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Fundamental Studies of Graphene/Graphite and Graphene Based Schottky Photovoltaic Devices

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Title:
Fundamental Studies of Graphene/Graphite and Graphene Based Schottky Photovoltaic Devices
Physical Description:
1 online resource (170 p.)
Language:
english
Creator:
Miao, Xiaochang
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
Publication Date:

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Physics
Committee Chair:
Hebard, Arthur F
Committee Members:
Biswas, Amlan
Cheng, Hai Ping
Tanner, David B
Appleton, Billy Ray

Subjects

Subjects / Keywords:
ferromagnetism -- graphene -- graphite -- magneto-transport -- photovoltaics -- schottky
Physics -- Dissertations, Academic -- UF
Genre:
Physics thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract:
In the carbon allotropes family, graphene is one of the most versatile members and has been extensively studied since 2004. The goal of this dissertation is not only to investigate the novel fundamental science of graphene and its three-dimensional sibling, graphite, but also to explore graphene's promising potential in modern electronic and optoelectronic devices. The first two chapters provide a concise introduction to the fundamental solid state physics of graphene (as well as graphite) and the physics at the metal/semiconductor interfaces. In the third chapter, we demonstrate the formation of Schottky junctions at the interfaces of graphene (semimetal) and various inorganic semiconductors that play dominating roles in today's semiconductor technology, such as Si, SiC, GaAs and GaN. As shown from their current-voltage ($I$-$V$) and capacitance-voltage ($C$-$V$) characteristics, the interface physics can be well described within the framework of the Schottky-Mott model. The results are also well consist with that from our previous studies on graphite based Schottky diodes. In the fourth chapter, as an extension of graphene based Schottky work, we investigate the photovoltaic (PV) effect of graphene/Si junctions after chemically doped with an organic polymer (TFSA). The power conversion efficiency of the solar cell improves from 1.9\% to 8.6\% after TFSA doping, which is the record in all graphene based PVs. The $I$-$V$, $C$-$V$ and external quantum efficiency measurements suggest that such a significant enhancement in the device performance can be attribute to a doping-induced decrease in the series resistance and a simultaneous increase in the built-in potential. In the fifth chapter, we investigate for the first time the effect of uniaxial strains on magneto-transport properties of graphene. We find that low-temperature weak localization effect in monolayer graphene is gradually suppressed under increasing strains, which is due to a strain-induced decreased intervalley-scattering rate. In chapter 6, we study the high vacuum thermal annealing effect on an unconventional ferromagnetism (FM) in highly oriented pyrolytic graphite (HOPG). The FM diminishes and eventually disappears in annealed samples accompanied by improved electrical transport properties and crystalinity. Our results indicate that the FM is mainly coming from the lattice imperfections.
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility:
by Xiaochang Miao.
Thesis:
Thesis (Ph.D.)--University of Florida, 2013.
Local:
Adviser: Hebard, Arthur F.

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Classification:
lcc - LD1780 2013
System ID:
UFE0045658:00001

MISSING IMAGE

Material Information

Title:
Fundamental Studies of Graphene/Graphite and Graphene Based Schottky Photovoltaic Devices
Physical Description:
1 online resource (170 p.)
Language:
english
Creator:
Miao, Xiaochang
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
Publication Date:

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Physics
Committee Chair:
Hebard, Arthur F
Committee Members:
Biswas, Amlan
Cheng, Hai Ping
Tanner, David B
Appleton, Billy Ray

Subjects

Subjects / Keywords:
ferromagnetism -- graphene -- graphite -- magneto-transport -- photovoltaics -- schottky
Physics -- Dissertations, Academic -- UF
Genre:
Physics thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract:
In the carbon allotropes family, graphene is one of the most versatile members and has been extensively studied since 2004. The goal of this dissertation is not only to investigate the novel fundamental science of graphene and its three-dimensional sibling, graphite, but also to explore graphene's promising potential in modern electronic and optoelectronic devices. The first two chapters provide a concise introduction to the fundamental solid state physics of graphene (as well as graphite) and the physics at the metal/semiconductor interfaces. In the third chapter, we demonstrate the formation of Schottky junctions at the interfaces of graphene (semimetal) and various inorganic semiconductors that play dominating roles in today's semiconductor technology, such as Si, SiC, GaAs and GaN. As shown from their current-voltage ($I$-$V$) and capacitance-voltage ($C$-$V$) characteristics, the interface physics can be well described within the framework of the Schottky-Mott model. The results are also well consist with that from our previous studies on graphite based Schottky diodes. In the fourth chapter, as an extension of graphene based Schottky work, we investigate the photovoltaic (PV) effect of graphene/Si junctions after chemically doped with an organic polymer (TFSA). The power conversion efficiency of the solar cell improves from 1.9\% to 8.6\% after TFSA doping, which is the record in all graphene based PVs. The $I$-$V$, $C$-$V$ and external quantum efficiency measurements suggest that such a significant enhancement in the device performance can be attribute to a doping-induced decrease in the series resistance and a simultaneous increase in the built-in potential. In the fifth chapter, we investigate for the first time the effect of uniaxial strains on magneto-transport properties of graphene. We find that low-temperature weak localization effect in monolayer graphene is gradually suppressed under increasing strains, which is due to a strain-induced decreased intervalley-scattering rate. In chapter 6, we study the high vacuum thermal annealing effect on an unconventional ferromagnetism (FM) in highly oriented pyrolytic graphite (HOPG). The FM diminishes and eventually disappears in annealed samples accompanied by improved electrical transport properties and crystalinity. Our results indicate that the FM is mainly coming from the lattice imperfections.
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility:
by Xiaochang Miao.
Thesis:
Thesis (Ph.D.)--University of Florida, 2013.
Local:
Adviser: Hebard, Arthur F.

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Classification:
lcc - LD1780 2013
System ID:
UFE0045658:00001


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FUNDAMENTALSTUDIESOFGRAPHENE/GRAPHITEANDGRAPHENEBASEDSCHOTTKYPHOTOVOLTAICDEVICESByXIAOCHANGMIAOADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2013

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c2013XiaochangMiao 2

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TomyparentsandRenjiaZhou 3

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ACKNOWLEDGMENTS Itisagreatpleasuretothankthosewhohavehelpedmeduringthepast5yearstowardsmyPhD.Firstofall,Iwanttoexpressmydeepestandearnestgratitudetomysupervisor,Prof.ArthurF.Hebard(Art)fortakingmeashisstudentandlettingmeworkonvariousprojectswithquiteafewexibilities.Iappreciatethehoursandhoursofdiscussionswithhimonmyprojects,questionsandideas.Hispositiveattitudeandpurecuriosityonthefundamentalphysicsgreatlystimulatemyresearchinterests.Tome,heisnotonlyagoodsupervisor,butalsoanperfectexampleofhowtobeasuccessfulandrespectfulphysicist.IamalsoindebtedtoallofmycommitteemembersDr.DavidTanner,Dr.Hai-PingCheng,Dr.AmlanBiswasfromDepartmentofPhysicsandDr.BillR.AppletonfromDepartmentofMaterialScienceEngineering(MSE).ThanksfortheirhelpfuladvicesandguidanceduringmyPhDstudy.Iconsideritanhonortohavetheminmycommittee.Moreover,IamgratefultoDr.AndrewG.RinzlerandDr.JiangengXuetogetherwithsomeoftheirstudents,especiallyMaureenK.Peterson,BoLiuandMitchellMcCarthy,fortheiramiablecollaborationandgeneroustechnicalsupportparticularlyinthegraphene/Sisolarcellproject.Iwouldliketothankmylabmates,KaraBerke,SimaSaeidi,HaoruHeandToddShumannnforsharingalltheupsanddownsintheexperimentsandbeingreliablesupportduringthepast4years.Inparticular,IwanttothankDr.SefaattinTongay(Sef),whoisnowapost-docatUC-Berkeley.IappreciateeverythinghehastaughtmesinceIjoinedthelab.Asabrilliantexperimentalistandlabmate,IfeltsoluckytoworkwithSefandlearnsuchagreatdealfromhim.Also,manythanksgotoentiremachineshopstaff(especiallyBillandMark),cryogenicsstaffJohnandGregtogetherwithJayHortonfortheirgreathelpandusefulinput(especiallyinthechemical-vapordepositionsystem),entireelectronicsshopstaff(especiallyDanforthecircuitboarddesign),TimNolandforhistechnicalHelp,ITspecialistDavidandBrent,andallcleanroomtechniciansatNRF 4

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(especiallyB.Lewis,A.OgdenandD.Hays)fortheirtrainingsandtimelyhelponvariousinstrument.IamalsothankfultoallofmyfriendsatUF,especiallyLiliPanandJieXiongfortheirsweetaccompany,JueZhangforbeingsuchalong-termfriendandclassmatestartingfromUniversityofScienceandTechnologyofChina(USTC),YanWangforbeingagoodneighborandteachingmeMatlabskills,JialongChengforjoyfultravelexperiences,XiangguoLiandIek-HengChufortheiralwayskindhelpandDr.Yu-NingWuforbeinganamazingcollegeseniorfromUSTCtoUF.Inparticular,IwouldliketothankDr.Hsin-JungLin(Keyo).ImissallofthewonderfulconversationsanddeliciousfoodwehadtogetherinGainesvilleandlookforwardtoreadinghersciencectionnovelinthenearfuture.Also,IwanttothankallmydearfriendsfromUSTC,especiallyLiuyanZhao(ColumbiaUniversity),SihuiChen(NorthCarolinaStateUniversity)andRunzheTao(UniversityofIllinois-Chicago)foreverythingwesharedtogether,andourfriendshipwilllastandprosperfarintomyfuturelife.Lastly,manythankstomydearparents,fortheirdevotedloveandsupportthathavebroughtmehere.Astheonlychild,Ihavereceivedtheirfullattentionaswellasexpectation.Theyalwaystrytoprovidemethebestqualityoflifeandeducationthattheycouldaffordandfullyrespectmypersonalpreferencesandallofchoicesinmylife.Ilovethemwithallmyheart.Iamalsofeelverygratefulformyhusband,RenjiaZhou,forbeingtheperfect`Mr.Right'inmylife.Iverymuchappreciatehislove,trustandunderstanding,andfeelincrediblyluckytosharemylifeandestablishanewfamilywithhim. 5

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 9 LISTOFFIGURES ..................................... 10 ABSTRACT ......................................... 12 CHAPTER 1INTRODUCTIONTOGRAPHENEANDGRAPHITE ............... 14 1.1CrystalStructureandReciprocalLattice ................... 16 1.2BandStructureofGraphene .......................... 19 1.2.1FromWallaceModeltoDiracHamiltonian .............. 19 1.2.2ChiralityandPseudo-spin ....................... 21 1.2.3TrigonalWarping ............................ 23 1.3BandStructureofGraphite:Slonczewski-Weiss-McClureModel ...... 24 2PHYSICSOFMETALANDSEMICONDUCTORCONTACTS:SCHOTTKYVSOHMIC ...................................... 33 2.1SchottkyBarrierattheMetal-SemiconductorInterface ........... 34 2.1.1SchottkyBarrierFormation ...................... 34 2.1.1.1Schottky-Mottmodel:idealSchottkycontact ....... 34 2.1.1.2Image-forcelowering .................... 36 2.1.1.3Bardeenmodel:Fermi-levelpinning ............ 38 2.1.2ChargeDepletionRegion ....................... 40 2.1.2.1Abruptjunctionapproximation ............... 40 2.1.2.2Electriceldandbuilt-inpotential .............. 40 2.1.2.3Interfacecapacitance .................... 41 2.1.3ElectricalTransportProperty ..................... 42 2.1.3.1Thermionicemissiontheory ................. 43 2.1.3.2Tunnelingeffect ....................... 46 2.1.4MeasurementofSchottkyBarrierHeight ............... 47 2.1.4.1I-Vmeasurement ...................... 48 2.1.4.2Activationenergymeasurement .............. 49 2.1.4.3C-Vmeasurement ...................... 50 2.2OhmicContact ................................. 51 3GRAPHENE/SEMICONDUCTORSCHOTTKYJUNCTIONS ........... 59 3.1Overview .................................... 59 3.2ExperimentalMethods ............................. 61 3.2.1GrapheneGrowthandTransfer .................... 61 6

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3.2.2DeviceFabricationandCharacterization ............... 62 3.3ResultsandDiscussions ............................ 63 3.3.1GrapheneCharacterization ...................... 63 3.3.1.1Hallmeasurement ...................... 63 3.3.1.2Ramanspectroscopy .................... 64 3.3.2SchottkyDeviceCharacterization ................... 66 3.3.2.1J-Vcharacteristics ...................... 66 3.3.2.2C-Vcharacteristics ...................... 71 3.3.3Voltage-DependentSchottkyBarrierHeight ............. 72 3.3.3.1Voltage-inducedFermienergyshiftofgraphene ..... 72 3.3.3.2Modicationofthermionic-emissiontheory ........ 74 3.4Conclusion ................................... 76 3.5FutureDirection ................................ 76 4GRAPHENE/SILICONPHOTOVOLTAICSBYCHEMICALDOPING ....... 85 4.1Overview .................................... 85 4.2BackgroundofSchottkySolarCells ..................... 87 4.2.1SolarSpectrum ............................. 87 4.2.2PhysicalMechanismofSchottkySolarCells ............. 88 4.3ExperimentalMethods ............................. 91 4.3.1DeviceFabrication ........................... 91 4.3.2Electro-OpticalCharacterizationsofPhotovoltaics .......... 91 4.4ResultsandDiscussion ............................ 92 4.4.1J-VCharacteristics ........................... 92 4.4.2C-VCharacteristics ........................... 97 4.4.3ExternalQuantumEfciencyandCarrierlifetime .......... 98 4.5Summary .................................... 99 4.6FutureWork ................................... 100 5STRAIN-MODULATEDWEAK-LOCALIZATIONEFFECTINCVD-GROWNGRAPHENE ..................................... 114 5.1Introduction ................................... 114 5.1.1Weak-LocalizationinGraphene .................... 114 5.1.2StrainEngineeringinGraphene .................... 118 5.2ExperimentalMethods ............................. 119 5.2.1SamplePreparationandmeasurements ............... 119 5.2.2StrainCalculation ............................ 120 5.3ResultsandDiscussions ............................ 122 5.3.1WeakLocalizationunderStrains ................... 122 5.3.2Electron-ElectronInteractionunderStrains .............. 126 5.4Conclusion ................................... 129 5.5FutureDirections ................................ 129 5.5.1GrapheneonDifferentSubstrates ................... 129 5.5.2OpticalStudiesofMX2underUniaxialStrains ............ 130 7

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6FERROMAGNETISMINHIGHLYORIENTEDPYROLYTICGRAPHITE .... 140 6.1Overview .................................... 140 6.2IntroductiontoTransportPropertiesofGraphite:Two-BandModel .... 142 6.3ExperimentalProcedure ............................ 145 6.4ResultsandDiscussions ............................ 146 6.4.1MagneticProperties .......................... 146 6.4.2X-rayDiffractionandRamanSpectroscopy ............. 147 6.4.3ElectricalTransportProperties .................... 149 6.5Conclusion ................................... 151 6.6FutureDirections ................................ 152 REFERENCES ....................................... 159 BIOGRAPHICALSKETCH ................................ 170 8

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LISTOFTABLES Table page 1-1InteractionparametersofSWMcCmodel ..................... 32 3-1ExtractedSBH,donordensity,valueofgrapheneworkfunctiononeachsemiconductorSchottkyjunctionsat300K. .................... 82 9

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LISTOFFIGURES Figure page 1-1Schematicsofgrapheneandgraphitecrystalstructures. ............. 28 1-2SchematicsofgrapheneandgraphiteBrillouinzone. ............... 29 1-3Fullbandstructureofgrapheneinreciprocalspace. ............... 30 1-4Schematicsofpseudo-spin/spintextureingraphene/topologicalinsulators. .. 31 1-5GraphitebanddispersionalongHKHdirection. .................. 32 2-1Banddiagramsatametalandann-typesemiconductorinterface. ....... 53 2-2Banddiagramsatametalandap-typesemiconductorinterface. ........ 54 2-3Modiedbanddiagramduetoimageforcelowering. ............... 55 2-4Detailedband-structureofanidealn-typeSchottkyjunction. .......... 56 2-5Proleofvariousphysicalquantitiesinthechargedepletionregion. ....... 57 2-6Banddiagramofann-typeSchottky ........................ 58 3-1RoomtemperatureHallmeasurementofgraphene/SiO2/Si. ........... 78 3-2RamanSpectraofmonolayergraphene. ...................... 79 3-3In-situRamanspectratakenongraphene/GaN .................. 80 3-4RoomtemperatureJ-Vcharacteristics ....................... 81 3-5DevicegeometryofgraphenebasedSchottkydiode. ............... 82 3-6Plotsoftheinverse-squarecapacitance(1=C2)vsappliedbias(V) ....... 83 3-7Interfacebanddiagram ............................... 84 4-1Schematicsofairmassratioatapolarangle. .................. 102 4-2SolarenergyspectraatAM0(blackcurve)andAM1.5(redcurve). ....... 103 4-3Basicsofasolarcell. ................................ 104 4-4Outlookofgraphene/Sisolarcells. ......................... 105 4-5RoomtemperatureJ-Vcharacteristicsofagraphene/SiSchottkysolarcell .. 106 4-6DarkroomJ-Vcharacteristicsinthesemi-logarithmicscale ........... 107 4-7Seriesresistance(Rs)ofpristineanddopedgraphene/Sisolarcells. ...... 108 10

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4-8TheJ-Vcurvesunderilluminationtakenupto3daysafterdoping. ....... 109 4-9Darkroomcapacitance(C)vsvoltage(V)characterization. ........... 110 4-10Externalquantumefciency(EQE)vswavelength ................ 111 4-11Transientphotovoltagevsdecayingtime. ..................... 112 4-12Dopingeffectonthebanddiagram ......................... 113 5-1Schematicsofelectronscatteringatlowtemperature. .............. 132 5-2Schematicsofelectron'smomentumandpseudo-spininKandK0valleys. .. 133 5-3Angulardistributionofscatteringprobabilities ................... 134 5-4RamancharacterizationoftheCVDgrowngrapheneonCopper ........ 135 5-5Specimengeometryunderstrain. .......................... 136 5-6Loweldmagnetoconductanceundervariousstrains ............... 137 5-7Variousttingparametersvsexternallyappliedstrain. .............. 138 5-8Zero-eldnormalizedconductivityvsstrain .................... 139 6-1Lowtemperaturemagneticpropertycharacterizations .............. 154 6-2RamanspectraofaHOPGsample ......................... 155 6-3XRDpatternsofHOPGsamples .......................... 156 6-4Temperaturedependenceofin-planeresistivity .................. 157 6-5Out-of-planeresistivityvstemperature ....................... 158 11

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AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophyFUNDAMENTALSTUDIESOFGRAPHENE/GRAPHITEANDGRAPHENEBASEDSCHOTTKYPHOTOVOLTAICDEVICESByXiaochangMiaoAugust2013Chair:ArthurF.HebardMajor:PhysicsInthecarbonallotropesfamily,grapheneisoneofthemostversatilemembersandhasbeenextensivelystudiedsince2004.Thegoalofthisdissertationisnotonlytoinvestigatethenovelfundamentalscienceofgrapheneanditsthree-dimensionalsibling,graphite,butalsotoexploregraphene'spromisingpotentialinmodernelectronicandoptoelectronicdevices.Thersttwochaptersprovideaconciseintroductiontothefundamentalsolidstatephysicsofgraphene(aswellasgraphite)andthephysicsatthemetal/semiconductorinterfaces.Inthethirdchapter,wedemonstratetheformationofSchottkyjunctionsattheinterfacesofgraphene(semimetal)andvariousinorganicsemiconductorsthatplaydominatingrolesintoday'ssemiconductortechnology,suchasSi,SiC,GaAsandGaN.Asshownfromtheircurrent-voltage(I-V)andcapacitance-voltage(C-V)characteristics,theinterfacephysicscanbewelldescribedwithintheframeworkoftheSchottky-Mottmodel.TheresultsarealsowellconsistwiththatfromourpreviousstudiesongraphitebasedSchottkydiodes.Inthefourthchapter,asanextensionofgraphenebasedSchottkywork,weinvestigatethephotovoltaic(PV)effectofgraphene/Sijunctionsafterchemicallydopedwithanorganicpolymer(TFSA).Thepowerconversionefciencyofthesolarcellimprovesfrom1.9%to8.6%afterTFSAdoping,whichistherecordinallgraphenebasedPVs.TheI-V,C-Vandexternalquantumefciencymeasurementssuggest 12

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thatsuchasignicantenhancementinthedeviceperformancecanbeattributedtoadoping-induceddecreaseintheseriesresistanceandasimultaneousincreaseinthebuilt-inpotential.Inthefthchapter,weinvestigateforthersttimetheeffectofuniaxialstrainsonmagneto-transportpropertiesofgraphene.Wendthatlow-temperatureweaklocalizationeffectinmonolayergrapheneisgraduallysuppressedunderincreasingstrains,whichisduetoastrain-induceddecreasedintervalley-scatteringrate.Inchapter6,westudythehighvacuumthermalannealingeffectonanunconventionalferromagnetism(FM)inhighlyorientedpyrolyticgraphite(HOPG).TheFMdiminishesandeventuallydisappearsinannealedsamplesaccompaniedbyimprovedelectricaltransportpropertiesandcrystallinity.OurresultsindicatethattheFMismainlycomingfromthelatticeimperfections. 13

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CHAPTER1INTRODUCTIONTOGRAPHENEANDGRAPHITECarbonisaversatileatominnature.With4electronsintheoutermostshell,electronorbitalscanbeeithersp-(inamorphouscarbon),sp2-(incarbonnano-tubeandfullerene)orsp3-hybridized(indiamond).Asaresult,carboncomesinavarietyofwaysandformsabigfamilyofallotropes.Amongallofthefamilymembers,graphiteandits2Dcounterpart,graphene,arethemoststudiedonesinrecentdecades.Inparticular,since2004whengraphenerstbecameexperimentallyavailable[ 1 ],researchinterestandeffortinthiseldhaveundergonearocketingresurgence.Asaresult,GeimandNovoselovsharedtheNobelPrizeinPhysics2010fortheirgroundbreakingexperimentsregradingthetwo-dimensionalmaterialgraphenewhichallbeginsfrombringingthewondermaterial,graphene,tothemundaneworldbyaseeminglytrivialmethodexfoliationfromits3Dparent(graphite)usingscotch-tape[ 2 ].Conventionally,asolidcanbecategorizedaseitherametalorinsulatoraccordingtoitsbandstructure.However,graphene/graphiteisastatein-betweenandcalledasemimetal.Ingraphite,duetoasmalloverlapbetweenitsconductionbandandvalenceband,electronsandholesco-existwithasmalldensityof1018cm)]TJ /F3 7.97 Tf 6.59 0 Td[(3(foreachtypeofcarrier).Consequently,theFermi-level(EF)ofgraphiteisonly20meV[ 3 5 ],whichistwoordersofmagnitudelessthanthatinaregularmetalsuchascopper[ 6 ].Inaddition,becauseoftheultra-cleannessofgraphite,momentumrelaxationtime(p)atroomtemperatureis10)]TJ /F3 7.97 Tf 6.59 0 Td[(12s[ 3 ]incontrasttothatof10)]TJ /F3 7.97 Tf 6.59 0 Td[(14sinaconventionalmetal.LowcarrierdensityandtheextraordinarilylongmomentumrelaxationtimeenablegraphitetobedrivenintothequantumHallregimewithamoderatemagneticeldwheretheelectronlevelsarequantizedintoLandaulevelswithanappreciableenergyseparationbetweentwoadjacentstates,whilethisishardtorealizeinregularmetals.Besides,graphiteisalsoawell-studiedanisotropicmaterial,asaresultofthedifferencebetweenintraplanarandinterplanarbindingnature(i.e.intraplanarbonds 14

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vsinterplanarVanderWaalsforces).Thus,whilethein-planeresistivity(ab)showsametallictemperaturedependencefromroomtemperaturedownto5K,theout-of-planeresistivity(c)variesnon-monotonicallyinthattemperaturerangewithastillmysteriousunderlyingtransportmechanism.Atroomtemperature,abistypically4-5ordersofmagnitudelessthanc.However,whenthecrystaldimensionreducesfrom3Dgraphitedownto2Dgraphene,theparabolicenergydispersionevolvesintothewell-knownlineardispersiondeningtheDiraccone.Whileinheritingsomesimilarsuperiorphysicalpropertiesfromgraphite,graphenehasitsuniquecharacteristicsandtheunderlyingphysicscanbequitedifferent.Ingraphene,electrons/holesbehaveasmasslessDiracFermionasaconsequenceofthelinearenergydispersion,thusmobilityisfoundtobeashighas200,000cm2/(Vs)whentheFermienergyisclosetotheDiracpoint[ 7 ].Also,originatingfromthetwononequivalentsublattices(AandB)inthehexagonalcarbonnetwork,carriersingraphenepossessanadditionalsymmetrycalledchirality,whichisrelatedtotheso-called`pseudo-spin'intheDiracHamiltonianandconsistentwithaBerryphaseof[ 8 ].Thisunconventionalsymmetrycastslightonaseriesofpeculiarphysicalphenomenaingraphene,suchasweakanti-localizationeffectinthemagneto-conductanceandKleintunneling.Additionally,grapheneisthemechanicallystrongestmaterialwithanintrinsicstrengthof130GPa[ 9 ],beinghundredsoftimesstrongerthansteel.Furthermore,graphenehashighopticaltransparency(withtransmittanceof97.7%)fromnearIRtonearUV[ 10 ],therebyisconsideredasapromisingalternativetoindiumtinoxide(ITO)fortransparentconductingelectrodeswhicharewidelyusedinoptoelectronics[ 11 ].Withallofthesuperiorandexoticphysicalproperties,grapheneindeeddeservestheworldwidecomplimentasa`wondermaterial'.Thusavastmajorityofresearchefforthasbeeninvestednotonlytoexploretherichfundamentalscience,butalsotoexploitgraphene'sfullpotentialinthenextgenerationofelectronics. 15

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Inthischapter,anintroductoryoverviewonthetheoreticalbackgroundofgrapheneandgraphiteisgivenbyrsttreatingcrystalstructures,wherealltheremarkablephysicsstarts.Asa2Dbuildingelementofgraphite,graphene'sbandstructurewillbediscussedasapreludetothatofgraphite,fromtheclassictightbindingapproximation(Wallacemodel[ 12 ])whereonlytheinplanecouplingsareconsidered.Then,acontinuumtransitiontotheDiracequationisfollowedtogetthefamousconicalbanddispersionofgraphenenearthesixcornersofrstBrillouinzone.Subsequently,theprevalentSlonczewski-Weiss-McClure(SWMcC)modelisintroducedtoderivethefullbandstructureofgraphitewhentheout-of-planecouplingsaretakenintoaccount.Thechapterconcludesbyshowinghowacontinuumbandevolutionfrom3Dto2DmanifeststheconsistencybetweenSWMcCandWallacemodels. 1.1CrystalStructureandReciprocalLatticeAsshowninFig. 1-1 (a),carbonatomsinamonolayergraphenearerepetitivelyarrangedinhexagonalpatterns,formingstrongintraplanarcovalentbondswiththeirthreenearestneighbors.TheresultingcrystalstructurecanbedescribedasasetoftwodifferentsublatticesA(yellowball)andB(blueball),asillustratedinFig. 1-1 (a),with2Dlatticebasisvectorswithcoordinatesgivenby a1=a 23,p 3,a2=a 23,)]TJ 9.3 10.54 Td[(p 3.(1)Here,a=1.42Aisthelatticeconstant.Eachcarbonatomhasthreenearestneighbors.In-planeatomicorbitals(s,px,py)hybridize,formingthreebonds.Thesp2hybridizationgivesrisetostronginter-atomicinteractionthatisresponsiblefortheremarkablemechanicalstrengthandthermalstabilityofgraphene,unlikeother2Dmaterials.Also,sincetherearefourelectronsintheoutmostshell,with3tightlybondedinxyplane,onlyoneelectronisleftinthepzorbital(out-of-planeorbital).Thiselectronisdelocalizedandcontributestothein-planeelectricalconductivity. 16

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GraphiteiscomposedofsuccessivelystackedgraphenelayersintheverticaldirectionheldtogetherbyVanderWaalsforce.Byvirtueofdifferentinter-andintraplanarbindingnature(VanderWaalsforceversusbonds),graphitemanifestshighanisotropicelectricalandmagneticproperties[ 4 12 13 ].Also,owingtotheadditionaldimensionalongthec-axis,graphenelayerscanbestackedinvariouswayswithrespecttotheiradjacentneighbors,suchasBernal(ABAB),rhobomhedral(ABCABC)andAAAstacking(knownassimplehexagonalgraphite).Thesestackingordersareinterchangeablewitheachotherthrougheithermechanicalorthermaltreatment.Besides,variantstackingphasesbarelyaffecttheoverallbulkpropertiesofthegraphitesinceneithertheintralayercarbon-carbonbondinglengthnorinter-layerdistanceissignicantlyaltered.However,theycanbedistinguishablebyadvancedmaterialcharacterizationtechniques,suchasX-raydiffraction(XRD),Ramanspectroscopyandtransmissionelectronmicroscope(TEM).Amongthosediversestackingphases,Bernalstacking,asindicatedinFig. 1-1 (b),isthemostcommonlyseenandstablestackingphaseindiversecategoriesofgraphiteincludinghighlyorientedpyrolyticgraphite(HOPG),naturalgraphiteandKishgraphite.Forexample,innaturalgraphite,Bernalphasetakesapproximatelyapercentageof85%whilerhobomhedralandsimplehexagonalhave15%intotal[ 14 ].Withthesamein-planelatticefeatureasthatofgraphene,thelatticebasisvectorsingraphiteare a1=a 23,p 3,0,a2=a 23,)]TJ 9.3 10.54 Td[(p 3,0,c=c(0,0,1),(1)wherec6.7Aisthelatticeconstantintheverticaldirection.Asaresult,theinter-planardistancebetweentwoadjacentgraphenelayersisjustc=2=3.35A.Accordingly,theunitlatticevectorsinreciprocalspacecanbecalculatedas b1=2 3a1,p 3,0,b2=2 3a1,)]TJ 9.3 10.54 Td[(p 3,0,b3=2 c(0,0,1).(1) 17

