .Finally,anInvOLSvalueof724.84nm/VwasdeterminedbyttingaGaussiancurvetotheInvOLShistogram(Figure 3-12 A).ThisInvOLSvaluecorrespondstohowmuchthenanoindenter'sexureiscompressingforagivenchangeinphotodiodevoltage.Sincethespringconstantoftheexureisknowntobe3,814N/m(fromthemanufacturerspecications),theforcecansimplybedeterminedbymultiplyingspringconstantbytheamountitwascompressed.Ifonenowwantstocalculatetheindentationforce,thefollowingequationcanbeused:P=VkInvOLS,(3)wherePistheindentationload,Visthechangeinvoltage(deection)measuredbythephotodiode,andkistheexure'sspringconstant.UsingthepresentcalibrationconstantsandEquation 3 ,achangeof1Vcorrespondstoaloadof(1V)(3.814N/nm)(724.84nm/V),or2,765N.OncetheInvOLSwascalibrated,thesapphire-balltipcouldberemoved,andthesapphiresubstratewasreplacedwiththeGaAs(001)sample. Figure3-12. A)ScatterplotandB)histogramusedforcalibratingthenanoindenter'sInvOLS.Thisrelatesthemeasuredchangeinvoltageofthephotodiodetothedeformationoftheexureinthenanoindenter.AGaussiantwasappliedtothehistogram,resultinginanInvOLSvalueof724.84nm/V. 54

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InordertocreateamicroscopicallyvisiblefeatureontheGaAssurface,athree-sideddiamondBerkovichindentertipwithanaxis-to-faceangleof65.3wasloadedintothenanoindenter.Thistipwasusedtomakea0.5-mmscratchintothesamplewithanormalforceof~8mN,anda45mx90marrowheadwasinscribedattheendoftheexistingscratch(Figure 3-13 )usingtheAFMsoftware'slithographytool.Subsequently,theBerkovichtipwasreplacedwiththediamondcube-cornertip(axis-to-faceangleof35.3)fornanoindentation,andthesystemwasallowedtoequilibratethermallyformorethan2hours.ByusingthededicatedBerkovichscribingtiptomakescratcheswhicharelargeenoughtobeseenwithouttheassistanceofamicroscope,unnecessarywearofthesharp,cube-cornertipwasavoided. Figure3-13. Opticalmicrographshowingthearrangementofcube-cornernanoindentationarrays,indicatedbyalargearrow(~550-mlong),inscribedintothesurfacewithaBerkovichtip.Regions1,2,and3eachcontainfourredundantarraysofindents,withalignmentmarkersoneithersideofeacharray. 3.3.3NanoindentationArraysAsummaryoftheparametersfornanoindentationarraysonGaAs(001)aretabulatedinTable 3-1 .Arraysofnanoindentationsweremadeatloadsof50,250,and1,000N,withspacingsof250,500,and1,000nm,respectively,betweenindentrowsandcolumns.Foreachindentation,theapproachandretractrateswere50nm/s,andthetriggerforce(therelativeincreaseinloadwhichdenesthezeropointofindentation) 55

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Table3-1. ParametersforGaAs(001)NanoindentationArrays. ArrayLoad(N)hf(nm)Load-Unload(s-s)mnl(m)a,b(nm)nh A50~91-1=234512112502.31B250~502-15298142.45C1,000~1105-19134121,0001.90 was3N.Theindenterwasoperatedinloadcontrol;oncethetriggerwasreached,theloadwasincreasedataconstantrateuptothemaximum,andunloadedataconstantrateuntilreleasingfromthesubstrate,withnoholdsegmentatthemaximumload.DuetothesoftwarelimitationsdiscussedinAppendixA,onlycertaincombinationsofrowsandcolumnswereallowed.Ultimately,thisresultedinrotatingatall,narrowarrayby90plussomesmallrotationangle,insteadofrotatingalong,shortarraybyjustthesmallrotationangle.Theanglesreportedherearejustthesmallangle,withthe90alreadyhavingbeensubtracted.TherotationangleswerechosensuchthattheFIBcrosssectionwouldcrosseachrowapproximatelytwice(nh2).Thiswasaveryconservativevalue,becausetheidealnumberofrowscrossedwouldbeexactlyone.ThehigherrotationanglewaschosenincasealignmentintheFIBwasfoundtobedifcult,oriftheFIBmillingandlift-outprocedureweretotruncateeachendofthearrays.ThespacingbetweenindentswaschosentobeapproximatelythreetimestheindentwidthmeasurebyAFM.Asummaryoftheorderofproceduresformakingtheindentarraysisasfollows: 1. CalibratetheindenterInvOLSwithasapphire-balltiponsapphire. 2. Replacethesapphiretipwithadiamondthree-sidedBerkovichtip,andreplacethesapphirecalibrationsamplewiththeGaAssample. 3. Scribealarge(>0.5mm)arrowintotheGaAssurface,pointinginthe+Xdirection. 4. ReplacetheBerkovichtipwithadiamondcube-cornertip. 56

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5. Translatethestage150mintheXdirection,and-40mintheYdirectiontocenterthetipinfrontofthearrow.(PrevioustestingshowedthatthisYdisplacementaccountsforanoffsetbetweentheBerkovichandcube-cornertips'axes.) 6. Makefourredundantindentarrays(RowCinTable 3-1 )withinthelimitsofthenanoindenter'spiezorangeof90m,spaced24-mapart. 7. Makealignmentmarkersoneithersideofeacharray,atloadsof2,000and500N,spaced24-and20-apart,respectively. 8. Translatethestage60mintheXdirectionforthenextregionofindentarrays. 9. Repeatsteps6-8fortheothertwosetsofarrays(RowsBandAinTable 3-1 ).Aftermakingthepatterns,eachonewascharacterizedviaAFM.AFMimagingwasperformedusingonlysupersharp,non-contact-modeSitips,withnominaltipradiispeciedas2nm(e.g.partnumberSSS-NCHR-10,NANOSENSORS,Neuchatel,Switzerland).Experienceshowsthatthesetipsfracturereadily,socarewastakentoreducethetip-sampleinteractionasmuchaspossible.Notypicalscanrateorvelocitywasused;thisgenerallydependedonthescan-windowsizeandmaximumpeak-to-peakfeatureheight.Imagesofindentationrowswerecollectedwithnon-squarescanwindows,suchas32x8m.Thissavedtimeandpreventedunnecessarytipwear.3.3.4InsituFIBLiftOutsTEM-specimenpreparationwasperformedusingaStrataDB235dual-beamFIB/SEM(FEI,Hillsboro,OR)withaliquid-metalgalliumionsource,intheUniversityofFlorida'sMajorAnalyticalInstrumentationCenter(MAIC).TheDB235anditsworkstationareshowninFigure 3-14 .Theinstrumenthasaverticalelectroncolumnwithaeld-emissiongunastheelectronsourceforinsituSEM.Anioncolumnisorientedata52anglewithrespecttotheelectroncolumn,andemitsGa+ionsfromaliquid-metalionsourceforimaging,milling,depositingPt,andweldingwithPt.TheOmniprobeinsitumicromanipulaterisdirectlybuiltintothechamber,andhasmotorizedX,Y,andZtranslation,whichiscontrolledfromtheuserworkstation.Thechambersitsonavibration-isolationtable. 57

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Figure3-14. DB235dual-beamFIB/SEM.Theelectronandioncolumnsaresituated52withrespecttoeachother,andaredesignedsuchthatthebeamsintersect.TheOmniprobeemphinsitumicromanipulatorisalsobuiltintotheinstrument. Duetothedestructivenatureofhigh-energyGa+ionsbombardingthesurfaceofGaAs,itwasimportanttoprotectthenanoindentedregionspriortoexposingthemtotheionbeam.Inearlytrials,thiswasachievedbydepositingprotectivePtcapsovertheregiontobeliftedout,usingtheelectronbeam,nottheionbeam.However,electron-beamdepositionofPtisseveraltimesslowerthanion-beamdeposition.Whiletheelectron-beamdepositionrateofPtcanbeincreasedbyreducingtheacceleratingvoltage 74 andincreasingthebeamcurrent(i.e.increasingthespotsize),thetimerequiredtocreateevenathin(~100nm)protectivecapwasapproximately30minutes,whichwasdeemedtooslowconsideringthenumberofarraystobeliftedout.Ultimately,itwasdecidedthatcoatingtheentiresamplepriortousingtheFIBwasabetteroption.Inallexperimentsreportedinthisdissertation,sampleswerecoatedwithaprotectivelayerofCintheMAICfacility,priortoFIBliftouts.ForGaAs(001),the 58

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carbon-lmthicknesswasapproximately80nm.Thecaveatwiththisprocedurewasthatsinceanentiresamplewascoveredwithathinlm,itcouldnotbeusedagainforfutureindentationarrays. Figure3-15. SamplemountingintheFIB.AnaluminumdualsampleholderinA)wasusedtomountboththeGaAs(001)sampleandaTEMgridparticularlydesignedforinsituliftouts,madebyOmniprobe.MagniedimagesoftheOmniprobegridareshowninB),C),andD).ArecessededgeintendedforprotectingmountedspecimensisindicatedbyaredarrowinD). Thepatterned,carbon-coatedGaAs(001)samplewasmountedtoastandardSEMpin-typespecimenholderusinganadhesive,electricallyconductivecarbontab.Thespecimenholderwasmountedtoadualsampleholderfabricatedinhousefromanaluminumblock,asshowninFigure 3-15 A.ThedualsampleholderwasmadesothatbothaTEM-gridholderandthemountednanoindentedsamplecouldbeplacedintheFIBchamber,withbothcomponentsutilizingpin-typeSEMmountsforeasyexchange.Thepinmountswerefastenedtothedualsampleholderusingsetscrewsintappedholes.ThecenterholeinFigure 3-15 Acontainedapinthatprotrudedbeneaththedualsampleholder(hiddenfromview),whichwasusedformountingtheentireassemblyontotheFIBstage.AllpartsofthecustomholderwerecleanedbysonicatingtheminethylalcoholpriortoinsertionintotheFIB'svacuumchamber.AnopticalmicrographofasingleOmniprobeINLOTEM`grid'(OmniprobepartnumberGRD-0001.01.0) 75 isshowninFigure 3-15 C.Figure 3-15 BshowshowtheTEMgridissituatedinitsholder(holderpreviouslysoldbyOmniprobe 75 ).TheoutsidediameteroftheTEMgridisapproximately3mm,whichisthestandardsizeof 59

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aconventionalTEMgrid,soitisdesignedtotintoastandardTEMgoniometer.Thecenterpillar,`B,'isintendedforside-mountedINLOspecimens,whilethepillars/anges`A'and`C'aredesignedformountingINLOspecimensinaV-shapedgroove.Allpillarshavearecessededge(indicatedintheSEMimageinFigure 3-15 D)toprovidedasafelocationformountingalifted-outcrosssection;thisprovidessomeprotectiontopreventthelifted-outcrosssectionfromcontactingasurfaceif,forexample,thegridisdroppedonitsfrontfaceduringhandling. Figure3-16. ScanningelectronmicrographstakenwithintheFIBchamber,showingthepreparationofacrosssection(foil)tobeliftedout:A)arotatedindentarrayissituatedbetweenalignmentmarkers;B)andC)aprotectivePtcapisdepositedontopartofthearray;D)andE)trenchesareion-milledaroundthePtcap;andF)thecrosssectionismilledtoathicknessof~1.5m.ThedashedlinesinF)outlinetheapproximatelocationofthepre-releasecutsmadepriortotheliftout.Insetsdepictrespectivecrosssectionsviewedfromtheside. OncethedualsampleholderwiththeattachedGaAs(001)sampleandTEMgridwereloadedinthetheFIB,thechamberwasevacuatedtoapressureof<810)]TJ /F7 7.97 Tf 6.58 0 Td[(5 60

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mbar.Next,theelectronandionbeamswereturnedon,thePtgasinjectionsystemwasheatedto40C,andthesurfacewasscannedwiththeelectronbeamuntilthepatternedregionwaslocated.Acceleratingvoltagesforelectronandionbeamswere15kVand30kV,respectively.Atthispoint,theeucentricheightwasfound,andthestagewastiltedto52fromthevertical,sothattheioncolumnwasnormaltothesurface.Theeucentricheightisthestageheightwhichcorrespondstotheaxisofrotationbeingsimultaneouslycoincidentwiththesurfaceofthesampleandtheelectronorionbeam.Infact,thebeamswerealreadyalignedtointersectattheeucentricheight,sothesamestageheightservedastheeucentricheightforbothbeamsatonce.Thismeantthatthestagecouldbetiltedaboutapointonthesurfacewhilemaintainingthepointinthecenteroftheimage,andkeepingthesamefocaldistance,forbothbeams.SnapshotsofdifferentstagesoftheFIB-lift-outprocessofrotatednanoindentationarraysaredetailedinFigure 3-16 ,forloadsof1,000NinGaAs(001).Inthisgure,allimagesareelectron-beamimages.Thestagewastiltedsuchthattheioncolumnwasnormaltothesamplesurface.Thustheelectron-beamimagesweretakenfromabird's-eyeview,at52fromsurfacenormal.Thearraywasrstbroughttothecenteroftheimage,andthestagewasrotatedsothatalinebetweenthealignmentmarkerswashorizontalintheion-beamimage.Thealignmenterrorwastypically0-2afterthisalignment.Subsequently,anerrotationwasappliedbyadjustingtheionbeamscandirection,resultinginamisalignmentoflessthan0.1.Thisguaranteedthatthelifted-outcrosssectionwouldintersecttheindentarrayattheproperangle.Thenextstepwastodepositathin,protectivePtstriporcapovertheregiontobeliftedout,showninFigure 3-16 B.Thisprocessinvolvesbringingavapor-phasePt-containingorganiccompoundincloseproximitytotheregionofinterestwithinthevacuumchamber.ThePt-containingmoleculesareadsorbedontothesamplesurface,andaredissociatedbythebeam(ionbeam,inthiscase).Ptatomsarethenadsorbedontothesurface,andmuchoftheorganicmoleculeisdesorbed.ThepurityofPtinthe 61

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depositedlmincreaseswithincreasingbeamcurrent 76 77 ,Therearetwocompetingmechanismsaffectingtheion-beam-induceddepositionrateofPt:depositionandsputtering(ormilling) 74 .Dependingonthemillingrateofthesurfacematerialandotherfactors,itispossibletomillawaymorematerialthanisbeingdeposited.Inthisresearch,itwasfoundthation-beamdepositionwasdestructiveduetosputteringoftheGaAssurfacewhenthebeamcurrentwasatorabove300pA,butwasnotdestructivetoalready-depositedPtat300pA,andthedepositionratewasseveraltimesfaster.Thusinitialdepositionwasperformedatalowercurrentofapproximately50or100pA,untilaheightof~250nm(Figure 3-16 B);thebeamcurrentwassubsequentlyincreasedto300pAforanother~1ofPt(Figure 3-16 C).ThePtcap'scrosssectionwasarectangularshape,approximately1.5wideby20-30mlong,dependingonthelengthoftheindentarray,andwasmadeparalleltothealignmentmarkers.Itshouldbenotedthatthetruebeamcurrentdependsontheaperturesize,whichincreaseswithuse,becausetheionbeamerodestheapertureandtherebyincreasesitsdiameter.Thereportedbeamcurrentcanthereforebetreatedasalowerbound.Next,staircase-shapedtrenchesweremadeoneithersideofthePtcapwitha5,000-pAaperture,usingtheFIBsoftware's`regularcrosssection'feature(Figure 3-16 DandE).Thistakeslesstimetomillthanremovingablockofmaterialintheshapeofarectangularprism.Thisstaircasefeaturewastypicallymade6mwide,~6-8mdeep,andlongerthanthePtcapbyabout0.5mononeside,and2-3montheoppositeside,whichaidedinthelift-outprocesslater.Atthispoint,thecrosssectionwas2-3mthick.Itwasthinneddowntoa1-1.5mthicknesswithsuccessivelylowerbeamcurrents(3,000pAand1,000pA)priortotheliftout(Figure 3-16 F).Next,thestagewastiltedto45relativetotheionbeam(7relativetotheelectronbeam),andpre-releasecutsweremade(Figure 3-16 F)suchthatthemilledcrosssectionwasonlyattachedbyasmallbridge.Theremaininginsitulift-outprocedures 62

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Figure3-17. Ion-beamimages(withtheexceptionofE))detailingtheinsitulift-outprocessusedherein:A)anL-shapedprereleasecuthasbeenmadetothefoilfromFigure 3-16 F,andanOmniprobemicromanipulatorisbroughtintocontactonthefarsidefromwherethefoilisstillattachedtothesubstrate;B)themicromanipulatorisweldedtothefoilwithPt;C)thefoilisreleasedbymillingawaytheremainingconnection,andthestageisloweredto`liftout`thefoil;D)andE)thefoilispositionedrelativetopillarBfromFigure 3-15 C;F)thefoilisweldedtothepillarwithPt;G)theOmniprobeisdetachedfromthefoil;H)themicromanipulatorisretracted;I)fromtopview,nalthinningto1m,inJ),isperformedwiththeionbeam.Thescalebaris10m,unlessotherwisespecied. 63

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areshowninFigure 3-17 .Allimagesinthisgureweretakenwiththeionbeam,exceptforE.Withthestagebacktoa0tilt(electronbeam),abuilt-inmicromanipulatorfromOmniprobewasgentlybroughtintocontactwiththefreeendofthecrosssectionandweldedtoitwithPt,usingtheionbeamanda100-pAaperture(Figure 3-17 AandB).Theendofthespecimenthatwasstillconnectedtothesamplewascutawaywiththeionbeam,andthespecimen,nowattachedonlytothemicromanipulator,wasliftedawayfromthesample(Figure 3-17 C).Thiswasactuallydonebymanuallyloweringthestageheight,notbyraisingthemicromanipulatorwithitsmotorizedcontrols,becausetheytendtohavesomehysteresiswhichcausesunpredictablemovementsandpossiblecollisionduringliftout.ThestagewasthenmovedsothatapillarontheTEMgridwasbroughttotheeucentricposition,andthelifted-outspecimenwasbroughtintocontactwiththepillar(Figure 3-17 DandE.Thespecimenwasthenweldedtothepillarat100pAandfollowedby300pA(Figure 3-17 F),andtheOmniprobemicromanipulatorwasreleasedfromthespecimenusingtheionbeam(Figure 3-17 G).Alow-magnicationviewinFigure 3-17 Hshowsthelifted-outspecimenattachedtothepillar,themicromanipulatoronthetoprightoftheimage,andpartofthePtnozzleonthetopleftoftheimage.Finally,thestagewasagaintiltednormaltotheionbeam,andthespecimenwasthinneduntilthePtcapwasalmostcompletelyeroded,usingprogressivelylowerbeamcurrentsof300and100pA(Figure 3-17 IandJ).3.3.5TransmissionElectronMicroscopySubsurfaceimagingwasperformedusingtwoTEMsintheMAICfacility:a2010Fanda200CX(JEOL,Tokyo,Japan).Inbothcases,theacceleratingvoltagewas200kV,andallimagingwasperformedalongthe[110]zoneaxisusingtwo-beambright-eldimagingwith)777(!g=[002]or[220].Althoughthe2010Fiscapableofhigh-resolutionTEMimages,the200CXhasanadvantageinimageacquisitionduetoamanualtiltingof 64

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thegoniometer,whichisusefulwhensmalltiltadjustmentsarenecessarytoreducebending-contourartifacts.3.3.6Post-ProcessingofElectronMicrographsPost-processingoftheTEMimageswasperformedusingthesoftwarepackagesImageJ 78 ,Amira(VisualizationSciencesGroup,FEICompany),andalsoMSPowerPoint.FulldetailsoftheImageJandAmiraproceduresareprovidedinAppendixB.Asummaryisgivenbelow.InitialimageprocessingwasperformedusingImageJanalysissoftware.XTEMimageswererotated,cropped,andbrightnessandcontrastwereadjusteddigitally.Consecutiveimageswerethenstacked,andGaussianblurswereusedtoeliminateisolatedbrightordarkpixels.Subsequently,theimageswerepreparedfor3Dvisualizationasfollows,dependingonthesoftwareused.Forpreliminary3DimagesinImageJ,thresholdingandimagemultiplicationwereemployedsuchthatthegrayscalewaspreservedinthedislocatedregions,whileotherregionsweremadeblack.Imageswerethenscaledinthethicknessdirectionaccordingtotheverticalindentspacing,dsin().Next,astackofimageswasprojectedin3D,treatingblackpixelsastransparent,andimageswereblurred(1-2pixels)inordertosmoothtransitionsbetweenimagelayers.Finally,differentcoloringschemeswereappliedtoenhancecontrast.For3DimagesinAmira,backgroundsubtractionwasusedtofurtherremoveartifactssuchasbendingcontours,andnallytheimageswereinverted.TheresultswereloadedintoAmira,andtheboundingboxwasscaledtogivetheappropriateslicethickness,asabove.TheVolrenfeaturewasusedforcreating3Dimages.Afterthis,colorschemesandlightingwasadjustedmanually.MSPowerPointhasaveryuseful`RemoveBackground'feature,whichwasemployedwhen`stitching'togetheradjacentimages.(Theseimageswerenotactuallymergedtogether,butwereratheroverlappedmanually.) 65

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3.4ResultsandDiscussionofGaAs(001)Samples3.4.1PreliminaryNanoindentationsandSurfaceCharacterization Severaloverlappingnanoindentationload-displacementcurves,withmaximumloadsrangingfrom10Nto2mN,areshowninFigure 3-18 .Theloadingsegmentsaresmooth,withnopop-inevents,andoverlapwellwithoneanother.Itshouldbenotedthatbecauseaforcetriggerof3Nwasusedtoindicatethebeginningoftheindentationloadcycle,anindentationwithadesignatedmaximumloadof10Nactuallyhasatruemaximumloadofapproximately13N.Therepeatabilityoftheload-displacementresponseisindicativeofahighlyuniformsample. Figure3-18. Overlappingload-displacementcurvesforpreliminarynanoindentationsonGaAs(001).Loadingandunloadingcurvesareallsmooth,withnopop-inorpop-outevents,andtheloadingsegmentsoverlapwell.Fromtheshallowestindentsintheinset,itcanbeseenthatplasticdeformationoccursformaximumloadswellbelow20N. 66

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TwotypesofAFMtipsanddifferentoperatingmodesweretestedformetrologyoftheindents'surfaceproles:asupersharptip(mentionedpreviously)inbothcontact-modeandnon-contact-modeoperation,andanall-diamondtipwithaverylowstiffness(<0.05N/mstiffness,partnumberND-CTIR1-4,AdvancedDiamondTechnologies,Inc.,Romeoville,IL)incontactmodeonly.Theadvantageofthediamondtipisthatitisextremelystableduetodiamondbeingveryhard,chemicallyinert,andhavingalowcoefcientoffriction;theextremelylowspringconstantalsomeansthetheforcesimpartedonthesamplearelow,evenrelativetootherAFMtips.ThenormalforceexertedonthesurfacebytheAFMtipcanbecalculatedbymultiplyingtherelativevoltageappliedwhileimagingbytheInvOLSvalueandthespringconstant.Forthediamondtipincontactmode,thenormalforceis(1.0V)(205.8nm/V)(0.02084nN/nm)4.3nN.Forthisparticularsupersharptipoperatingincontactmode,thisis(0.1V)(81.3nm/V)(14.66nN/nm)119nN.Thusthediamondtipexertsaforce1-2ordersofmagnitudelowerthanthatofthesupersharptipincontactmode.Itsmajordisadvantageisitstipradiusof15-30nm(manufacturerspecied).SelectedAFMimagescorrespondingtothesethreecombinationsoftipsandimagingmodesareshownforscansofthesameindentinFigure 3-19 A,B,andC,withrespectivelineprolesthroughtheshallowestpixelineachimageinD,E,andF.InFigure 3-19 A-C,onecanobservethattheAFMimagesproducedbythesupersharptiparesmoother,whereastheimageobtainedwiththediamondtipisslightlystreaky.Thiswasatrendobservedforthesmallestimagescansizes(~1N),evenwhentestingwithdifferentscanningparameters,suchastheappliedforce/voltagesetpoint.Thetipradiusof15-30nmwasalsoobservedtoaffectthemetrologyoftheshallowestindentfeatures,whosedepthsweregenerallymeasuredtobelesswiththistipthanwiththeothertwotips. 67

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Figure3-19. Comparisonof1-mAFMimagesandlineprolesofthesame50-NnanoindentonGaAs(001),takenwithdifferenttip/imaging-modecombinations:A)andD)supersharptip,ACornon-contactmode;B)andE)supersharptip,contactmode;andC)andF)diamondtip,contactmode. Figure 3-19 showsacomparisonofresidualdepthsmeasuredbyAFMforonlyoneindent.InFigure 3-19 A,depthsformultipleindentsarecomparedforthethreedifferenttips/modes,normalizedtothenaldepthmeasuredbyindentation.Ingeneral,forultralow-loadindents,thediamondtipandthesupersharptipinACmodeproducedepthvalueslowerthanthesupersharptipincontactmode,andallproducedepthslowerthanthemeasureddepthfromtheload-displacementcurve.Thismightreasonablybeattributedtoartifactsduetomeasuringverysmallimpressions.Duetoelasticrecoveryoccurringinbothverticalandlateraldirections,theacuityoftheresidualindentimpressionmaydifferforindentsofdifferentsizes,evenwhenmadewiththesameindentertip. 68