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Keepingthexycomponentsinb1andb2,andneglectingb3,weobtainthereciprocallatticevectorbasisforgraphene.Aschematicdiagramofgraphite'srstBrillouinzone(BZ)isshowninFig. 1-2 (a),indicatingthatthe6-foldsymmetryinthelatticestructureisstillpreservedinreciprocalspacewithallhighsymmetrypointsaslabeled.TheFermisurfaceusuallylocatesintheproximityofzoneedgesalongHKHandH0K0H0,thus,generatingelectronandholepocketsaroundH(K0)andK(H0)points.Forintrinsicgraphite,theFermisurfaceisalignedinsuchawaytoperfectlycompensatesthenetofchargefromelectronsandholes(i.e.ne=nh).MorespecicswillbeintroducedinSec. 1.3 .The2Dcross-sectionofgraphite'sBZalongKK0planegivesthatofgraphene,whichcanotherwisebedeterminedfromtheenergycontour-plotasdepictedinFig. 1-2 (b).KandK0arethefamousDiracpoints,wheretheconductionandvalencebandofgraphenecoincidewitheachother.Theirrelativecoordinatestothecenter()]TJ /F1 11.955 Tf 6.94 0 Td[()oftheBZcanbewrittenas K=2 3a1,1 p 3,K0=2 3a1,)]TJ /F6 11.955 Tf 15.47 8.09 Td[(1 p 3.(1)Here,KandK0arerelatedtoeachotherbytimereversalsymmetry,sinceKiscentral-symmetricwithK0inthereciprocalspaceasreectedinFig. 1-2 (b).Theyarealsoreferredtoaschargeneutralitypoints,sinceinapieceofundopedpristinegraphene,theFermilevel(EF)locatesatthoseDiracpoints,leavingacompletelyfullvalenceband(EV)andcompletelyemptyconductionband(EC).Asaresult,thedensityofchargecarriers(n)vanishes.However,electron/holehaszeroeffectivemassattheDiracpoints,thereby,inprinciplethecarriermobility,=e=m,canbeinnitelylarge.AccordingtotheDrudemodel,theconductivity=nebecomesaproductofzeroandinnity.Herecomesthelong-standinginquiryontheminimumconductivity(min)ingraphene,especiallyforexperimentalists.Thepresenceofelectron-holepuddlesingraphenecomplicatesthedenitionofconductivitywhencarrierdensityisapproaching 18

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zero,therebyleavinganaccuratemeasurementoftheprefactorintheexpressionofminoutofthequestion[ 15 18 ]. 1.2BandStructureofGraphene 1.2.1FromWallaceModeltoDiracHamiltonianAsrstderivedbyJ.Wallacein1942fromthetightbindingapproximation[ 12 ],mono-layergraphenewasrevealedtobeasemiconductorwithzeroband-gap,thoughatthemomentgraphenewasnotaswellknownasitistodayandtheinitialmotivationforWallace'sworkwastostudygraphite'sbandstructurebyusinggrapheneasa2Dbuildingblock.TheWallacemodeltakesaccountoftwohoppingenergiesfromonesitetoitsrst(0)andsecondnearestneighbors(00),whileneglectingalltheout-of-planecouplings.Thus,theHamiltoniancanbewrittenas[ 12 19 ] H=)]TJ /F7 11.955 Tf 9.29 0 Td[(0Xi6=j,s(ays,ibs,j+H.C.))]TJ /F7 11.955 Tf 11.95 0 Td[(00Xi6=j,s(ays,ias,j+bys,ibs,j+H.C.).(1)Here,ai,s(ayi,s)denotesthecreation(annihilation)operatorofanelectronwiths(s=1 2)spinontheithsublatticeA.AsimilardenitionappliestooperatorsbandbyonthesublatticeB.Accordingly,bysolvingthesecularequation,thefullbanddispersion, (q)=0vuut 3+2cosp 3qya+4cos p 3 2qya!cos3 2qxa+200"cosp 3qya+2cos p 3 2qya!cos3 2qxa#, (1) isobtained.Fig. 1-3 showsafullbanddispersionaccordingtoEq.( 1 ).Theasymmetryof+(q)and)]TJ /F6 11.955 Tf 7.09 1.79 Td[((q)originatesfromanon-vanishing00,whichisusuallyoneortwoordersofmagnitudesmallerthan0[ 19 ].Sincebandextremalocateatthesixcorners(KandK0)oftheBrillouinzone,expandbanddispersiontotherstorderatoneofthoseDiracpointsandneglect00,yielding (k)~vFjkj.(1) 19

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Here,kisthewavevectormeasuredfromtheDiracpoints.vF=30a=(2~)istheFermivelocityofgraphene,withavalueof106m/s,afactor(1/300)ofthelightspeedinvacuum.Eq.( 1 )givesthewell-knownlineardispersionofgraphene,aswellastheeigenvaluesofDiracHamiltonian,whichcanbewrittenina(22)matrixas HK=~vF0B@0kx)]TJ /F4 11.955 Tf 11.95 0 Td[(ikykx+iky01CA=~vFk.(1)Likewise,theDiracHamiltoniancanalsobederivedfromthetight-bindingHamiltonianinEq.( 1 )asdiscussedinRef.[ 19 ]withmorespecics.Here,wejustskipthemathematicaldocumentationsincethesurplusalgebraisnotourmainfocus.AppearinginEq.( 1 ),=(x,y)arethePaulimatricesrelatedtotheelectronspin.However,ingraphene,doesnotrepresenttherealspin,butoriginatesfromthetwofoldsublattices(AandB)inrealspace,andcanbedescribedequivalentlybythexycomponentsofPaulimatricesinmathematics.Therefore,isalsoreferredtoaspseudo-spiningraphene.Inaddition,thoughthemasslessnatureofthechargecarrier(electronorhole)canbereectedmathematicallyinEq.( 1 ),itismoreessentiallycomingfromsymmetryrestriction.Specically,bothtimereversalsymmetryandinversionsymmetryrequirethemasstermintheDiracequationtovanish[ 20 ].Also,underthetimereversalsymmetrywithrespecttotheKvalley,theHamiltonianatK0valleyisgivenby HK0=~vFk,(1)whereisthecomplexconjugateof.Consequently,theeigenfunctionsofEq.( 1 )andEq.( 1 )inmomentumspacearesolvedtobe K(k)=1 p 20B@e)]TJ /F8 7.97 Tf 6.59 0 Td[(ik=2eik=21CA,K0(k)=1 p 20B@eik=2e)]TJ /F8 7.97 Tf 6.59 0 Td[(ik=21CA(1) 20

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withk=arctan(kx=ky).Theeigenfunctionsareanalogoustothetwo-componentspinorwave-functionwiththepolarangle=(correspondingtothesuperscript`'inKandK0)andtheazimuthalangle'=k(with`+'atKand`)]TJ /F1 11.955 Tf 9.3 0 Td[('atK0).Asmentionedbefore,suchatwo-componentfeatureresultsfromthetwodistinctsetsofsublatticesinthehexagonalcrystalstructure.Theangles=90areduetothe2Dnatureofthegraphenelattice,whiletheoppositesignofthe'atKandK0isadirectresultoftheirtimereversalsymmetry.Regardlessofthedifferentwave-functionsatKandK0,theeigenvalues(k)=~vFkarebothfour-folddegenerate.AccordingtoKramer'stheorem,foranyspin-1=2systemwithtimereversalsymmetry,theHamiltonianisatleasttwo-folddegenerate,whichgivesrisetothetwo-foldvalleydegeneracyhere.Inaddition,anothertwo-folddegeneracyoriginatesfromunliftedspin-degeneracypreservedbyaweakspin-orbitalcouplingingraphene,notonlybecauseoftherelativelysmallatomicnumberforcarbon,butalsoduetothe2Dnatureofthecrystallinestructure,whichminimizesthecouplingbetweenout-of-planeandin-planeorbitals[ 21 ]. 1.2.2ChiralityandPseudo-spinBeingmathematicallyequivalenttospin,twosetsofsublatticesingraphenesystementerintotheHamiltonianasanextraquantumdegreeoffreedomcalledpseudo-spin.BylookingattheexpressionfortheHamiltoniananditseigenvalues,onecaneasilygureoutthatintheKvalleythepositivesignink(forconductionband)meansthattheelectron'smomentumisparalleltoitspseudo-spininconductionband,whilethenegativesignmeansthattheananti-parallelcouplingforholesinthevalenceband.(ThecouplingisreversedinK0valley.)Therefore,thepseudo-spinislockedwithmomentuminasinglevalley,whichisusuallydescribedbyaquantumnumbernamed 21

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helicity(h)anddenedas h=p jpj=8>><>>:)]TJ /F6 11.955 Tf 9.3 0 Td[(1,ifk)]TJ /F11 11.955 Tf 10.69 0 Td[(p,1,ifkp. (1) Thus,themasslessDiracfermioningraphenehasanexplicitchirality.Apparently,hisgoodquantumnumbersinceitcommuteswiththeDiracHamiltonianinEq.( 1 ).Inthissense,themomentumislockedwiththepseudo-spin,therebyleadingtoaprohibitionofback-scattering,orevenlargeanglescatteringeventsingraphene.Boththespin-momentumlockingandDiracFermionnatureingrapheneremindsusofanother2Dsystemtopologicalinsulator,whichisalsoacurrentlypopularresearchareaincondensedmatterphysics.Theyindeedshareawidevarietyofsimilarities.Forinstance,frompreviousSTMstudies[ 22 23 ],theelectron-holepuddlesareobservedbothingrapheneandtopologicalinsulatorwhenEFisclosetotheDiracpoint,duetothepresenceofchargedimpurities.However,grapheneandtopologicalinsulatorsarefundamentallydifferentfromeachother.Themostcrucialdistinctionisthat,inatopologicalinsulator,itistherealspinthatcouplestothecarrier'smomentum,incontrasttothepseudo-spininthegraphenecase.Thatuniquefeaturemakestopologicalinsulatoramoredesirableandpromisingmaterialinthesenseofspintronicsapplications,wherespinmanipulationcanberealizedbyanexternalelectriceld.Second,asillustratedinFig. 1-4 ,duetothestrongspin-orbitcoupling,thespininatopologicalinsulatorisorthogonaltothemomentum,whileingraphene,pseudo-spiniseitherparalleloranti-paralleltothemomentum.Also,ingraphene,thereareafour-folddegeneracyintheenergydispersionrelationandtwodistinctDiracconesintherstBrillouinzone,whileonlyasingleDiracconeexistsinthetopologicalinsulatorandenergyisonlytwo-folddegenerateattheDiracConeaspredictedbyKramer'stheorem.Suchadegeneracyisprotectedonlybythetimereversalsymmetryofthesurfacestates,unlikethesublattice-inducedvalleydegeneracyingraphene.Asaresult, 22

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thespintextureissupposedtobemorerobustinatopologicalinsulator,therebythesuppressionofback-scatteringandgaplessfeatureareonlyvulnerabletomagneticimpuritieswhileinerttonon-magneticdefects.Incontrast,back-scatteringismoreeasilyresumedwheneverUmklappprocessesarepresentduetoanyshort-rangeinteraction(magneticornon-magnetic)tolinkKandK0valleysandbreaktheconservationofhelicity.Thatiswhygraphenemoreoftenshowsapositivemagnetoconductanceinlowtemperaturetransportstudies(knownasweak-localizationeffect)[ 24 25 ],whileintopologicalinsulatorsatransitionfromweakanti-localizationtoweaklocalizationisexperimentallyobservedwhenmagneticimpuritiesarepresent[ 26 ].MoretransportpropertiesaretobediscussedwhenitcomestotheweaklocalizationeffectingrapheneinCh. 5 ofthisthesis.Here,acomparisonismadebetweengrapheneandtopologicalinsulator,aimingtohelpthereaderunderstandthetwoseemingly-alikesystemsatamoreprofoundlevel. 1.2.3TrigonalWarpingFromEq.( 1 )toEq.( 1 ),allnon-lineartermsand00termsareneglectedwhenkxa,kya<0.1.However,whenkisfurtherawayfromDiracpoint,thebandprolestartstodeviatefromtheconicalfeature,whereallthehigher-ordertermscomeintoplayandchargecarriersbecomemassive.SuchamodicationtotheDiracequationiscalledthetrigonalwarpingeffect.Thus,thecross-sectionoftheDiracconenolongerlookscircularandtheenergyspectrumbecomesanisotropicinmomentumspace.Thetrigonalwarpingeffectisbelievedtodegradethecarriertransportpropertyingraphene,sinceitbreaksbothchiralsymmetryandtimereversalsymmetrywithinasinglevalley[ 19 27 ].Asaresult,back-scatteringcanbeturnedon,andgivesrisetoacrossoverfromelectronweakanti-localizationtoweaklocalizationaspreviouslyobservedintransportmeasurement[ 24 ].SincethetrigonalwarpingiscloselyrelatedtothepositionofEF,themagnitudeoftrigonalwarpingeffectistunablebyeitherchemicaldopingorelectrostaticgating.TrigonalwarpingbecomesappreciablewhenEFisaway 23

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fromthechargeneutralitypointby0.5eV,correspondingtoacarrierconcentration(nc)of1.61013cm)]TJ /F3 7.97 Tf 6.58 0 Td[(2.Accordingly,trigonalwarpingisfoundtobemoreprominentinCVDgraphenethaninmechanicallyexfoliatedakes,duetothedifferentsampleprocessingproceduresandamountofcrystaldefects.Usually,inCVDgraphene,post-transfertechniquesandconsiderableamountofgrainboundariesfacilitatetrappingofoxygenandwatermolecules[ 28 30 ].Consequently,thecarrierconcentrationcanbefeasiblybroughtabovenc[ 25 ].Thus,postthermaltreatmentinH2/Ar2forminggasat300CforasamplemadefromCVDgrapheneissometimesnecessarytoeliminatethoseabsorbatesandimprovesamplequality[ 29 31 ]. 1.3BandStructureofGraphite:Slonczewski-Weiss-McClureModelSincetheVanderWaalsforcestackingbetweensuccessivegraphenelayersismuchweakerthanbondingwithineachgrapheneplane,theWallacemodeldoesnotgiveapreciseenergyspectrumofgraphiteasitonlycountstheinplanecouplingandneglectsalloftheout-of-planecouplings.However,aslaterdemonstratedbySlonczewsk,WeissandMcClure(SWMcC)inthelate1950s[ 32 33 ],theout-of-planecouplingsleadtoaniteoverlapbetweenconductionandvalencebandingraphite,incontrasttoazero-gapfeaturedenergydispersionofgraphene.AsadescendentoftheWallacemodel,theSWMcCmodelismorecomprehensiveandthemostprevailingtheoreticalframeworkthathasbeensuccessfullyappliedtoexplainavastmajorityofinvitingphysicalphenomenaingraphite,suchasdiamagnetism[ 34 ],deHaas-vanAlpheneffect[ 35 ],ShubnikovHaasoscillation[ 36 ]andopticalproperties[ 37 38 ].BasedontheclassicaltightbindingapproximationoftheBernalstackingsequence,theSWMcCmodelgivesathree-dimensionalbandstructureinmomentumspaceusing7differentinteractionparametersaslistedinTable. 1-1 withcarefulconsiderationsofinterlayercouplings.ThegeneralHamiltoniancanbewrittenasa(44)matrixasadoptedfromRef.[ 4 ] 24

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H=0BBBBBBB@E10H13H130E2H23)]TJ /F4 11.955 Tf 9.3 0 Td[(H23H13H23E3H33H13)]TJ /F4 11.955 Tf 9.3 0 Td[(H23H33E31CCCCCCCA(1)withalldiagonalcomponents E1=+21coskzc 2+25cos2kzc 2, (1) E2=)]TJ /F6 11.955 Tf 11.95 0 Td[(21coskzc 2+25cos2kzc 2, (1) E3=22cos2kzc 2. (1) ThesecularequationoftheSWMcCHamiltoniancanbeanalyticallysolvedwhenthetrigonalwarpingeffect(i.e.3)isnegligible.Theobtainedeigenvalues1and2giveathreedimensionalbanddispersionink-space,whichcanbeexpressedas 1=1 2(E1+E3)s 1 4(E1)]TJ /F4 11.955 Tf 11.95 0 Td[(E3)2+20)]TJ /F6 11.955 Tf 11.95 0 Td[(24cos2kzc 22, (1) 2=1 2(E2+E3)s 1 4(E2)]TJ /F4 11.955 Tf 11.95 0 Td[(E3)2+20+24cos2kzc 22. (1) Here =3 2ak(1)isadimensionlessparameterwithkrepresentingtheinplanewavevectorasmeasuredfromtheK(K0)point[ 4 ].Theparametera=1.46Aistheclosestdistancebetweentwocarbonatomsinthesameplane.SinceEFofgraphiteisclosetotheverticalzoneedge,thebandstructurealongHKHismostinvolved.Bysetting=0andplugginginrelevanttightbindingparametersfromTable. 1-1 ,thebanddispersioncanbeplottedasshowninFig. 1-5 .Asseenfromthebanddispersionrelation,E3isalwaysdoubledegeneratealongHKH,whilethedegeneracyofE1andE2isliftedwhenKisawayfromHpoint. 25

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Inaddition,anitebandoverlap,originatingfromthetheinterlayercoupling(2),givesrisetothecoexistenceofelectronsandholes,whichareindicatedaspinkandlightblueshadingareasinFig. 1-5 ,respectively.ElectronsattheKpointaretermedasmajorityelectrons.Andsuchachargecarriertypeisdeterminedbyanegativevalueof2.However,thesignof2hadbeencontroversialattheearlystageofgraphiteresearchandwasnotidentieduntil1986byM.S.Dresselhausandhercoworkersfromtheirlasermagneto-reectionexperiment[ 39 ].Holesattheextremalholepocket(somewherebetweenKandH)aremajorityholes.Thenumberofmajoritycarriersarebothontheorderof1018cm)]TJ /F3 7.97 Tf 6.59 0 Td[(3[ 3 35 ],ordersofmagnitudelesscomparedtoregularmetals.Besides,holesthatareclosetotheHpointaretheminorityholes,andtheirdensityiscloselyrelatedto.TheminorityholeislaterfoundtoberesponsiblefortheDiracFermionbehavioringraphiteasobservedinSTM[ 40 ],ARPES[ 41 ]andmagneto-opticalstudies[ 42 ].Allthecarrierscontributeequallytotransportpropertywithslightlydifferentmobilities(e>h)[ 35 ],thusrequiringatwo-bandmodeltointerpretbothlongitudinalandtraversalmagnetoresistivity[ 3 5 ]whichisuniqueforsemimetals.Thistwo-bandmodelwillbelaterdiscussedinmoredetailinCh. 6 ofthisthesiswhenweaddressthetransportpropertiesofgraphite.Besides,ifalloftheout-of-planebindingparametersarevanished(i.e.i=0,i=f2,3,4,5g)and=0whichisbacktothegraphenecase,Eq.( 1 )andEq.( 1 )arereducedto 1,2=3 2a0k=~vFk,(1)where1,2istheexactDiracenergydispersionrelationdescribedbyEq.( 1 )withfour-folddegeneracy,giventhatvF=30a=(2~).ThissuggeststhattheWallacemodelissomehowembracedintheSWMcCmodel.However,theinplanebindingparameter0isbarelyaffectedwhengraphenelayersaresuccessivelystackingalongthec)]TJ /F1 11.955 Tf 9.3 0 Td[(axis.Thisisattributedtothenatureofstronginplanebindings.Moreover,theSWMcCmodelisalsowidelyappliedtounderstandingthefundamentalphysicsingraphiteintercalation 26

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compounds,whereintroducedforeignatomsaretreatedasaperturbationtothebandstructureofpristinegraphite[ 4 ].Theinterlayercouplingsareweakenedasaresultoflatticeswellinginthec-axis.Theenergydispersioncanbedriventographenelimitedatalowdoseofintercalatedatoms[ 4 ].ThediscussiontothispointisbasedontheBernalstackingcrystalstructure,sinceitisthepredominantstackingphaseingraphite,especiallyinhighlyorientedpyrolyticgraphite(HOPG)withsmallmosaicspreadangles.Althoughdifferentstackingsequencesaredescribedbyuniquecrystalsymmetryandsymmetrygroup,theyhaveverylittleeffectonthebandstructureofbulkgraphitederivedfromtheSWMcCmodelwithslightmodicationstotheout-of-planecouplingparameters.Nevertheless,fortri-andbi-layergraphene,correspondingbandstructuresaresensitivetostackingorderwheretheinversionsymmetryplaysanvitalrole.Therefore,variousstackingorderscangiverisetodistinctlydifferentphysicalphenomenaasobservedinRamanspectroscopy[ 43 44 ],infraredabsorptionspectroscopy[ 45 ]andtransportexperiments[ 46 ].However,morespecicsonthebandstructureoffewlayergrapheneisoutofthescopeofthisthesis,andtheyarenotwelldescribedbytheSWMcCmodel. 27

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Figure1-1. Schematicsofgrapheneandgraphitecrystalstructures.A)Thehoneycomblatticestructureofgraphenecanbedepictedasrepetitivelytranslatingaunitcellwithtwocarbonatoms(AandB)by2latticevectorsa1anda2asdened.B)Graphiteiscomposedofmultiplegraphenelayersstackingintheverticaldirection.TheBernalstackingsequencefollowsanABABABpattern,orrather,onelayerrotates60withrespecttoitssuccessiveneighbor.Duetothesymmetryofthehoneycomblattice,therstandthirdlayerareequivalent.Accordingly,atomscanbelabeledasA1andB1intherstlayer,A2andB2inthesecondlayer. 28

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Figure1-2. SchematicsofgrapheneandgraphiteBrillouinzone.A)Brillouinzoneofgraphiteastakenfromref.[ 4 ].B)2Denergycontour-plotofgraphenealsoshowstheproleoftherstBrillouinzoneofgraphenewithDiracpointsK(lightbluedot)andK0(navydot)atthesixcorners. 29

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Figure1-3. Fullbandstructureofgrapheneinreciprocalspace.Thezoominimage(intheblackpanel)ofthebanddispersioninthevicinityoftheDiracpointK(K0)showsaconicalprole. 30

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Figure1-4. Schematicsofpseudo-spin/spintextureingraphene/topologicalinsulators.A)Ingraphene,electron'spseudo-spinisparalleltoitsmomentuminKvalley,whileitisanti-paralleltomomentuminK0valley.Forhole,thecouplingisintheoppositemannerwithrespecttothatforelectroninthesamevalley.B)Inatopologicalinsulator,spinisperpendiculartomomentum.Forelectron,spinrotatespositivelyaroundtheenergycontouroftheconductionband,whiletheholespinrotatesnegativelyaroundtheenergycontourofthevalenceband. 31

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Table1-1. InteractionparametersofSWMcCmodel InteractionparameterPhysicaldescriptionValuein(eV)[ 4 5 47 ] 0InteractionbetweenAandBatomsinthesameplane3.201InteractionbetweennearestB1andA2inadjacentlayers0.402InteractionbetweentwonearestB1orB2atomsfromthesecondnearestlayerwithaseparationofc)]TJ /F1 11.955 Tf 9.3 0 Td[(0.023InteractionbetweennearestA1andB2inadjacentlayers0.324InteractionbetweenB1andB2insuccessivelayers0.045InteractionbetweentwonearestA1orA2atomsfromthesecondnearestlayerwithaseparationofc0.04Anisotropyofthecrystallineeldinasingleplane0.04 Figure1-5. GraphitebanddispersionalongHKHdirection.FermilevelintersectsE3andgivesrisetothecoexistenceofelectronandholepocketsalongthezoneedge. 32

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CHAPTER2PHYSICSOFMETALANDSEMICONDUCTORCONTACTS:SCHOTTKYVSOHMICTheintimatecontactofmetalandsemiconductor(SC)isubiquitousinsolid-stateelectronics.Becauseoftheirindispensableapplicationinsemiconductorindustriesandadvancedmodernelectricaltechnologies,thephysicalpropertiesofmetal-semiconductorcontactshavebeenwidelystudiedsincethebeginningof20thcentury.Giventhefundamentaldifferenceinthebandstructuresbetweenametalandasemiconductor,theinterfacephysicsismainlygovernedbythepositionsofFermilevelsatbothsidesbeforetheyarebroughtintocontact.Ingeneral,twodifferentbehaviorsarenamedintermsofthechargetransportpropertiesacrosstheinterface,i.e.(1)Schottkyand(2)ohmiccontacts,whicharegoingtobediscussedrespectivelyinmorespecicsinthefollowingtwosectionsofthischapter.First,theoriginofSchottkyBarrierformationwillbeintroducedstartingfromtheidealcasedescribedbySchottky-Mottmodel.Subsequently,twomostcommonlyseennon-idealeffects,(1)imageforceloweringand(2)Fermi-levelpinning,arealsodiscussedrespectivelytoshowthedeviationsintheSchottkybarrierheight(SBH)predictedbytheSchottky-Mottmodel.Inadditional,theuniqueelectricaltransportpropertyandinterfacecapacitance,aswellastherelatedexperimentalmethodstodeterminetheSBH,willalsobebrieyreviewed.Finally,theohmiccontact,asanessentialroleinsemiconductordevices,andthecommonrecipestofabricateohmiccontactarebrieyintroduced.Thischapterprovidesabackgroundoverviewonthephysicsatmetal-semiconductorinterface,servingasaprecludeforgraphenebasedSchottkyjunctionsdiscussedinlaterpartsofthisthesis.ForamoreadvanceddiscussionbothonsemiconductorandSchottkybarrierphysics,pleaserefertoRef.[ 48 ]andRef.[ 49 ]. 33

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2.1SchottkyBarrierattheMetal-SemiconductorInterfaceSchottkybarrierphysicshasbeenextensivelyexploredsincetheearlyestablishmentofitsprimitiveframeworkbySchottkyandMottin1930's[ 50 51 ].ThebarrierheightisaresultofthemismatchedFermilevelsofthemetalandsemiconductor.AsshowninthermionicemissiontheoryrstdevelopedbyBethein1942[ 52 ],theSBHgovernstheessentialelectricaltransportpropertiesacrosstheinterface.TheI-Vcharacteristicsshowrectifyingbehaviorwhichcloselyresemblesthatofap-njunction.Orrather,currentfollowinaSchottkydiodeisunidirectionalandexponentiallydependentontheappliedbias.Schottkydiodesarethekeycomponentsinmetal-semiconductoreldeffecttransistors(MESFETs)andhighelectronmobilitytransistors(HEMTs),thusplayingancrucialroleinmodernelectronicandoptoelectronicdevices. 2.1.1SchottkyBarrierFormation 2.1.1.1Schottky-Mottmodel:idealSchottkycontactBanddiagramsofametalandann-type(p-type)semiconductorpriortotheircontactisshowninFig. 2-1 (a)(Fig. 2-2 (a).Inann-typesemiconductor,thenumberdensityofelectronscanbeexpressedas n=NCexp)]TJ /F4 11.955 Tf 10.5 8.09 Td[(EC)]TJ /F4 11.955 Tf 11.95 0 Td[(EF kBT.(2)Here,theFermienergyEF(equivalenttothechemicalpotential)lieswithinthebandgapwherecarriersareforbidden.TheexpressionforEFcanbeinferredfromEq.( 2 )as EF=EC)]TJ /F4 11.955 Tf 11.96 0 Td[(kBTlnNC n,(2)whereNC,intheunitsofcm)]TJ /F3 7.97 Tf 6.59 0 Td[(3,istheeffectivedensityofstatesoftheconductionband(EC).DuetothedissimilarityoftheFermilevelsonbothsides(EMetalFandESCF),whenthemetalandsemiconductorcomeintocontact,theexcesscharges(electronsinn-type 34

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semiconductor;holesinp-typesemiconductor)owfromthesemiconductorsidetothemetalside.Consequently,theESCFnlowersdown(ESCFprisesupinp-typesemiconductor),whileEMetalFusuallyxedintactduetothelargedensityofstatesaroundEFinametal.Thereby,thewholesystemarrivesatanewthermalequilibriumwithauniversalFermilevel(EF)onbothsidesasillustratedinFig. 2-1 (b)(Fig. 2-2 (b)).First,let'sconsiderthesimplestidealcasewherethesurfacestateisabsentandmetalandan-typesemiconductorareinanintimatecontactwitheachother(i.e.nointerfacialdipoleoroxidationlayer).AccordingtoSchottky-Motttheory,theresultingn-typeSchottkyBarrierHeight(0Bn)canbeexpressedas 0Bn=W)]TJ /F7 11.955 Tf 11.95 0 Td[(,(2)whereWistheworkfunctionofametalandistheelectronafnityofasemiconductor,representingtheminimumenergypenaltyrequiredtoreleaseanelectronfromametalorsemiconductor,respectively.Likewise,thep-typeSchottkyBarrierHeight(0Bp)asillustratedinFig. 2-2 (b)isgivenby e0Bp=Eg)]TJ /F4 11.955 Tf 11.95 0 Td[(e0Bn=Eg)]TJ /F4 11.955 Tf 11.95 0 Td[(e(W)]TJ /F7 11.955 Tf 11.96 0 Td[().(2)Therefore,thesumofanidealn-typeandanidealp-typeSchottkybarrierheightsbasedonthesamemetal-semiconductorcombinationisjustthebandgap(Eg)ofthesemiconductor,i.e. e(0Bn+0Bp)=Eg.(2)However,theSchottky-MottmodelonlygivestheSchottkybarrierheight(SBH)undertheidealcondition.Inreality,therearesomeothereffects:(1)existenceofinterfacelayer(especiallyforSilicon,thereisanativeoxidationlayeronthesurface),(2)imageforceloweringand(3)Fermi-levelpinningthatallcanleadtonoticeablediscrepanciesintheexpectedvaluesofSBH.Wewilldiscussthoseeffectsinthe 35