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Figure3-20. ComparisonofresidualdepthsmeasuredbyAFMandnanoindentation:A)AFMdepthswiththreetipsnormalizedtothemeasuredindentationnaldepths;andB)log-logplotcomparingAFMdepthsmeasuredwiththesupersharptipinACmodewiththatmeasuredbyindentation. Thediamondtipproduceswhatislikelyanerroneouslysmallmeasureoftheindentdepthforthecaseoftheshallowestindent(Pmax=10N,hf3nm.Itisalsopossiblethatsomeplasticdeformationisrecoveredaftertheindentismadeinthecaseofthelowest-loadindents,duetoaplasticzonethatisnotfullydeveloped,anddislocationsthatremainnearthesurface,whichthenrelaxwithinminutesaftertheindentationloadisremoved.Lilleoddenetal.previouslyobservedthistooccurforsub-100-NindentsinGaAs,usinginsituimagingwithananoindentertip 79 .InFigure 3-20 B,indentationdepthsareplottedinadifferentwaytocomparethedepthsmeasuredfromtheload-displacementcurvewiththosefromtheAC-modeAFMimages,onalog-logplot.Itcanbeobservedthattheindentdepthsmeasuredfromtheload-displacementcurvesagreereasonablywell(usuallywithin10%)withtheAFMdepths,forloadsabove~50N(depthsabove~9nm).Thusfutureindentationdepthswillbereportedasthatmeasuredfromtheload-displacementcurve,asinFigure 3-18 .Onemoreimportantobservationwasthatthestiff,supersharptipactuallycreatedgougesontheGaAssurface.Withatipradiusof<2nmandarelativelylargenormalforcewhenscanning,theSitipleftbehindarectangularregionoflowerdepththan 69

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thesurroundingsurfaceaftercollectinganimage.ThiswasnoticedinsomecasesafterreplacingtheAFMtipandre-imagingthesameindents.Theimagequalityalsoseemedtodegraderelativelyquickly,indicatingthatthetipwasalsobeingbluntedduringimaging.Consideringtheabove,asupersharptipwasusedinnon-contactmodeforcollectingtheremainingAFMimages.3.4.2NanoindentationArrays Figure3-21. AtomicforcemicrographsofnanoindentationarraysonGaAs(001),withmaximumindentationloadsof50NinA)andB),250NinC)andD),and1,000NinE)andF). SelectedAFMimagesofnanoindentationarraysonGaAs(001)areshowninFigure 3-21 .Notethatthe[110]directionisapproximatelyalignedwiththeverticaldirectionoftheimages.Theaveragesurfaceroughnesswasmeasuredtobe0.19nmand0.15nmfromsquareAFMwindowsizesof1mand5m,respectively.Thisverysmooth 70

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surfaceisindicativeofahighlyuniformsample,andthesimilarityoftheindentsineachAFMimagequalitativelysuggestthattheindents'sizeandshapewasveryrepeatable.TheimagesinFigure 3-21 C-Fshowmaterialpileuparoundtheindents,indicatingplasticowupwards,aroundtheindentertip,duringindentation.Thisistypicalfornanoindentationsinmaterialsthatdeformplastically,andisanindicationthatthematerialisnotworkhardeningappreciablyduringindentation 80 81 .AsseeninFigure 3-21 C,therearenoalignmentmarkersforthisarray.Thiswasamistake;thestagewasmovedbeforemakingthealignmentmarkers,andbythattimeitwastoolatetomovethestageback,duetohysteresisinthestage.However,thiswasnotaproblem,becausethealignmentmarkersfromanotherregioncouldbeusedtoalignwiththepropercrystallographicdirectionintheFIB,andthentheFIBstagecouldbetranslatedtothispattern.Fortunately,theseindentswerelargeenoughtobediscerniblebytheFIB/SEM.3.4.3TEMResults Figure3-22. Threestitchedbright-eldtransmissionelectronmicrographsof50-NnanoindentationsinGaAs(001),viewedalongthe[110],with)777(!g=[002]. Figure 3-22 showsthreestitchedbright-eldtransmissionelectronmicrographsof50-NnanoindentationsinGaAs(001),viewedalongthe[110]directionwithatitleconditionof)777(!g=[002].Eachofthesevenfeaturescorrespondtoadifferentsegmentofanindentationplasticzone.Whilethisgureonlyshowssevenindent'splasticzones,therewereactually37containedinthespecimen.TheindentcentersinFigure 3-22 arespaced250-mapart.UsingEquation 3 ,withanarrayrotationangleof3,theshiftawayfromanindent'scenterfromonefeature 71

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tothenextinFigure 3-22 is250nmsin(3)13.1nm.Thusthesevenfeaturescoveradistanceofapproximately80nm,notaccountingforthewidthofthespecimen. Figure3-23. Transmissionelectronmicrographsof250-NnanoindentationsinGaAs(001),viewedalongthe[110]:A)stitchedimagesofallindentationsinthespecimen;andB-D)magniedviewsofindividualindents. Figure 3-23 Ashowsastitchedimageofallplasticzonesforthe250-NindentsinGaAs(001).Theimagesinthisgurearealsobright-eldTEMimageswitha[110]beamaxisandtiltedto)777(!g=[002].Withindentsspacingsof500nmandanarrayrotationof5,theshiftfromoneindenttothenextiscalculatedtobe43.6nm.ThemagniedimagesinFigures 3-23 B,C,andDcorrespondtosegmentsofplasticzonesapproximately240,110,and20nmoff-center.StitchedimagesoftheGaAs(001)specimenwith1,000-NindentsareshowninFigure 3-24 ,withthesameimagingconditionsastheothers.Theseimagesareconsiderablynoisier,probablyasaresultofspecimenthickness.Theseparationbetweenindentshereis1m,andthearrayrotationangleis9,correspondingtoashiftof156.4nmfromoneindenttothenext.Duetotherotationanglebeinggreaterthanwasnecessarytoincludeonefullrowofindents,onecanseethatthecentersoftwoindentsfromadjacentrowsare 72

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Figure3-24. Stitchedtransmissionelectronmicrographsof1-mNnanoindentationsinGaAs(001),viewedalongthe[110]. includedinthisspecimen(i.e.thethirdandninthplasticzonesinFigure 3-24 .Theseareseparatedbysixspacingsof1,000nminthisspecimen.Wealsoknowthattheseindentswereoriginallylocatedonrowsspaced1-mapart(b=1minFigure 3-2 B).Asmentionedabove,theshiftawayfromanindent'scenterfromonefeaturetothenexthereisapproximately156.4nm,sosixshiftscorrespondstoapproximately940nmintheYdirectionbetweenthesetwofeatures.Thisis60nm,or6%,lowerthantheactualrowspacingof1,000nm,anerrorwhichcouldeasilybeaccountedforbythethicknessoftheTEMspecimenbeinggreaterthan60nm.3.4.43DReconstructionsofGaAsIndentsA3DreconstructionofsegmentsofindentationplasticzonesfromTEMimagesof50-NindentsinGaAs(001)isshowninFigure 3-25 ,orientedatrotationsof0,30,60,and90.ThesereconstructionswerecreatedusingImageJ,withthe`Fire'coloringscheme.Thecolorsdonothaveameaningofanysignicance.Thismethodofreconstructingplasticzones(i.e.usingImageJ)wasfoundtobelimiting,becauseitonlyallowsveryspecicrotations,notransparencyadjustments,andno`surface'reections.ThecommercialsoftwarepackageAmirawasthereforeemployedtoproducehigher-quality3Dimages.Amiraisaprogramthattomographicallygenerates3Dvolumesandsurfaces,andhasbeenusedfortheFIB/SEMserial-sectioningtechnique 40 82 .SeveralAmira-generatedimagesareshowninFigure 3-26 .Figure 3-26 Aisabird's-eyeviewofa3D-reconstructed250-Nindent'splasticzone,withacorrespondingAFMimagesuperimposedontothetopsurface.InFigure 73

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Figure3-25. ImageJ-produced3DreconstructionofananoindentationplasticzonefromTEMimagesof50-NindentsinGaAs(001),rotatedatA)0,orthe[110]direction,B)30,C)60,andD)90,orthe110direction. 3-26 B,threeofseventeencrosssectionsareshownwithnothickness,usingtheOrthoslicefeatureinAmira.Figure 3-26 CandDshowtherepresentativeplasticzonefromthe[110]and110directions(or0and90rotations).TheultimateresolutionofthismethodisbasedonthethicknessoftheXTEMspecimenandtheshiftfromcenterfromoneindenttothenext.Theshiftiswhatdenesthethicknessoftheslicesinthe3D-reconstructedimage,andalthoughAmirahasasmoothingalgorithm,onecanstillmakeoutdifferentslicesintheimageinFigure 3-26 D.However,theoverallshapeoftherepresentativeplasticzonecanbeclearlybeseen,inawayneverbeforebeenexperimentallydemonstrated.Itshouldbenotedthatthesizeoftheplasticzoneforthis250-Nindentisontheorderof0.5m,i.e.muchlargerthanthethicknessofasingleTEMspecimen,andyetTEMcanbeusedtovisualizethisstructure.Reconstructionsof1,000-Nand50-NindentationplasticzonesareshowninFigure 3-27 A-CandD-E,respectively.TheimagesinDandEareanalogoustothoseinFigure 3-25 AandD,respectively.However,thebendingcontoursareresponsiblefor 74

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Figure3-26. 3Dreconstructionsofa250-NindentationplasticzoneinGaAs(001),producedinAmira:A)bird's-eyeviewwithanAFMimageofasimilarindentsuperimposedontothetopsurface;B)3(of17)selectedslicesdisplayedwithinaboundingbox;andperspectiveimagesfromtheC)[110]andD)110directions. thesmoothnessoftheoutlinedshapeinFigure 3-25 ,whichisbasedonTEMimagescollectedfromtwo-beamconditiontiltedto)777(!g=[002].Thebendingcontourswerelessvisiblewhentiltedto)777(!g=[220],andimagescollectedwiththisviewingorientationwereusedformakingthereconstructedimagesinFigure 3-27 D-E.Inthecaseofthe50-Nindents,dislocationswereconsistentlydeeperontheleftside.Thiscanbeobserved,forexample,inFigure 3-22 ,Figure 3-25 A,andalsoinFigure 3-27 DandE.FromtheAFMimagesinFigure 3-21 ,onecanseethatallindentslefttriangularimpressionswithonevertexfacingtotheright,andtheopposite(left)base 75

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Figure3-27. 3Dreconstructionsof1,000-and50-NindentationplasticzonesinGaAs(001),producedinAmira:A)andD)bird's-eyeviews;andorthographicprojectionsalongtheB)andE)[110],andC)andF)110directions. ofthetrianglebeingapproximatelyvertical.Theh110idirectionsintheseimagesaretheverticalandhorizontaldirections. Figure3-28. Molecular-dynamicsresultofananoindentationonGaAs(001),withapenetrationdepth<3nm.Dislocationloopsareobservedbeneaththeindent.ReproducedfromRef84withpermission. 76

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Anotherobservationisthatthepileupoccurspredominantlyalongthebasesofthetriangles,notnearthevertices,implyingthatupwardplasticowoccurredpredominantlyalongthesidefacesoftheindents.Themidpointofthetriangularimpression'sbasesarealsothepointofgreatesttensilestressforanindentationwithathree-sidedpyramid 83 .Oneexplanationoftheleft-side-dominantdeformationisthatdislocationactivitywasenhancedneartheleftface,whichwasnormaltoah110idirection,sinceGaAsdislocationsextendalongh110idirections 61 .Thebiaseddeformationismostexaggeratedinthecaseofthesmallest(50-N)indents,perhapsbecausetheplasticzonewasnotfullydeveloped.Atlargerloads,asthepressuredistributionbeneaththetipbecomesmoreregular,otherslipsystemsareactivated.Figure 3-28 showsamoleculardynamicssimulationofananoindentationofGaAs(001)fromtheliterature 84 .Theaxescorrespondtoh100icrystaldirections.Dislocationloopsareobservedbeneaththeindentertip,andareproducedatanextremelysmallload,likelyduetotheradiusoftheindentertipbeingmuchsmaller(sharper)thanthatoftipsusedinexperiments.Atomistic-simulationsizesandtimesarelimitedduetothecomputingresourcestheyrequire.Nevertheless,ifasimulationwerescaledtotheappropriatesize,theexperimentalresultshereincouldbeusedtovalidatethepredictivequalityofnumericalsimulations.Multiscalemodelingprovidesawaytoovercomethelimitationsofcomputationalresources 85 86 ,sothisisadirectionthatcouldbetakeninthefuture.3.4.5IndentationPlasticZoneNanoindentationplasticzonesareoftenassumedtotaketheshapeofahemisphericalcavity,followingthemodelofJohnseon 87 .Itiscommonforresearcherstoreportplastic-zoneradiiasameasureofhowfartheplasticdeformationextendsfromtheindentsite 88 .InFigure 3-29 ,apparentplasticzonesareoutlinedbysemicircles.IftheFIB-milledcrosssectionhadbeenmadeparalleltoarowofindents,ratherthanatananglesuch 77