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followingsubsectionswithmorespecics.Forsimplicity,allofthefollowingdiscussionswillbefocusedonn-typeSchottkyifnototherwisespecied. 2.1.1.2Image-forceloweringWhenachargeisplacedinthevicinityofagroundedmetal,duetotheinducedpolarization-chargeonthesurfaceofmetal,thesolutionofelectriceldisnolongerthesameasthatofachargeinfreespace.Aclassicalandanalyticalsolutioninelectromagnetismistointroduceanimagechargewiththesamemagnitudebutanoppositesignonthemetalside.Consequently,theeffectontheelectriceldfromthesurfacepolarization-chargeisabletobesimulatedbysuchaimaginarycharge.Similarly,inanintimateSchottkycontactunderzerobias,whenanelectronistravelingclosetothemetal,itsimagewillbeinducedinsidethemetalasindicatedinFig. 2-3 .TheconsequentattractiveCoulombforcefacilitatestheelectron'stransportfromsemiconductortothemetal,whichinprincipleisequivalenttoaneffectivelyreducedSBH(Bn).Let'sdenotesuchareductioninmagnitudewith.AccordingtoCoulomb'slaw,theattractiveforceF(x)betweentheelectronanditsimageatadistanceof2xcanbeevaluatedby F(x)=)]TJ /F4 11.955 Tf 34.8 8.09 Td[(e2 40s(2x)2=)]TJ /F4 11.955 Tf 29.92 8.09 Td[(e2 160sx2,(2)where0=8.8510)]TJ /F3 7.97 Tf 6.58 0 Td[(12F/misthevacuumpermittivityandsistherelativepermittivityofthesemiconductor.Thus,theresultingpotentialenergy,Uim(x)isgivenby Uim(x)=Zx1F(x0)dx0=)]TJ /F4 11.955 Tf 27.45 8.08 Td[(e2 160sx.(2)Takingintoaccounttheoriginalelectricalpotentialacrossthedepletionregion,V(x),describedbyEq.( 2 )(tobederivedinSec. 2.1.2.1 ),theoverallelectronpotentialenergyisgivenby U(x)=Uim(x))]TJ /F4 11.955 Tf 11.96 0 Td[(eV(x)=)]TJ /F4 11.955 Tf 27.46 8.09 Td[(e2 160sx)]TJ /F4 11.955 Tf 13.15 8.09 Td[(e2ND 0sWDx)]TJ /F6 11.955 Tf 13.15 8.09 Td[(1 2x2,(2) 36

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whereNDandWDdenotethedensityofshallowdonorionsandthewidthofdepletionregion,respectively.ToobtainthemaximumvalueofU(x),let dU(x) dx=e2 160sx2)]TJ /F4 11.955 Tf 13.15 8.09 Td[(e2ND 0s(WD)]TJ /F4 11.955 Tf 11.96 0 Td[(x)=0.(2)Sincetheimpactfromtheimagechargeismostsignicantintheproximityofthemetal-semiconductorinterfaceindicatingthatxWD,Eq. 2 canbeapproximatedas dU(x) dxe2 160sx2)]TJ /F4 11.955 Tf 13.15 8.09 Td[(e2ND 0sWD=0.(2)Therefore,xissolvedtobe xm=r 1 16NDWD.(2)Thesubscript'm'ofxmdenotesthepositionofmaximumU(x).Andcanbecalculatedas =0)]TJ /F4 11.955 Tf 13.15 8.09 Td[(U(xm) e=e 0sr NDWD 4.(2)SubstitutingEq.( 2 )(tobederivedinSec. 2.1.4.3 )withV=0toeliminateWD,itgives =e3NDVbi 82(0s)31=4(2)Thus,asseenfromFig. 2-3 ,theeffectiveSBH(Bn)forchargetransportisgivenby Bn=0Bn)]TJ /F6 11.955 Tf 11.96 0 Td[((2)ThemagnitudeofisusuallytensofmV'sforSilicon(Si)withmediumdopinglevel,anorderofmagnitudelessthan0Bn.Furthermore,underforwardbias,WDdecreasesgivingrisetoasimultaneousslightdecreasein.Therefore,imageforceloweringisnotastrongphenomenoninaSi-basedSchottkyjunctionwithahigh-work-functionmetal(W>4.8eV),suchasstronglyholedopedgraphene. 37

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2.1.1.3Bardeenmodel:Fermi-levelpinningTheSchottky-Mottmodelneglectsthepresenceofsurfacestates,thusassumingthattheindexofinterfacebehavior(S)equalstounity,whereSisdenedas Sd0Bn dW.(2)However,surfacestatesatasemiconductorsurfaceareaninherentpropertyofthesemiconductorandmayoriginatefromuncompensatedchemicalbondsoftheoutermostatoms(especiallyincovalentsemiconductors)orunavoidabledefectsinducedinthevicinityoftheinterfaceduringmetaldepositionprocess(particularlyforIII-Vcompounds).InaSchottkycontact,thesurfacestatesusuallybehaveassurfacechargetrapsandconsequentlyinducesurfacedipolesifmetalandsemiconductorareseparatedbyanultrathininterfaciallayer,whichinpracticemaysignicantlymodifytheSBHfromthatgivenbyEq.( 2 )dependingonthedensityofthosestates.AsacomplementtotheSchottky-Mottmodel,theBardeenmodelwasdevelopedin1947tostudytheeffectofsurfacestatesonSBHandtoaddressthefailureoftheSchottky-MottmodelinderivationforSBHsformetal/Sipointcontacts[ 48 49 ].WithintheframeworkofBardeenmodel,theexpressionfortheSBHwasdeducedtobe 0Bn=0(W)]TJ /F7 11.955 Tf 11.95 0 Td[()+(1)]TJ /F7 11.955 Tf 11.96 0 Td[(0)Eg e)]TJ /F7 11.955 Tf 11.96 0 Td[(CNL0W+1 (2) with 0=0in 0in+e2Ds(2)and 1(1)]TJ /F7 11.955 Tf 11.95 0 Td[(0)Eg e)]TJ /F7 11.955 Tf 11.96 0 Td[(CNL)]TJ /F7 11.955 Tf 11.96 0 Td[(0.(2)Here,inandaretherelativedielectricconstantandthicknessoftheinterfaciallayer,respectively.CNListhechargeneutralitylevelatthesurfaceofthesemiconductor, 38

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whichdemarcatesthenatureofthosesurfacestatesasacceptor-ordonor-type.Specically,theacceptor-(donor-)typesatesresideabove(below)CNL,andarenegativelycharged(neutral)whenoccupiedandneutral(positively)whenempty.Dsisthedensityofacceptor-typesurfacestatesperunitareaperenergy.Inthisscenario,theindexofinterfacebehavior,S,explicitlyreliesonthedensityofsurfacechargetraps(Dtr)through Sd0Bn dW=0=0in 0in+e2Dtr(2)Here,let'slookattwoextremelimits: 1. whenDtr!0,i.e.intheabsenceofthesurfacechargetrapsites,0!1(alsoS!1).Eq.( 2 )reducestoEq.( 2 ),i.e.goesbacktoSchottky-Mottmodel. 2. whenDtr!1,i.e.inthepresenceofextremelylargedensityofsurfacechargetrapsites,0!0.Asaresult,Eq.( 2 )reducesto 0Bn=Eg e)]TJ /F7 11.955 Tf 11.95 0 Td[(CNL.(2)Underthiscircumstance,SBH(0Bn)isindependentofmetal'sworkfunction,thusleadingtoS0.Thisphenomenoniscalled`Fermi-levelpinning'andiscommonlyseeninSchottkyjunctionsbasedonIII-Vcompoundsduetoahugedensityofsurfacestates[ 48 49 ].Physically,itmeanswhenthemetalandsemiconductorarebroughtintocontact,alloftheexcesselectronsowingfromsemiconductortometal(astoreachtheequilibriumstate)aretrappedattheinterfacesothattheresultedSBHbarelydependsonthemetal'sworkfunction,andinsteadreliesmostlyonthesurfacepropertyofthesemiconductor.Inpractice,usuallythereareanitenumberofchargetrapsatthesurfaceofasemiconductor,resultingaSBHcasein-between(i.e.0<0<1).BystudyingvariousSchottkycontacts(withdifferentspeciesofmetals)onasametypeofsemiconductingsubstrates,wecanobtainnumericalvaluesfor0and1,fromwhichvaluesof(CNL)andotherimportantparametersforasemiconductorcanbeestimated/extracted.Inthissense,detailedstudiesofSchottkydiodeprovideanopportunitytoinvestigatetheintrinsicproperties,especiallyatthesurface,ofasemiconductor. 39

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2.1.2ChargeDepletionRegionAsmentionedabove,whenametalandasemiconductor(stillfocusonn-typesemiconductor)withdifferentFermi-levelscomeintointimatecontactwitheachother,majorityelectronsfromthesemiconductorsideowintothemetalsideinordertoequilibrateFermi-levelonbothsidessothatthenetcurrentiszero(i.e.thewholesystemisatequilibrium).Asaresult,therewillbeachargedepletionregionleftbehindinthesemiconductorneartheinterfaceasindicatedinFig. 2-4 ,incontrasttotheatbandregion(i.e.chargeneutralregion)wherethereisnoelectriceldandhenceremainschargeneutral.TheinterestinganduniquefundamentalphysicsofaSchottkyjunctionderivesfromthepresenceofthisdepletionregion. 2.1.2.1AbruptjunctionapproximationTheconceptof`Abruptjunctionapproximation'wasrstdevelopedforp-njunctionswherethechargedistributionattheinterfacewasassumedtohaveaboxprole.Thisassumption/approximationgreatlysimpliesthecomplicatedinterfacephysicsinp-njunction.Duetoitssuccessandmanysimilaritiesbetweenp-njunctionandSchottkydiode,wecanstillapplytheabruptjunctionapproximationtoSchottkyjunctiononthesemiconductorside,i.e.assumethatchargeisuniformlydistributedoverthedepletionregioninthesemiconductorasillustratedinFig. 2-5 .Atroomtemperature,assumethatalloftheshallowbanddopants(i.e.shallowdonorsinn-typesemiconductor)arecompletelyionized,thusnND,whereNDisthedensityofshallowdonors.Therefore,thechargedensityisgivenby (x)=8>><>>:eND,0xWD0,x>WD,(2)whereWDisthewidthofdepletionregion. 2.1.2.2Electriceldandbuilt-inpotentialAccordingtoPoisson'sEquation, 40

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dE(x) dx=8><>:eND 0s,0xWD0,x>WD,(2)wheresistherelativepermittivityofthesemiconductor.Withtheboundarycondition:E(x=WD)=0,wecansolvePoisson'sEquationandobtaintheexpressionforelectriceld E(x)=8><>:eND 0s(x)]TJ /F4 11.955 Tf 11.95 0 Td[(WD),0xWD0,x>WD.(2)GiventhatV(x=0)=0andV(xWD)=Vbi,integratingoverthespaceyieldselectricalpotentialas V(x)=8><>:eND 0s(WDx)]TJ /F6 11.955 Tf 13.15 8.09 Td[(1 2x2),0xWDVbi,x>WD.(2)Here,Vbiisthebuilt-inpotential.Takingaccountofthecontinuityoftheelectricpotentialatx=WD,Vbiisfoundtobe Vbi=eND 20sW2D.(2)Besides,asindicatedinFig. 2-4 ,theenergydifferencebetweene0BnandeVbiisjust(EC)]TJ /F4 11.955 Tf 11.95 0 Td[(EF).CombinedwithEq.( 2 ),Vbicanalsobeexpressedas Vbi=0Bn)]TJ /F4 11.955 Tf 13.16 8.09 Td[(kBT elnNC ND.(2)Eq.( 2 )showsthatVbianintrinsicpropertyofaSchottkycontactandanindirectmeasureofSBH(0Bn).Notethatfornon-degeneratesemiconductor,ND
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asaparallel-platecapacitorifthedopedsemiconductorinthechargeneutralregionasinFig. 2-4 andmetalareregardedastheconductiveplateswithaccumulatedspacechargeQDperunitareaataseparationwidthofWD.BasedonEq.( 2 ),WDandQDarefoundtobe WD=r 20s eND(Vbi)]TJ /F4 11.955 Tf 11.95 0 Td[(V)(2)and QD=eNDWD=p 2e0sND(Vbi)]TJ /F4 11.955 Tf 11.96 0 Td[(V),(2)whereVistheexternallyappliedbias.Ithasapositive(negative)signforforward(reverse)bias,wheretheEFinthesemiconductorsideisliftedup(lowereddown)andelectronseeslower(higher)barrierheightwhentravelingfromsemiconductortometal.Fromtheparallel-platecapacitormodel,theinterfacecapacitance(CD)perunitareaiscalculatedas CD=0s WD=s e0sND 2(Vbi)]TJ /F4 11.955 Tf 11.96 0 Td[(V).(2)RewriteEq.( 2 ),itgives 1 C2D=2(Vbi)]TJ /F4 11.955 Tf 11.95 0 Td[(V) e0sND.(2)Eq.( 2 )suggestsalinearrelationshipbetween1=C2DandappliedbiasV,whichhasbeenwidelyappliedincapacitance-voltage(C-V)measurementtodeterminethebuilt-inpotential(Vbi)anddopinglevel(ND)ofthesemiconductor(tobediscussedinSec. 2.1.4.3 ). 2.1.3ElectricalTransportPropertyElectricaltransportpropertyisoneofthemostimportantandinterestingpropertiesofaSchottkyjunctionthatneedstobeclariedtounderstandtheirapplicationsinmodernelectronics.Foranidealjunction,transportismainlygovernedbythermionicemissiontheory,wheretheSBHcanbeextractedfromtheI-Vcharacteristics.Otherthanthat,tunnelingisalsoanothercommonly-seentransportmechanismattheinterface,whichisstronglyrelatedtothedopingdensityofthesemiconductor.To 42

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evaluatetowhatextenttheinter-facialtransportpropertyisdeterminedbythermionicemission,aphysicalquantity,calledidealityfactor(),isdened.Whenisclosetounity,electronsaremainlybeingthermionicallyemittedovertheSBH.Whenisgreaterthanunity,othermechanisms(liketunneling)alsocomeintoplay.Inthefollowingtwosub-sections,wewilldiscussthewell-knowthermionicemissiontheoryandtunnelingeffect,thatofwhicharealsoaprerequisitesforSec. 2.1.4 2.1.3.1ThermionicemissiontheoryAsreectedinthename,thermionicemissionreferstoathermally-activatedowofchargecarriersoverasurfacepotential.Thus,inaSchottkyjunction,whenelectronsarethermally-excitedfromthesemiconductortothemetalside,theinducedthermioniccurrentdensitycanbedescribedas Js!m=Z1ECevxdn.(2)wherevxdenotesthevelocityofelectronsemittingfromsemiconductortometal.Thelowerboundoftheintegralmeansonlythoseelectronsintheconductionbandareparticipatinginthermionicemission.And dn=N(")f(")d",(2)whereN(")isdensityofstatesperunitvolumeperenergy,f(")istheFermi-Diracdistributionfunctionanddnisthethenumberofelectronswithintheenergyrange(","+d").Quantum-mechanically,k-spaceisnotacontinuousspacebutcomposedofaserialofphasecellswithaunitvolumeof(2)3.Accordingly,thedensityofstatesink-spacecanbederivedas N("(k))dk=21 (2)34k2dk.(2)Thefactorof2originatesfromelectron'sspindegeneracy. 43

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Sincethemomentumofanelectronwithaneffectivemassmisgivenby mv=~k,(2)thedensityofstatesinvelocity-spacecanbeobtainedas N(v)dv=2 (2)3m ~34v2dv=2m h3dvxdvydvz.(2)Also,atsufcientlyhightemperaturewherethermionicemissionplaysavitalroleintheinterfacialelectricaltransportprocess,theFermi-DiracdistributioniswellapproximatedbytheBoltzmanndistribution,i.e. f(")exp)]TJ /F7 11.955 Tf 10.49 8.09 Td[(")]TJ /F4 11.955 Tf 11.95 0 Td[(EFn kBT.(2)wheretheenergy"andEFnareusuallymeasuredwithrespecttothebottomofvalenceband(EV).Inaddition,assumingthatalltheelectronenergyisfromitskineticenergy,itfollowsthat ")]TJ /F4 11.955 Tf 11.95 0 Td[(EC=1 2m)]TJ /F4 11.955 Tf 5.48 -9.68 Td[(v2x+v2y+v2z,(2)wherevx,vyandvzarethevelocitycomponentsinthex,yandzdirections,respectively.SubstitutionofEq.( 2 )andEq.( 2 )intoEq.( 2 )yields, Js!m=2em h3exp)]TJ /F4 11.955 Tf 10.5 8.08 Td[(EC)]TJ /F4 11.955 Tf 11.95 0 Td[(EFn kBTZ+1vx0vxexp)]TJ /F4 11.955 Tf 11.91 8.08 Td[(mv2x 2kBTdvxZ+1exp)]TJ /F4 11.955 Tf 10.91 8.95 Td[(mv2y 2kBTdvyZ+1exp)]TJ /F4 11.955 Tf 11.92 8.09 Td[(mv2z 2kBTdvz=4emk2B h3T2exp)]TJ /F4 11.955 Tf 10.5 8.09 Td[(EC)]TJ /F4 11.955 Tf 11.95 0 Td[(EFn kBTexp)]TJ /F4 11.955 Tf 10.5 8.09 Td[(mv2x0 2kBT (2) wherevx0,theminimumvelocitythatanelectronneedstoovercometheSBH,canbederivedfromenergyconservation 1 2mv2x0=e(Vbi)]TJ /F4 11.955 Tf 11.95 0 Td[(V).(2) 44

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Therefore,Eq.( 2 )canbefurthersimpliedas Js!m=4emk2B h3T2exp)]TJ /F4 11.955 Tf 10.5 8.09 Td[(e0Bn kBTexpeV kBT,(2)giventhateVbi=e0Bn)]TJ /F6 11.955 Tf 11.95 0 Td[((EC)]TJ /F4 11.955 Tf 11.95 0 Td[(EFn)asindicatedinFig. 2-4 .Likewise,thecurrentdensitycausedbyelectronthermionicemissionfrommetaltosemiconductoris Jm!s=4emk2B h3T2exp)]TJ /F4 11.955 Tf 10.49 8.08 Td[(e0Bn kBT.(2)NotethatJm!sisbias-independent.Thisisbecausetheemissionbarrierforanelectronfromthemetalsideisnotaffectedunderbias.CombiningEq.( 2 )andEq.( 2 ),thenetcurrentdensitybythermionicemissioniscalculatedtobe J=Js!m)]TJ /F4 11.955 Tf 11.96 0 Td[(Jm!sJsexpeV kBT)]TJ /F6 11.955 Tf 11.96 0 Td[(1, (2) with Js=AT2exp)]TJ /F4 11.955 Tf 10.49 8.09 Td[(e0Bn kBT(2)and A=4emk2B h3.(2)JsisthesaturatedcurrentdensityexponentiallydependentoftheSBHatthemetal-semiconductorinterfaceandisirrelevanttoappliedvoltageacrosstheSchottkyjunction.ItisacriticalphysicalquantitytodetermineSBHwhichcanbeextractedfromI-Vcharacteristics.MorespecicswillbediscussedinSec. 2.1.4.1 .TheRichardsonconstant,A,variesfordifferentsemiconductingmaterials.Itmayalsobedifferentforelectronsandholesduetotheirdifferenteffectivemasses.Richardsonconstantisacriterionoftheabilitytoemitchargecarriersatacertaintemperatureanditsfreeelectronvalue(A0)is120A/(cm2K2). 45

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Furthermore,atrstglance,Eq.( 2 )suggestsasimilarexponentialtermofvoltageincurrentdensityasthatofap-njunction.However,theunderlyingphysicsregardingcarriertransportisdifferent.Inap-njunction,thecarriertransportmechanismismainlygovernedbyminoritychargediffusionintotheneutralregionsonbothsides,whichinvolvesbothelectronsandholes.However,inaSchottkyjunction,thecarriertransportacrosstheinterfacebarriermainlyoriginatesfromthermionicemission,whereonlymajoritychargecarriersareinvolved.Consequently,aSchottkydiodecanbeturnonandoffatamuchfasterspeedthanap-njunction,thusplayingakeyroleinswitch-modepowersupplies. 2.1.3.2TunnelingeffectQuantum-mechanically,anelectroncantransmitthroughabarrier,wheresuchbehaviorisclassicallyprohibited.Duetothewave-particledualitynatureofchargecarriers(electronsorholes),tunnelingisanotherimportantelectricaltransportprocessatametal-semiconductorinterface,especiallywhenthesemiconductorisheavilydoped(N>1018cm)]TJ /F3 7.97 Tf 6.59 0 Td[(3)oratlowtemperature.Physically,thetunnelingcurrentfromonesidetotheothershouldbeproportionaltothenumberofelectronsreadytotunnelinonesideandtheemptystatesthatareavailabletoaccommodatetunneledelectronsontheotherside,aswellasthetunnelingprobability~T.Accordingly,tunnelingcurrentdensityfromsemiconductortometalandthereversecanbegenerallydescribedas JTUNs!m/Zfs(")~T(")[1)]TJ /F4 11.955 Tf 11.95 0 Td[(fm(")]d"(2)and JTUNm!s/Zfm(")~T(")[1)]TJ /F4 11.955 Tf 11.96 0 Td[(fs(")]d",(2)respectively.Here,fs(")andfm(")aretheFermi-Diracdistributionfunctionforthesemiconductorandmetal,respectively.Despitetheunavailabilityofanexplicitmathematicalexpressionforthenettunnelingcurrentdensity,theoverallJ-VcharacteristicsofaSchottkyjunction,when 46

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thermionicemissionandtunnelingarebothtakenintoaccount,canbeempiricallydescribedas J=JsexpeV kBT)]TJ /F6 11.955 Tf 11.96 0 Td[(1.(2)Forsolethermionicemission,theidealityfactor,,isequaltounity.Whenthetunnelingcomesintoplay,willsubstantiallydeviatefromunity.Theterm,thermionic-eld-emission(TFE),istherebyintroducedtodepictacombinedchargetransportmechanismofthermalexcitationandtunneling.Additionally,animportantparameter,E00,denedas E00=e~ 2r N m0s(2)iscommonlyusedtoestimatetheeffectoftunnelinginametal-semiconductorjunction,whereNistheextrinsicdopinglevelofthesemiconductor(NDfordonortype,andNAforacceptortype).WhenkBTE00,thermalactivationdominates,andisclosetounityintheabsenceofdepletion-layerrecombinationandimageforcelowering.WhenkBTE00,tunnelingdominateswhilethermionicemissionissuppressed.WhenkBTE00,carriertransportismainlythroughTFEprocess.Sincetunnelingblursthepictureofthermionicemissionandmayevenleadtocurrentleakageunderreversebias,itisnotaverywelcomeeffectinaSchottkyrectier.However,itgivesanimportanthinttoohmiccontactrecipeofasemiconductorbycreatingaheavilydopedlayeratthesurface.Thismethodispracticallyusefulformostp-typesemiconductors,whereasimplemetal-basedohmiccontactrecipeisimpossible.WewillrevisitthistopicwhentalkingaboutohmiccontactinSec. 2.2 attheendofthischapter. 2.1.4MeasurementofSchottkyBarrierHeightThoughtherearemultipletechniquesthathavebeeninvolved/developedtoinvestigatethephysicsatametal-semiconductorjunction,I-V,activationenergyandC-Vmeasurementsarethemostcommonlyusedexperimentalmethodsamong 47

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them.Thefollowingthreesub-sectionswillgiveabriefintroductiontothosethreemeasurementsrespectively. 2.1.4.1I-VmeasurementCurrent-voltage(I-V)measurementisthemoststraightforwardwaytotestaproducedSchottkyjunctionatacertaintemperature.WhenVkBT,andtheSBHishomogenouswithaknownactiveareaAandanegligibleresistanceRs,thetotalcurrentpassesthroughthatarea(I=AJ)accordingtoEq.( 2 )is I(V,T)Is(T)expeV kBT(2)with Is(T)=AAT2exp)]TJ /F4 11.955 Tf 10.49 8.09 Td[(eBn kBT.(2)Here,Bnmaydeviatefrom0Bnassubjecttomodicationfromimageforceloweringor/andsurfacedipoles.Eq.( 2 )indicatesanexponentialdependenceofVifBnisessentiallyvoltage-independent.Thus,I-Vcharacteristicsareplottedonasemi-logarithmicscale,theeffectiveSBH(Bn)ateachtemperaturecanbeextractedfromtheintercept(lnIs),andidealityfactor()canbedeterminedfromtheslope(e=kBT).Inpractice,isusuallyfoundtobegreaterthan1.Tunnelingalonesometimesisnotenoughtoexplainsuchadeviation.Effects,suchasabias-dependentSBHeitherduetoimageforcelowering(Eq. 2 )orshiftedEFunderbias(forexample,graphene),thelateralinhomogeneityofSBHandchargerecombinationattheinterface,shouldalsobetakenaccountof.Besides,atahigherforwardbiasrange,adeparturefromlinearityinlnIusuallycomesintosightinmostSchottkyjunctionsbecauseofaniteseriesresistance,Rs.TherebyamoreaccuratedescriptionofI-Vcharacteristicis IIsexpe(V)]TJ /F4 11.955 Tf 11.96 0 Td[(IRs) kBT.(2) 48

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Alittlebitmorealgebragives dV d(lnI)=IRs+kBT e.(2)Thus,RsisjusttheslopewhenplottingdV=(dlnI)vsI[ 53 54 ].TheoriginofRsisusuallyfromaunsatisfactoryohmiccontacttothesemiconductoror/andaniteresistanceofmetal,whichisgoingtobediscussedmorewhenwetalkaboutgraphene/Sisolarcells. 2.1.4.2ActivationenergymeasurementForairregularshapeorincompletelycontactedSchottkyjunction,wheretheactiveareaisunknown,itisimpossibletodeterminetheSBHfromtheI-Vmethoddiscussedpreviously.Instead,oneneedstoinvestigatethesaturationcurrent(Is)fromI-Vcharacteristicsatvarioustemperatures.Accordingtothermionicemission,electrongainshigherthermalenergyandcanbemoreeasilyexcitedovertheinterfacebarrieratelevatedtemperatures.Thus,atzerobias,Isislargerathighertemperatures.Basedontherelationshipthat lnIs T2=ln(AA))]TJ /F4 11.955 Tf 13.15 8.09 Td[(eBn kBT,(2)Bncanbededucedfromtheslopeofln(I=T2)vs1=Tcurve,whichistheso-calledac-tivationenergyplot.Itslinearitysuggeststheformationofainterfacebarrier.Themostprominentadvantageofanactivationenergymeasurementisthatadifcultestimationoftheactivearea,A,canbecircumventedwhenthereislittlespacialvariationsinSBHs.However,thismethodtodeterminetheSBHbecomesinaccuratewhenthelateralinhomogeneitiesinSBHsisappreciable,suchasingraphene/semiconductorSchottkyjunctions.TheSBHandidealityfactormaybecometemperature-dependent,andtheextractedBnisusuallysmallerthan300KBn[ 55 ].FlatbandcorrectionisnotsufcienttocountforsuchadiscrepancywhenthespacialuctuationsinSBHsaresignicant. 49

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2.1.4.3C-VmeasurementDuetothepresenceofthechargedepletionregion,capacitancemeasurementisanotherimportantexperimentaltechniqueandusuallyservesasacomplementarymethodtoothermeasurementsastocomprehensivelyinvestigatetheinterfacepropertyinaSchottkyjunction.Toavoidcurrentleakage,interfacecapacitancemeasurementsareusuallymadeusingaDCreversebias(VR)uponwhichissuperimposedanadditionalACsignalwithanamplitudeofVm.Usually,VmismuchsmallerthanVR.BearingEq.( 2 )inmind,underreversebiasvoltageconditionthatV=)]TJ /F4 11.955 Tf 9.3 0 Td[(VR, 1 C2D=2(Vbi+VR) e0sND.(2)Accordingly,VbiandNDcanbederivedfromtheinterceptofabscissaandtheslopeofa1=C2DvsVRplot.Thus,BncanbecalculatedthroughEq.( 2 ).Inprinciple,thevaluesofSBHdeterminedfromI-VandC-Vshouldbeidentical.However,thisisnotthecasewhentheSBHislaterallyinhomogeneousoverthemetal-semiconductorinterface.InanI-Vmeasurement,electronsusuallypickthemostconductivepathsdominatedbysmalleffectiveSBHs,whileaC-VmeasurementprobesanaveragevalueofSBH.IfweassumeaGaussiandistributionoftheseinhomogeneousbutnon-interactingSBHpatches,theBn'sfromI-V(I)]TJ /F8 7.97 Tf 6.59 0 Td[(VBn)andC-V(C)]TJ /F8 7.97 Tf 6.59 0 Td[(VBn)measurementswereshowntorelatedby[ 56 ] I)]TJ /F8 7.97 Tf 6.58 0 Td[(VBn=C)]TJ /F8 7.97 Tf 6.59 0 Td[(VBn)]TJ /F4 11.955 Tf 13.15 8.09 Td[(e2SBH 2kBT.(2)HereSBHdenotesthestandarddeviationofSBHs.InthelaterdiscussionofgraphenebasedsemiconductorSchottkyjunction(Sec. 3.3.2.2 ),wewillseethattheresultingSBHattheinterfaceisratherinhomogeneous.I)]TJ /F8 7.97 Tf 6.59 0 Td[(VBnisusuallyfoundtobesmallerthanC)]TJ /F8 7.97 Tf 6.59 0 Td[(VBn.Besides,theaccuracyofcapacitancemeasurementissubjecttodeepcarriertrapsordopantsinsidethesemiconductor(whosecontributioncanbeeliminatedathigh 50

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frequencies),non-negligibleRsandsurfacecleanliness(mainlyinterfacestates).Thus,carefulprecautionisrequiredwhendoingdataanalysis. 2.2OhmicContactWhencomparedwithSchottkycontact,ohmiccontactisof,atleast,equalimportanceinsemiconductor-basedelectronics.Agoodohmiccontactensuressuperiorcurrenttransportinandoutofthefabricateddevicewithlittleenergydissipationduetotheohmicloss.Inparticular,suggestedbyMoore'slaw,miniaturizationofmodernelectronicsrequiressemiconductordevicestobedenselycompactedonasmallchip,whichmeanshighercurrentdensityandmakeshighqualityohmiccontactevenmoredesirablethanbefore.Asitsnameimplies,theI-Vcharacteristicofanohmiccontactbetweenmetalandsemiconductorislinearandnon-rectifying,suggestinganinvariantbutnegligibleresistance(withrespecttothatofthewholesemiconductordevice)withinanadequatevoltagerange.Ingeneral,therearethreemechanismsthataremostfrequentlyusedtocreateohmiccontacttoasemiconductordevice.TheattempttochooseametalwithmatchedFermi-leveltothatofasemiconductoristhemostintuitiveandsimplestapproachtoformohmiccontactforaspecicsemiconductingmaterial.Whentheinter-facialbarrierheightiszeroornegligible,currentisabletopassthroughthejunctionregardlessofthedirectionofappliedbias.Thisstraightforwardohmiccontactrecipehasbeenwidelyandsuccessfullyusedinorganicandorganic-inorganichybridelectronics,wherethemobilityoforganicsemiconductorispoorandthedevicecanbemadewithalargearea[ 57 ].However,thetechniquetoachieveanohmiccontactwithlowresistivityforaninorganicsemiconductingmaterial,especiallywhenitcomestoap-typewidebandgapsemiconductorlikegroupIII-Vcompounds,isusuallymoredemandingandcomplicatedthanasinglemetal-basedrecipe[ 58 59 ].Oneofthemostwidelyadoptedmethodsistocreateaheavilydopedsurfacelayerinasemiconductor(usuallythroughion 51

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implantationorthermaldiffusion)priortoitscontactwithametal,wherethedopinglevelusuallyexceeds1020cm)]TJ /F3 7.97 Tf 6.59 0 Td[(3andmostofcurrentacrosstheinterfaceisfromtunnelingassuggestedbyEq.( 2 ).Forexample,inaSip-njunctionsolarcell,ap++regionisusuallyfabricated(byboronatomsusuallyviathermaldiffusion)onrearsideofp-typeregion,whichistheso-calledbacksurfaceeld.Itcannotonlyreducechargerecombinationrateattherearsurface,butalsoservesasanohmiccontacttothep-typeside.Lastly,rapidthermalannealing(RTA)toformmetal-semiconductoralloyisanotherwaytoformlow-resistanceohmiccontact,especiallyonGaAsandGaN[ 58 60 ].Likewise,growthofanalloyinglayerontopofsemiconductoralsogivesrisetotheformationofaheavily-dopedsurfacearea.PriortoRTA,amultilayer-metal-depositionisdoneineitherathermalore-beamevaporationsystem,whereAuorPtisusuallyinvolvedasabasismetaltoimprovecontactadherenceonthesemiconductorsurface.Besides,someothermetalsarealsorequiredinthecompoundsandfunctionasdopingspecies,suchasZn,NiandIn.Also,afterformationoftheappropriatealloy,anadditionalmetalcappinglayerissometimesnecessarytoprotectohmiccontactfromagingduetotheatmosphericexposure. 52

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Figure2-1. Banddiagramatmetalandan-typesemiconductorinterface.A)Banddiagrambeforethemetalandsemiconductorarebroughtintocontact.B)Banddiagramatthemetal/semiconductorintimate-contactinterfaceunderzerobiasintheabsenceofsurfacestatesandinter-facialdipolelayer. 53

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Figure2-2. Banddiagramsatmetalandap-typesemiconductorinterface.A)Bandprolewhenthemetalandsemiconductorareseparated.B)Bandprolewhenthemetalandsemiconductorarebroughtintocontactunderzerobiasintheidealcondition. 54

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Figure2-3. Modiedbanddiagramofametalandn-typesemiconductorwhenimageforceeffectistakenintoaccount.Duetotheadditionalelectricalpotentialinducedbyimagecharge,theintrinsicSchottkybarrierheight0Bnisloweredbyaneffectiveamountof. 55

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Figure2-4. Detailedband-structureofanidealn-typeSchottkyjunction. 56

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Figure2-5. Proleofvariousphysicalquantitiesinthechargedepletionregion.A)Theproleofchargedistribution.B)Theproleofelectriceld.C)Spatialdistributionofelectricpotentialinthedepletionregion. 57

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Figure2-6. Banddiagramofann-typeSchottkyunderA)zero,B)forward,andC)reversebias,respectively. 58

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CHAPTER3GRAPHENE/SEMICONDUCTORSCHOTTKYJUNCTIONS 3.1OverviewIncontrasttoregularmetalcontact,graphene/graphiteisaverystablematerialintermsofanti-oxidationandanti-corrosionatambient,otherthantheirexceptionalelectricaltransportpropertiesthathavealreadybeendiscussedinCh. 1 .Also,thehightemperatureresilienceandsuperiorthermalconductivityofgraphene/graphite[ 61 ]assuretheexcellentdeviceoperationsatelevatedtemperatures[ 62 63 ]andimproveoveralllifetimeofthedevices.Besides,inaregularmetal/semiconductorSchottkydiodes,impurityatomscandiffuseintothesemiconductorsathightemperatureandformundesirableohmiccontacts,whilegrapheneandgraphiteprovideinterfacialdiffusionbarriersandhenceprotecttheunderlyingsemiconductorswhenoperatingathightemperatures.Therefore,graphene/graphitebasedsemiconductorSchottkyjunctionsareexpectedtohavemuchreliableandsustainabledeviceperformancewhichiscrucialtotheextensiveapplicationofmetal-semiconductoreldeffecttransistors(MESFETs)andhighelectronmobilitytransistors(HEMTs).Researchalongthisdirectionwasrststartedongraphite/semiconductorinterfacesbackto2009inourlab,byeither(1)pressingapieceofthinhighlyorientedpyrolyticgraphite(HOPG)akeor(2)droppingHOPGpaintonaseriesoffreshlycleanedsemiconductorsurfaces(namely,Si,4H-SiC,GaAsandGaN)[ 62 65 66 ].ThesubsequentelectricalandcapacitancecharacterizationsprovedtheformationofSchottkybarriersattheirinterfaces.Accordingtothebondpolarizationtheory[ 49 ],thepropertyatmetal-semiconductorinterfaceismainlydeterminedbytheoutmostafew ThischapterisareprintofRecticationatGraphene-SemiconductorInterfaces:Zero-GapSemiconductor-BasedDiodesbyS.TongayandX.MiaoetalpublishedinPhys.Rev.X.2,011002(2012)[ 64 ]. 59

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atomiclayersincontact.SinceHOPGiscomposedofindividually-stackinggraphenelayers,graphene/semiconductorsinterfacesareexpectedtohavesimilarproperties.However,thebandstructurediffersfromgraphitetographene.Thelatterisanatomicallythinzero-bandgapsemiconductor.Ourinitialmotivationwastoaddresstwoproblems:(1)whetherthereisrecticationatgraphene/semiconductorinterface;(2)ifthereis,howitdiffersfromgraphitecounterparttakenaccountofthebandstructuredifferencebetweengrapheneandgraphite?Inthischapter,wedemonstraterecticationeffectsduetheformationofSchottkybarriersatgraphene/semiconductorinterfacesonasurprisinglywidevarietyofsemiconductors,includingSi,GaAs,4H-SiCandGaNthatarealltechnologicallyimportantandarecriticalcomponentsinmodernoptoelectronicandelectronicdevicesforhighpowerandhighfrequencyapplications.Inadditiontocurrent-voltagemeasurements,weutilizeHall,capacitance-voltageandRamanspectroscopytogaincomprehensiveinsightsintotheuniquephysicstakingplaceatthegraphene/semiconductorinterfaces.Wefoundthatgraphene'sFermilevel(EGF)issubjecttovariationduetoelectrostaticgatingasreectedinelectric-eld-modulatedRamanspectra,insharpcontrasttoconventionalmetal/semiconductorSchottkyjunctionswhereEFofthemetalstaysconstantduetoahighdensityofstatesattheFermilevel.ThesevariationsbecomeparticularlypronouncedathighreversebiaswhentheamountofinducedelectronsingrapheneissufcienttoincreaseEGFandtherebydecreaseSBHs,whichleadstohighercurrentleakagecomparedwithgraphite/semiconductorSchottkyjunctions.Alongthisdirection,wemadeamodicationtoconventionalthermionicemissiontheorytoaddresssuchabias-dependentSBHspecicallyingraphenebasedsemiconductorSchottkydiodes. 60

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3.2ExperimentalMethods 3.2.1GrapheneGrowthandTransferLargeareagraphenegrownbychemicalvapordepositionmethod(CVD)enablesitsintegrationwithregularsemiconductors,therebyboostinggrapheneresearchprogressonoptoelectronicandelectronicdeviceapplications[ 67 ].BasedonthereciperstdevelopedbyRuoff'sgroupfromUniversityofTexasatAustinin2009[ 68 ],wesynthesizedgrapheneonCufoilsviamultiplestepsinahome-builtCVDsystem.First,apieceof25-m-thickCufoilwasloadedintoaquartztubefurnaceoperatinginCVDmode.Thesystemwasevacuatedbelow4mTorratroomtemperatureandsubsequentlyheatedto500CunderH2withbackpressureof300400mTorr.Aftera30-minutesoak,thetemperaturewasraisedto900CunderthesameH2pressurefor1530minutestocompletelyremovenativeoxidesontheCusurface.Thentemperaturewasincreasedto1025Cfor60minutestopromotetheformationoflargeCugrainsize.Afterthat,thetemperaturewasdecreasedto1015Cfor30100minutestogeneratealowdensityofgraphenenucleationsiteswithamixtureofCH4andH2atatotalpressureof90mTorrwiththeirowratesat0.5and2.0sccm,respectively.DuringthisstagegraphenegrewslowlyacrosslargeCugrainsandgapsbetweenthegraphenegrainsarelledbyincreasingCH4owrateupto30sccm(900mTorr)at1000forapproximately10minutessothatfullareacoverageofgraphenewasachieved.Finally,thewholesystemwasnaturallycooledtoroomtemperaturewithin3hoursunderthesamegasow.Aftergraphenegrowth,alayerof1.5mthickpoly(methylmethacrylate)(PMMA)wasspun-castontoCufoilsat2000rpmfor1minute.Subsequently,reactive-ionetching(RIE)removedunwantedgrapheneontheothersideofCufoil(toavoidmulti-layerformationonsomespotduringwetetchingprocessasdescribednext).TheCuwasthenremovedbyetchingina0.05mg/LsolutionofFe(NO3)3.ThePMMA/graphene 61

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lmwasthenwashedinseveraldeionized-waterbathspriortothetransferontoseveralsemiconductorsubstrates.Theas-grownandtransferredgraphenelmswerecharacterizedinaHoriba-Yvonmicro-RamanSpectrometerwitha532nm(2.33eV)greenlaser.Besides,roomtemperatureHallmeasurementswerealsopreformedtodetermineelectricaltransportpropertiesofgraphenesheetsusinga17HzACresistancebridge(LR700).PMMA/graphenesheetsweretransferredontoseveralSiO2/Sisubstrateswithpre-patternedAu/CrcontactsinHallbargeometry(asshownintheinsetofFig. 3-1 )beforebeingloadedinaphysical-property-measurement-system(PPMS)fromQuantumDesign,whereamagneticeldupto7Tcanbeapplied. 3.2.2DeviceFabricationandCharacterizationCommerciallyavailablesemiconductorwaferswerepurchasedfromdifferentvendors.Allthesemiconductorsusedinthisexperimentweren-type.Then-Siandn-GaAssamplesweredopedwithphosphorous(261015cm)]TJ /F3 7.97 Tf 6.59 0 Td[(3)andSi(361016cm)]TJ /F3 7.97 Tf 6.59 0 Td[(3),respectively.Epilayersofn-GaNandn-type4H-SiCweregrownonsapphiresubstratesdopedwithSi(131015cm)]TJ /F3 7.97 Tf 6.59 0 Td[(3)andnitrogen(131015cm)]TJ /F3 7.97 Tf 6.58 0 Td[(3),respectively.Thedopingdensities(NHallD)ofthesemiconductorswerecharacterizedat300KintheHallbarcontactgeometry.ThevaluesofNHallDarelistedinTable. 3-1 .Priortographenetransfer,thewaferswerecleanedusingtypicalsurface-cleaningtechniques.OhmiccontactstoeachofsemiconductorswereformedusingconventionalOhmic-contactrecipes[ 48 69 71 ].Multilayermetallicthinlmsweregrownonsemiconductorsurfacesandpostannealing(mostlyRTA)athightemperature(>300C)eitherundervacuumorN2gasatmospherewasnecessarytoinitiatetheformationoflow-resistanceOhmiccontacts.Afterthat,a0.51.0mSiO2windowweregrownonvarioussemiconductorsinaplasma-enhancedchemical-vapor-deposition(PECVD)system,followedbydepositionofAu(60nm)/Cr(10nm)electrodesontopasohmiccontacttographenesheets.ThethickSiOxlayerpreventedelectricalshorting 62

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betweenAu/Crelectrodesandtheunderlyingsemiconductingsubstrates.Subsequently,PMMA/graphenelmsweretransferredontothesemiconductorsubstrate.Applicationofadropofisopropylalcohol(IPA)improvesthechanceofsuccessfultransferrate.Someofthedevicesweresittinginanacetone-vapor-richcontainerforseveralhourstoremovePMMA.However,theyshowlittledifferencefromthosewithundissolvedPMMAinrectifyingcharacteristics.Therefore,weconcludethatthegraphenemakesgoodcontactwiththesemiconductorviathevanderWaalsforce.TheSchottkydevicegeometryisdepictedinFig. 3-5 .Thesizeofthewindowareaisusuallyabout0.1cm2.Ourdesignofthedevicegeometryallowscurrent-densityvsvoltage(J-V),capacitancevsvoltage(C-V)andelectric-eld-modulatedRamanmeasurements.J-VmeasurementsweretakenindarkroomconditionusingeitherKeithley6430orKeithley2400.C-VmeasurementsweretakenbyHP4284Acapacitancebridgeatlowfrequencyrange(typicallyfrom100to1000Hz).Thelinearrelationshipof1=C2vsVisbarelyaffectedbythefrequencywithinthatrange. 3.3ResultsandDiscussions 3.3.1GrapheneCharacterization 3.3.1.1HallmeasurementFig. 3-1 showsatypicalresultfromHallmeasurementsatT=300Kingraphene.Ingeneral,theHallmobilityofourCVD-growngraphenesheetsusedinthediodesisintherangeof14002100cm2/Vs.ThepositiveslopeinFig. 3-1 indicatesthehole-dopednatureofgraphenewithhole-densityusuallyvaryingbetween21012and81012cm)]TJ /F3 7.97 Tf 6.59 0 Td[(2.Suchanunintentionaldopingeffectisexpectedtoresultbothfrom(1)residualwaterorchemicals(suchastheuseofIPAdropforgraphenetransferandFe(NO3)3inCuetchingprocess)eitheronthetopofgraphenesurfaceortrappedbetweengrapheneandtheunderlyingSiO2/Sisubstrate[ 28 31 72 ],and(2)substrate-induceddopingeffectduetothepresenceofoxygendanglingbonds(thatcanbeminimizedwhenusingBoron-Nitridesubstrate[ 73 ]orinsuspended-graphene[ 74 ]).Postannealingat 63

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temperature300CeitherinvacuumorH2/Ar2forminggasisusuallyamusttoremovethoseundesirablechemicals/dopants,therebyimprovingtheelectricalpropertiesofgrapheneasdemonstratedinpreviousstudies[ 28 30 ].Moreover,recentlyagold-assistgraphenetransferprocesshasbeenusedinsteadofPMMAduringFETfabricationprocedure.Anditwasshowntodramaticallyimprovegraphene'ssurfacecleanlinessandtheresulteddeviceperformanceintheabsenceofPMMAresidualafteritsremovalinacetone-bath[ 75 77 ]. 3.3.1.2RamanspectroscopyRamanSpectroscopyisapowerfultooltocharacterizeandidentifyawidevarietyofphysicalpropertiesingraphene[ 78 ],suchasnumberoflayers[ 79 80 ],disorders[ 81 82 ],dopinglevel[ 81 83 ],stackingsequence[ 43 44 ]andstrains[ 84 85 ]etc.TherearethreemostimportantpeaksinatypicalgrapheneRamanspectroscopy.InaincreasingsequenceofRamanshifts,theyareD(1350cm)]TJ /F3 7.97 Tf 6.58 0 Td[(1),G(1580cm)]TJ /F3 7.97 Tf 6.59 0 Td[(1)and2D(2700cm)]TJ /F3 7.97 Tf 6.59 0 Td[(1)peakswiththeirpositionspecicallydependingonincident-photon-energy[ 78 ].TheDpeak,ifthereisany,originatesfromdisorderordefects.Therefore,anegligibleDpeakintensityalongwithhigh2D-to-Gintensityratio(I2D=ID2)oftenindicatesagoodcrystallinityofthegraphene.TheGpeakarisesfromtheradialbreathingmodeofsp2bindingsandaredoublydegenerateatthecenteroftheBrillouinzone(BZ)protectedbyE2gsymmetry[ 82 85 ].Itisthesignatureofthesp2carbonnetworksinRamanspectroscopy.Thepeakproleisstronglyrelatedtothein-planephononmodes,whichcanbeaffectedbydoping,strainandstackingsequence[ 78 ].Finally,the2Dpeak(alsonamedasG0peak)istheovertoneoftheDpeakresultingfromasecondorderdouble-phonon-resonanceRamanprocess.Thepeakintensityandpositionareverysensitivetothestackingorders,numberofgraphenelayersanddopinglevels.HerewemainlyemployedRamanspectratocharacterizethequalifyofgraphenebeforeandaftertransferontosemiconductorsubstratesandmonitorG-and2D-peak 64

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shiftsunderappliedbiasasillustratedinFig. 3-2 andFig. 3-3 ,respectively.TheresultsshowninFig. 3-2 havebeenreproducedatmorethan20randomspotsandaregoodrepresentationofthequalityofthegrapheneontheCufoilsandontheindicatedsemiconductorsaftertransfer.AsindicatedinFig. 3-2 (a),I2D=IG2andID0inas-growngraphene,thedescribedCVDmethodinSec. 3.2.1 yieldsdecentqualityofmonolayergrapheneonCufoilbeforewettransfer.RegardlessoftheinvarianceofI2D=IG,DpeaksemergingwithsmallintensitiesareobservedintheRamanspectraasindicatedinFig. 3-2 (b)oncegraphenesheetshavebeentransferredontodifferentsemiconductorsubstrates.Thisresultsuggestsaslightdegradationofgraphenequalitypossiblyduetoinducedthedefects/disordersduringtheCuetchingandPMMAremovalprocesses.ThevarianceinbothGand2DpeakpositionsasreectedinFig. 3-2 (c)(d)ondifferentsamplesaremainlycomingfromvariationsinthepropertiesofgraphenesheetsmostlyowingtounintentionaldopingduringtransferprocessandthedistinctinteractionsofthegraphenewithdifferentsubstrates.Additionally,RamanspectroscopycanalsobeusedtodetectshiftofEFingraphene(EGF)viamonitoringevolutionsofbothG-and2D-peakproles,whichhavebeenalreadydemonstratedinelectriceldgatingexperimentsonmechanicallyexfoliatedgraphenedepositedonSiO2/Si[ 83 ].TheGpeakwasfoundtohaveablueshiftanddecreasedfull-width-at-half-maximum(FWHM)duetoremovalofKohnanomalyfrom)]TJ /F1 11.955 Tf 10.26 0 Td[((thecenterofBZ)andconsequentlyincreasedphonon-lifetimebychangingofEGFbydoping[ 78 81 ].Also,suchaG-peak-stiffeningisinsensitivetothedirectionofEGFshiftandIGisalmostinvariantwiththepositionofEGF.Incontrast,the2Dpeakresponsesdifferentlytoelectronandholedoping(movingEGFupanddownrespectively)aredifferent,sincestrongelectron/hole-dopinggivesrisetophononsoftening/stiffeningattheKpoint.Inthissense,thetypeofdopingcanbeidentiedfromtheshiftof2Dpeakposition.Besides,I2Ddecreaseswithincreasingcarrierdensity(forbothelectronsandholes)asaresultofdoping-inducedexcited-state-broadening[ 86 ]. 65

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Basedontheseconsiderations,wetookRamanspectraonagraphene/GaNSchottkyjunctionasafunctionofappliedbiastoestimatethebias-inducedmodulationsinEGF.However,ourmeasurementsdifferfromthosereportedinRef.[ 83 ]inthefollowingaspects:(1)weareusingCVD-growngrapheneinanareaof0.1cm2ratherthanmicron-sizedmechanicallyexfoliatedgraphene;(2)thegrapheneisindirectcontactwithGaNratherthanSiO2,thusanydifferenceinsubstrate-inducedself-dopingeffectmustbeconsidered;(3)thegrapheneismeasuredinsituasapartoftheSchottkyjunctionratherthanagatedeldeffecttransistor(FET).InFig. 3-3 ,weshowtheevolutionoftheRamanspectraat0V,1Vand)]TJ /F1 11.955 Tf 9.3 0 Td[(10V.WhiletheGand2Dbandsarealmostidenticalwiththesamepeakintensitiesandpositionsat0Vand1V,theGbandblueshiftsbyapproximately63cm)]TJ /F3 7.97 Tf 6.58 0 Td[(1andthe2Dbandredshiftsbyapproximately73cm)]TJ /F3 7.97 Tf 6.59 0 Td[(1whenthedeviceisreverselybiasedat)]TJ /F1 11.955 Tf 9.29 0 Td[(10V.Meanwhile,I2D=IGreducesfrom2.6to1.2whenthebiasdecreasesfrom0Vto)]TJ /F6 11.955 Tf 9.3 0 Td[(10V.TherelativeshiftsintheRamanpeaksalongwiththesimultaneouschangeinI2D=IGimplythatthegraphenesheettransferredontoGaNwaselectron-dopedbyahighnegativebias.IfcomparedwithresultsfromRef.[ 83 ]despitethedifferenceinthemeasurementsmentionedabove,theshiftinEGFcanbeestimatedtobeintherangeof0.2)]TJ /F1 11.955 Tf 9.29 0 Td[(0.5V.MorespecicswillbediscussedinSec. 3.3.3 3.3.2SchottkyDeviceCharacterization 3.3.2.1J-VcharacteristicsAsdiscussedinCh. 2 ,theelectricaltransportinaSchottkydiodeisunidirectional.Inotherwords,itishighlyconductiveunderforwardbiasandhighlyresistiveunderreversebias.AsshowninFig. 3-4 ,J-V(mainpanels)anditsequivalentsemi-logarithmicplots(insets)fromvariousgraphene/n-typesemiconductorjunctionsdemonstratestrongrecticationsasaconsequenceoftheSchottkybarrierformationattheinterface,whereelectronowsfromthesemiconductortographenetoequilibratetheFermi-levelonbothsidesasillustratedinFig. 3-7 (a). 66

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AccordingtotheSchottky-Mottmodel,arstorderestimationofthebarrierheight(SBH)issimplydeterminedbythedifferencebetweentheworkfunctionofthegraphene(WG)andelectronafnityofthen-typesemiconductor().Mathematically,itcanbewrittenas SBH=WG)]TJ /F7 11.955 Tf 11.96 0 Td[((3)Also,electrontransportinsuchaSchottkyjunctioniswelldescribedbythermionic-emissiontheorythathasbeenpreviouslyintroducedinSec. 2.1.3.1 .TheJ-Vcharacteristicisgivenby J(V,T)=Js(T)expeV kBT)]TJ /F6 11.955 Tf 11.95 0 Td[(1.(3)Thecurrentdensity,J(V,T),representsthecurrentowingperunitareatheinterfaceunderappliedbiasVatacertaintemperatureTandistheidealityfactor.TheSchottkybarrierheight(SBH),SBH,isexplicitlyincludedinthesaturationcurrentdensityJsas Js(T)=AT2exp)]TJ /F4 11.955 Tf 10.49 8.08 Td[(eSBH kBT,(3)whereAdenotestheRichardsonconstant.AsshowninalloftheinsetsinFig. 3-4 ,eachofthesemi-logarithmicplotsofJ-Vcurvesdisplaysalinearregioninforwardbiasasindicatedbytheblackdashedstraightlines,suggestingthatelectricaltransportacrosstheinterfacebarrierisdominatedbythermionicemission.Suchalinearityspans2)]TJ /F6 11.955 Tf 12.37 0 Td[(4decades,thusallowingextractionofJsandforeachtypeofjunctionaccordingtoEq.( 3 ).Thedeviationsfromlinearityathigherbiasaremostlyduetoincreasingcontributionfromseries-resistance.FromtheextractedJs,theSBHs(denotedasJ)]TJ /F8 7.97 Tf 6.58 0 Td[(VSBH)canbecalculatedandthevalues,togetherwiththoseof,arelistedinTable 3-1 .Theidealityfactor,,rangingfrom1.3to5.0,showslittleobviouscorrelationtothetypeofsemi-conductingsubstrates,andissignicantlyhigherthanwhathasbeenobservedingraphitecounterparts[ 65 ].Idealitygreaterthanunityhasbeen 67

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attributedto(1)animage-forceinducedSBHlowering,(2)abias-dependentSBHspecicallyforgraphene(tobediscussedinSec. 3.3.3 ),(3)lateralinhomogeneitiesinSBHsduetotheuctuationsofgraphene'schemicalpotentialsand(4)theexistenceofadditionalcurrenttransportprocessessuchasthermionic-eld-emissionacrossthemetal/semiconductorinterface[ 48 49 ].Here,despiteofabias-dependentSBH,wedonotexpectconsiderablechangesintheSBHsundertheforwardbias,sincetheextractedvaluesofSBHs(listedinTable 3-1 )wereobtainedfromlowforwardbiasvoltageintherange(0.3V1.0V).Withinthissmallrange,theshiftsinSBHsarenegligibleaccordingtolatercalculationsinSec. 3.3.3.2 .Therefore,thethreeothermechanismsdiscussedabovearethekeyfactorsthatcausetodeviatefromunity,especiallytheimage-forceloweringeffect.Itcanleadtosignicantdeviationin[ 49 ],andmaybethemaineffectingraphene/semiconductorSchottkydiodeswhere3.0.Andtherelativelyhighercomparedtothatofgraphitecounterparts,isprobablyduetothecomparativelylargeructuationsongraphene'schemicalpotentialsattheinterface,whichgiverisetolargerspatialinhomogeneitiesinSBHs.Ontheotherhand,thevaluesofJ)]TJ /F8 7.97 Tf 6.59 0 Td[(VSBHarewelldescribedusingeithertheBardeenorSchottky-Mottmodel.IntheBardeenmodel,theinterfacephysicsismainlygovernedbyinterfacestateswhich,byaccumulatingfreecharge,changethechargedistributionattheinterfaceandcausetheSBHtobeinsensitivetotheworkfunctionofthemetal(termedFermi-levelpinningasintroducedinSec. 2.1.1.3 ),forinstance,asfoundinGaAs[ 48 ].Ontheotherhand,SBHsbasedonthewide-band-gapsemiconductorsSiCandGaNarewelldescribedbytheSchottky-Mottmodel,wheretheinteractionofinterfacestatescanbeoverlooked.Inthiscase,theSBH(SBH)issimplygivenbySBH=WG)]TJ /F7 11.955 Tf 10.41 0 Td[(asshowninEq.( 3 ).UsingtheextractedvaluesofJ)]TJ /F8 7.97 Tf 6.58 0 Td[(VSBHandtheknownvaluesofforallthesemiconductorsthathavebeenusedinthiswork(Si4.05eV,GaAs4.1eV,GaN4.1eV4H)]TJ /F8 7.97 Tf 6.58 0 Td[(SiC3.4eV),wecancalculatetheworkfunctionofgraphene(WG).TheresultsarelistedinTable 3-1 .Thecalculatedvaluesofthe 68

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workfunctionaretypicallyhigherthantheacceptedvalues(4.6V)whenEGFisatthecharge-neutralitypoint.ThedeviationfromthisstandardvaluecanbeattributedtotheholedopingnatureofgrapheneasdemonstratedinHallmeasurement(Fig. 3-1 ).AlthoughtheSBHsonSi,GaAs,andGaNcanberoughlyexplainedwithintheSchottky-Mottmodel,inpractice,GaAshasahugedensityofsurfacestatesonthesurfaceandthusexhibitscharacteristicFermi-levelpinning.WithinthetheoreticalframeworkoftheBardeenmodel,GaAs-basedSchottkyjunctionsgenerallyhaveSBHsintherangeof0.75)]TJ /F6 11.955 Tf 13.25 0 Td[(0.85eV[ 48 ],whichareingoodagreementwithourobservation.ProperinterpretationoftheSBHongraphene/GaAsjunctionsrequiresmorespecictheoreticalcalculationsandexperimentalmeasurementsgroundedontheBardeenmodel.Forexample,duetothehugedensityofstateswhichmakesSBHsinsensitivetoWGandhenceEGF,theuctuationsinEGForthebias-inducedshiftsinEGFareexpectedtohavelessorlittleeffectontheSBHbasedontheexactamountofdensityofsurfacestates.Specially,SBHongraphene/GaAsshouldinprinciplehavelessinhomogeneitiescomparedwithothergraphene/semiconductorcounterpartsiftheuctuationsinEGFistheonlyreasonfortheSBH.However,suchassumptionmayturnoutbeoversimpliedinrealityandneglectsotherpossiblefactorssuchas(1)unevendistributionofsurfacedipolesand(2)variationsofmetal-contactqualitiesthatmayalsocontributetothespatialinhomogeneitiesofSBHsovertheinterface.Besides,ouroverallresultsareingoodagreementwiththendingsoftheearlierworkongraphiteormany-layer-graphene/semiconductorjunctions[ 65 66 ]wherethelayerinclosestproximitytothesemiconductorisasinglesheetofcarbonatom(mono-layergraphene),thusvalidatingthepredictionfrombondpolarizationtheory.Nevertheless,barriersformedonthe4H-SiCsubstratesgiveanextraordinarilylowvalueofWG(Table 3-1 )andthereforecannotbeexplainedbyeitherBardeenorSchottky-Mottmodel.Suchanunusualdeviationthuscallsforconsiderationofmoreadvancedtreatmentsofmetal-inducedgapstatesorbondpolarizationasdescribed 69

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inRef.[ 49 ].Forexample,sincethelatticemismatchbetweengrapheneand4H-SiCisrelativelysmallwhencomparedwiththeothersemiconductors(namely,Si,GaAsandGaN),thecoupling/interactionbetweenthemmightbefundamentallydifferentfromothercounterparts.Withintheframeworkofbondpolarizationtheory,thisdifferencemightresultintheobserveddeviation.Sofar,wehaveonlyfocusedonJ-Vcharacteristicsintheforwardbiasrange.However,thereverse-biascharacteristicingraphene/semiconductorSchottkydiodesisspecialandworthadetaileddiscussion,especiallyathighreverse-biasrangewhereEGFissignicantlymodiedduetoelectrostaticgating.Inconventionalmetal/semiconductorjunctions,theworkfunctionofthemetalispinnedindependentofthebiasvoltageduetothehighdensityofstatesatEF,whileunderreverse(forward)bias,theEFofsemiconductorshiftsdownward(upward),allowingobservedrectifyingcurrentviaanincrease(decrease)inVbi.Unlikeconventionalmetals,grapheneissemimetalicwithavanishingdensityofstatesattheDiracpoint.Inthisscenario,EGFandthusWG,canbeeasilytunedthroughelectricalgatingasalreadydemonstratedinpreviouswork[ 1 83 ].Thus,theSBHisnotaconstantunderhighvoltages,thoughitbarelyshiftsatlowforwardbias(V<1V).However,deviationfromlinearityobservedinsemi-logarithmicplotsathighforwardbiasmaybeassociatewithcurrentdegradationcausedbyacombinationofseriesresistanceandslightlyincreasedSBH(thelaterisillustratedinFig. 3-7 (b)and(c)).Underhighreversebias(V<)]TJ /F1 11.955 Tf 9.3 0 Td[(10V),shiftofEGFbecomesnoticeable(reectingastheshiftinRamanpeaksinFig. 3-3 )andinvalidatestheassumptionofabias-invariantSBH.Specically,EFincreasessincegrapheneisnegativelybiased,therebyWGdecreases.Asaresult,SBHdecreasesasillustratedinFig. 3-7 (c).AsobservedinallofthepanelsintheFig. 3-4 ,thiseffectcausesthetotalreversecurrenttoincreaseasthemagnitudeofthebiasincreases,thuspreventingtheSchottkydiodefromreachingreverse-currentsaturation.Suchaneffectisactuallydeleterioustodeviceperformanceathighreversebias,sincethe`off'statecanbe 70