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asinthisexperiment,allXTEMimageswouldcorrespondtothesamesectionofanindent'splasticzone.Inthatcase,itispossiblethattheimageswouldlooklikethatineitherFigure 3-29 AorB.Thedifferenceinradiiofthetwosemicirclesis28%,sothereisnosingleimagethatcanbeusedtoreportanappropriateplastic-zoneradius. Figure3-29. Twotransmissionelectronmicrographsofnominallyidentical250-NindentsinGaAs(001),withindentsslicedatA)~110nmoffcenter,andB)within~20nmofthecenter.Theapparentplastic-zoneradiusisapproximately28%largerinA). Therefore,notonlycanthesizeofthedeformedregionbeneathanindentnowbecondentlyfound,butwecanconcludethatthesizesreportedinstudiesfromasingle2Dimageareverylikelyerroneous.3.4.6RepeatabilityandLimitationsTherepeatabilityoftheindentationdimensionscanbequalitativelyassessedfromAFMimagesinFigure 3-21 .Foramorequalitativeanalysis,thenaldepthsofanarrayof1-mNindentsweretakenfromtheload-displacementcurves.AsshowninFigure 3-30 ,theaverageandstandarddeviationofthenaldepthswere130.2nmand11.9nm(or9.1%),respectively.Forthesetofexperimentsinthischapter,thenumberofrowscrossedbytheFIBsliceswasapproximatelytwoforallindentarrays(nh2).ThiswasdoneincasepartofeithersideofthearrayswasaccidentallynotcutoffintheFIB,whichcanhappenwhenmakingthepre-releasecutsduringaliftout.Thiswasanoverlyconservativeapproach, 78

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Figure3-30. Histogramofnal-depthvalues,hf,forall52indentsina1-mNarrayonGaAs(001),withasuperimposedGaussiant. sincefarlessthanhalfofeacharraywascutoffintheFIB,andfutureexperimentsusednhvaluesofapproximately1.0-1.5.However,oneinterestingresultobtainedwiththisexperimentwasthatoneoftheTEMspecimenscontainedthecentersofindentsfromtwodifferentrows.Thiscanbeseenbylookingcloselyatthe1-mNindentsinFigure 3-24 ,whichisreproducedinFigure 3-31 A.Thecentersofindents3and9arecontainedwithinthisspecimen,asseenbythetriangularindentimpressionsinbothofthese.InFigure 3-31 BandC,thesetwoindentshavebeenmagniedandcroppedsuchthatcorrespondingfeaturesareinthesamepositionsofbothimages.UsingImageJ,thesetwoimagesweresimplyaveraged,andtheresultisshowninFigure 3-31 D.DuetotheremarkablesimilarityoftheTEMimagesinBandC,theaveragedimageretainsmanyofthedetailsinbothimage,andalsoappearssomewhatlessnoisy.Thisprocedurewasrepeatedforindents2and8,inFigure 3-31 EandF,respectively,withtheaveragedimageinG.Theabilitytoaverageimagescorrespondingtosimilarregionsofsimilarindentsduetoaveryreproduciblesubsurfacedeformationproleispromisingforfutureapplications 79

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Figure3-31. Demonstrationofaveragingimagesofplastic-zonecrosssectionsof1-mNindents,forimagescorrespondingtothesameshiftsfromthecenter. ofthismethod.Forexample,averagingsimilarimagescouldbeusedtogeneratemorerepresentativeXTEMimagesforeachsegmentofanindent'splasticzone,whichcouldthenbeusedtoreconstructsmoother,morerealistic3Dimages. 80

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CHAPTER4APPLICATIONTOOTHERMATERIALSYSTEMSTheutilityofmethoddescribedinChapter2isnotlimitedtoaparticularmaterialsystem,norisitnecessarytoperform3Dreconstructionsofafeatureinordertobenetfromthetechnique.Inthischapter,themethodisappliedtostudythedeformationundernanoindentationsinothermaterialsystems,specicallyanInAsthinlmonGaAs(001),andazirconium-carbidethinlmonSi(001).SincethemethodologyforincreasedthroughputofFIBliftoutsviananopatterninghasalreadybeeninvestigated,samplepreparationisexpectedtobesomewhatroutine.4.1Background 4.1.1DeformationofNanolaminatesUnderstandingthemechanicalbehaviorofnanolaminatematerialsisbecomingincreasinglyimportant.Nanolaminatematerialsorcompositesarecomposedoftwoormoredifferentmaterialswiththicknessfromafewatomiclayerstoapproximately100nm.Thedimensionsofthesematerialsoftenresultinenhancedpropertiesthatarenotpossibleinthebulkformofeitherconstituentmaterial,includingincreasedstrength 89 ,enhancedradiationprotection 90 ,andlowerthermalconductivity 91 .Theapplicationsarebroad,includinghigh-efciencysolarcells,exibleelectronics,andradiation-andthermal-barriercoatingsforaerospacecomponents.Ingeneral,therearetwotypesofinterfacesbetweenadjacentlayersofcrystals:coherentandincoherent 89 .Coherentinterfacescorrespondtoasmoothtransitionbetweenlayers,whichcanoccurifthetwoconstituentmaterialsareofthesamecrystalsystemandhaveasimilarlatticeconstant(i.e.below~2%mismatch,dependingonlayerthickness).Incoherentinterfacesincludethosethatdonotmatchsmoothly,e.g.alargelatticemismatchordifferentcrystalstructures.Whenamaterialisgrownor 81

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depositedontolattice-mismatchedsurface,thegrownlmoftenaccommodatesthedifferentlatticeconstantsbyformingmistdislocationsand/orsurfacereconstructions 92 .GaAshasalreadybeenshowntodeformatnanoscalevolumesviadislocationnucleationandslipinChapter3.Foralattice-matched(coherent)systemsuchasGaAs/AlAs,dislocationloopscanpassthroughtheinterfacesbetweenlayerswithminimalresistance 93 .Asthelatticemismatchincreases(>2%),thebarrierstrength(theextenttowhichtheinterfaceimpedesdislocationtransmission)increases,duetomiststrainandinteractionsbetweenmobileandinterfacialmistdislocations 94 96 .Thisdislocation-blockingmechanismisappealingforapplicationswherealmorcoatingservesasaprotectivelayer,becausetheplasticdeformationcanbelocalizedwithinthethinlm 97 .Thisresultsinanobservedincreasedstrengthwithdecreasinglayerthickness 98 (uptoafactorofatleast2.5 89 ).Inthischapter,deformationofInAs/GaAsandZrC/SithinlmsisobservedusingthemethodpresentedinChapter3.TheInAs/GaAssystemhasiscommonlyusedforoptoelectronicdevicesoperatingintheinfraredrange.InAslmshavebeendemonstratedtohavestrongquantumconnementeffects,theabilitytotunetheelectronicbandgapwiththickness,andhighelectronmobilityasultrathintransistors 99 .ThelatticemismatchbetweenInAsandGaAsisapproximately7%,andtheinterfaceisgenerallyincoherentformorethan1.5-2monolayersMLofInAsdepositedonGaAs 92 .ZrCisametal-carbidematerialwithwhichisextremelyhard,wearresistant,thermallystable,andchemicallystable 100 .Ithaspotentialuseinhigh-heatapplicationssuchasnuclear-reactorcoatings.Inthischapter,deformationofananograinedZrClmonSi(001)isobservedusingthemethodfromChapter3.Additionally,mechanicalcharacterizationofthelmisperformedusingnanoindentationinordertodeterminethehardnessasafunctionofgrowthtemperature. 82

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4.1.2Mechanical-PropertyDeterminationusingNanoindentionOneofthegreatadvantagesofananoindenter,comparedtotraditionalmicroindenters,istheabilitytomeasurethemechanicalpropertiesofthinlms.Atraditionalindentationtestreliesoncapturinganopticalmicrographoftheindentimpressionandmeasuringitsdimensionsinordertodeterminetheindentationhardness,H,whichistheratiooftheappliedload,P,tothecross-sectionalarea,A,ofthepermanentimpression:H=P A.(4)However,internationalstandardsspecifythattheindentationdepthbeatleast200nm 101 formicroindentation.Additionally,inordertomakeawell-dened,microscopicallyvisibleindentimpression,anindentisgenerallyseveralmormoreinlength.The`ruleofthumb'generallyfollowedbyresearchersisthatthesampleorlmthicknessmustbeatleasttentimesgreaterthantheindentationdepth 101 105 ,oralternativelythreetimestheindentdiameter,whicheveristhegreaterofthetwo 101 .Thustraditionalindentationexperimentswouldbelimitedtomeasuringthehardnessoflmsontheorderofseveralmthick.Forsmallerindents,electronmicroscopyisnecessarytodeterminethesizeoftheresidualindentimpression 106 107 .Withtheincreaseddemandofrobust,reliablethinlmsinthesemiconductorindustry 108 ,nanoindentationhasbecomeacriticaltoolintestingthemechanicalpropertiesoflms,becausetotaldepthscanbeconsiderablyless.Nanoindentationinvolvesthesimultaneousmeasureofloadanddisplacement,andwasformerlyreferredtoasdepth-sensingordisplacement-sensingindentation 103 109 .Awealthofinformationaboutthematerialbeingtestedcanbeextractedfromtheresultingload-depthcurveinananoindentationtest.Examplesofatypicalquasi-staticnanoindentationschemeandacorrespondingload-displacementcurveareshowninFigure 4-1 .Aforceisappliedontheindentertipuptoamaximumload,Pmax,atwhichtheloadisheldcontacttoallowthematerial 83

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Figure4-1. A)Nanoindentationscheme,andB)atypicalload-displacementcurve,showinghowinformationoftheformercanbeobtainedbythelatter. tocreep,andthentheloadisremoveduntilthetipisnolongerincontactwiththespecimen.BulychevandcolleaguesproposedusingtheinitialunloadingslopetocalculatetheYoung'smodulus,orelasticmodulus,ofamaterial 110 .Thisslopeisdenedasthemeasuredstiffness 103 ,S,andisgivenby:S=dP dhu=2 p Erp Ac,(4)wherehistheindentationdepthordisplacement,dP=dhistheslopeoftheload-displacementcurve,udenotesthattheslopeisevaluatedatthebeginningoftheunloadingsegment,(=1to1.067) 111 adjustsfordeviationsfromaxialsymmetry,Acistheprojectedareaoftheindentertipatmaximumcontact,andEristhereducedmodulus.Thismeasuredmodulusaccountsforcontributionstotheelasticrecoveryfromboththespecimenandindentertip 112 ,andisgivenby:1 Er=1)]TJ /F3 11.955 Tf 11.96 0 Td[(2s Es+=1)]TJ /F3 11.955 Tf 11.95 0 Td[(2i Ei,(4) 84