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`turnedon'again,thusimposingalimitationinhighvoltageapplications.However,thisnon-saturatingreversecurrenthasnotbeenobservedingraphite-basedSchottkyjunctionsduetothestabilityofgraphite'sEFathighvoltage[ 62 ]. 3.3.2.2C-VcharacteristicsComplementarytoJ-Vcharacteristics,C-VmeasurementsaretakenunderreversebiastominimizethecurrentleakageforacomprehensivestudyoftheSchottkyphysicsattheinterfacebetweengrapheneandsemiconductor.Otherthanthebarrierheight,C-Vmeasurementsprovideusefulinformationaboutthedistributionanddensityofionizeddonors(ND)inthesemiconductor.AsdiscussedinSec. 2.1.4.3 ,undertheapproximationofabrupt-junctionandassumptionofauniformdistributionofND,theSchottky-Mottrelationshipbetween1=C2andthereverse-biasinthemagnitudeofVRtakestheform 1 C2=2(VR+Vbi) eND0s.(3)AsindicatedinFig. 3-6 ,thelinearbehaviorinbothgraphene/Siandgraphene/GaAsjunctionssuggeststhatSchottky-Mottmodelprovidesagooddescriptioninbothcases.(However,wehavenotbeenabletoobtainreliableC-VmeasurementsforGaNandSiCbasedgrapheneSchottkyjunctions,becauseofhighseriesresistanceinthesewide-band-gapsemiconductors.)Thebuilt-inpotentialVbicanbeextractedfromthetheinterceptsontheabscissaandreads0.82Vand0.88Vforgraphene/Siandgraphene/GaAsSchottkyjunctions,respectively.Accordingly,theSBHcanbeconvertedfromEq.( 2 )giventhatNC=3.21019cm)]TJ /F3 7.97 Tf 6.58 0 Td[(3forSiand4.01017cm)]TJ /F3 7.97 Tf 6.58 0 Td[(3forGaAs.Besides,fromtheslopeofthestraightline(1=C2vsV),wecancomputethedensityofionizeddonors(NC)]TJ /F8 7.97 Tf 6.58 0 Td[(VD).BothC)]TJ /F8 7.97 Tf 6.58 0 Td[(VSBHandNC)]TJ /F8 7.97 Tf 6.59 0 Td[(VDfromgraphene/Siandgraphene/GaAsarelistedinTable 3-1 .NC)]TJ /F8 7.97 Tf 6.59 0 Td[(VDofbothSiandGaAsingoodagreementwiththeresultsfromHallmeasurements,suggestingthevalidationofourcapacitancemeasurements.However,wenotefromTable 3-1 thattheextractedC)]TJ /F8 7.97 Tf 6.59 0 Td[(VSBHvaluesonthegraphene/Siandgraphene/GaAsjunctionsaregenerallyhigherthantheirJ)]TJ /F8 7.97 Tf 6.59 0 Td[(VSBH.Thediscrepancy 71

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betweentheSBHsdeterminedbythetwomethodscanbeattributedtothefundamentaldifferencesinthesetwotechniqueswhentheSBHsarelaterallyinhomogeneous[ 87 ].Morespecically,aspredictedbythetheoryofthermionic-emission,theprobabilityofanelectronbeingthermallyexcitedoveraninterfacialbarrierisexponentiallysensitivetothebarrierheight.Thus,underthepresenceofspatialvarianceintheSBHs,J-VtendstoprobeaminimumvaluefortheSBH,whileC-Vreectsalaterally-averagedvalue[ 56 ].IfassumeanGaussiandistributionofthebarrierheight,valuesobtainfromJ-VandC-Vcharacteristicscanberelatedas J)]TJ /F8 7.97 Tf 6.58 0 Td[(VSBH=C)]TJ /F8 7.97 Tf 6.58 0 Td[(VSBH)]TJ /F7 11.955 Tf 21.67 8.08 Td[(2SBH 2kBT=e,(3)whereSBHisthestandarddeviationoftheinhomogeneousSBHs[ 49 56 87 ].Consequently,basedonthevaluesofJ)]TJ /F8 7.97 Tf 6.58 0 Td[(VSBHandC)]TJ /F8 7.97 Tf 6.59 0 Td[(VSBHobtainedinthosetwosetsofmeasurements(aslistedinTable 3-1 ),SBHingraphene/Siandgraphene/GaAsareestimatedtobe0.055Vand0.078V,respectively.TheinhomogeneitiesinSBHsingraphenebasedSchottkyjunctionsmainlyoriginatefromrandomuctuationsingraphene'schemicalpotentialsalongitssurface,whichgiverisetoelectron-holepuddles[ 22 ]. 3.3.3Voltage-DependentSchottkyBarrierHeight 3.3.3.1Voltage-inducedFermienergyshiftofgrapheneThelinearityofthe1=C2vsVasshowninFig. 3-6 isconsistentwiththeSchottky-Mottmodelandtheabrupt-junctionapproximation.ThisgoodagreementinvitesamorequantitativeanalysisoftheEGFshift,whichhasbeenidentiedastheoriginofnon-saturatingcurrentunderhighreversebiasasdiscussedinSec. 3.3.2.1 .Webeginbywritingtheelectron-chargedensityQperunitareonthegrapheneas Q=eni=CD(Vbi+VR),(3) 72

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whereCDisthedepletioncapacitanceattheinterface,niisthenumberofelectronsperunitareaunderareversebiasofVRinmagnitude.Giventhat CD=s e0sND 2(Vbi+VR),(3)nicanbecomputedas ni=r 0sND 2e(Vbi+VR),(3)whichprovidesanestimationoftheelectric-eldinducednumberofelectronsperunitareawithinthedepletionwidth.However,nidoesnotaccountfortheinitialdensityofholes(n0)ingrapheneduetounintentionaldopingeffect.Thus,theoverallcarrierdensityincludingcontributionsfromtheas-preparedgrapheneandthechargetransfersassociatedwithelectricalgatingeffect(duetothepresenceofSchottky-Mottcapacitance)canbeexpressedas ntot=n0)]TJ /F4 11.955 Tf 11.96 0 Td[(ni.(3)Substitutingntotintothewell-knownexpressionforgraphene'sEFyields EGF=)]TJ /F16 11.955 Tf 9.3 0 Td[(~vFjkFj=)]TJ /F16 11.955 Tf 9.3 0 Td[(~vFp ntot=)]TJ /F16 11.955 Tf 9.29 0 Td[(~vFp (n0)]TJ /F4 11.955 Tf 11.96 0 Td[(ni).(3)IncombinationwithEq. 3 ,Eq.( 3 )canbefurtherwrittenas EGF=)]TJ /F16 11.955 Tf 9.3 0 Td[(~vF("n0)]TJ /F13 11.955 Tf 11.95 19.09 Td[(r 0sND 2e(Vbi+VR)#)1=2.(3)ToestimateatypicalvaluefortheshiftinEGF(EGF)priortographenetransferuponthesemiconductor,weusethefollowingvaluesforparametersthathavebeeninvolvedinEq.( 3 ):0=8.8410)]TJ /F3 7.97 Tf 6.59 0 Td[(14F/cm2,~=6.510)]TJ /F3 7.97 Tf 6.59 0 Td[(16eVs,e=1.610)]TJ /F3 7.97 Tf 6.58 0 Td[(19C,vF=1.1108cm/s,Vbi0.6V,s10foratypicalsemiconductorandn051012cm)]TJ /F3 7.97 Tf 6.59 0 Td[(2,thevalueadoptedfromHallmeasurementaspresentedinFig. 3-1 .Accordingly,EGF(0)=)]TJ /F6 11.955 Tf 9.29 0 Td[(0.287eV,belowthecharge-neutralitypointasaresultoftheunintentionaldopingeffect.Whenthegrapheneissittinguponthesemiconductor, 73

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equilibrationofthechemicalpotentialsandconcomitantformationofaSchottkybarrierresultsinatransferofnegativechargetothegrapheneandanincreaseinEGFintherangeof3)]TJ /F6 11.955 Tf 12.05 0 Td[(11meV(onlyduetoVbiatzerobias)whenNDisintherangeof11016to11017cm)]TJ /F3 7.97 Tf 6.59 0 Td[(3.Furthermore,theapplicationofa)]TJ /F6 11.955 Tf 9.3 0 Td[(10V-reversebiascreatesasignicantshiftinEGF.BasedonEq.( 3 )andtheaforelistedparameter-values,EGFiscalculatedtobeintherangeof)]TJ /F6 11.955 Tf 9.3 0 Td[(0.271to)]TJ /F6 11.955 Tf 9.3 0 Td[(0.233V,correspondingtoEF15)]TJ /F6 11.955 Tf 12.34 0 Td[(53meV.Thus,EGFisbroughtclosertothecharge-neutralitypoint.SuchanumericalestimationofEGFshowsthat,forthen-dopedsemiconductors,itiseasytoinduceFermi-levelshiftsontheorderof50meVunderasufcientlylargereversebias.However,aspreviouslydiscussedinthelatehalfofSec. 3.3.1.2 ontheRamanmeasurements,theshiftinEGFat)]TJ /F6 11.955 Tf 9.29 0 Td[(10Vcomparedtozerobiasisapproximatelyintherangeof200to500meV,whichissignicantlyhigherthanthatobtainedfromourcalculation.SuchadiscrepancymightbeattributedtoanunpreciseestimationofEFusingrelativepeakshiftsinthefeaturedRaman-peakpositions(asalreadymentionedinSec. 3.3.1.2 )basedonexfoliatedgraphene/SiO2,wheretheinteractionbetweengrapheneandunderlyingsubstrateisdifferent. 3.3.3.2Modicationofthermionic-emissiontheoryAsdiscussedpreviously,anupwardshiftinEFof50meVleadstoasimultaneousreductionintheworkfunctionofgraphene(WG)withthesameamount.Sincetheelectronafnity()ofthesemiconductorremainsconstant,accordingtoSchottky-Mottrelation,SBHisexpectedtodecreaseby50mV.Orrather,SBHshouldinprincipleshowasimilarbiasdependencegivenby eSBH(V)=e0SBH+eSBH(V)=e0SBH)]TJ /F6 11.955 Tf 11.95 0 Td[(EF(V),(3)wheree0SBHdenotesthezero-biasSBHandeSBH(V)representsthecorrectiontotheSBHatacertainvoltageV.TheminussignpriortoEGFindicatesaoppositeevolutiontrendsineSBH(V)withrespecttoV.Thus,underreversebias,usingEq.( 3 )and 74

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Eq.( 3 ),andassumingnin0,itgives eSBH(VR)=)]TJ /F6 11.955 Tf 9.3 0 Td[(EF(VR)=~vFhp (n0)]TJ /F4 11.955 Tf 11.95 0 Td[(ni))]TJ 11.96 8.54 Td[(p n0i)]TJ /F6 11.955 Tf 29.75 8.09 Td[(1 2~vFp n0ni n0=)]TJ /F6 11.955 Tf 10.49 8.09 Td[(1 2~vFs 0sND(Vbi+VR) 2en0. (3) Asaresult,thecurrentdensity(J)canberewrittenas J(V)=AT2exp)]TJ /F4 11.955 Tf 10.49 8.09 Td[(e0SBH+eSBH(V) kBTexpeV kBT)]TJ /F6 11.955 Tf 11.96 0 Td[(1.(3)TheoriginalformoftheRichardsonequationispreserved,withslightmodicationtothesaturationcurrentdensityJs,whichisnowgivenby Js(V)=AT2exp)]TJ /F4 11.955 Tf 10.49 8.09 Td[(e0SBH+eSBH(V) kBT.(3)SBH(V)isthecorrectionto0SBHunderreversebiaswithaminussignasindicatedinEq.( 3 ).Thus,Jsbecomesvoltage-dependentandincreasesunderhigherreversebias,suggestinganincreasingcurrentathighVR,incontrasttothatinaregularmetal/semiconductorSchottkyjunctionandthegraphitecounterpartstudiedpreviously[ 65 ]wheretheFermi-levelsarepinnedbyhighdensitiesofsurfacestates.IntheconventionalJ-VanalysisusingEq.( 3 ),thezero-biassaturationcurrentJsisextractedbyextrapolatingthecurrentdensitytothezero-biaslimitbyusingtheJ(V)dataintheforwardbiasrange(usuallybetween0.3Vto1.0V,sinceathigherrange,currentdegradationfromseriesresistancebecomesnoticeable).Inthislimit,thecorrectiontotheSBHisexpectedtobenegligible,sincetheEGFisnotsubjecttoanyconsiderablevariations(asreectedinFig. 3-3 ).However,onecanstillestimatetheSBHatcertainvoltagebypluggingtheextrapolatedJ)]TJ /F8 7.97 Tf 6.59 0 Td[(VSBHintoEq.( 3 ). 75

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3.4ConclusionInsummary,wehavedemonstratedtheformationofSchottkybarrierswhengraphene,azero-gapsemiconductor,isinintimatecontactwithaseriesoftechnicallyimportantn-typeinorganicsemiconductorsincludingSi,GaAs,GaNand4H-SiC.SuchSchottkyjunctionshavebeencharacterizedbycurrent-voltageandcapacitance-voltagemeasurements.TheresultsshowsurprisinglygoodagreementwithSchottky-Mottphysicswithinthecontextofbond-polarizationtheory,simplyduetothefactthatthesuchamodelwasinitiallydevelopedformetal-semiconductorinterfaces,notforatomically-thinzero-bandgapsemiconductorinterfacesdiscussedhere.Furthermore,duetoalowdensityofstates,graphene'sFermilevelshiftsduringthechargetransferacrossthegraphene-semiconductorinterfaces.Thisshiftdoesnotoccuratmetal-semiconductororgraphite-semiconductorinterfacewhereEFofthemetalremainsxedbothduringSchottkybarrierformationandapplicationofhighvoltages.Electric-eld-modulatedRamanspectroscopymeasurementshaverevealedthatlargevoltagesacrossthegraphene/semiconductorinterfacechangethechargedensityandhencetheFermilevelofgrapheneasdeterminedbyrelativechangesintheGand2Dpeakpositions.Thebias-inducedshiftintheFermienergy(andhencethetheworkfunction)ofthegraphenecausessignicantchangesinthediodecurrent.ConsideringchangesinthebarrierheightassociatedwithbiasinducedFermilevelshift,wemodifythethermionicemissiontheoryaccordinglybyaddinganbias-inducedcorrectiontotheSBHatzerobiasintheexponentialterm,whichturnsouttoberesponsibleforincreasingcurrentleakage(asshowninFig. 3-4 )underincreasingreversebias.Also,fromtheSchottky-Mottmodel,wecanestimatethechangeinthebarrierheightatxedappliedbias. 3.5FutureDirectionTherecticationeffectsobservedonawidevarietyofsemiconductorssuggestanumberofapplications,suchastosensorswhereinforwardbiasthereisexponential 76

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sensitivitytochangesintheSBHduetothepresenceofadsorbatesonthegrapheneortoMESFETandHEMTdevices,forwhichSchottkybarriersareintegralcomponents.ThisideahasrecentlybeendemonstratedbyH.Y.Kimetal[ 88 ].Grapheneisparticularlyadvantageousinsuchapplicationsbecauseofitsmechanicalstability,resistancetodiffusionandresilienceathightemperatures.Besides,thankstographene'shightransparencyinthevisiblerange,italsosuggestspromisingapplicationsinphotovoltaics,whichisgoingtobediscussedinthefollowingchapter.Furthermore,Schottkyworkcanalsobeextendedonotherlayeredmaterialsinsteadofgraphene/graphite,suchasBi2Se3,whichisatopologicalinsulatorwithsurfacestatesprotectedbytime-reversalsymmetry.OurpreliminaryresultssuggestBi2Se3/SiformsSchottkyjunctionsascharacterizedbyJ-VandC-Vmeasurements.However,giventhattheSchottkyphysicsisverysensitivetotherstafewatomiclayersattheinterface,Bi2Se3Schottkyjunctionsprovideagoodplatformtoexploretheunderlyingphysicsofthesurfacestatesandtheirinteractionswithinorganicsemiconductors.Especially,Bi2Se3isshowntobesensitivetosomegasmoleculessuchasO2andNO2[ 89 ],whileitisinerttoNOandH2,duetothedistinctinteractionswithSevacancies.Accordingly,Bi2Se3basedSchottkydiodescastlightongassensingapplication,whichmaybeevenadvantageousovergraphenecounterparts.FutureeffortwillbeinvestedintounderstandingtheSchottkyphysicsattheBi2Se3andSiinterfaceandtheircapabilitiesingassensingapplications. 77

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Figure3-1. RoomtemperatureHallmeasurementofgraphene/SiO2/Si.Typically,themobilitiesofourCVD-growngraphenesheetsareintherangeof5.62)]TJ /F6 11.955 Tf 11.95 0 Td[(21001012cm2/Vsandwithcarrier(hole)densitiesof2)]TJ /F6 11.955 Tf 11.95 0 Td[(81012cm)]TJ /F3 7.97 Tf 6.59 0 Td[(2.Insetshowsthecontactgeometry. 78

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Figure3-2. RamanSpectraofmonolayergrapheneonvarioussubstratesaremeasured.A)RamanSpectroscopytakenonmonolayergrapheneasgrownonCufoilbyCVDmethod.B)Measurementstakenongraphenesheetsafterbeingtransferredontovarioussemiconductorsubstrates.TheemergenceofmoderateDpeaksafterwettransferindicatesslightdegradationofgraphene'squalityduetopossiblyintrudeddefects/disordersduringthetransferprocess.C)GpeaksfromtheRamanspectra.Theblackcurveisfromgraphene/Cu,andothersarefromgrapheneonthosesemiconductorsasindicatedinB).D)2DpeaksfromtheRaman-spectra.ThecolordenitionisthesameasthatinC). 79

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Figure3-3. In-situRamanspectratakenongraphene/GaNunderdifferentbias:0V(blackline),+1V(redline),and)]TJ /F6 11.955 Tf 9.3 0 Td[(10V(blueline).ThedirectionoftheshiftinGand2Dpeakpositionsareindicatedbybluearrowswhenthedeviceisreverselybiasedat)]TJ /F6 11.955 Tf 9.3 0 Td[(10V. 80

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Figure3-4. RoomtemperatureJ-VcharacteristicsmanifestrecticationduetotheformationsofSchottkybarriersattheinterfacesgrapheneandvarioussemiconductors.A)TheJ-Vcharacteristictakenonagraphene/Sijunction.B)TheJ-Vcharacteristictakenonagraphene/GaAsjunction.C)TheJ-Vcharacteristictakenonagraphene/4H-SiCjunction.D)TheJ-Vcharacteristictakenonagraphene/GaNjunction. 81

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Table3-1. ExtractedSBH,donordensity,valueofgrapheneworkfunctiononeachsemiconductorSchottkyjunctionsat300K. Schottkyjunctions J)]TJ /F8 7.97 Tf 6.59 0 Td[(VSBH(V)C)]TJ /F8 7.97 Tf 6.59 0 Td[(VSBH(V)NC)]TJ /F8 7.97 Tf 6.59 0 Td[(VD(cm)]TJ /F3 7.97 Tf 6.59 0 Td[(3)NHallD(cm)]TJ /F3 7.97 Tf 6.59 0 Td[(3)WG(V) Graphene/Si 3.580.860.924.010153.010154.91Graphene/GaAs 1.350.790.913.510163.010164.89Graphene/4H-SiC 3.490.84)]TJ 51.56 0 Td[()]TJ /F1 11.955 Tf 65.95 0 Td[(1.010164.24Graphene/GaN 4.940.76)]TJ 51.56 0 Td[()]TJ /F1 11.955 Tf 65.95 0 Td[(1.010174.86 Figure3-5. DevicegeometryofgraphenebasedSchottkydiode. 82

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Figure3-6. Plotsoftheinverse-squarecapacitance(1=C2)vsappliedbias(V)takenat300Kand100Hzforgraphene/Si(redsquaresandmarkingsontheleft-handyaxis)andgraphene/GaAs(greencirclesandthemarkingsontheright-handyaxis). 83

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Figure3-7. InterfacebanddiagramunderA)zerobias,B)forwardbiasandC)reversebias.TheshiftinEGFunderbiasgivesrisetoavoltage-dependentSBHinB)andC). 84

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CHAPTER4GRAPHENE/SILICONPHOTOVOLTAICSBYCHEMICALDOPING 4.1OverviewBecauseofitssuperioropticalandelectricalproperties,graphenereceiveshighexpectationforfutureapplicationinphotonicsandoptoelectronics.Afocusongraphenebasedsolarcellsis,forexample,particularlyattractiveduetotheurgentdesireforrenewableenergies.However,mechanicallyexfoliatedgrapheneisnottechnicallyapplicableinphotovoltaics(PVs),wherelarge-areaandscalablegrapheneproductionisusuallyrequired.Instead,priortothedevelopmentofCVDmethods,researchongraphenebasedPVswasrststartedwithsolutionprocessedthinlmsofreducedgrapheneoxides(RGO)[ 90 91 ],bywhichlarge-areaRGOsheetscanbeeasilysynthesizedandconsequentlyallowsitsintegrationwithbothorganic[ 92 ]anddye-sensitizedsolarcells(DSSC)[ 93 ].Inbothdevicearchitectures,graphenesheetswerefunctioningastransparentconductingelectrodes(TCEs)tocollectfreecarriersafterphoton-inducedexcitondisassociations.Themotivationistoreplaceindiumtinoxides(ITO),sinceITO(aswellasothertransparentconductiveoxides)ismechanicallybrittle,thuspreventingitsapplicationinexibleelectronics.Also,duetoacommerciallyscarcity,theproductionexpenseofITOismuchhigherthanthatofeitherCVD-grownorsolutionprocessedgraphene.Inaddition,graphenecanalsobeintegratedwithinorganicsemiconductorstoformSchottkysolarcells,suchasSi[ 95 96 ],CdS[ 97 ]andCdSe[ 98 ]withpowerconversionefcienciesrangingfrom0.1%to2.86%.ProgressinthiseldhasbeengreatlystimulatedbythedevelopmentofCVDmethods.TheCVDgraphenequalityismuchhighercomparedwithRGOasmanifestedbyamuchlowersheetresistance(R2) ThischapterisareprintofHighEfciencyGrapheneSolarCellsbyChemicalDopingbyX.MiaoetalpublishedinNanoLett.12,2745(2012)[ 94 ]. 85

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andhighercarriermobilities[ 67 90 99 100 ],whicharecriticaltodeviceperformance.IngraphenebasedSchottkyPVs,graphenesheetsnotonlyserveasTCEsbutalsoareinvolvedinactivelayers,wheretheyforminterfacepotentialswithinorganicsemiconductors(asintroducedinCh. 3 )andhencehelpchargedisassociationafterphoto-excitation.Ontheotherhand,grapheneisasemimetalwithlowdensityofstatesaroundEF,whichallowseasychemicalfunctionalizationofgraphene'selectricalpropertiesastofullyrealizegraphene'sversatilityinPVsandotheroptoelectronicdevices.Especially,chemicaldopingisthemostcommonlyusedandeasiestwaytoreducethehighsheetresistanceofas-grownCVDgraphene(R21k),whichisthemainobstaclethathindersgraphene'scompletesubstitutionofITOasTCE[ 101 ].Therehavebeennumerousstudiesondopinggraphenewithdifferentchemicals,suchasAuCl3[ 102 ],HNO3[ 103 ],thionylchloride(SOCl2)[ 104 ]andtetracyanoquinodimethane(TCNQ)[ 76 ]etc.However,theresultingdopingeffectsaresubjecttoagingandnoticeablydegradeopticaltransparenciesandcarriermobilitiescomparedwiththeundopedparentsheets.Incontrast,bis(triuoromethanesulfonyl)amide(TFSA)isfoundtobeastrongandstableorganicdopantinpreviousstudies[ 105 106 ],whichholedopesgrapheneandsignicantlyreducesR2ofgrapheneupto70%withlittlesacriceinitsopticalpropertiesandcarriermobility.Moreimportantly,thedopingeffectofTFSAislong-termstable.Therefore,itsusesuggestsapromisingapplicationinallgraphenebasedPVs.Inthischapter,wewillshowthatTFSAdopingincreasesthepowerconversionefciency(PCE)ofasingle-layer-graphene/n-SiSchottkyjunctionsolarcellfrom1.9%to8.6%.ResultsfromJ-V,C-Vandexternalquantumefciencymeasurementswillbediscussedrespectivelytounderstandtheunderlyingphysicsthatleadstosuchremarkableenhancementsinthedeviceperformance.Here,wechooseSiasthesemiconductingsubstratemainlybecause:(1)wealreadyhavedevelopedtheknowledgeofgraphene/SiSchottkyjunctionsinourpreviousworkasdescribedinCh. 3 86

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and(2)single-crystalSiisaverysophisticatedandwell-understoodmaterialintheapplicationoflightharvestingthusprovidinganidealplatformforourinvestigation.Tobeginwith,ashortintroductiontothebackgroundofSchottkysolarcellsisgivenassupplementarytothewholecontentinthischapter. 4.2BackgroundofSchottkySolarCells 4.2.1SolarSpectrumSolarradiationisthepowersupplyforsolarcellsandoriginatesfromthenuclearfusionprocessesinthesun.Thesolarspectrumcanbesimulatedastheelectromagneticradiationsemittedbyablackbody(namely,thesun)withatemperatureof5800Kandradiativeenergyrangingfrominfraredtoultravioletspectralranges.Toaccuratelyestimatethefullspectrumatthesurfaceoftheearth,attenuationbytheatmospheresurroundingtheearthmustbetakenintoaccount.Thetotalabsorptionofthesunlightbytheatmosphereisproportionaltothelengthofthesunlightpassage(l)throughthegaseouslayer.Theminimumatmosphericpath(lmin)occurswhenthesunisatzenith.Theratioofl-to-lmincanbeevaluatedasthesecantoftheangle()betweenlandlminasillustratedinFig. 4-1 ,whichisalsodenedasairmass(AM)ratio.Itisanevaluationofatmosphericimpactonthesunlightarrivingatthesurfaceoftheearth.AM0isthesolarradiationimpingingontheearthintheabsenceofatmosphere,andAM1.0isthesolarradiationpassingthroughtheatmospherewhenthesunisatzenith(i.e.,=0).AtypicalsolarspectrumisusuallygivenatAM1.5(=48),asshowninFig. 4-2 ,takingintoaccountthegeneralclimateandterrestrialconditions.Thetotalincidentpower(Pin)canbeobtainedbyintegratingthesolarradiation(powerperunitareaperunitwavelength),S(),overthewholespectralrange,i.e. Pin=ZS()d.(4)Pin=135mW/cm2and100mW/cm2forAM0andAM1.5,respectively. 87

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4.2.2PhysicalMechanismofSchottkySolarCellsForatypicalsolarcell,ap-typeandann-typesemiconductingmaterialwithsuitablebandgaps(usuallyintherangeof1.01.8eV)arebroughttogether.Theirinterfaceprovidesthebuilt-inpotential.Whenasolarphotonisabsorbedineitherofthesemiconductors,anelectron-holepairorexcitoniscreated.Subsequently,theelectron-holepairisdisassociatedintofreecarriersbythebuilt-inpotentialattheinterface.Theyaresubsequentlycollectedbycorrespondingelectrodes(cathodeforelectronsandanodeforholes),therebygeneratingthephotocurrent(Iph).ThisconceptcanbeequivalentlyappliedtoaSchottkysolarcell,withthebuilt-inpotential(Vbi)createdbythemetalandsemiconductorasdescribedinCh. 2 .TheI-VcharacteristicsareshowninFig. 4-3 (a)foratypicalsolarcell.Whenthecellisindark,I-VisnodifferentfromthatinausualSchottkyjunction.However,whenthecellisunderillumination,giventheadditionalphotocurrentterm,Iph,theoverallI-Vcharacteristicsaregivenby I=Is(T)expeV kBT)]TJ /F6 11.955 Tf 11.96 0 Td[(1)]TJ /F4 11.955 Tf 11.95 0 Td[(Iph,(4)whereIs(T)isthesaturationcurrentandistheidealityfactorofthecell.AsindicatedinFig. 4-3 ,theinterceptoftheI-Vcurvewhentakenunderilluminationrepresentstheshortcircuitcurrent,Isc.Inanidealsolarcellwithnegligibleseriesresistance(Rs),Isc=)]TJ /F4 11.955 Tf 9.3 0 Td[(Iph.Inaddition,theinterceptofabscissagivestheopencircuitvoltage,Voc,denotingthevoltagedifferenceacrosstheanodeandcathodewhentheloadimpedanceisinnitelylarge.TheexpressionforVoccanbederivedfromEq.( 4 )bysettingI=0as Voc=kBT elnIph+Is IskBT elnIph Is,(4)basedonthefactthatIphIs. 88

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Moreover,outputpowercanbeobtainedby Pout=IV=IsVexpeV kBT)]TJ /F6 11.955 Tf 11.95 0 Td[(1)]TJ /F4 11.955 Tf 11.95 0 Td[(IphV.ThemaximumPout(Pmaxout)canbederivedbysolvingdP=dV=0,whichisillustratedbytheareaofshallowyellowboxintheFig. 4-3 (a).AnotherwaytoevaluatePmaxoutisbyintroducingaphysicalquantitycalledllfactor(FF),whichisdenedas FF=ImVm IscVoc.(4)Here,ImandVmarethecorrespondingcurrentandvoltageatPmaxout.Thus, Pmaxout=ImVm=FFIscVoc.(4)Consequently,thepowerconversionefciency(PCE)canbeobtainedas PCE=Pmaxout PinA=FFIscVoc PinA=FFJscVoc Pin.(4)Here,Aistheactiveareaofthecellunderillumination.Jsc=Isc=Aistheshortcircuitcurrentdensity.ThePCEevaluatestheefciencyofaphotovoltaiccellinconvertingsolarenergytoelectricity.Itisacriticalparameterthatdirectlyreectstheperformanceofaas-producedPV.ThePCEisfarfrombeing100%incurrentsolarcellindustriesandscienticstudies.Thedeviationismainlyascribedtotheinevitablechargerecombination,ohmiclossesowingtoaniteseriesresistanceandincompletelightabsorptionduetosurfacereection[ 107 ].ThehighestPCEachievedis25.0%forcrystallineSisolarcells[ 108 ](withoutlightconcentrator)veryclosetoitstheoreticallimit[ 109 ],whiletherecordPCEfororganicthin-lmsolarcellis10.0%[ 108 ].Additionally,theexternalquantumefciency,EQE,givesincident-photon-to-charge-carrierefciency(alsotermedasIPCE)andisadetailed 89

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evaluationofenergyconversionefciencyataspecicwavelength.Itisdenedas EQE=numberofcollectedelectrons numberofincidentphotons.(4)Accordingly,JsccanbeobtainedfromEQEas Jsc=ZeEQE()S() hcd.(4)Here,hisPlanck'sconstant,cisthespeedoflightandS()isthepowerofsolarradiationperunitareaatagivenwavelength,.Sofar,theeffectofseriesresistance(Rs)showninFig. 4-3 (b)hasnotbeenconsideredinthediscussion.However,inpractice,Rscannotbesimplyneglected,duetothenitebulkresistanceofthesemiconductorandresistanceofohmiccontactsbetweenmetalelectrodesandsemiconductors.Itcanberegardedastheinternalresistanceofabattery.Consequently,theequivalentcircuitofarealsolarcellcanbeapproximatedasacombinationofincludingaphotocurrentsource,adiodeandaniteseriesresistanceasillustratedinFig. 4-3 (b).Inthisscenario,theI-Vcharacteristicsaremodiedtobe I=IsexpeV)]TJ /F4 11.955 Tf 11.95 0 Td[(eIRs kBT)]TJ /F6 11.955 Tf 11.96 0 Td[(1)]TJ /F4 11.955 Tf 11.96 0 Td[(Iph.(4)AspreviouslyintroducedinSec. 2.1.4.1 ,RscanbeextractedfromtheslopeofadV=(dlnI)vsIplot,giventhat dV d(lnI)=IRs+kBT e.(4)Usually,theeffectofRsbecomespronouncedatahighvoltagerange(V>0.5V)andsignicantlydegradestheoutputcurrentanddeviceperformance.Thus,itisimportanttoengineeralowRsinordertofacilitatechargecollectionprocessesafterexcitondissociationsandminimizeohmicloss. 90

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4.3ExperimentalMethods 4.3.1DeviceFabricationMonolayergraphenewasgrownbyCVDmethodaspreviouslydescribedinSec. 3.2.1 .n-Si(111)waferswerepurchasedfromUniversityWaferwitha1m-thickthermaloxide(SiO2)andadopinglevel(phosphorous)of11015cm)]TJ /F3 7.97 Tf 6.58 0 Td[(3.Au/Crwindows(asshowninFig. 4-4 )weredepositedontotheSisubstratesaslow-resistancecontactstothegraphenesheets.Subsequently,theexposedparts(33mmarea)oftheSiO2wereremovedusingbufferedoxideetch(BOE)withNH4/HF(6:1)for10mintoyieldtheunderlyingSi.Thenthewholedevicewasexposedtoairfor12hourspriortographenetransfer.Thisadditionalprocesshasbeenshownincarbonnanotube(CNT)/Sisolarcellstobebenecialforthedeviceperformance[ 110 ],probablyduetotheoxygenpassivisationofsurfacestatesaspreviouslyreportedforconventionalMISPVs[ 111 ].Indeed,theprocedurealsoworksforourgraphene/Sisolarcells.However,longerwaitingtimewouldcauseformationofthickernativeoxidesontheSisurface,whichdegradethedeviceperformance.Subsequently,thegraphenesheetsweretransferredontotheSisubstratesinasimilarwayasdescribedinSec. 3.2.1 followedbyacompleteremovalofPMMAinanacetone-vaporbathandseveralsubsequentacetonesolventbathformorethan12hours.TFSAwasdissolvedinnitromethane.Theresultingsolutionwithaconcentrationof20mMwasspun-castontothedeviceat10001500rmpfor1mintoachieveuniformcoverageontheactiveareaofthePVs.OhmiccontactstotheSiwafersweremadebyusinggalliumindiumeutecticpaint(fromAlhpaAesar,ProductNo.12478,99.99%metalbasis).Finally,thedevicewasmountedonastainlesssteelplatetoallowconnectiontoTungstenwiresaselectricalleadsasillustratedinFig. 4-4 (c). 4.3.2Electro-OpticalCharacterizationsofPhotovoltaicsTheJ-Vcharacteristicsweremeasuredunderstandardsolarcelltestconditions,wherethesimulationofsolarspectrumatAM1.5isgeneratedbyaXenonlamp(Oriel 91

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6255)incombinationwithaseriesoffusedsilicalens,neutraldensity(ND)ltersandotheropticalelements(seeRef.[ 112 ]).Theintensityoftheilluminationonthesamplesurfacewascalibratedtobe100mW/cm2byaNewport1916-RHandheldopticalpowermeter.Thesizeofthehomogenouslightspotwasfoundtobe1cm2withvariationslessthan5%inthelightintensity.J-VmeasurementsweretakenbyaKeithley2400underthecontrolofLabTrace2.0software.C-Vcharacteristicsweretestedindark(tominimizecurrentleakage)byaHP4284Acapacitancebridgeatafrequencyof1000Hz.Tomeasuretheexternalquantumefciency(EQE),thedeviceswereundertheilluminationofmonochromaticlightthatwasmechanicallychoppedat400Hz,andthephotocurrentwasrecordedbyaStanfordResearchSystem830DSPlock-inampliertogetherwithaKeithley428currentamplier.AXe-arclampwasusedasthethewhitelightsourceandanOrielmonochromatorwasadaptedtogeneratemonochromaticlightatvariouswavelengths.TheresultinglightintensitywasmeasuredusingacalibratedNewport818-UVSidetector.Tomeasurethecarrierlifetime,transientphotovoltageswereinducedby632nmlaserpulseswithlightintensitymodulatedbyaseriesofNDlters[ 113 ].Theresultingvoltagesignalswerethenmonitoredbyaoscilloscope.AllthecharacterizationsofthePVswereconductedatroomtemperature. 4.4ResultsandDiscussion 4.4.1J-VCharacteristicsThediscussioninCh. 3 showedthatthemismatchofEFingrapheneandSigivesrisetotheformationofaSchottkybarrieratthegraphene/Siinterfacewhentheyareinintimatecontactwitheachother.ConcomitantwiththeformationofaSBH,achargedepletionregioniscreatedontheSisidewithassociatedbuilt-inpotential(Vbi)acrossit.Consequently,whenthedeviceisunderAM1.5illumination,photonsareabsorbedbySiafterpenetratingthroughthetopgraphenelayer.Asaresult,electron-holepairsaregeneratedintheSiandsubsequentlyseparatedwithinthedepletionregionbytheelectriceldassociatewithVbi,andhencebecomefreeelectronsandholes.Eventually, 92

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thesephoto-excitedfreechargecarriersarecollectedbycorrespondingelectrodes,therebygeneratingphotocurrentinthecircuits.Fig. 4-5 showsbothJ-Vcharacteristicsindark(blackline)andunderAM1.5illumination(blueline)ofapristinegraphene/Sisolarcell.TheparametersJsc=14.2mA/cm2,Voc=0.42V,FF=0.32andPCE=1.9%arefound.SimilarmeasurementshavebeentakenonninedifferentsamplespriortoTFSA-dopingwithPCEintherangeof0.88%to2.7%.Thetrendsreportedherehavebeenreproducedonallthesamplesandaregoodrepresentationsoftheoverallresults.Basedonpreviousworkdonebyourgroup[ 105 ],itisknownthatTFAShole(p-)dopesgraphene,thusreducingthesheetresistance(R2)upto70%concomitantwithanincreaseinworkfunctionofgraphene(WG).Advantageously,TFSAisatransparentorganicpolymer.Consequently,dopingwithTFSAdoesnotdegradegraphene'shighopticaltransparency.Moreover,thedopingeffectofTFSAislong-termstable,whichisadvantageousoverothergraphenedopants[ 102 103 ].AsshowninFig. 4-5 ,theJ-Vcurveunderilluminationinthesamegraphene/SiPVafterTFSAdoping(redline)manifestssignicantlyenhancedJscandVoccomparedwithwiththepristinedevice.Specically,Jscincreasesfrom14.2to25.3mA/cm,Vocrisesfrom0.43to0.54V,andFFenhancesfrom0.32to0.63.Asaresult,thePCEimprovesfrom1.9%to8.6%,i.e.afactorof4.5timesincrease.Thisdramaticimprovementcanbeattributedto(1)improvementingraphene'selectricalconductivityand(2)asimultaneousincreaseinVbi(aswellasSBH)associatedwithdopinginduced-downshiftinEGF.First,theimprovementingraphene'selectricalconductivitybyTFSAdopinggivesrisetoa30%deceaseinseriesresistance(Rs)ofthegraphene/SiPV.AsillustratedinFig. 4-7 ,Rsdecreasesfrom14.9to10.8,therebyreducingohmiclossesandfacilitatingthechargecollectionprocessafterelectron-holepairseparationinthedopeddevice. 93

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Inaddition,SBHcanbeextrapolatedfromthelinearregionsinthesemi-logarithmicJ-VplotsinFig. 4-6 toinvestigatetheeffectofdopingonthebandstructure.Basedonthermionicemissiontheory,thecurrentdensity,J,inaSchottkyjunctionisgivenby J(V)=Js(T)expeV kBT)]TJ /F6 11.955 Tf 11.96 0 Td[(1,(4)with Js(T)=AT2exp)]TJ /F4 11.955 Tf 10.49 8.08 Td[(eSBH kBT,(4)whereAistheRichardsonconstant.TheextractedvaluesshowthatSBHincreasesfrom0.79to0.89V.AccordingtotheSchottky-Mottmodel,whereSBH=WG)]TJ /F7 11.955 Tf 11.18 0 Td[(Si,suchanincreaseinSBHisadirectresultoftheraisedWGbyhole-dopingnatureofTFSAasdepictedinFig. 4-12 .GiventhelinearrelationshipbetweenSBHandVbisuggestedbyEq.( 2 ),asimilarincreaseisexpectedinVbiafterdoping.Furthermore,sinceVocisgenerallyproportionaltoVbi,thechangeinSBHcanalsobeassociatedwiththechangeofVoc.Indeed,asshowninFig. 4-5 (b),Voc,asmentionedabove,increasesby0.1Vafterdoping.ThisincreaseisnowwellexplainedbytheincreaseinSBH.However,accordingtothepreviousstudiesofTFSAdopedgraphene[ 105 ],theshiftinEGFcanbeashighas0.7eV.SuchachangeinEFshouldgiveaconsiderablyhigherchangeinSBHthantheobserved0.1Vincrease.Weattributethisdiscrepancytothefundamentaldifferencesbetweenthetwoexperimentaltechniques.InthepreviousHallmeasurementsbasedonfour-terminalcontactgeometry,thegraphenesheetwastransferreddirectlyontoaSiO2/Sisubstrate,therebylimitingthechargetransferbetweengrapheneandthesubstratesunlikewhathappensduringtheformationofaSchottkybarrier(refertoSec. 3.3.3 ).Asaconsequence,theeffectofTFSA-dopingisoptimizedwithoutanyothercontaminantsideeffects(suchasSchottkyeffect)thatwouldblurthedoping-inducedchangesintransportproperties.Moreover,sincetheelectricalcurrentpreferentiallyowsthroughthemostconductivepaths(giventheelectron-holepuddlesinthegraphenesheet),thismeasurementthereforetendstooverestimatethe 94

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changeinEF.Likewise,themostconductivepathsinaSchottkydiodecorrespondingtothepatcheswithlowestSBH.GiventheSchottky-Mottmodel,thelowestSBHcorrespondingtothelowestWG,thushighestEGF.Therefore,theJ-Vmeasurementconductedinagraphene/SiSchottkyjunctiontendstounderestimatethechangeinEGF.Inaddition,theidealityfactor,,ofthegraphene/Sisolarcell,isfoundtobeintherangeof1.62.0inpristinedevices,whileimprovingtovaluesfallingwithin1.31.5indopeddevices.Typically,thedeviationinfromunityingraphenebasedSchottkyjunctionscanbeascribedtoanumberofpossiblephysicalmechanisms:(1)additionalchargetransportprocesssuchastunnelingoccurringattheinterfaceotherthanthermionicemission,(2)abias-dependentSBHasdescribedinSec. 3.3.3 ,(3)imageforceloweringeffect[ 48 49 ],and/or(4)lateralinhomogeneitiesofSBHsinthedevices.Here,thebias-dependentSBHeffectisnotsignicant,sinceweonlyexamtheJ-Vcharacteristicsfrom-1Vto1V,wherethebias-inducedshiftinEGFisnotappreciablebasedonthecalculationsinSec. 3.3.3 .Furthermore,TFSAdopingbringsEGFfurtherdownfromthechargeneutralitypoint,wherethedensityofstatesismuchhigher.Ahigherdensityofstateswouldreducethebias-dependenceoftheSBH.However,thespatialuctuationsinSBHsisexpectedtohaveamoreprominenteffectonthedeviationoffromunityinpristinegraphene/Sidevices.Suchuctuationsoriginatefromthenonuniformchemicalpotentialsingraphenesheets(e.g.existenceoftheelectron-holepuddles).Therefore,TFSAdopingisanticipatedtoyieldabetterhomogeneityingraphene'schemicalpotentialandconsequentlyreducethelateralinhomogeneitiesinSBHsatthegraphene/Siinterface.Thismaygiverisetotheimprovedindopeddevices.Sofar,wehavenotfullyexplainedthedramaticincreaseinJscafterdopingasobservedfromFig. 4-5 .The30%reductioninRsofthedopedcellisnotbyitselfsufcienttoaccountfortheaccompanyingfactorof1.8increaseinJsc.Whenthedeviceisunderillumination,Eq.( 4 )ismodiedbycountingthephotocurrentdensityterm, 95

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Jphandgivesthenetcurrentdensityas J(V)=JsexpeV kBT)]TJ /F6 11.955 Tf 11.96 0 Td[(1)]TJ /F4 11.955 Tf 11.96 0 Td[(Jph.(4)Jphisusuallyregardedasaconstantunderacertainincidentlightintensity,orrather,thePin.Here,Rsissettozeroonpurpose,sincewewouldliketoclarifyhowmuchtheJscwouldchangesolelybecausetheSBHincreasesfrom0.79to0.89eVbydoping.Atzerobias,wehaveJsc=)]TJ /F4 11.955 Tf 9.3 0 Td[(Jph,andforzeronetcurrent(V=Voc),wehave JphJs(T)expeVoc kBT.(4)Generally,VockBTsothatthe)]TJ /F6 11.955 Tf 9.3 0 Td[(1termisnegligiblecomparedwiththeexponentialterminsidetheparenthesesinEq.( 4 ).Thus, Jsc)]TJ /F4 11.955 Tf 28.56 0 Td[(Js(T)expeVoc kBT=)]TJ /F4 11.955 Tf 9.3 0 Td[(AT2exp)]TJ /F4 11.955 Tf 10.5 8.09 Td[(eSBH kBTexpeVoc kBT. (4) SubstitutingtheexperimentallyobtainedvaluesofSBH,VocandinpristineandTFSAdopedsamples,Jsciscalculatedtoincreasebyafactorof1.5,whichisveryclosetothefactorof1.8directlyinferredfromFig. 4-5 (b).However,thisvalueisanunderestimate,sincewehavenotyetconsideredthe30%reductioninRsinthecalculationnorthepossiblebenetsfromanti-reectioneffectoftheTFSAoverlayer.Inaddition,theenvironmentalstabilityofthegraphene/SiPVhasalsobeencontinuouslytestedupto3daysafterdopingbytheJ-VmeasurementsaspresentedinFig. 4-8 .Theresultsindicatesthereislittledegradationintheperformanceofthedopeddeviceafter3days,whichisconsistentwiththestabledopingnatureofTFSAasfoundinpreviouswork[ 105 ].AssuggestedbyearlierstudiesdoneonCNT/SiSchottkysolarcells[ 110 112 ],suchlittledegradationisprobablyduetotheoxidationontheSisurfacebyintercalationofO2moleculesundergraphenelayer,leadingtotunnelingbarriersthatincreaseohmiclossesand/orinterfacedipolesthatmayserveaschargerecombination 96

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centers.ComparedwithCNT/SiSchottkyPV,thegraphene/Sicounterpartshowsamuchloweroxidationrate[ 110 ].ThisisbecauseoxygendiffusesmucheasierintothepercolatingnetworkofCNTs,whilethehoneycombgraphenelatticehasamuchhigherdiffusivebarrierforoxygen,especiallyifthereareonlyafewlatticeimperfectionsinducedduringthegraphenegrowth/transferprocess.Thus,encapsulationofthewholedevice,suchasspin-coatinganextralayerofPMMAorTiO2ontopoftheTFSA/graphene/Si,maypreventoxidationontheSisurface,andisthereforeexpectedtoimprovetheenvironmentalstabilityofthegraphene/SiPV.Moreover,suchovercoatsmayalsosignicantlyincreasetheJsc,therebyenhancingPCE,duetotheadditionalbenetfromanti-reectioneffect[ 114 115 ]. 4.4.2C-VCharacteristicsIncomplementtoJ-Vcharacteristics,darkroomC-Vcharacterizationisperformedbeforeandafterdopingtogiveadirectmeasurementofthebuilt-inpotential,Vbi.WithintheSchottky-Mottmodelandabruptjunctionapproximation,1=C2scaleslinearlywithappliedvoltage.Theirrelationshipisgivenby 1 C2=2(Vbi)]TJ /F4 11.955 Tf 11.96 0 Td[(V) e0sND(4)Here,Vistheappliedvoltage.NDisthedensityofionizeddopantsinSi.0isthevacuumpermittivityandsistherelativedielectricconstantofSi.AsdemonstratedinFig. 4-9 ,thelinearityofthe1=C2vsVcurvesbeforeandafterTFSAdopingsuggeststhattheSchottky-Mottmodelandabruptjunctionapproximationgiveasatisfactorydescriptionoftheinterfacephysicsatgraphene/SiSchottkyjunctions,whichisalsoinaccordwiththepreviousdiscussioninSec. 3.3.2.2 .ThedashedlineextrapolationstothevoltageaxisyieldthevaluesofVbi=0.36VandVbi=0.56Vinpristineanddopedcells,respectively.TheshiftinVbiisadirectresultofdopinginduceddown-shiftinEGF,asillustratedinFig. 4-12 ,andwithdrawsmoreelectronsfromSitographenetoequilibrateEFonbothsidesduringtheformationofSchottkybarrieratthe 97

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graphene/Siinterface.ThecorrespondingSBHscalculatedfromEq.( 2 )are0.63Vand0.82Vbeforeandafterdoping.TheseresultsareingoodagreementwithwhathavebeenobtainedfromJ-Vcharacteristicsofadifferentsample(Fig. 4-5 andFig. 4-6 )regardlessofthefundamentaldifferencesinthosetwoexperimentaltechniques.Specically,asdiscussedinSec. 3.3.2.2 ,resultsfromaJ-VmeasurementusuallygivealowerboundofSBH,whilethosefromaC-VmeasurementgivesanaveragevalueofSBH.Suchadoping-inducedincreaseinVbileadstoasimilarenhancementinVocasobservedinFig. 4-5 (b).Asaresult,thedoping-inducedincreaseinVbifacilitateselectron-holepairdisassociationattheinterface,therebygeneratingmorefreecarriersforchargecollectionandpartiallycontributingtothedramaticimprovementinPCE. 4.4.3ExternalQuantumEfciencyandCarrierlifetimeOtherthanJ-VandC-Vcharacterizations,wehavealsomeasuredtheexternalquantumefciency(EQE)inaseparategraphene/SisolarcellasshowninFig. 4-10 .ThePCEinthisdeviceincreasesfrom2.7%to6.2%afterTFSAdoping.TheEQEofthepristinecellissimilartostate-of-artSisolarcells[ 116 ]andimpliesthatinourdevicewithtransparentgrapheneelectrodes,onlytheSiabsorbsphotonsandsubsequentlycreateselectron-holepairs.AnEQEnear50%inthewavelength()rangeof400to850nmindicateseffectiveelectron-holepairgenerationandthesubsequentfacilecollectionoffreechargecarriersbycorrespondingelectrodes.AfterTFSA-doing,theEQEconsiderablyincreasesto65%withinthesamewavelengthrange,representinga30%improvementcomparedwiththepristinecell.Giventhealmostidenticalphoto-generationforthepristineanddopeddevices,thehigherEQEafterTFSAdopingisascribedtomoreefcientchargeseparationandchargecollectionduetotheincreasedbuilt-inpotential(Vbi)andreducedRs,respectively.Toinvestigatethedopingeffectonthecarrierlifetime,transientphotovoltagemeasurementshavebeenperformedandtheresultsareshowninFig. 4-11 .The 98

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temporalphotovoltageresponsecanbewelldescribedbyabi-exponentialdecayingfunctioninEq.( 4 )forSisolarcellsasdemonstratedinpreviousstudies[ 113 117 ]. Vphoto=V1exp)]TJ /F7 11.955 Tf 10.49 8.09 Td[(1 t+V2exp)]TJ /F7 11.955 Tf 10.49 8.09 Td[(2 t+V0,(4)Here,V1andV2arethemagnitudesofthetwoexponentialcomponents,andV0isabackgroundterm.Thecarrierlifetimebothatgraphene/Siinterface(1)andinsidethebulkSi(2)canbeextractedoutbyttingthetransientphotovoltagewithEq.( 4 ).Forthepristinedevice,pristine1=0.710.01msandpristine2=4.490.02ms.SuchlongcarrierlifetimesareduetothehighqualityofcrystallineSiweusedhere.FortheTFSA-dopeddevice,doped1=0.460.01msanddoped2=5.680.01ms.1,whichiscloselyrelatedtopropertyofthegraphene/Siinterface,isnotsignicantlyalteredbyTFSA,indicatingthattheoverlayercoatingwithTFSAdoesnotintroduceanysurfacechargerecombinationcenters.Likewise,2,whichisdeterminedbythebulkpropertiesofSi,isnotaffectedbyTFSAdopingeither.TheseresultssuggestthattheseintrinsicallylongcarrierlifetimesinSiarenotamainfactortothedoping-inducedimprovementofthedeviceperformance.Hence,theenhancementintheJscandtheoverallPCEismainlyaconsequenceoftheincreaseintheSBH(built-inpotential,Vbi)andthesimultaneousdecreaseinRs,asalsomanifestedinthenoticeableincreaseinEQE. 4.5SummaryWehaveshownimprovedlightharvestinginchemicallydopedgraphene/SiSchottkysolarcells.DopingwithTFSAoverlayersresultsinanoverall35timesincreaseinpowerconversionefciencies(PCEs)andthehighestPCEis8.6%.Weattributethesignicantimprovementindeviceperformanceto(1)reductionofgraphene'ssheetresistanceandhenceofRsand(2)anincreaseinthebuilt-inpotential,Vbi,asdemonstratedbythreecomplementaryexperimentaltechniques:J-V,C-V,andEQEmeasurements.Whilethedecreaseingraphene'ssheetresistancereduces 99

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theohmiclosses,theenhancementinVbifacilitatesseparationofelectron-holepairsgeneratedbyabsorbedphotons.Thetechnicalmethodsofdevicefabricationaresimpleandscalableinvolvingonlyplanarthin-lmgeometries,conventionalgrapheneproductiontechniquesandeasyspin-castingoforganicsolutions. 4.6FutureWorkThoughTFSAdopinghasbeenshowntogreatlyenhancetheperformanceofthegraphene/SiPVs,thereisstillroomforfurtherimprovement.Oneofthepossibledirectionsistoreducethelightback-reectionfromtheatSisurface.Thiscanbeachievedbytwostrategies.First,amorphizationoftheSisurfacewithKOH(orNaOH)andIPAisshowntopromotethePCEincrystallineSisolarcells[ 118 ].TherandomtexturesassociatedwithchemicalreactionontheSisurfacepromoteeffectivelightabsorptionandisnowanimportanttechnicalprocessinsolarcellmanufacturing.Likewise,ratherthancreatingrandomlydistributedfeaturesontheSisurface,onecanintentionallydesignperiodicnanoarrayswithdifferentgeometricshapesandperiodicities[ 119 121 ]togenerateplasmoniceffectsandhencegreatlyimprovelighttrappingandenhancebroadspectral-rangeabsorptions.Thosemethodscanbeadoptedingraphene/SiPVsincombinationwithchemicaldopingtofurtherenhancePCE.Besides,thepresentCVDmethodneedstobeimprovedtoyieldlargegrainsizegraphene,whichisdesirablenotonlyinthesenseofabetterelectricaltransportproperties,butalsotopreventtheunderlyingSisurfacefromoxidation.Forinstance,encapsulatingCufoilinametallicboat/cellunderareducedCH4partialpressure(smallerthan50mTorr)isdemonstratedtoproducehighqualityofgraphenesheetswithsubmillimeter-sizedgrains[ 77 122 123 ].TheresultingelectricalpropertiesoftheproducedgrapheneonSiO2iscomparabletothatofexfoliatedgrapheneaccordingtoPetroneetal[ 28 ].Thosemethods,ifadoptedinourprocess,willreducetheseries 100

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resistanceinthepristinegraphene/Sicellandfurtheroptimizethedeviceperformanceafterdoping.Furthermore,electricalgatingofgraphenesheetbyionicliquidcanalsobeappliedtoimprovethedeviceperformanceincomplementarytochemicaldopingmethod.IthasbeenshowninpreviousworkofCNT/SiPVs[ 110 ],electricalgatingisabletomodulatethepositionofFemi-levelinCNTandinterfacedipoles,leadingtoandramaticincreaseinPCEfrom4%to11%.Inourstudies,theamountofsurfacedipolesisfoundtobeoneofthemainfactorsthatdegradesthepristinedeviceperformance(PCE<1.0%),andusuallystemfromover-orunder-passivationoftheSisurface.Electricalgatingisexpectedtoreduce,ifnotcompletelyremoval,thosesurfacestates.Moreover,thecarrierdynamicscanbecontrollablyinvestigatedunderelectricalgatingincombinationwithEQEandtransientabsorptionmeasurement,fromwhichcarrierlifetimeandhotcarrierrelaxationdynamicsatvariousbuilt-inpotentialscanbeinvestigated.Thosestudieswillprovideaclearpictureofcarrierdissociationprocessingraphene/SiPV. 101

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Figure4-1. Schematicsofairmassratioatapolarangle. 102

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Figure4-2. SolarenergyspectraatAM0(blackcurve)andAM1.5(redcurve). 103

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Figure4-3. Basicsofasolarcell.A)AtypicalI-Vcharacteristicsofasolarcell.B)Schematicsofanequivalentsolarcellcircuit.Thedioderepresentsthebuilt-inpotentialandRsistheseriesresistance,whichshouldbekeptassmallaspossibletominimizeohmicloss. 104

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Figure4-4. Outlookofgraphene/Sisolarcells.A)Devicegeometryofapristinegraphene/Sisolarcell.B)ThesamedevicegeometryafterTFSAspun-casting.C)OpticalimageofacompletedTFSAdopedgraphene/n-Sisolarcellswithcontactleads. 105

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Figure4-5. RoomtemperatureJ-Vcharacteristicsofgraphene/SiSchottkysolarcellinlinearscaleisshown.A)TheJ-Vcharacteristicsfrom-1Vto1VtakenbeforeandafterTFSAdoping.B)TheJ-Vcharacteristicsfrom)]TJ /F1 11.955 Tf 9.3 0 Td[(0.20Vto0.65VofthesamedevicebeforeandafterTFSAdoping. 106

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Figure4-6. DarkroomJ-Vcharacteristicsinthesemi-logarithmicscalebefore(blacktriangle)andafterTFSAdoping(orangecircle).ThedataisfromthesamedeviceasinFig. 4-5 .TheextractedSchottkybarrierheightareshowntoincreasefrom0.79eVto0.89eVafterdoping. 107

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Figure4-7. Seriesresistance(Rs)ofpristine(blacksquare)anddoped(redtriangle)graphene/SisolarcellsextrapolatedfromtheplotsofdV=d(lnI)vsIcurves. 108

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Figure4-8. TheJ-Vcurvesofasamegraphene/Sisolarcellunderilluminationtakenupto3daysafterdoping. 109

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Figure4-9. Darkroom1=C2vsappliedvoltage(V)ofagraphene/SisolarcellbeforeandafterdopingwithTFSA. 110

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Figure4-10. Externalquantumefciency(EQE)vswavelength()ofpristine(blacksquare)andTFSA-doped(redtriangle)graphene/Sisolarcells. 111

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Figure4-11. TransientphotovoltagesasafunctionofdecayingtimeforpristineandTFSA-dopedgraphene/Sisolarcells. 112

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Figure4-12. Dopingeffectonthebanddiagramisshown.A)Thebanddiagramatgraphene/Siinterfaceofapristinedevice.B)TheinterfacebanddiagramafterdopingwithTFSA. 113