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whereisPoisson'sratio,andsubscriptssandidenotethespecimenorindentermaterials,respectively.Perhapsthemostchallengingaspectofindentationtestingiscorrectdeterminationofthetip-areafunction,ortheprojected(cross-sectional)areaasafunctionofdistancefromtheindentertip.Becauseindentertipsdeviatefromtheiridealshapes,particularlyattheapex,usingthetip-areafunctionthatcorrespondstoanidealtipproduceslargeerrorsatlowdepths,e.g.below~200nm 109 ,dependingonthetip.Earlymethodstoexperimentallydeterminethetip-areafunctionreliedonproducingaseriesofindentsatvaryingdepths,creatingmoldedreplicasoftheindents,andmeasuringtheareasofthereplicasusingTEM 107 109 .Morerecently,AFMhasbeenusedtomeasuretipgeometry 113 .However,boththesemethodscanbetedious,andprovidenoindicationfromdirectindentationdataastothestateofdegradationofthetip.Themoststandardandmostcompletemethodtomeasurethetip-areafunctionandsubsequentmaterialpropertiesforroutinenanoindentationexperimentsisthatdevelopedbyOliverandPharr 81 103 .Inthismethod,apower-lawtisappliedtotheunloadingsegmentofaload-displacementcurve,andtheinitialunloadingslope,(dP=dh)u,isdeterminedfromthederivativeevaluatedatthemaximumload.Thecontactdepth,hc,isdeterminedfrom:hc=hmax)]TJ /F3 11.955 Tf 11.96 0 Td[(Pmax S,(4)wherehmaxandPmaxarethemaximumdepthandload,respectively,and(=0.72to1.0)isacoefcientadjustingforthetypeoftip(e.g.spherical,conical,etc.) 103 .ThisisequivalenttoextrapolatingalinefromthetopoftheunloadingcurveinFigure 4-1 B,withaslopeof(dP=dh)u,andmakingaslightadjustment(inthepositivehdirection)toaccountforthetipshape.Thetip-areafunctioniscalibratedbymakingaseriesofindentsoverarangeofdepthsonasampleofknownreducedmodulus,Er,ndingthecorrespondingvaluesS 85

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andhcusingtheabovemethod,andthensolvingforAcfromEquation 4 .ThevaluesforAcarethenplottedversushc,andacurveisttoitoftheform 103 :A(hc)=C0h2c+C1hc+C2h1=2c+C3h1=4c+...+C8h1=128c,(4)whereCnarettingcoefcients.Oncethistip-areafunctionisdeterminedforaparticulartip,thereducedmodulusofamaterialcanbedeterminedfromtheload-displacementcurveofanindentationonthematerial,bysolvingforErinEquation 4 .4.2MaterialsandMethods4.2.1InAs-FilmGrowthviaMolecularBeamEpitaxy TheInAslmusedhereinwasgrownonGaAs(001)viamolecularbeamepitaxy(MBE)bycollaboratorsattheAirForceResearchLaboratory(Wright-PattersonAirForceBase,OH)toanintendedlmthicknessof200nm.ConventionalgrowthofInAslmsonGaAs(001)involvesgrowthunderAs-richconditions,wherebyalargemiststrainresultsinrapidrelaxationat1.5-2MLofInAs 92 .Atthispoint,growthtransitionsfrom2-D(planar)to3-D(island)growth,whichcanbeusefulforformingself-assembledquantumdots.Inthisstudy,growthwasperformedunderIn-richconditionsinordertosuppressthesurfacekineticsandpreventrelaxationviaislandformation 114 .Instead,miststrainisrelaxedbytheformationofLomer(pure-edge)dislocationsattheInAs/GaAsinterface,spacedapproximately8nmapart,dependingonthelmthickness 115 ,andaplanarInAslmismaintained.ThesampletemperatureduringgrowthwasmeasuredwithaBandiTtemperaturemonitor(k-Space,Dexter,MI)andadjustedtoavalueof368C.Thebeamequivalentpressure(BEP)attheendofgrowthwas1.099510)]TJ /F7 7.97 Tf 6.59 0 Td[(7Torrfortheindiumcellwithatemperatureof630.9CandtheAsBEPwas4.09410)]TJ /F7 7.97 Tf 6.58 0 Td[(7TorrusingtheAscellwithacrackertemperatureof600C,asublimatortemperatureof355C,andavalvesettingof196.TheseBEPsproducealmosta1:1incorporationofInandAsallowingmetal-richgrowthwithoutsignicantmetal-dropletformation. 86

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Usingtheseconditions,theMBEshutterswererstclosedtoallowexcessAsontheGaAssurfacetodesorb.TheInshutterwasthenopenedfor30stoputanexcessofInonthesurface,forcingmetal-richconditions.TheAsshutterwasopened,andInAswasgrownfor1hr,14min,30s.Afterthis,thethicknessofthelmshouldhavebeenpastthepointwhererelaxationwaspossible.ThesurfacewascappedwithAs,andfurthergrowthwasperformedunderAs-stabilizedconditionsfor6hr,45min,onanotherday.Aftergrowth,thesamplewasquenchedto25C.Thetotalgrowthtimewas8hr.4.2.2ZrC-FilmGrowthviaPulsed-LaserDepositionZirconiumcarbidelmsweregrownbyMAICcollaboratorsviapulsed-laserdepositiontothicknessesofapproximately200nm,usingaKrFexcimerlaser(=248nm,pulseduration=25ns,8.0J/cm2uence,40Hzrepetitionrate).Thelmsweredepositedonp-typeSi(001)usingaZrCtarget(fromPlasmaterials,Inc.,Livermore,CA).Fordetermininglmpropertiesasafunctionofdepositiontemperature,lmsweredepositedatnominaltemperaturesof30,300,and500C.ThesecorrespondingsamplenameswereZC30,ZC300,andZC500,respectively.Moredetailsregardingnon-mechanicalcharacterizationofthelmsaredetailedbyCraciunandcolleagues 100 .4.2.3NanoindentationArrayswithGuidelinesIntheexperimentsinChapter2,materialanisotropyandthenon-axisymmetricindentertipledtoXTEMimagesofplastic-zonesegmentswhichwereasymmetrical.Whilethiswasanexpectedresult,itcomplicatedalignmentofimagestacksduringpost-processing.Inordertomakealignmentmorestraightforwardandlesssubjective,alignmentguidelinesweremadebetweenindentcolumnsinfutureexperiments.Guidelineswereachievedbyscribingwithananoindentertipimmediatelypriortomakingeachindentarray.Theguidelinesweremadeinaserpentinepattern,spacedevenlybetweencolumnsofindents,androtatedatthesameangleastheindentarray.TheguidelinesweremadebycarefullydrawingaserpentinepathmanuallyinIGORPro,intheAsylumResearchsoftwarepackage.Thetipwasdraggedacrossthesurface 87

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Table4-1. ParametersforInAs/GaAsNanoindentationArrays. ArrayLoad(N)hf(nm)Load-Unload(s-s)mnl(m)a,b(nm)nh A2510.51-1=224512112501.54B125402-1=22.5298145001.22C5001065-13.5216201,0001.22 atavelocityof1m/s,andwithanormalforceofapproximately10Nappliedtotheindentertip.Indeterminingproperindentloadsforthisexperiment,thegoalherewastobeabletocompareplasticzonesofindentsshallowenoughtohavelittleornointeractionwiththeInAs/GaAsinterfacetoindentsdeepenoughsothattheplasticzonewouldinterferegreatlywiththeinterface.BasedontheMBEchamber'scalibrationatthegrowthconditionssimilartothoseusedtocreatetheInAslmusedherein,itwasestimatedthatthe8-hourInAslmwasapproximately200-nmthick.Preliminaryindentationsweremadeoverarangeof25to1,000NontheInAssample,andthenaldepthswereplottedversusmaximumload(notshown).Acurvewasttothegraphtodeterminetheloadsnecessarytoproduceresidualindentsofapproximately10,40,and100nmindepth,correspondingto5%,20%and50%oftheexpectedlmthickness,respectively.Therespectiveloadswerefoundtobeverycloseto25,125,and500N.UsingEquation 3 ,rotationangleswerechosensuchthattheFIBslicewouldcross1-1.5rowsofindents(1
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Table4-2. ParametersforZrCNanoindentationArrays. ArrayLoad(N)hf(nm)Load-Unload(s-s)mnl(m)a,b(nm)nh A1,200415-12.961298145001.50B6,00020710-26.582134242,0001.50 showedthatloadsashighas1,200and6,000Nwererequiredtocreateresidualindentsofapproximately40nmand200nm,respectivelyCalculatingtheparametersmanuallywastediousduetolimitationsinthesoftwarethatallowforonlyevennumbersforcertainarraydimensions,androw:columnratiosofpowersof2only.ThusaMATLABprogramwasmadetomakethisprocessmoreefcient.ThecodeandresultsforoneexamplearegiveninAppendixA.UsingthisMATLABprogram,arrayrotationangleswerefoundwhichcorrespondedtoexactly1.5rowsbeingcrossedbyaFIBslice(nh=1.5).Theresultingvaluesofwereroundedtothenearestthreedecimals,andusedastherotationanglesintheAsylumsoftware.TheparametersoftheZC500arraysaregiveninTable 4-2 .4.2.4InsituFIBLiftOutsandTEMInthersttrialforInAs/GaAs(001),signicantbendingofthelifted-outspecimenwasobserved,despitehavingfollowedthesamerecipeasinChapter3,forGaAs(001).ThebentspecimenisshowninFigure 4-2 .ThislikelyoccurredduetoresidualstressesintheInAslm.AstheFIB-milledspecimenbecamethinner,itsstiffnessdecreased,allowingittoexduetoanisotropicresidualstresses.Thisunintendedbendingbecamemorepronouncedasthespecimenbecamethinner,untilitbecamedifculttothinthespecimenfurtherwitharectangularmillingcrosssection.Becausethespecimenwasonlyxedononeend,itbentlikeacantileverbeam(Figure 4-2 B).Thusamethodwassoughtwhichwouldconstrainthespecimenonbothends.Fortunately,theOmniprobegridalreadycontainedtwoV-shapedmounts 89

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Figure4-2. Scanningelectronmicrographsofabent,lifted-outcrosssectionofInAs/GaAs(001).Theregionindicatedontherightwasthinningmorerapidlythanthanontheleft,asseenbyalightercontrastinA),andfromatopviewinB).Theinset,stretchedintheverticaldirection,showswherethebendingtookplace. asalternativestotheverticalpillarsusedpreviously(referto`A'and`C'inFigure 3-15 C).Imagesofthemodiedlift-outprocedureareshowninFigure 4-3 .Priortomountingthespecimen,theionbeamwasusedtomillnotchesintheV-shapedmount,withthelengthoftheopeningapproximately2mshorterthanthatofthespecimen(Figure 4-3 A).A5,000-pAbeamcurrentwasusedforthisstep.Thespecimenwasthencarefullybroughtintocontactwiththemount,anditwasweldedonbothlowercorners(Figure 4-3 B),usingproceduressimilartothoseinChapter3.Finally,withbothendsconstrained,thespecimenwasmilledtoelectrontransparency,oruntiltheprotectivePtcapandcarboncoatingweresputteredaway.ThismodiedprocedurewasusedforboththeInAs/GaAs(001)andZrC/Si(001)specimens.4.2.5HardnessTestingofSuperhardThinFilmsATI900Triboindenter(Hysitron,Inc.,EdenPrairie,MN)wasusedfortestingthemechanicalpropertiesoftheZrClms.TheTriboindenterusesathree-platecapacitivetransducertomeasureloadanddisplacement,withaloadresolutionand 90

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Figure4-3. FIBmicrographsshowingthemodiedinsitulift-outprocedures,includingA)theV-shapedmount,B)millingnotcheswiththeFIBat5,000pA,C),bringingthespecimenintoposition,andD)weldingthespecimenonbothends. noiseoorof<1nNand100nN,respectively,andadisplacementresolutionandnoiseoorof0.0004nmand0.2nm,respectively.TheTriboindenterishousedwithinanenvironmentalenclosurewhichpassivelydampenstemperaturechanges,airow,andacousticnoise.Insidetheenclosure,thenanoindenterisxedtoablockofgranite,whichreducesitsnaturalfrequencyofvibration,andtheentireassemblysitsonapassivevibration-isolationtable.TheTriboindenterhasmotorizedX)]TJ /F1 11.955 Tf 9.3 0 Td[(,Y)]TJ /F1 11.955 Tf 9.3 0 Td[(,andZ)]TJ /F1 11.955 Tf 12.62 0 Td[(translationforcoarsemovement,atube-typepiezoelectricscannersimilartothoseofstandardscanningprobemicroscopes(SPMs)fornetranslation.Forultranez)]TJ /F1 11.955 Tf 9.3 0.01 Td[(translationduringindentationtests(i.e.<~4m),thetransducerisusedindependently.Inthisexperiment,ZrCsampleswereattachedtomagneticpucksusingCrystalbond-1(bothproductsfromTedPella,Inc.).Thesesamples,plusafusedquartzsample(fromHysitron,Inc.)mountedpermanentlytoamagneticpuck,weremagneticallyheldbytheindenterstage'sbuilt-inpermanentmagnetsforindentationtesting.Fusedquartzisusedforcalibratingthenanoindentertip-areafunction,becauseitiswell-knownelasticpropertiesanddeformsisotropically.Becausethemechanicalpropertiesaredeterminedfromatip-areafunction,itisveryimportantthatthegeometryoftheindentertipremainsthesamethroughoutthetesting.Otherwise,recalibrationofthetip-areafunctiononfusedquartzisnecessary. 91

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Table4-3. ParametersforNanoindentationTestingofZrCFilms. StepSamplePurposeNo.IndentsMax-LoadRange(N)Approx.Max-DepthRange(nm)Load-Hold-Unload(s-s-s) 1FQclean41,000to1,000180to18010-5-52FQcalibrate49500to3120to42-1-13ZC500test100750to565to32-1-14FQclean41,000to1,000180to18010-5-55ZC300test100750to565to32-1-16FQclean41,000to1,000180to18010-5-57ZC30test100750to590to32-1-18FQclean41,000to1,000180to18010-5-59FQcalibrate49500to3120to42-1-1 Twofactorscaneffectthegeometryoftheindentertip:tipwearanddebrisonthetip.Ingeneral,therearethreestagesofwearforatool:(1)rapidinitialwear(break-inofthetool),(2)steadywearatalowerrate,and(3)rapidwearleadingtofailure.Theregimeinwhichonewouldwanttooperateisthesecond,becauseitisthemoststable.Thusitisundesirabletouseanewtipthathasnotbeenworn,particularlyonaveryhardsurface;ontheotherhand,arelativelysharptipisstilladvantageousbecauseitproducesawell-developedplasticzoneatashallowdepth.Sometimes,whenatipisunloaded,debrisfromtheindentedmaterialremainsonthefacetsofthetip.Thisaffectsthetip'sgeometry,aswellasthemechanicalbehaviorofthetip,thusproducingerroneousvaluesofmechanicalproperties.Onewaytodeterminewhetherthetipiscontaminatedwithdebrisistoindentagainonfusedquartz,andcomparetheloadingresponsewiththethosefromthemostrecentcalibration.Ifatipiscontaminated,itissometimespossibletocleanitbymakingadeepindentinamaterialtoeitherpushthedebrisfurtherawayfromthetip,ortoattractthedebriswithelectrostaticattraction. 92

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Inthisexperiment,anunusualamountofcarewastakentoensurethatthetipgeometrydidnotchangeduetoeitherwearorcontamination,becausehundredsofindentsonsuperhardlmscouldeasilywearanindentertip,andwehadpreviouslyobserveddebrisontipsviaAFMimagingafterindentingonsimilarsamples.ANorthStarcube-cornertip(purchasedfromHysitron,Inc.)waschosenfortheseexperiments.Thistiphadbeenpreviouslyusedforthousandsofindents,includingseveralhundredsonsuperhardlmssuchastitaniumnitride,whilelimitingloadsbelow2mNforhardnesstesting(althoughloadedupto11mNonsoftaluminumfortip-optics-offsetcalibrations).Thetipwascalibratedonfusedquartzimmediatelypriortoindentationonthezirconiumcarbidesamples,andrecalibratedimmediatelyafterward.Thetwocalibrationswerecomparedinordertoassesswhetherornotthetiphaddegradedsignicantlyduringtesting.ThekeytestingparametersaretabulatedinTable 4-3 .4.3ResultsandDiscussionAtomicforcemicrographsofsectionsof125-Nand500-NindentarraysareshowninFigure 4-4 AandB,respectively.TheaverageroughnessvaluesfromsquareAFMscansizesof1and5mweremeasuredtobe2.30nmand2.61nm,respectively.TheeffectoftheroughnessontheuniformityofindentgeometrycanbeobservedbycomparingFigure 4-4 AwithFigure 3-21 D.Intheformercase,theindentgeometryappearstodependonwhetherornottheindentissituatedonapeakortrough.Also,theroughnessisindicativeoflm-growthconditionsthatmaynothavebeenideal,suchasrelaxationduetodislocationformation.Thereisalsodebrisobservedonthesurfaceduetotheaddedscribingprocedure,whichisdiscussedinmoredetailbelow.TheindentdepthsinFigure 4-4 Aareinrangeof12-17nm.Sinceroughnesshasalessenedeffectforlargerindentations,theindentsinFigure 4-4 Bappearmoreuniform.Infact,theAFM-measureddepthsofthesefourindentsareallintherangeof106.0-107.5nm.Thescribelinethatiscenteredbetweenthecolumnsofindentscanclearlybeseeninthisimage.However,inFigure 4-4 A,thelineswere 93

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Figure4-4. AtomicforcemicrographsofpartsofarraysofA)125-NandB)500-NnanoindentationsonInAs/GaAs(001).Theheightrangeis30nmforbothimages. madeinthesamemanner,buttheyarelessrecognizable.Itispossiblethattherewassomeinteractionbetweenthescribeslinesandtheindents'plasticzonesthatcausedthelinestoshiftwhentheindentsweremade.Theplowingoftheindentertipduringscribingalsocausedaggregatesofmaterialonthesurfacetobedepositedatintervals,particularlywhenchangingdirections,suchasattheendsofeachscribeline.ThiscanbeseeninFigure 4-5 A.Eyinketal.previouslydemonstratedthatremovingthesurfaceoxidesofinscribedInAssamplesbydippinginHFremovesmuchofthedebriscausedbyscribing 116 .Onepossibleexplanationforthisisthatmuchofthesurfacematerialthatisdisplacedbyscribingconsistsoftheoriginaloxidelayer.Afterscribing,HFdisproportionatelyremovesthethisdisplacedmaterialasatwouldaregularoxidelayer.Figure 4-5 BshowstheresultoftreatingtheindentedandscribedInAssamplewithHF.NotethatthisisthesameregionasshowninFigure 4-5 A.Theindentsareallclearlyvisible.However,thereisstillconcernregardingtheuniformityoftheindents,becausethescribelinesweremadepriortotheindents.Hadtheybeenmadeafter,theywouldhavehadanegligibleeffectontheindentations. 94

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Figure4-5. Atomicforcemicrographsofarraysof125-NindentsonInAs/GaAs(001)A)beforeandB)aftercleaningwithHF.Theheightrangeis40nmforbothimages. 4.3.1InAsDeformationTransmissionelectronmicrographsof125-Nand500-NindentsintheInAs/GaAs(001)sampleareshowninFigures 4-6 and 4-7 ,respectively.InFigure 4-6 A,allindentsectionsinthespecimenhavebeenstitchedtogether,andselectedimagesaremagniedinBandC.Thebulkregion(i.e.fromoutsideofthearray)isshowninD.Fromthisimage,itisclearthattheInAslmcontainsmorethanjustmistedgedislocationsattheInAs/GaAsinterface,asseveraldislocationscanbeseentopropagatetothesurface.Thusthelmispartiallyrelaxed,anditsstructurepriortoindentationisnotcompletelyknown,northesameforatallindentlocations.Insomecases,suchasinFigure 4-6 C,dislocationsarepresentwhichconnectfromtheinterfacetotheplasticzonebeneathanindent.Duetotheradiusoftheplasticzonebeinglessthanhalfofthelmthickness,thesedislocationsareexpectedtohaveoriginatedattheinterface.Itisalsopossiblethatthelocalstressfromthe 95

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Figure4-6. Transmissionelectronmicrographsof125-NnanoindentationsinInAs/GaAs(001),viewedalongthe[110]. indentationwasenoughtocauseexistingdislocationstomigratethroughthelm,sothesedislocationsmayhavebeenshorterpriortoindentation.Figure 4-7 Acontainsstitchedimagesoftheentirespecimen,andmagniedindentsareshowninB-D,withscribemarksindicatedwithovals.Thenalindentationdepthfortheseindentswasapproximatelyonefourthofthelmthickness,andsotheplastic-zoneradiuswouldbeexpectedtobeontheorderofdoublethelmthickness,inthecaseofacontinuous,homogeneousmaterial.InFigure 4-7 B,theshapeoftheplasticzoneisclearlydistortedbytheInAs/GaAsinterface.Dislocationspropagatelaterallyawayfromtheindent'saxis,butnoneareobservedtotransmitthroughtheinterface.ThisisconsistentwiththemodeldescribedbyMisraetal.,inwhichdislocationsareimpededbyanincoherentinterface,andmigrateparalleltotheinterfaceinsteadofthroughit 95 96

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Figure4-7. Transmissionelectronmicrographsof500-NnanoindentationsinInAs/GaAs(001),viewedalongthe[110],withA)astitchedimageoftheTEMspecimen,B)asegmentnearthecenterofanindent,andC)aregionfurtherfromthecenter.Scribemarksareindicatedbyredovals. 4.3.2ZrCDeformationAtomicforcemicrographsof4-mscansofthe1.2-mNand6-mNindentarraysinZC500areshowninFigure 4-8 AandB,respectively.ThescribelineshereappearcleanerthanthoseinInAs,perhapsduetoahardersample,lowersurfaceroughness,andlargespacebetweenindents.TheaverageroughnessvaluesfromsquareAFMscansizesof1mand5monthissamplewere0.37nmand0.38nm,respectively.Themeasured-depthrangeforthe1.2-mNand6-mNindentsintheseimagesare32-39nmand203-208nm,respectively.TEMresultsoftheZC500samplearepresentedinFigure 4-9 .SEMandTEMimagesoftheentirespecimenareshowninFigure 4-9 AandB,respectively,andmagniedviewsofindividualindentsareshowninC,D,andE.Atleastvemediancracksareobservedinthisspecimen(Figure 4-9 B),andmoremayhavebeenpresentbeneathindentsfaroff-centerfromthespecimen.Itshouldbenotedthatnhwasdesignatedtobe1.5forthisspecimen,soalmostexactly1.5indentrowsshouldbeincludedinthisspecimen.ReferringtoTable 4-2 ,andalsoEquation 3 ,theshiftfrom 97

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Figure4-8. AtomicforcemicrographsofpartsofarraysofA)1.2-mNandB)6-mNnanoindentationsonZC500(ZrConSi).Theheightrangeis38nmforbothimages.DebrisfromscribingisobservedtohavepiledupatthetopandbottomofthearrayinA). oneindenttothenextisgivenby2,000nmsin(6.582),orapproximately230nm.ThustheindentinFigure 4-9 Dis~230nmoff-center.ThenanograinedZC500lmisthedark-contrastlayer,asindicatedinFigure 4-9 E.InimageC,muchofthecarbonhasbeeneroded,andassumingthecarbonlayerhasatrapezoidalshape,itislikelythatpartoftheZrClmwasalsoeroded.Thelmonthebacksideofthespecimenmayhavebeenslightlyeroded,whilethefrontremainedrelativelyintact,orviceversa.Thismayexplaintheapparentdiscontinuityinthetopofthelm.Whereasnocrackisobservedbeneaththisimage,aquasi-hemisphericalregioncanbeseenintheSiregiondirectlybeneaththeindent.IntheSiaroundthishemisphericalregion,bandsofstresscontoursareverydense,buttheyvanishastheyencounterthehemisphericalregion.ThiscanbeexplainedbyaphasetransformationintheSiduetoextremelyhighlocalizedstresses,creatingatransformedzonesurroundedbythehighlystressedcrystal.ThisphenomenoniscommonfornanoindentationsinSi 23 117 .Figure 4-9 Ecorrespondstoacross-sectionalviewthroughthecenteroftheindent.Thetriangularimpressionleftbythecube-cornertipisslightlyacutefromthisviewing 98

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Figure4-9. A)SEMandB-E)TEMimagesof6-mNnanoindentationsontheZC500lmonSi(001):A)thenal,thinnedspecimeninsidetheFIB;B)astitchedimageshowingallindents;C)acenteredindentwithnocrack;D)anindentoff-centerby~230nm,withamediancrackintheSiregion;andE)acenteredindentwithamediancrackintheSiregion. orientation,whereastheproleofthecube-cornertipiseitherarightangleorslightlyobtuse,dependingontheviewingorientation.Duetotheclarityoftheimage,thisacuityislikelynotanartifactduetoasuperpositionoflayersatdifferentdepths,soonemustassumethattheimpressionisindeedacute.Thisimpliesthatelasticrecoveryoccurredpredominantlyfromthesidesoftheindent,comparedtounderneaththeindent'sapex,orinotherwords,thatplasticdeformationwasaccommodatedmoreintheverticalratherthanlateraldirections,allowingforlittleelasticrecoveryintheverticaldirection.Thisisareasonableresult,consideringthatverylittleplasticdeformationoccurredintheZrClmitself.TheyellowdashedlinesinFigure 4-9 EcorrespondtoanoutlineofthetopsurfaceoftheZrContherightsideoftheimage.TheselineshavebeencopiedandpastedontothetopoftheSisurface,attheZrC/Siinterface,toshowhowmuchthelmwascompressedasaresultoftheindentation.Itappearsthatonlythepartofthelm 99