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CHAPTER5STRAIN-MODULATEDWEAK-LOCALIZATIONEFFECTINCVD-GROWNGRAPHENE 5.1Introduction 5.1.1Weak-LocalizationinGrapheneInamoderatelydirtyconductor,electron'sthermalwavelength,th=h=p 2mkBT,iscomparabletoitsmeanfreepath(L)atlowtemperature.Asaresult,beforeloosingtheircoherentphasesduetoinelasticscatterings,electronscanbeback-scatteredafterseveralelasticcollisionswithaseriesofscatteringcentersasillustratedinFig. 5-1 .Thepresenceofback-scatteringhinderstheelectron'sforwarddiffusion,givingrisetoadecreasedconductivitywithdecreasingtemperature.Suchinsulator-liketemperaturedependenceofconductivity,rstproposedbyAnderson[ 124 ],iscalled`weaklocaliza-tion'(WL),wheretheconcentrationofdefectsisnotsufcienttoopenaband-gapandthusdiscriminatefrom`stronglocalization'.Weaklocalizationisalow-temperaturequantumeffectobeyingtime-reversalsymmetry.Assumeelasticscatteringisarandomeventinadirtysystem,thusanelectroncanundergomultipletrajectoriesbeforeitisback-scatteredtoitsoriginalsiteatpointA.Quantum-mechanically,theprobabilityamplitudefortheithtrajectoryisdenotedbyaie)]TJ /F8 7.97 Tf 6.58 0 Td[(ii,whereaiisthemodulusandiisthephase[ 27 ].Thus,thetotalprobabilityofback-scatteringisgivenby P(A!A)=Xiaie)]TJ /F8 7.97 Tf 6.59 0 Td[(ii2=Xijaij2+Xi6=jaiaje)]TJ /F8 7.97 Tf 6.59 0 Td[(i(i)]TJ /F19 7.97 Tf 6.58 0 Td[(j)=Xijaij2+2Xi
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assumingthataiisrealandpositive.Thersttermisaclassicalterm(denotedbyPCL),whilethesecondisapureresultofquantuminterferencethataveragestozerointheabsenceoftimereversalsymmetry.However,undertimereversalsymmetry,assumethe(2i)thtrajectoryhasatime-reversalcounterpart,(2i+1)th,asillustratedinFig. 5-1 withredandbluearrowsrespectively.Inthisscenario,a2i=a2i+1,2i=2i+1.Thus,Eq.( 5 )canbewrittenas P(A!A)=2Xija2ij2+2Xija2ij2=2PCL(A!A),(5)whileinterferenceswithothernon-time-reversalsymmetrictermsareaveragedtozero.Eq.( 5 )impliesenhancedchanceofback-scatteringundertimereversalsymmetryandhencefurtherconnestheelectronlocallyaroundsiteA.Theaveragesizeoftheback-scatteringloopsisdenotedbythephasecoherentlength,L,asshowninFig. 5-1 .Inthediffusiveregime,kFL1,Lisdenedas L=p D(5)with D=1 2vFL=1 2v2Ftr.(5)Here,Disthediffusivityandisrelatedtoconductivity()bytheEinsteinrelationdenedas[ 125 126 ] =e2(EF)D,(5)where(EF)isthedensityofstatesatEF.Ingraphene, (EF)=2jEFj (~vF)2.(5)PluggingEq.( 5 )intoEq.( 5 ),Dingraphenecanbesolvedas D=(~vF)2 2jEFj=hvF 4e2kF=hvF 4e2R2p n,(5) 115

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giventhatjEFj=~vFkF,kF=p n,nisthedensityofchargedcarriersandcanbedeterminedfromHallmeasurement,R2=1=isthesheetresistanceandvF1.0108cm/sistheFermivelocityofgraphene.Thephasebreakingrate,)]TJ /F3 7.97 Tf 6.59 0 Td[(1,duetoinelasticscatteringsisgenerallytemperaturedependentandcloselyrelatedtothedimensionalityofthesystem.In2Dgraphene,)]TJ /F3 7.97 Tf 6.59 0 Td[(1isshowntoscalelinearlywithtemperatureasamainresultofelectron-electroninteractionasdemonstratedinpreviousstudies[ 127 130 ].Physically,denotesatimescale,withinwhichelectronstillkeepsitsphasememoryafterscatteringbacktoitsoriginalsiteviaseveralelasticcollisions,whichoccuratanaveragerateof)]TJ /F3 7.97 Tf 6.59 0 Td[(1tr.Thus,toexperimentallyobserveweaklocalization(WL)effect,theconstraint)]TJ /F3 7.97 Tf 6.59 0 Td[(1)]TJ /F3 7.97 Tf 6.58 0 Td[(1tr[ 131 ]mustbesatised.Nevertheless,applyingamagneticeld(B)perpendicularlytoelectron'smotionplane,duetoAharonovBohmeffect[ 132 ],electronsgainanadditionalphasegivenby B=e ~IAdl=e ~ZZ(rA)dS=e ~ZZBdS (5) Fortwotime-reversallysymmetrictrajectoriesasillustratedinFig. 5-1 ,Bisoppositeinsign.Asaresult,theoriginalconstructiveinterferenceterminEq.( 5 )isnowrevisedas2Pija2ij2cos(2B,2i),suggestingadecreasedprobabilityofback-scattering.Duetothebrokentimereversalsymmetrybymagneticeld(B),theelectronisnowmoreeasilyforwardscattered.Consequently,theconductivityincreasewithincreasingBatloweldrangegivesrisetoapositivemagnetoconductance(MC).PositiveMCisusuallyconsideredastheexperimentalsignatureofWL.Incontrasttoconventional2Dmaterials,suchasFe,MgandAuthinlms[ 131 133 ],quantuminterferenceinpuregrapheneisaffectedbychiralsymmetry.AspreviouslydiscussedinCh. 1 ,theAandBsublatticesofgraphene'shoneycomb 116

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latticestructuremanifestthemselvesastwocomponentsofaspinorwave-functionintheDiracHamiltonian,whichistheso-called'pseudo-spin'.Pseudo-spiniseitherparalleloranti-paralleltothemomentum,whichisreectedfromthewelldenedhelicity(h)givenbyEq.( 1 ).Accordingly,h=+1()]TJ /F6 11.955 Tf 9.3 0 Td[(1)forelectronsinK(K0)valleyasillustratedinFig. 5-2 ,whileitsvalueisoppositeforholeswithrespecttothatofelectronsinthesamevalley,therebygivingrisetothewell-known`chiralsymmetry'or'chirality'.Duetothepseudo-spin-momentumlockingnatureingraphene,ippingthecarrier'smomentumaloneisnotallowedwithoutchangingitspseudo-spinorhelicity.Thus,back-scatteringisforbidden,inanalogytothesituationinatopologicalinsulatorasmentionedinSec. 1.2.2 .Consequently,insteadofWL,weakanti-localization(WAL)accompaniedbyanegativemagnetoconductance(MC)atloweldistheoreticallyexpectedingrapheneatlowtemperature.Thiscanbeotherwiseconsideredasaresultofanunusual-Berryphaseinmonolayergraphene,whichgivesrisetoacompletelydestructiveinterferencebetweentwotime-reversallysymmetrictrajectoriesandhenceprohibitslarge-anglescatterings.SuchauniqueBerryphaseisrelatedtothepolarangleofmagnitudeof(refertoSec. 1.2.2 )inthespinor-likeeigenfunctionsgiveninEq.( 1 ).Thus,theangulardistributionofscatteringprobabilityP()canbeexplicitlycalculatedas P()=1 DK,K0()K,K0(=0)E2=1 cos2 2.(5)Here,isthescatteringangle.Thefactorof1=isnormalizationcoefcient,whichassuresthattheintegrationofP()over2is1.AsshowninFig. 5-3 ,theprobabilityoflarge-scatteringingrapheneisstronglysuppressed,whilethatofsmall-scatteringisgreatlyenhanced.Thisisinsharpcontrasttoanisotropicangularscatteringprobability(P()=1=2)inaregularmetalthinlmwithausualBerryphaseof2.However,WALisonlyexpectedtobeseenindefect-free(orsuspended)graphenesamplesandissuppressedbyatrigonalwarpingscatteringrate()]TJ /F3 7.97 Tf 6.59 0 Td[(1w),whichbreakstime-reversalsymmetrywithinasinglevalleyandbecomesmoresignicantwhenthe 117

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EGFisfarawayfromtheDiracpointaspreviouslymentionedinSec. 1.2.3 .Inaddition,WALisalsoeliminatedatahighchiralitybreakingrate()]TJ /F3 7.97 Tf 6.59 0 Td[(1z)duetosurfaceripples,grainboundariesanddislocations[ 130 134 135 ].Accordingly,WLisreadilyobservedinimperfectgraphenesamplesalreadyharboringdefectsasreportedinpreviouswork[ 127 136 137 ].WLissensitivenotonlytotheinelasticphasebreakingrate()]TJ /F3 7.97 Tf 6.59 0 Td[(1),butalso(incontrasttonormalmetals)toavarietyofelasticscatteringmechanismsthatmixhelicitiesbybothintervalleyandintravalleyscatteringsillustratedbyredandbluedashedarrowsrespectivelyinFig. 5-2 .Especially,forlarge-areagraphenegrownbyCVDmethod,impurities,defectsandgrainboundariesareomnipresent,renderingWLadominatephenomenonatlowtemperatureratherthanWAL.ThepresenceofWLisattributedtothedominanceofintervalleyscatteringoccurringatarateof)]TJ /F3 7.97 Tf 6.59 0 Td[(1ithatreectsthepresenceofshort-rangeinteractionsrelatedtoatomicallysharpdefectsandchargedimpurities.ThisintervalleyscatteringhappensbetweenadjacentDiracconeswithoppositehelicities,thusallowingback-scatteringwithoutalteringthepseudo-spin.Additionally,thepresenceofintravalleyscattering(atarateof)]TJ /F3 7.97 Tf 6.59 0 Td[(1)duetolong-rangeinteractionisabletoturnonback-scatteringbysimultaneouslyippingmomentumandpseudo-spin(whilethehelicityisconserved)withinasinglevalley.Therefore,WLingrapheneissensitivelydefect-dependentandcanbeemployedasapowerfultooltoinvestigatethefundamentalphysicsandvariousscatteringmechanismsthatarepresentingraphenefabricatedbydifferentmethods/techniques. 5.1.2StrainEngineeringinGrapheneOntheotherhand,duetothesuperiormechanicalstrengthofgraphene,strainengineeringisexpectedtohaveawidevarietyofapplications,includingvalley-polarizedelectronics,spintronicsandelectronbeamcollimators[ 138 142 ].Latticedistortionaltersthehoppingenergy(0),whichismathematicallyequivalenttoanadditivegauge-eldtermintherevisedHamiltonian[ 19 ].Suchagauge-eldisthesocalled 118

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'pseudo-magneticeld'(Bs).Ithasbeenobservedtobemorethan300TinpreviousSTMstudies[ 143 ],wherezero-eldquantumHalleffectingraphenehasbeencharacterizedbyaseriesofpeaksingraphene'slocaldensityofstates.Suchastrongpseudo-magneticimpliesopeningofabandgapE0.035p BsduetoLandau-levelsplitting.ToinduceanuniformBs,itrequiresatriangularsymmetricstrainvaryingsharplyoverinteratomicdistanceasproposedbyGuineaetalisrequired[ 144 ].Inthisscenario,forastrain"10%,E0.25eVcorrespondingtoaBs40T[ 144 ].Nevertheless,forauniaxialstrain,thepseudomagneticeldhasoppositesigninKandK0valleys,sincethetime-reversalsymmetryofthewholelatticeisstillpreserved.However,thetwoDiracconesatKandK0arenowshiftedinoppositedirectionsasaresultofBrillouinzonedistortion,wheretheoriginalhexagonalsymmetryisnowaffected.Especially,theE2gsymmetryoftheopticalphononisbrokenatthe)]TJ /F1 11.955 Tf 10.27 0 Td[(point.Consequently,thetwofolddegeneracyoftheGpeakisliftedandhencesplitintoG+andG)]TJ /F1 11.955 Tf 10.41 -4.34 Td[(peaksasobservedbypolarizedRamanspectroscopyingrapheneunderuniaxialstrain[ 84 85 145 ].Besides,underanultrahighuniaxialstrain(>20%),abandgapopeningistheoreticallysuggestedduetothemergingoftwoadjacentDiraccones[ 146 ].Inthischapter,astrain-inducedsuppressionofWLinCVD-growngraphenewillbediscussedintermsofvariousscatteringmechanisms.Inzero-magneticeld,alogarithmictemperature-dependentconductivitycorrection,resultingfromstrongelectron-electroninteractions,isalsoshowntobeaffectedbystrainmodulation.Theresultsareallingoodagreementwiththeoreticalworks.ForamorecomprehensivebackgroundandperspectiveofissuesregardingWL,electron-electroninteractionandstrainengineeringingraphene,readersareencouragedtoreadRef.[ 19 27 144 147 ]. 119

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5.2ExperimentalMethods 5.2.1SamplePreparationandmeasurementsMonolayergraphenesheetsweregrownon25m-thickCufoilbyawell-developedCVDmethodasdescribedinSec. 3.2.1 .Theas-growngraphenewascharacterizedbymicro-Ramanspectroscopywitha532nmlaserasshowninFig. 5-4 .Thelargepeak2DtoGintensityratio(I2D=IG2)andthepeakpositions(G:1580cm)]TJ /F3 7.97 Tf 6.59 0 Td[(1and2D:2700cm)]TJ /F3 7.97 Tf 6.59 0 Td[(1)suggestthattheproducedgraphenesheetissingle-layer.Aftergrowth,asimilarPMMA-assistmethodasaforedescribedinSec. 3.2.1 wasadoptedtotransfergrapheneontoexibleKaptonsubstratespre-patternedwithCr(6nm)/Au(60nm)contactelectrodesarrangedinaHallbargeometry.Aftertransfer,PMMAwasremainedontopofgraphenesheetandwasnotwashedawaybyacetone.StrainwasappliedbybendingtheKaptonsubstratesusingaspecially-designedCupieceasillustratedinFig. 5-5 (b).Priortoelectricalmeasurement,goldwireswereattachedtoCr/Aucontactsbymeltingindiumdots.Measurementsweretakenconsecutivelyonthesamesampleunderdifferentstrainswithoutbreakingthegoldwirecontacts.CarewasalsotakentoavoidexcessheatingofthesamplefromthesolderinggungiventhatPMMAlmisnothigh-temperatureresilient.However,attemptstocharacterizesampleswithcurvatureoppositetothatshownintheFig. 5-5 (b)gaverisetoelectricalshortingofthecontactswiththebaseoftheCuholderandalsointroduceddifcultiesinrepairingbrokencontacts.TransportmeasurementswereperformedbyusingaLR70017HzACresistancebridgeonsamplesloadedintoaphysicalpropertymeasurementsystem(PPMS)fromQuantumDesign.Thetemperaturecanbecontrollablyvariedfrom5to300Kandmagneticeldupto7TappliedperpendiculartothebaseofCuholder. 5.2.2StrainCalculationBasedontheimageofthebentsamplesasillustratedinFig. 5-5 (b),thestrainofthegraphene/Kaptonlmcanbeapproximatedasthatgeneratedbytwoidentical 120

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bendingmomentsexerted(bythecopperrailsinpractice)ontwosidesofthemembraneassuggestedinFig. 5-5 (a).AccordingtoRef.[ 148 ],theresultingverticaldeectioninz-direction,v,satisesthegoverningdifferentialequationthatcanberewrittenas @4v @x4+@4v @x2@y2+@4v @y4=0.(5)Atrivialsolutioncanbeobtainedas v(x,y)=c1x2+c2y2,(5)wherec1andc2aretheconstantcoefcientsdeterminedbyboundaryconditions.Inourcase,duetoanegligibleelasticmodulusinthey-direction,Eq.( 5 )canbesimpliedas v(x,y)c1x2,(5)suggestingaparaboliccurvatureofthestrainedgrapheneplane.GiventhegeometricdimensionsasillustratedinFig. 5-5 (b),theboundaryconditionisgivenby vx=d 2=c1d 22=h.(5)Consequently,c1issolvedtobe c1=4h d2.(5)Here,histhepeakheightofthecurvature,anddisthespanoftheKaptonarcmeasuredattheCubaseasillustratedinFig. 5-5 (b).Additionally,accordingtoRef.[ 148 ],thex-componentofstrainisdenedas "=1 2t@2v @x2.(5)tisthethicknessofthethinlm.SubstitutingEq.( 5 )andEq.( 5 ),thegeneratedstrainingraphene/KaptonsamplewithacurvatureshowninFig. 5-5 (b)canbe 121

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estimatedtobe "=1 2t2c1=4ht d2.(5)Here,tisthetotalthicknessofPMMA/graphene/Kapton.Eq.( 5 )hasbeenadoptedtoevaluateallstrainsintheourexperiments.Italsosuggeststhatthestrainismacroscopicallyuniformalongthesurfaceofthesamples. 5.3ResultsandDiscussions 5.3.1WeakLocalizationunderStrainsFig. 5-6 showsthattheexperimentallydeterminedcorrectiontothemagnetoconductance(MC)atT=5K,(B),ispositiveaswouldbeexpectedforweaklocalization(WL).(B)isdenedas (B)=(B))]TJ /F7 11.955 Tf 11.95 0 Td[((B=0)(5)Inaddition,theWLasmeasuredby(B)issuppressedatallmagneticeldswithincreasingstrain(").Furtherinsightintotheunderlyingmechanismsresponsibleforthisstrain-inducedsuppressionofWLrequiresknowledgeofatheorydevelopedbyMcCannetal[ 149 ],whichexplicitlyprovidesanexpressionforthecorrectiontotheMCofgrapheneinthediffusiveregimeas (B)=e2 22~"F )]TJ /F3 7.97 Tf 6.58 0 Td[(1B )]TJ /F3 7.97 Tf 6.58 0 Td[(1!)]TJ /F4 11.955 Tf 11.96 0 Td[(F )]TJ /F3 7.97 Tf 6.59 0 Td[(1B )]TJ /F3 7.97 Tf 6.59 0 Td[(1+2)]TJ /F3 7.97 Tf 6.58 0 Td[(1i!)]TJ /F4 11.955 Tf 11.96 0 Td[(F )]TJ /F3 7.97 Tf 6.59 0 Td[(1B )]TJ /F3 7.97 Tf 6.59 0 Td[(1+)]TJ /F3 7.97 Tf 6.59 0 Td[(1i+)]TJ /F3 7.97 Tf 6.59 0 Td[(1!#,(5)where F(z)=lnz+1 2+1 z(5)and )]TJ /F3 7.97 Tf 6.59 0 Td[(1B=4eDB? ~.(5)(x)isthedigammafunction.Hereweaveragethemagneticeld(B)overtheparabolicallycurvedgrapheneplaneas B?=d `B.(5) 122

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Here,`isthetotallengthofthecurvedportionofthestrainedsample.Sincethespin-orbitcouplingingrapheneisnegligible[ 150 151 ],hereonlytheperpendicularcomponentofappliedmagneticledcontributestothephasebreakingevents.AspreviouslynotedinEq.( 5 ),)]TJ /F3 7.97 Tf 6.58 0 Td[(1isthephasebreakingrateduetoinelasticscattering,whereastheintervalleyscatteringrate)]TJ /F3 7.97 Tf 6.58 0 Td[(1iandintravalleyscatteringrate)]TJ /F3 7.97 Tf 6.58 0 Td[(1areelasticscatteringrates.)]TJ /F3 7.97 Tf 6.59 0 Td[(1ingrapheneisusuallygivenby )]TJ /F3 7.97 Tf 6.58 0 Td[(1=)]TJ /F3 7.97 Tf 6.59 0 Td[(1w+)]TJ /F3 7.97 Tf 6.59 0 Td[(1z(5)with )]TJ /F3 7.97 Tf 6.59 0 Td[(1w=tr30a2 2~n2(5)fromtrigonalwarpingeffect[ 130 149 ]and)]TJ /F3 7.97 Tf 6.59 0 Td[(1zdenotingchiralitybreakingrate.Theremainingparametersarethemomentumrelaxationtimetr,thehoppingenergytonearestcarbonsite0,thelatticeconstantaaspreviouslymentionedinCh. 1.2.1 andcarrierdensityndeterminedfromHallmeasurement.Thestraindependenceofthesethreeunknownscatteringrates()]TJ /F3 7.97 Tf 6.58 0 Td[(1,)]TJ /F3 7.97 Tf 6.59 0 Td[(1iand)]TJ /F3 7.97 Tf 6.59 0 Td[(1)canbeextractedoutbyimplementationofaleast-squaresregressionalgorithmusingthedata(symbols)inFig. 5-6 withEq.( 5 )followingasimilarproceduredescribedinRef.[ 137 ].ThequalityofthetsisshownbythesolidlinesinFig. 5-6 andthedependenceofthebest-tscatteringrates,)]TJ /F3 7.97 Tf 6.59 0 Td[(1and)]TJ /F3 7.97 Tf 6.58 0 Td[(1i,onthestrainisplottedinFig. 5-7 (b).Fromthetswendthat)]TJ /F3 7.97 Tf 6.58 0 Td[(1exceedsbythreeordersofmagnitudethevaluesofvaluesof)]TJ /F3 7.97 Tf 6.58 0 Td[(1and)]TJ /F3 7.97 Tf 6.59 0 Td[(1i,therebyrenderingthelastterminEq.( 5 )negligibleandthedeterminationof)]TJ /F3 7.97 Tf 6.59 0 Td[(1imprecise.Forthesereasons,weonlyplot)]TJ /F3 7.97 Tf 6.58 0 Td[(1and)]TJ /F3 7.97 Tf 6.59 0 Td[(1iinFig. 5-7 (b).Thevaluesof)]TJ /F3 7.97 Tf 6.59 0 Td[(1and)]TJ /F3 7.97 Tf 6.59 0 Td[(1iatzerostrainareingoodagreementwiththosereportedinpreviousworks[ 128 130 137 152 ].Withstrainincreasingfrom0to0.6%,)]TJ /F3 7.97 Tf 6.58 0 Td[(1idecreasesbyafactorof44.6,whichissignicantwhencomparedwithafactorof5.2reductionin)]TJ /F3 7.97 Tf 6.58 0 Td[(1.Physically,theseresultsshowninFig. 5-7 (b)suggesta 123

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dramaticallyweakenedintervalleyscatteringandarethemaincauseoftheobservedsuppressionofWLinthepresenceofexternallyappliedstrains.Inaddition,thediffusivity(D),denedinEq.( 5 ),canbeevaluatedusingthemeasuredvaluesofthesheetresistanceR2,carrierdensitynandtheknownFermivelocityvF1.0106m/sforgraphene.ThedependenceofDonstrain"showninFig. 5-7 (a)revealsadramaticdecreasefrom43to6cm2/swhenstrainincreasesby0.6%.ThisdecreaseisprimarilyduetothesignicantincreaseinR2(from2.1to18k=2)withincreasing".Thesestrain-inducedtrendsareconsistentwiththephysicalnotionsthatlatticedistortiondecreasesthenearest-neighborhoppingenergy(0)andsimultaneouslyintroducesmoreripplesanddefectsingraphenesheetwhichactasscatteringcenters.Analternativeperspectivetounderstandingthestrain-inducedsuppressionofweaklocalizationingrapheneisgainedbyevaluatingthephasecoherencelength(L)andintervalleyscatteringlength(Li)asgivenbyL,i=p D,iusingthedatashowninpanels(a)and(b)ofFig. 5-7 .AsseeninFig. 5-7 (c),LremainsrelativelyconstantwithdifferentstrainsduetothecoincidentcompensationbetweenadecreaseinDandanincreasein.IncontrasttoL,Liincreasesbyafactorof2.5.ThisincreasecanbeascribedtoarelativeincreaseinithatmorethancompensatesforthedecreasedD.Accordingly,asstrainincreases,adramaticallyincreasedLiaccompaniedbyanalmostinvariantLconrmsthatWLissuppressedandcarrierswilldiffusealongerdistancebeforeundergoingascatteringeventinwhichphasememoryislost.WLingrapheneistheoreticallypredictedtobesuppressedunderstrain[ 27 130 135 ],sincebyalteringthehoppingenergy,latticedistortionisequivalenttoalocaleffectivegaugeeldthatbreakstimereversalsymmetrywithineachDiraccone.However,underuniaxialstrain,thetimereversalsymmetrybetweenKandK0valleyisstillconserved,therebyresultinginoppositelyorientedpseudo-magneticeldsinthesetwovalleys.Theonlymodicationbyuniaxialstrainsismanifestedintherelative 124

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motionofKandK0valleys.Morespecically,theyeithermovetowardsoragainsteachotherasresolvedpreviouslyinpolarizedRamanSpectroscopy[ 145 ].Inourcase,wedidnotwashthePMMAoffthegrapheneaftertransferringthePMMA/grapheneontoKapton.Accordingly,thegrapheneismoretightlyattachedtothePMMAthanitistotheKaptonsubstrate.Asaresult,strainappliedtoourPMMA/graphenesamplesbybendingtheKaptonsubstratesintotheconvexshapeshownintheFig. 5-5 (b)introducescompressivestrainsandhencemoreripplesonthePMMA/graphenesheet,thusweakeningitscouplingwiththeunderlyingKapton.RipplesareanimportantsourceoflatticedeformationleadingtothedestructionofWLbasedonresultsfrompreviousmagneto-transportmeasurements[ 134 ],buthereitisnotthedominatingcauseoftheobservedsuppressionofWLsinceasaforementioned,theglobaltimereversalsymmetriesarenotbrokenbytheapplieduniaxialstrains.Amoreimportantmechanismisexpectedtobethestrain-modulatedelectron-electroninteractionsandCoulombinteractionswithchargedimpuritiesfromthesurfaceofthesubstrates,whichisgoingtobediscussedinmoredetailinSec. 5.3.2 .Forgraphenelooselyattachedtoitssubstrate,accordingtoMcCannetal[ 149 ],itisreasonabletoexpectthattheintervalleyscatteringrateislessthanthephasebreakingrate(i.e.)]TJ /F3 7.97 Tf 6.59 0 Td[(1i<)]TJ /F3 7.97 Tf 6.59 0 Td[(1).Inourcase,theratioof)]TJ /F3 7.97 Tf 6.59 0 Td[(1i=)]TJ /F3 7.97 Tf 6.59 0 Td[(1reducesfrom0.814to0.095asstrainincreasesfrom0upto0.6%.Moreover,thedramaticallydecreasedintervalleyscatteringisthekeyfactortothesuppressionofWL.Ingraphene,restrictedbythechiralnatureofthecarriers,back-scatteringisprohibitedwithinasinglevalley.However,back-scatteringcanberestoredbyintervalleyscatteringthroughmixingtwovalleyswithoppositehelicities(h=1inKvalleyandh=)]TJ /F6 11.955 Tf 9.3 0 Td[(1inK0valley),thusgivingrisetotheexperimentallyobservedWL.Accordingly,WLbecomeslessprominentwithadecreasingintervalleyscatteringrate()]TJ /F3 7.97 Tf 6.59 0 Td[(1i)andanincreasingintervalleyscatteringlength(Li)inmorestrainedsamples. 125

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Thedecreaseof)]TJ /F3 7.97 Tf 6.59 0 Td[(1withincreasedstrain,whichlookscounter-intuitiveatrstglance,maybeexplainedintermsofweakenedCoulombinteractionsasaresultofstrain-induceddecouplingbetweenthegraphenesheetandtheKaptonsubstrate.ThegrapheneisstronglyattachedtothePMMAbeforetransferontotheKapton.Whenunderexternallyappliedstrain,thegrapheneisslightlyseparatedfromtheKaptontapebyintroductionofmoreripplesonthesurface.Ourexperimentalobservationsalsoshownoticeablyreducedconductanceuctuations(CF)underhighmagneticeld(B>0.5T)withincreasingstrainasshownintheinsetofFig. 5-6 .Themagnitudeofthesereproducibleuctuationsisapproximately0.01e2=~,whichistwoordersofmagnitudeslessthanthevaluesofuniversalconductanceuctuationsobservedpreviouslyinmicron-sizedgraphenesamples[ 134 136 153 ].GiventherelativelylargesizeofourgraphenesampleswhereLL,mesoscopicuctuationsareaveragedoverlarge-areainhomogeneities[ 137 ]andsuchobservedCFmayattributetoimpuritiesassociatedwiththescatteringcentersonthesubstrates[ 154 155 ].Therefore,adecreasedcouplingbetweengrapheneanditsKaptonsubstrateleadstoareducedinteractionwiththoseimpurities,therebylessCFunderhigherstrains.Likewise,suchadecouplingmayalsoreducetheshortrangeinteractions(V0)withpointdefectscatteringcentersonKaptonsubstrates,whichresultsinthedramaticdecreaseof)]TJ /F3 7.97 Tf 6.59 0 Td[(1i,since)]TJ /F3 7.97 Tf 6.59 0 Td[(1i/V20[ 147 156 ]. 5.3.2Electron-ElectronInteractionunderStrainsThemainpanelofFig. 5-8 showsalogarithmictemperaturedependenceofnormalizedconductivityfrom5to150Katzerostrain.Thisdependenceextendstohighertemperature(250K)atthehigheststrainof0.6%.TheconductivityisnormalizedwithrespecttothevaluemeasuredatT0=5K[ 131 ],i.e. N(T)=e2 22~(T))]TJ /F7 11.955 Tf 11.96 0 Td[((T0) (T0)ARlnT T0(5) 126

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whereARisthenormalizedprefactorofthelnTdependence.However,attemperaturesontheorderof150Kandabove,opticalphononsarefrozenout[ 19 ]andtheacousticelectron-phononinteractiondominates.Thetemperatureboundaryfortheonsetofelectron-phononscatteringforgrapheneismarkedbytheBloch-GruneisentemperaturedeterminedbyTBG=54p nK[ 128 157 ].Here,nisthecarrierdensitymeasuredinunitsof1012cm)]TJ /F3 7.97 Tf 6.59 0 Td[(2.Foroursamples,nspansfrom1.451013to1.701013cm)]TJ /F3 7.97 Tf 6.59 0 Td[(2at300KbasedontheHalleffectmeasurementsperformedundereachofthosestrains(indicatingnisessentiallyconstantundervariousstrains).SuchnvaluescorrespondtoaTBGrangingfrom206to223K,whichisingoodagreementwithourexperimentalobservationsasreectedinFig. 5-8 thatthelogarithmiccorrectionstotheconductivityareunaffectedbyphononsatT
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Thecoefcient,A(F0)isdeterminedbythestrengthoftheinteractionandF0istheFermi-liquidconstant.Giventhatinourcase)]TJ /F3 7.97 Tf 6.59 0 Td[(1,)]TJ /F3 7.97 Tf 6.58 0 Td[(1i)]TJ /F3 7.97 Tf 6.58 0 Td[(1,)]TJ /F3 7.97 Tf 6.59 0 Td[(1tr(theseratesareallindependentoftemperatureexcept)]TJ /F3 7.97 Tf 6.59 0 Td[(1),thesecondterminEq.( 5 )isnegligiblewhenconsideringtemperaturedependence,andthersttermisalwaysmuchsmallercomparedtothevalueofEq.( 5 )atallstrains,implyingalowtemperaturecorrectiontoconductivityatzeromagneticeldmainlyfromEEI.However,forthesamplewithR2<1k,ahigher)]TJ /F3 7.97 Tf 6.58 0 Td[(1iisobserved,suggestingthatWLmaybecomecomparabletoEEI,henceexplainingahigherARforthisparticularsample.Therefore,whenconductivityisnormalizedwithrespecttoitsvalueat5K,thetemperaturedependenceisspecicallyderivedas N(T)EEI=ARlnT T0,(5)where ARA(F0)=1+c1)]TJ /F6 11.955 Tf 13.15 8.09 Td[(ln(1+F0) F0.(5)TheparametercdenotesthenumberoftripletchannelsinvolvedinEEI.Inourcase,~=i0.Therefore,thehuge)]TJ /F3 7.97 Tf 6.59 0 Td[(1ismainlyduetoalargechiralitybreakingrate()]TJ /F3 7.97 Tf 6.59 0 Td[(1z)understrain.Hence,F0becomesmorenegativeandgivesrisetoadropinAR. 128