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directlybeneaththeaxisoftheindentertiphasbecomethinnerfromtheindentation.Furthermore,step-likepatternscanbeseenattheZrC/Siinterface.ThesearenotconsistentwiththesizeandshapeoftheZrCgrains,whicharesmaller(~20nm) 100 andelongated.However,thestepdirectionsdoappeartobealong110idirections,i.e.orthogonaltotheimagingdirection,whichisconsistentwithslipdirectionsforSi.ThusitislikelythatZrCgrainshaverotatedand/orslidslightly,butthebulkoftheplasticdeformationandfractureoccurredintheSiregion.AlsoinFigure 4-9 E,atransformedzonecanbeseenintheSiregion,centeredbeneaththeindent.Amediancrackprotrudesdownwardfromtheplasticzone.Thelminthisimagehasdelaminateduptoalengthof780-790nmoneithersideoftheindent(measurementnotshown),butdelaminationwasnotobservednearallindents.Asindicatedinthegure,thedepthoftheindentwasmeasuredtobe185nmfromtheXTEMimage.Thisisjustslightlylessthanthetypicalnaldepthsmeasuredwiththenanoindenterof195-200nm,andtheAFMdepthsof203-208nm. Figure4-10. Schematicdepictionsofdifferenttypesofcrackswhichcanbeformedduringindentation(witha4-sidedVickersindenterinthiscase):A)radialcracks;B)lateralcracks;C)mediancracks;andD)half-pennycracks.ReproducedfromRef118withpermission. InthecaseoftheindentinFigure 4-9 D,whichisapproximately230nmoff-center,themediancrackextendsnearlytotheZrC/Siinterface.Ifweassumethattheindentthatcausedthiscrackalsohadahemisphericalamorphousregionbeneathit,thenthecrackmayhavebeenblockedfromreachingtheinterfacebytheamorphousregion.However,here,230nmawayfromtheindent'saxis,whichalsohappensto 100

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theapproximateradiusoftheamorphousregion(e.g.inFigure 4-9 E),thecrackextendsuptotheinterface.ThisdoesnotconrmthatthedeformationbeneathindentsinDandEaresimilar,butitisanexplanationofhowamediancrackcouldextendalongtheboundaryoftheamorphousregion,propagatetotheinterface,andbecomeahalf-pennyorradialcrack.DifferenttypesofcrackswhichcanbeproducedduringindentationaredenedschematicallyinFigure 4-10 118 .4.3.3HardnessTestingofZrCFilmsThreeload-displacementcurvesforeachofthethreesamplestestedareshowninFigure 4-11 .IndentsinZC500wereconsistentlyslightlyshallowerthanindentsinZC300,whichwerefarshallowerthanindentsinZC30.Thisindicatesanincreasinghardnesswithgrowthtemperature. Figure4-11. Load-displacementcurvesforZC30,ZC300,andZC500forthreedifferentmaximumloads. HardnessandreducedmodulusareplottedinFigure 4-12 asafunctionofcontactdepth.Theareafunctionusedtocalculatethehardnessandmodulusvalueswastheoneobtainedfromthecalibrationimmediatelypriortotheindentationtesting.Onecanseethattheinitially,theplotsHandErbothstartnearzero,rapidlyincrease,andstabilizeatapproximately10-15nmcontactdepths.Thistrendistypical 101

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fornanoindentationtestingveryhardmaterials,andisreportedlycausedbyaplasticzonethatisnotyetfullydeveloped 55 119 .HardnessvaluesinFigure 4-12 Aarereasonablystablebetweencontactdepthsofapproximately20nmand30nm(10%to15%ifthelmthickness),whereasmeasuredmodulusvaluesdecreasecontinuouslyfromdepthsatorbelow10nm.Theyseemtobeapproachingavaluesomewhathigherthantheexpectedsubstratemodulus. Figure4-12. A)Hardness,andB)reducedmodulusofZC30,ZC300,andZC500samples,plottedversuscontactdepth. Correctlydeterminingthemechanicalpropertiesofthinlmsisanongoingresearchchallenge.Asanindentertippenetratesdeeperintoalm,theunderlyingsubstratebeginstoaffectthemeasurementanincreasingamount.Theaforementionedruleofindentingtonomorethanacriticaldepthof10%ofthelmthicknessisnotaconcreterule;thecriticaldepthdependsonmanyfactors.Ingeneral,thecriticaldepth-to-thicknessratioisgreaterthan0.1forsoftlmsonhardsubstrates(e.g.upto0.3forAlonSi,fromnite-elementsimulations) 104 ,andaslowas0.06orlessforahardlmonasoftsubstrate(e.g.CrBlmsonvarioussubstrates,experimentallyobserved) 120 .Otherfactorsthanhardness,suchasadhesion,lmcracking,indentergeometry,andtheelasticmoduliandwork-hardeningbehaviorofthelmandsubstrate 102

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materials,inuencetheresponseofalmonasubstratewhensubjectedtoindentationloading.Furthermore,whiletheabovedepth-to-thicknessratiosaregivenforhardnessmeasurements,duetothenatureofelasticdeformationextendingfarbeyondanindent'splasticzone,thecalculationofelasticmodulusisfarmoresensitivetopenetrationdepthintoalmthanisthehardness 105 .Unfortunately,thereisnotjustanupperlimittoindentationdepthsinlms,butthereisalsoalowerlimitforaccuratemeasurements.Aninnitelysharpindentertipwouldplasticallydeformamaterialuponinitialcontact,butinreality,tipsareroundedattheends,soplasticdeformationdoesnotoccurimmediately,particularlyinhardlms.Eventhesharpestcube-cornerdiamondindentertipscommerciallysoldhavenominaltipradiiofapproximately40nm 121 .Abasicassumptioninthemethodologyofindentationtestingrequiresthataplasticzonebefullydeveloped 55 122 ,sohardnesstestingbelowacriticalpenetrationdepthisnotmeaningful.Inaddition,itisrecommendedtoindenttoadepthatleasttwentytimesgreaterthantheRMSsurfaceroughness,accordingtointernationaltestingstandards 101 .Perhapsmostlimitingisthewell-knownIndentationSizeEffect(ISE),whichresultsinanexponentialdecreaseinobservedhardnessaspenetrationdepthincreases;atlowdepths,hardnessvaluesareinatedtoveryhighvalues 102 122 123 .Duetotheupperandlowerlimits,itisoftennecessaryforresearcherstochooseanappropriateofvaluestoaveragewhenreportingthemechanicalpropertiesofthinlms 55 124 125 .Severalmodelshavebeenproposedtodecouplethemechanicalpropertiesofalmandsubstratefromthemeasured(composite)values 102 109 126 127 .Effectivelydecouplingtheseallowsmoreexibilityintherangeofdepthsthatcanbereliablyusedforreportingmechanicalproperties.However,assumptionsinthesemodelsmustusuallybemadewhichseverelylimittheirutility,andnosuchmodelswereusedinthisanalysis.Fortheresultsofthisresearch,hardnesswasaveragedwithintherangeof20-30nm.Thevaluescalculatedfromarea-functioncalibrationsfrombothbeforeandafter 103

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Table4-4. HardnessvaluesforZrCsamplesfor20nm
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Figure4-13. Effectofusingarea-functioncalibrationsfrombeforeversusafterindentationtests:A)selectedload-displacementcurvesonfusedquartz;B)HandErcalculatedfromthetwoareafunctions;C)theareafunctionsplottedupto100nm;andD)theratioofthe`before'to`after'areafunctions,showinghowlargerdeviationsoccuratdecreasingcontactdepths. e.g.upto75%forAlonglass 105 .Furthermore,thiswasaccomplishedwithouttheuseofcomplicatedequationsthatdependonaveryspecicsetofcriteriaandknowledgeofthematerialsinvolvedthatarenotalwaysavailableorconvenient,otherthanthecriterionofmatchedelasticmoduli.SahaandNixtookadvantageofthendingbyJoslinandOliverthatloaddividedbystiffnesssquared,P=S2,isnotdependentontheareafunction 128 .UsingEquation 4 ,thisisgivenby: 105

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P S2=P 2 p Erp Ac=1 2 41 E2rP Ac.(4)RecognizingthatH=P=Ac,P S2=1 2 4H E2r.(4) Figure4-14. PlotofP=S2valuesasademonstrationofarelativelysteadyvalue,evenformodulus-mismatchedlm-samplecombinations. Asonecansee,P=S2isafunctionofEr,soitonlyremainssteadyifthemodulusofthespecimenisthesameeverywhere,hencetheimportanceofmatchingthelmandsubstratemoduli.Evenwithvastlymismatchedmodulifromthepresentexperiment(Er,ZrC350,Er,Si120),thevalueP=S2remainsrelativelyconstantwhenplottedagainstcontactdepth,asshowninFigure 4-14 .ThehardnessisobtainedbyaveragingvaluesofP=S2,andrearrangingEquation 4 toget:H=24 P S2(4)whereEristakenasthereducedmodulusofboththelmandsubstrate.NoteagainthatP=S2istakendirectlyfromtheload-displacementcurve,anddoesnotdepend 106

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ontheareafunction.Sinceitwaspreviouslyrecognizedthatanothersourceoferrorcomesfromthechangingtip-areafunctionduetodegradationoftheindentertipoverthecourseoftestingonthesuperhardZrClms,calculatingHinthiswaywouldbeparticularlyadvantageous.Infutureexperiments,choosingproperlm-substratecombinations(e.g.growingZrClmsonsapphire)couldresultinmoreaccuratemeasuresofH. 107

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CHAPTER5SUMMARYANDFUTUREWORKVisualizingmaterialdeformationattheatomicscalecanrevealinformationaboutamaterial'sdeformationmechanisms,hardness,andhowinterfacesaffectdeformation.TheTEMistheultimatetoolforimagingatomicdefectswhichareformedwhenamaterialplasticallydeforms.However,preparationofsite-specicTEMspecimensischallengingandlowinthroughput,andresultingimagesprovidelimitedinformationregardingthe3Dnatureofadeformedvolume.Fewresearchers,ifany,haveeverattemptedtostudyindentation-inducedplasticityinthreedimensionsusingaTEM.Inthisdissertation,anewmethodhasbeenexperimentallydemonstratedwhichincreasesthethroughputofsite-specicXTEM-specimenpreparationforstudyingcrosssectionsofnanofeatures.Itwasshownthatwhenpreparedintheproposedmanner,asingleXTEMspecimenisguaranteedtocontainmultiple(approximately10-50)features,eachcorrespondingtoadifferentcross-sectionalsliceofthepatternednanofeature.Furthermore,bypatterningthefeaturesinarectangulararray,thefeaturesintheresultingXTEMimageswereregularlyspaced,sodeterminingwhichsectionoftheoriginalfeatureeachimagecorrespondedtowassimple.Withthisinformation,theimageswerecompiledintoavirtualstackandrenderedintoa3Dimagetorepresentthesubsurfacevolumeofasinglenanofeature.Thismethodwasrstappliedtostudytheplasticzonesbeneathcube-cornernanoindentationsonGaAs(001)forthreedifferentloads.Theoverallshapeandsizeoftheanisotropicplasticzonewasobservedtobeextremelyrepeatableforsimilarpositions(e.g.thecenters)ofnanofeatures.Additionally,oneinterestingresultwasthedirectobservationofjusthowdifferentthecrosssectionofaplasticzoneisatdifferentdistancesfromanindent'scenter.ThisimpliesthatalthoughpreviousstudiesseemtohavealwaysreliedonasingleTEMimageforagivenloadfromwhichtodraw 108

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conclusionsabouttheoverallplasticity,oneimagecannotbeusedalonetorepresenttheplasticzone'ssizeandshape.Thedrawbacksofthismethodarethatitreliesontheabilitytopreciselypositionnanofeaturesinanarraywithnear-nmaccuracy,andthepatternedfeaturehastobehighlyrepeatableif3Dimagesaredesired.Ifthefeatureisnotrepeatable,thentheresulting3Dimagemaybeblurry,oradjacentslicesinitmaynotmatchsmoothly.InChapter4,themethodwasappliedtostudythedeformationoftwothin-lmsystems:InAsonGaAs(001),andZrConSi(001),withthelattergrownatthreedifferenttemperatures.Intheformercase,thedislocation-dense,mismatchedInAs-GaAsinterfacewasobservedtocompletelyblockdislocationsfromtransmittingfromtheInAslmtotheGaAsregion.ThenanograinedZrClmwasdevoidofdislocations,anditaccommodatedplasticdeformationpresumablybygrainrotationandsliding.TheZrC-Siinterfaceappearsalsotohavenotbeenbroken,astherewaslittle-to-nointermixingoftheZrCandSi,evenwhenthenal(plastic)indentationdepthwas90%ofthelmthickness.MuchoftheplasticdeformationwasabsorbedbythebulkSiregion.Itunderwentphasetransformationscenteredbeneaththeindent,andmediancrackswereobservedinmanycases.MechanicalcharacterizationwasalsoperformedontheZrClms.Thehardnessandreducedmoduluswerebothobservedtoincreasewiththegrowthtemperature,andthehighesthardnessvalueobtainedwasapproximately42GPa.SomedegradationofthediamondindentertipwasobservedasaresultoftestingonthesuperhardZrClms,socaremustbetakenwheninterpretingtheresults.Futurestudiesonmodulus-matchedsubstrates(e.g.sapphire)weresuggestedinordertoreduceerrorduetoboththeunderlyingsubstrateandthechangingtip-areafunction.Asmentionedabove,themethodpresentedherereliesonveryhighrepeatability.Onepotentialwaytoovercomevariabilityinpatternedfeatureswouldbetorepeatthesameprocedureforseveralspecimens,andthentoaveragetheimageswhich 109

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correspondtothesamepartofafeature,aswasdonefortwopairsofimagesinFigure 3-31 .IftheTEMspecimenwerelongenough,thiscouldbeachievedinasinglespecimenbycrossingseveralrows,insteadofonlyoneortwo.SomeissuesaroseinthisresearchduetopoorcontrastintheTEM.Someofthiswascausedbyspecimenthickness,andsomebybending/straincontours.OptimizingtherecipesforthinningeachmaterialdownintheFIBto50-100nmwithouterodingtheprotectiveCandPtlayerswouldhelpgreatlywithimageresolution.However,bendingcanbecomemoreextremeasthesamplebecomesthinner.Awaytoreducebendingistoxthespecimenatbothends,asdemonstratedinSection 4.2.4 .Thiswasnotaseasyasexpectedthough,becauseitinvolvedpreciselypositioningaspecimenontoacurvedsurface,withviewingorientationslimitedtotopandbird's-eyeviews,notafrontview.Thereforemorepracticeisrequiredwiththisprocedurethanwithsimplymountingaspecimentothesideofapillar,asinSection 3.3.4 .Anotherwayofimprovingthismethodwouldbetomillthespecimentoathicknessascloseaspossibletothecriticalthicknesscorrespondingtoperfectoverlapofreconstructedslices(usingEquation 3 ).Unlessperfectoverlapisachieved,thethicknessesofreconstructedsegmentdonotcorrespondtotheactualcross-sectionthickness.Itwouldbeidealtomakethesethicknessesmatch,andthenoverlaptheminthestacked3Dimage.Itisrecommendedthatscribelinesbemadebetweencolumnsofindents,tousewhenaligningstackedTEMimagesduringpost-processing.Thescribelinesshouldbemadeaftertheindentationsaremade.Otherwise,aggregatesofplowedmaterial,whicharedepositedinunpredictablelocationswithanarray,caninterferewiththeindentations.Theresolutionofthe3Dimageismostlylimitedbythewidthoftheindividualslices,whichcorrespondstotheshiftintheYdirectionfromonefeaturetothenext.Thisiswhytheimagesrotatedby90appearpixelated.Theslicethicknesscanonlybe 110

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reducedbyeitherreducingthespacingbetweenfeatures(althoughtheminimumsizeislimitedbyinteraction/overlapoffeatures),orbyreducingtherotationangle(whichmightresultinlessthanawholerowbeingcrossedbytheFIBslice).Analternativewaytoovercomethisresolutionlimitinthedirectionofthespecimenthicknesswouldbetorepeattheproceduresatanotherangleonthesamesample.Forexample,ifthesameprocedureswerecarriedouttoproducea3Dreconstructionofanarraycreatedwithadifferentrotation,analgorithmcouldbemadetomergetheresultstogether.Using3D-TEMtomographycombinedwiththemethodpresentedinthisworkcouldproduceveryinterestingresults,becauseeachTEMimagecouldbereconstructedin3Dindividually,andacompositeofthese3Dimagescouldbeobtained.Thiswouldprovideahigher-resolutionresultwithbettercontrastthatwhatwasobtainedinthisresearch.Futureexperimentson3Dvisualizationofsubsurfacedamageonabroadrangeofmaterialswouldalsobeofinterest,suchasindentation-inducedcrystallizationofbulkmetallicglasses.Also,theeffectoftipgeometryonplastic-zoneshapeandsizecouldbestudiedforasinglematerial,toimprovetheunderstandingofthepressuredistributionaroundanon-axisymmetrictipduringindentation.Anotherrecommendationistocomparethe3Dimageswithplasticzonesmodeledusingniteelement,atomistic,ormultiscalesimulations.Accuratemodelingofmaterialdeformationsupportedby3Dexperimentalobservationscouldadvancethepredictiveabilitiesofsimulations,whichcouldthenbeusedtodesignand`test'virtualmaterialprototypesbeforephysicallymakingthem.Lastly,thismethoddescribedhereinisnotlimitedtovisualizingnanomechanics.Anyfeaturethatcanbepatternedandslicedtorevealitscrosssectioncouldbeacandidateforusingthismethod.Ionimplantationandmixing,forexample,couldbeinvestigatedbypatterningfeatureswithaFIB.Theregularspacingofnanostructuresmadefromnanosphere-lithographytemplatescouldbeexploitedfor3Dvisualization.Themethodcanalsobeappliedforobservationsoutsideanelectronmicroscope.Ifa 111

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microscalefeaturewerepatternedonablockofmaterial,theblockcouldpotentiallybepolishedfromthesidetoexposethecrosssectionsofthesefeatures,andaseriesofopticalmicrographscouldprovidesufcientdetailtoreconstructa3Dimage.Therefore,thepotentialfutureapplicationsarenumerous,andhopefullythisdissertationhasonlypresentedtherstofmanyuses. 112

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APPENDIXAMATLABCODEFORROTATED-ARRAYPARAMETERSDuetothelimitationsoftheAsylumResearchsoftwareusedformakingthenanoindentationarrays,determiningthearrayparameterswasnotastrivialasfollowingEquation 3 .ThusMATLABwasemployedtoautomaticallyproducethearrayparameters,estimatethetimerequiredtomakeeacharray,andcalculatethecriticalthicknessoftheFIBslice.ThecodeisgiveninFigures A-1 A-2 ,and A-3 ,and A-4 .Theinputparametersandcorrespondingoutputs(Figure A-5 )wereusedforcreating1.2-mNindentsintheZrCsample. FigureA-1. MATLABcodefordeterminingarray-rotationangleandotherparameters(1of4). 113

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FigureA-2. MATLABcodefordeterminingarray-rotationangleandotherparameters(2of4). 114

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FigureA-3. MATLABcodefordeterminingarray-rotationangleandotherparameters(3of4). 115

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FigureA-4. MATLABcodefordeterminingarray-rotationangleandotherparameters(4of4). TheoutputintheMATLABcommandwindowcorrespondingtotheaboveprogramisshowninFigure A-5 FigureA-5. OutputofMATLABprogram,givingarray-rotationangleandotherparameters. 116

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APPENDIXBPOST-PROCESSINGPROCEDURESTOCREATE3DIMAGESReconstructing3Dimagesofindentationplasticzonesfrom10-20segmentsofnominallyidentical,butrealisticallyvaried,indentfeaturescanbenontrivial.Onemajorchallengeinvolvesenhancingimagecontrasttohighlighttheindividualdislocationloops,whilereducingimageartifacts,suchasbendingcontoursintheTEMimagescausedbyhighlocalstrains.Anotherchallengeisndingawaytoreconstructthevariousimagesegmentsasseamlesslyaspossible,sothatthesegmentsarenotobviouslydistinct.Effectivelyprocessingtheimagesresultsinbothmorerealisticandusefulrepresentations.InitialprocessingwasperformedusingImageJ 78 129 .SnapshotsofimportantstepsusedwhenprocessingtheTEMimagesoftheGaAsspecimencontaining250-NindentscanbeseeninFigure B-1 .FifteenofseventeenindentsinthesingleTEMcrosssectionareincludedinFigure B-1 A.Resolutionatthisscaleiscompromisedduetobendingcontoursandslightmisalignmentsofthebeamwithrespecttothesample'scrystallographicdirections(whichisimpossibletoxfortheentirespecimenatonceifitiscurved).Proceduresaredetailedbelow.First,snapshotsofallimagesinFigure B-1 BareloadedintotheImageJsoftwareandstacked(Image!Stack!ImagestoStack).Theimagesarethenrotateduniformlysothatthesurfaceishorizontal(Figure B-1 C).Thenextandmosttediousstepistoalignimagesbytranslatingeachoneindividually.(Guidelineshelpedsignicantlywiththisstepinlaterexperiments.)Oncealigned,theimagestackiscroppedjustenoughtoincludealldislocationsinallimages(Figure B-1 D).Next(Figure B-1 E),theimages'brightnessandcontrastareadjusted,andnoiseisreducedby'blurring'oraveragingneighboringpixels(Process!Filters!GaussianBlur),choosing2.0pixelsastheblurringparameter.Thispreparestheimagesforthenextstep,whichistoapplyauniformbackgroundsubtraction(Process!SubtractBackground)toall 117

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FigureB-1. Snapshotshighlightingpost-processingproceduresofTEMimagesinImageJ,showingA)allindentsinthespecimen,B)rawTEMimagesofindividualindents,whicharestackedtogether,aligned,rotatedinC),croppedinD),smoothedwitha2-pixelGaussianblur,contrast-adjustedinE),enhancedwithabackgroundsubtractioninF),andinvertedinG). images,whichhelpsreducenoiseandotherartifactsfromtheimage,thusmakingtheresultmorerepresentativeoftheactualfeature(Figure B-1 F).Forthisstep,theslidingparaboloidoptionwasused,with500pixelsusedinthecalculation.Finally,theimagesareinverted(Figure B-1 G),andcontrastisadjustedifnecessary.Thedarkbackgroundisusefulwhencreatingthe3Dimages.Afterprocessingtheimages,itisnecessarytoidentifytheimagescorrespondingtoasinglerow,suchas2-14inFigure B-1 B,anddeletetherest.Ifonecontinuousrowisnotfoundinthecrosssection,imagesfromadjacentrowscanberearrangedinawaytherepresentsonefullrow,andthusonefullindent.Theproceduresusedfor3D-imagecreationinAmiraareoutlinedinFigure B-2 .First,thestackedimagelefromImageJisreadin.ThedefaultZdimension(thickness)correspondstothenumberofimagesinthestack,andthisisadjustedbychangingtheZdimensionoftheboundingbox.Thenumberofpixelscorrespondingtoeachimage(slice)isthencalculated: 118

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FigureB-2. Proceduresforcreatinga3DimageinAmira:A)whenreadinginstack,theboundingboxZdimension(thickness)isadjustedtotheappropriatesize,B)aboundingboxisaddedanda3DimageiscreatedusingtheVolrenfeature,C)thecolorschemeischangedtotemperature,D:)thecolorrangeisadjustedfrom0-255to35-45,andE)adjustmentsaremade,includingmakingtheboundingboxmorevisible.AscreenshotofthenalparametersisshowninG). P=asin()C,(B)whereCistheconversionfactorinpixelspernm,whichcanbefoundinImageJbymeasuringthesizeofaTEMimage'sscalebar.PisthenmultipliedbythenumberofslicestogettheZdimensionoftheboundingbox.Figures B-2 B-Fshowthedisplayingofaboundingbox,creatinga3DimageusingtheVolrenfeature,adjustingthecolorscheme,andsmoothingtheimage.Figure B-2 showsascreenshotofthenalparameters. 119

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BIOGRAPHICALSKETCH EdwardwasbornandraisedinFairfaxCounty,VA,byhisparents,AllanandJessica,andhasanelderbrothernamedSean.HeattendedVirginiaCommonwealthUniversity(VCU)forhisbachelor`sdegreeinMechanicalEngineering,duringwhichtimehewasanactivevolunteerandmentorforhighschoolFIRSTRoboticsteams.HeremainedatVCUforhismaster`sdegree,underthesupervisionofDr.CurtisTaylor.Thetitleofhismaster'sthesiswasMechanicalCharacterizationofNanocompositeCdSeQuantumDotMEH-PPVPolymerThinFilmsviaNanoindentation.EdwardsubsequentlyfollowedDr.TaylortotheUniversityofFloridaforhisPh.D.studies.Hehashadsixinternshipsthroughouthiscollegetenure,inadditiontoasummerresearchstintinSingaporefundedjointlybytheU.S.NationalScienceFoundationandSingapore'sNationalResearchFoundation.HishobbiesincludeBrazilianJiuJitsu,MuayThaikickboxing,andCrossFit.Helovestotravel,takephotographs,cook,read,andtrynewanddifferentfoods. 130