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Ontheotherhand,strainalsodecouplesgraphenefromitssubstratebyintroducingmoreripples.AccordingtothenatureofCoulombinteractionsingrapheneonasubstrate,despiteaslightlydecreaseddielectricconstant(lessscreening),theinelasticscatteringbychargedimpuritiescanbesuppressedasaresultofanincreasedaveragedistance(zc)betweenexternalchargedimpuritiesandthegraphenesheet,whichbehavesasanexponentialfactor(e)]TJ /F8 7.97 Tf 6.59 0 Td[(qzc)intheCoulombpotential,(q)[ 125 126 160 ].Soevenasmallseparationisabletogiveanoticeabledecreasein)]TJ /F3 7.97 Tf 6.58 0 Td[(1.However,since)]TJ /F3 7.97 Tf 6.59 0 Td[(1doesnotshownadramaticstrain-induceddecrease,theCoulombpotentialshouldnotchangeconsiderablylargebystrain.Otherwise,itwouldhaveoverwhelmedtheincreaseinthemagnitudeofF0bychiralitybreakingandleadtoanincreaseinAR. 5.4ConclusionInsummary,wendthatWLinCVD-growngrapheneissuppressedbyapplyinguniaxialstrains,whichcanbeexplainedintermsofreducedintervalleyscatteringasaresultofthestrain-induceddecouplingbetweenPMMA/grapheneandunderlyingKaptonsubstrates.Also,thelogarithmictemperaturedependenceofconductanceatzeromagneticeldbelowBloch-Gruneisentemperatureinhighlyresistivesamples(R2>2k)mainlyoriginatesfromelectron-electroninteraction.Thesmallvalueoftheprefactor,AR,athighstrainisattributedtohugechiralitybreakingratewherelargeanglescatteringisallowedandleadstoarelativelyhighamplitudeofangle-averagedCoulombpotential(orFermi-liquidconstant,F0).Alltheresultsnotonlyprovideacoherentunderstandingofstrain-modulatedtransportpropertiesingraphene,butalsogiveapenetratinginsightintothedifferentscatteringprocessingraphenewhensubjectedtoexternalstrains. 5.5FutureDirections 5.5.1GrapheneonDifferentSubstratesAsrevealedinthiswork,thecouplingbetweengrapheneandtheunderlyingsubstratesareveryimportant.Forexample,thetransportpropertiesongraphene/SiO2 129

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aresubjectedtointeractionwithpolaropticalphononofSiO2,therebysettinganupperboundtothecarriermobilityof4104cm2/Vs[ 161 ].Besides,thedanglingbonds(fromuncompensatedoxygenbonds)andchargetrapsonthesurfaceofSiO2giverisetouctuationsofgraphene'schemicalpotential(alsoknowasrandompotentials)[ 22 ].Incontrast,hexagonalboronnitride(h-BN)isfreeofdanglingbondsandpossessesasimilarlatticestructurewiththatofgraphene,thusgraphene/h-BNareshowntohavesuperiorelectricaltransportpropertieswithcarriermobilitiesashighas1.4105cm2/VsneartheDiracpoint[ 73 ].Inaddition,previousSTMstudiesrevealthatthechargeuctuationsareinhighqualitygraphene/h-BNmuchsmallerthanthatingraphene/SiO2butaresimilarwiththoseobservedinsuspendedgraphene,therebysuggestingasignicantsuppressionofback-scatteringbothingraphene/h-BN,aswellasinsuspendedgraphene[ 74 162 163 ].However,asystematicmagneto-transportstudyconcentratingontheWLeffect(whetherthereisany)hasnotbeendoneyet.Especially,magneto-conductanceevolutionwithexternallyappliedstrainsinsuspendedgraphenehasnotbeeninvestigatedeither.Futureresearchdirectionsmightllinthoseblankareasandprovidesmoreinsightintointeractionsbetweengrapheneandvarioussubstratesandstraineffectonsuspendedgraphene. 5.5.2OpticalStudiesofMX2underUniaxialStrainsSinglelayertransitionmetaldichalcogenides(MX2),suchasMoS2,MoSe2,WS2andWSe2etc,haverecentlyemergedasacomplementarypeertographene.Unlikegraphene,MX2hasadesirableenergybandgap(1.6.9eV)withinthevisiblespectralrange,whichisessentialforsophisticatedtransistorsandopticalcomponents.Asrevealedbypreviousstudies[ 164 ],monolayerMX2hasexcellentmechanicalpropertiesandhenceisapromisingcandidateforexibleelectronics.Inaddition,theelectronicstructureandtheout-of-planephononmodearefoundtobesensitivelydependentofthethickness,whichaffectstheinteratomiccouplingstrength.Especially,thedirectexcitonictransitionenergystronglydependsonthedorbitalcouplinginM(M=Mo,W) 130

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atoms[ 165 166 ],sincetheconductionbandminimum(CBM)atKisdecreasingwithincreasingstrainaccordingtotheresultsfromtheoreticalcalculations[ 166 167 ],whichalsoshowthattheelectron'seffectivemassisaffectedbyeithertensileorcompressivestrains.Also,transitionfromdirecttoindirectbandgapisalsosuggestedtooccurinMoSe2understrainupto3%[ 168 ].Inaddition,boththein-planeandout-of-planephononmodesinmonolayerMX2aresensitivetolatticestretching,whichmaymanifestthemselvesasshiftsinE2gandA1gpeaksinRaman[ 168 ].However,thosestrain-inducedeffectshavenotbeenexperimentallyobservedyet.Todothat,mono-layerMX2needstobetransferredontoaexiblesubstrate,suchasPDMSandPETplasticlms,followingsimilartransfermethodsthathavebeenpreviouslyusedtotransfergraphenefromSiO2toPDMS[ 85 ]orBN[ 73 ].ThesamplecanbemountedintheCupieceweusedforWLstudiesinthischaptersuchthattheamountofstraincanbeevaluatedinthesamewayasintroducedinSec. 5.2.2 .PolarizedRamanspectroscopyandPLwouldbeemployedtomonitorthestrain-modulatedchangesinphononmodesandelectronicbandstructures. 131

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Figure5-1. Schematicsofelectronscatteringatlowtemperature.Inamoderatelydirtysystem,electronscanbeback-scatteredafterseveralcollisionswithvariousscatteringcenters(grayballs)asillustratedbythebluearrowsandtheirtimereversalcounterparts.Thesizeoftheback-scatteringloopischaracterizedbytheelectroncoherencelength(L). 132

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Figure5-2. Schematicsofelectron's(blackballs)momentumandpseudo-spininKandK0valleys.Momentumisparallel(anti-parallel)topseudo-spininK(K0)valley,denotingby+1()]TJ /F6 11.955 Tf 9.3 0 Td[(1)helicity,h.Withinasinglevalley,hhasoppositesignforholes.Intervalleyscatteringandintravalleyscatteringareillustratedbyredandbluedashedarrows,respectively.Theyarebothelasticscatterings. 133

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Figure5-3. Angulardistributionofscatteringprobabilitiesingraphene(redcurve)andaregularmetalthinlm(bluecurve).Theanglerepresentsthescatteringangle.Incontrasttoanisotropicdistributioninaregularmetal,theprobabilityoflarge-scatteringisstronglysuppressedasconnedbychiralsymmetry. 134

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Figure5-4. RamancharacterizationoftheCVDgrowngrapheneoncopperwithGand2Dpeakslabeled. 135

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Figure5-5. Specimengeometryunderstrain.A)Schematicsofathinlmbentbyanidenticalbendingmoment(m)ontwosides,whiletheothertwosidesarefreeboundaries.B)Opticalimageofabentgraphene/KaptonmountedontheCuholderwithcoordinatesystemandrelevantdimensionofthecurvatureaslabeled. 136

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Figure5-6. LoweldmagnetoconductanceatT=5Kundervariousstrainslabeledforeachcurve.ThesymbolsarethedatafromexperimentalmeasurementsandthesolidlinesaretstoEq.( 5 ).Inset:magnetoconductancemeasuredoveralargereldrange(uptoB=1.5T)atthesametemperature,wheretheconductanceuctuationsthatareclearlyobservedinthenon-strainedsample(topcurve)becomesuppressedunderstrains. 137

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Figure5-7. Variousttingparametersvsexternallyappliedstrainareshown.A)Diffusivity,B))]TJ /F3 7.97 Tf 6.58 0 Td[(1and)]TJ /F3 7.97 Tf 6.59 0 Td[(1i,C)LandLiplottedasafunctionofexternallyappliedstrain(").Inallpanelsthestandarddeviations(errorbars)determinedbythettingprocedurearecomparabletosizesofthesymbols. 138

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Figure5-8. Zero-eldnormalizedconductivityN(T)underdifferentstrains(")showsalogarithmicdependenceontemperature(T).Inset:ARvs"fortwodifferentsamples.ARistheprefactoroflnTdependenceshowninEq.( 5 ). 139

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CHAPTER6FERROMAGNETISMINHIGHLYORIENTEDPYROLYTICGRAPHITE 6.1OverviewAlthoughhighqualitygraphitehasbeenstudiedformorethanfourdecades,manyofitsfundamentalphysicalproperties,suchasout-of-planeelectronictransportandintrinsicferromagnetism,haveyettobefullyunderstood.Inparticular,observationofferromagnetism(FM)withasurprisinglyhighCurietemperature(TC>500C)inhighlyorientedpyrolyticgraphite(HOPG)crystalsthatareknowntobefreeofmagnetictransitionmetalimpurities[ 169 170 ]areparticularlypuzzling,sincecarbonisalightatomwithnegligiblespin-orbitcouplingincontrasttothatinconventionalferromagnetsbasedonFe,CoandPt.Thus,suchanunusualFMinHOPGandothercarbonbasedmaterialshasgeneratedvigorousresearchactivitiestoclarifypossiblephysicalmechanismsofitsorigin.Basedonpreviousstudies[ 172 175 ],thecurrentconsensusontheoriginofFMingraphene/graphiteisthatthemagnetismismainlyattributedtolatticedefects,suchasvacancieswithdanglingbonds,zigzagedgeswithinducedspinpolarizationsviaelectron-electroninteractions,dislocationsandinterstitialbridgingatomsbetweengraphenelayers.Thisconsensusissupportedbyscanningtunnelingmicroscopyexperimentsonsingleatomvacanciesongraphitesurfaces[ 176 ]andtheincreaseinmagnetismassociatedwithirradiationofgraphitebyprotons[ 177 ],carbonatoms[ 178 ]andheliumions[ 179 ].Thelineartemperaturedependenceofthemagnetizationinproton-irradiatedgraphitesuggeststhatthemagnetizationhasatwo-dimensional(2D)graphene-likefeature[ 177 ]possiblyrelatedto2DperiodicnetworksofpointdefectsasproposedlaterbyCervenkaetal[ 170 ].Thisinterpretionisalsoconsistentwiththe ThischapterisareprintofExtinctionofFerromagnetisminHighlyOrderedPyrolyticGraphitebyAnnealingbyX.MiaoetalpublishedinCarbon50,1614(2012)[ 171 ]. 140

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anisotropicFMinlow-doseheliumirradiatedgraphite,wherethedefects,inducedbyachemicallyinertimplant,mainlylocatedonthegrainboundariesalignedalongc-axis.Inspiteofthepresentunderstandingofthecontributionfromzigzagedgesanddefects[ 172 173 ],questionsabouttheoriginsofFMstillassumeabroadperspective.Accordingly,furtherexplorationsonthissubjectarecontinuouslyinprogress,especiallysincestimulatedbyrecentlydiscoveredtechniquestoobtainsinglelayersheetsofgraphene[ 2 68 ]andgraphenederivatives[ 180 181 ].Forexample,magnetizationstudiesofsonicallyexfoliatedgraphenenanosheetsshownoevidenceofferromagnetism[ 182 ]whereaspartiallyhydrogenatedepitaxialgrapheneshowsroom-temperatureFMthatisbelievedtobeassociatedwithunpairedelectronsoccupyingtheremnantdelocalizedbondingnetwork[ 183 ].Moreover,recentspintransportmeasurementsandtherealizationofazero-magnetic-eldspinHalleffectinhydrogenatedgrapheneakespreparedbymechanicalexfoliationsuggestsanenhancedspin-orbitcouplingwithamagnitudeof2.5meVinmicron-sizedgraphenesheetbyadsorptionofHydrogenatomsonthesurface[ 184 185 ].Tofullyunderstandthephysicalmechanismsformagnetisminbothgrapheneandgraphite,theroleofdimensionalityneedsmoretheoreticalandexperimentalinvestigations.Suchdimensionalityconsiderationsapplytonitegraphenenanostructures,graphenenanoribbonswitharmchairorzigzagedgecongurations,graphenewithmagnetisminducedbythepresenceofdefectsorchemicalmodicationsandinert-atomirradiatedgraphitewheretheinteractionsbetweenbombardedatomsandsurfacecarbonatomsarecritical.Allthesesubjectsareimportantandneedfurtherclaricationssoastofullyexploitgraphene/graphite'sversatileroleinspintronicsapplicationseitherasaspininjectororspinconserver.Inthischapter,ratherthanfocusingoneffortstoenhanceferromagnetisminHOPG,wewillshowthattheobservedFMofHOPGsamplescanbediminishedbythermalannealingunderhighvacuumconditionsinacontrolledandreproducible 141

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manner.Atsufcientlyhightemperatures(T2300C),FMiseventuallyextinguished.Themagneticsamplesareannealedforvaryingtimestotemperaturesashighas2300Candresultscorrelatedwithmeasurementsofmagnetization,crystallinequalitybyX-raydiffraction(XRD),Ramanspectraandelectricaltransportproperties.Theanneal-inducedreductionofthesaturationmagnetization(Ms)fromitsoriginalvaluetozeroisaccompaniedbyanimprovementinelectricalpropertiesandcrystallinity,therebyimplyingthattheFMinHOPGiscloselyrelatedtocrystallinedisorderandhencedefect-freeHOPGisinherentlynon-ferromagnetic.Thischaptermainlyfocusesonthemagneticpropertiesofgraphene/graphiteandservesasacomplementtothediscussionsinpreviouschapters.Also,thetransportpropertiesofgraphitebasedonatwo-bandmodelarediscussedinthebeginningsectionofthischapter,sincethetransportpropertieshaveplayedanindispensableroleinunderstandingnotonlytheannealing-inducedeffectsinthiswork,butalsoinvariousofotherstudiestorevealtheunderlyingphysicsingraphite[ 3 186 ]. 6.2IntroductiontoTransportPropertiesofGraphite:Two-BandModelInaconductororsemiconductorwithonlyasinglepartiallylledband,chargedcarrierscanbeeitherholesorelectrons.AccordingtoRef.[ 6 ],theinducedcurrentdensityjbyanexternallyappliedin-planeelectriceld(withamagnitudeofEx)inthepresenceofout-of-planemagneticeldB=(0,0,B)isgivenby j=E=)]TJ /F3 7.97 Tf 7.59 0 Td[(1E(6)Here,E=(Ex,Ey,0)andEyisthetransverseelectriceldoriginatingfromHalleffect.The2-ranktensorisdenedas =)]TJ /F3 7.97 Tf 7.59 0 Td[(1=0B@)]TJ /F4 11.955 Tf 9.3 0 Td[(RBRB1CA(6) 142

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with =1 ne(6)and R=1 ne.(6)RistheHallcoefcientandpositive(negative)forholes(electrons).ThecarrierdensityncanbedeterminedfromRinHallmeasurements.However,ingraphite,asshowninFig. 1-5 ,electronsandholescoexist,thusrequiringatwo-bandmodeltodescribethetransportproperty.Thenetcurrentdensity,j,isnowgivenby j=je+jh=()]TJ /F3 7.97 Tf 7.6 0 Td[(1e+)]TJ /F3 7.97 Tf 7.6 0 Td[(1h)E)]TJ /F3 7.97 Tf 7.59 0 Td[(1E.(6)Here =()]TJ /F3 7.97 Tf 7.59 0 Td[(1e+)]TJ /F3 7.97 Tf 7.59 0 Td[(1h))]TJ /F3 7.97 Tf 6.58 0 Td[(1(6)with i=0B@i)]TJ /F4 11.955 Tf 9.3 0 Td[(RiBRiBi1CA.(6)i=fe,hgdenotingtherelatedphysicalquantitiesforelectronsandholes,respectively.Nowlet'strytosolveinmatrixformandobtaintheanalyticalexpressionsforthelongitudinalmagnetoresistivityandHallcoefcient.First,basedonEq.( 6 ),theinverseofiiscalculatedtobe )]TJ /F3 7.97 Tf 7.59 0 Td[(1i=1 2i+R2iB20B@iRiB)]TJ /F4 11.955 Tf 9.3 0 Td[(RiBi1CA.(6)Subsequently,thenetconductivitytensorcanbeobtainedas =)]TJ /F3 7.97 Tf 7.59 0 Td[(1e+)]TJ /F3 7.97 Tf 7.59 0 Td[(1e=0BB@e 2e+R2eB2+h 2h+R2hB2ReB 2e+R2eB2+RhB 2h+R2hB2)]TJ /F8 7.97 Tf 20.1 4.7 Td[(ReB 2e+R2eB2)]TJ /F8 7.97 Tf 22.76 5.11 Td[(RhB 2h+R2hB2e 2e+R2eB2+h 2h+R2hB21CCA (6) 143

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Thus,thenetresistivitytensorisjusttheinverseofandfoundtobe =)]TJ /F3 7.97 Tf 7.59 0 Td[(10B@)]TJ /F4 11.955 Tf 9.3 0 Td[(RBRB1CA(6)with xx(B)=eh(e+h)+(eR2h+hR2e)B2 (e+h)2+(Re+Rh)2B2(6)and R=Re2h+Rh2e+ReRh(Re+Rh)B2 (e+h)2+(Re+Rh)2B2(6)Here,andRarethelongitudinalmagnetoresistivity(alsodenotedasxx)andHallcoefcient,respectively,inatwo-typecarriersystemlikegraphite.Substitutingthefollowingrelations 8><>:e=1 eneeh=1 enhhand8><>:Re=)]TJ /F3 7.97 Tf 14.62 4.7 Td[(1 neeRh=1 nhe(6)intoEq.( 6 ),theHallresistivity,xy(B),canbeobtainedas xy(B)RB=()]TJ /F4 11.955 Tf 9.3 0 Td[(ne2e+nh2h)B+2e2h(nh)]TJ /F4 11.955 Tf 11.96 0 Td[(ne)B3 e(nhh+nee)2+e2e2h(nh)]TJ /F4 11.955 Tf 11.96 0 Td[(ne)2B2.(6)Additionally,fromEq.( 6 ),thelongitudinalresistivityatzeromagneticeld(B=0)isfoundtobe xx(0)=eh e+h=1 e(nee+nhh).(6)Therefore,dividingbye2xx(0)onbothsidesofEq.( 6 )leadstotheresult xy(B) e2xx(0)=)]TJ /F2 11.955 Tf 5.48 -9.68 Td[()]TJ /F4 11.955 Tf 9.29 0 Td[(ne2e+nh2hB+2e2h(nh)]TJ /F4 11.955 Tf 11.96 0 Td[(ne)B3 1+e22xx(0)2e2h(nh)]TJ /F4 11.955 Tf 11.95 0 Td[(ne)2B2.(6)Eq.( 6 )andEq.( 6 )obtainedfromthetwo-bandmodelaresuitabletodescribethemagneto-transportpropertiesinasystemwhereelectronsandholescoexist(suchasgraphiteandBismuth)orinasystemwhereonlyone-typecarrierexistsbuttheyarefromtwopartiallylledenergybandswithdifferenteffectivemasses. 144

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Nevertheless,thismodelcanbeextendedtosystemswheretheFermi-levelinterceptswithmultiplebands(nbandsintotal)byrevisingEq.( 6 )as = i=nXi=1)]TJ /F3 7.97 Tf 7.59 0 Td[(1i!)]TJ /F3 7.97 Tf 6.58 0 Td[(1=0B@)]TJ /F4 11.955 Tf 9.3 0 Td[(RBRB1CA(6)orrather, =i=nXi=1i.(6)ihasthesameformasthatinEq.( 6 ),withelementsiandRidenedinthesamewayasthatintheaforementionedtwo-bandmodel.Also,consideringtheDrudemodel,icanalsobegivenby i=)]TJ /F3 7.97 Tf 6.59 0 Td[(1i=mi e2nii.(6)wheremi,iandnidenotetheeffectivemass,momentumrelaxationtimeanddensityofthecarriersintheithpartiallylledenergyband,respectively.PluggingexpressionsforiandRiintoEq.( 6 ),theoveralllongitudinalmagnetoresistivityandHallcoefcientRcanbesolvedforamultiple-bandsystem. 6.3ExperimentalProcedureGraphitesampleswerecutfromhighlyorientedpyrolyticgraphite(HOPG)pieceswithvariousmosaicspreadanglesrangingfrom0.4to3.4andin-planeresistivity,ab,spanninga445cmrangeatroomtemperature.GoldwireswereattachedtotheHOPGsamplesusingcommerciallyavailablesilverpastefromSPIsuppliesandarrangedinaHallbargeometry.Samplesweremountedinaphysicalpropertymeasurementsystem(PPMS)fromQuantumDesignwherethetemperaturecanbecontrollablyvariedfrom5Kto300Kwithamagneticeldupto7T.ElectricaltransportmeasurementsweretakenbyaLR700,lowfrequencyresistancebridge,inacombinationwiththePPMS.ThemagneticpropertieswerecharacterizedinaQuantumDesignsuperconductingquantuminterferencedevice(SQUID)inasametemperaturerange.Magneticeldwasappliedperpendiculartothec-axisupto5Ttomeasurethe 145

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inducedmagneticmoment(M?).Inthisgeometry,thediamagneticbackgroundsignalisminimized,sincethemagnitudeofsusceptibilitydia?ismorethananorderofmagnitudelowerthanthesusceptibilitydiakwherethemagneticeldisappliedparalleltoc-axis.TheHOPGsampleswereannealedinahighvacuumchamberatapressureof510)]TJ /F3 7.97 Tf 6.58 0 Td[(7TorrbyJouleheating,i.e.,bypassingadirectcurrentof200260AthroughaattungstenboatinthermalcontactwiththeHOPGsamplescorrespondingtoatemperatureintherangeof21002300C.TheannealingtemperaturewasmeasuredusingaC-typethermocouple.Sampleswereannealedforabout5minuteseachtime.PristineandannealedsamplewerecharacterizedusingX-raydiffraction(XRD)andRamanspectroscopy.XRDpatternswerecollectedbyaPhilipsdiffractometerusingCu-Kradiationina-2conguration.RamanspectraweretakeninaHoribaJobin-YvonLabRAMAramisRamanspectrometerfrom1200to3000cm)]TJ /F3 7.97 Tf 6.59 0 Td[(1withagreenlaserbeam(532nm). 6.4ResultsandDiscussions 6.4.1MagneticPropertiesFig. 6-1 (a)and(b)showM?vsHdata(blacksquares)at5Kbeforeandaftersubtractingthediamagneticbackground(Mdia?)onasameHOPGsample,respectively.Priortothethermalannealing,HOPGsamplesgivetypicalsusceptibilitiesdia?intherangefrom)]TJ /F6 11.955 Tf 9.29 0 Td[(8.510)]TJ /F3 7.97 Tf 6.59 0 Td[(7to)]TJ /F6 11.955 Tf 9.29 0 Td[(5.010)]TJ /F3 7.97 Tf 6.59 0 Td[(7emu/(gOe),inaccordwithvaluesreportedintheliterature[ 170 187 ].However,basedonthedatatakenfrom11HOPGsampleswithdifferentmosaicspreadrange(morespecically,2sampleswith0.4spread,1samplewith0.5spread,2sampleswith0.7spread,1samplewith0.9spreadand5sampleswith3.4spread),themeasuredsaturatedmagneticmoment(Ms)valuesarefoundtodiffernoticeablyforsampleswithdifferentmosaicspreadwithoutanyobviouscorrelationbetweenmosaicspreadandMs.ThisspreadinvaluesmaybeattributedtodifferenttotalgrainboundaryareasanddensitiesofdefectswithintheHOPGsamplethatare 146

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uncorrelatedwithcrystallinequality,i.e.,mosaicspreadasdeterminedbyX-rayrockingcurves.Afterthemagnetizationmeasurements,thesamesamplewasannealedupto2100Cfor5minutesandthenslowlycooleddowntoroomtemperaturebeforereloadingitintotheSQUIDforsubsequentmagnetizationcharacterizations.WeobservedthatannealedHOPGsamplesbecomelessferromagnetic.ThesaturatedmagnetizationMsdecreasesby60%70%.Furthermore,annealingthesamesampleforanother5minutesupto2300Cextinguishesallsignsofferromagnetismandthediamagneticresponse(straightlinewithnegativeslope)dominatesasshowninFig. 6-1 (a)and(b).ThethreetracesofFig. 6-1 (a)showthatthebackgrounddiamagneticsusceptibilitydia?ofthepristineferromagneticsampleincreasesbyafactorof4from)]TJ /F6 11.955 Tf 9.3 0 Td[(4.9810)]TJ /F3 7.97 Tf 6.58 0 Td[(7to)]TJ /F6 11.955 Tf 9.3 0 Td[(2.0410)]TJ /F3 7.97 Tf 6.59 0 Td[(6emu/(gOe)foritsfullyannealednon-ferromagneticdescendant.Similartrendshavebeenobservedforintercalatedgraphitecompoundswhichhaveasmallerdiamagneticsusceptibilitythanpristinegraphite[ 4 186 ]. 6.4.2X-rayDiffractionandRamanSpectroscopyTofurtherunderstandtheeffectofannealingonthemagneticpropertiesofHOPG,XRDmeasurementsandRamancharacterizationswereperformedonpristineandannealedsamples.Fig. 6-2 showsRamanspectraofthesamplesbeforeandafterannealingwithanexpandedviewoftwoprominentfeatures,Gand2Dpeaks,illustratedintheinsets.SimilartotheRamanpeaksingrapheneasintroducedinSec. 3.3.1.2 ,theobservedGpeakisduetothesp2-bondstretchingingraphite,whilethe2Dpeak,consistingof2D1and2D2incontrasttoasingleLorentzian-shapedpeakingraphenecase,isareectionofsecondorderscatteringfromlatticeimperfectionswithparticularsensitivitytothestackingdisorderalongc-axis.Additionally,ourHOPGsamplesdonotshowanynoticeableDpeaks(1350cm)]TJ /F3 7.97 Tf 6.59 0 Td[(1),whicharisesfromrst-orderRamanscatteringbydefects.TheratioofintensityoftheDpeaktothatoftheGpeak(i.e., 147

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ID=IG)isinverselyproportionaltothein-planecrystallinesize[ 78 82 ].However,incontrasttotheevolutionoftheDpeakwithincreasingdisorderasreportedinthepreviousstudiesonpolycrystallinegraphite[ 188 ]andonheliumionbombardedHOPGsampleswithvaryingdoses[ 179 ],theabsenceofDpeaksinourcaseindicatesthattheHOPGsamplesareofhighcrystallinequalityandcontainnegligibleamountsofdisorderwithinthedetectionofRamanspectroscopy.Hence,Ramanspectratakenonpristineandannealedsamplesdonotshownoticeabledifferencesanddonotallowustoprobethedensityofdefects,eg.vacancies,brokenbonds,dislocationsandconcentrationofamorphouscarbon),therebynoconclusioncanbedrawnfromRamancharacterization.Inaddition,asshowninFig. 6-3 ,XRDpatternsoftheHOPGsamplesdisplaysharp(002)and(004)peaksinthedetectionrangeasexpected.IntheinsetofFig. 6-3 ,thedetailedprolesof(004)peaksbeforeandafterannealingshowthatthefullwidthathalfmaximum(FWHM)decreasesafterannealingasindicatedbythearrows.AccordingtoScherrer'sformulainEq.( 6 ) RGS=K d004cos,(6)theaveragedgrainsize(RGS)increasedby30%bythermaltreatment,ingoodagreementwithanneal-inducedcrystallitesizeincreaseobservedinpreviousstudies[ 82 189 ].Here,K0.9istheshapefactor,1.54AisthewavelengthoftheCu-Kradiationandd004istheFWHMofthe(004)peakinradians.Ourobservedanneal-inducedimprovementincrystallinequalityconcomitantwiththeextinctionoftheFMisconsistentwiththetheoreticalconsensusthatindefectedgraphitealargenumberofzigzagedgeswithcarbene-liketripletgroundstates[ 172 ]alongthegrainboundariesplayanimportantroleinunderstandingtheunconventionalmagneticproperties[ 173 ].Asdemonstratedinpreviouswork[ 19 ],zigzagedgesbreakthesymmetryofthegraphenesublatticeandgiverisetolocalizedelectronstatesneartheFermi-level.Therepulsiveelectron-electroninteractionsinducespin 148

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polarizationalongthoseedgesandhenceareresponsiblefortheunusualFMingraphene/graphite[ 190 193 ].However,asshownfromdensityfunctionaltheoryandrstprinciplecalculations,thezigzagedgemaybemetastable[ 82 193 195 ],andplanararmchair-like(acombinationofonepentagonandoneheptagon)edgereconstructioncanbetriggeredatroomtemperature[ 194 ].ThistransformationinedgecongurationsfromzigzagtoarmchairprocesswillgreatlydepresstheFM[ 193 ].Meanwhile,chemisorptionofoxygenispossiblearoundtheedges(especiallyzigzagedges)[ 172 ]andheattreatmentabout200Cwillremovethoseoxygenatomsasfoundingrapheneoxides(GO)[ 196 ].However,inHOPGtheoxygenratiosareundetectableincontrasttothatinGOs,wheretheoxygencontainingchemicalgroupsareubiquitous.Furthermore,annealingHOPGabove2100Cisclosetothegraphitizationtemperature(2400C),thusnotonlyhighenoughtoremoveabsorbedoxygenatoms,ifthereareany,butalsoabletoexpandthecrystallinesizebyrestoringthecarbonbondingatthegrainboundaries[ 82 ]asconrmedbyXRDmeasurement.Additionalconsequencesoftheannealingprocessincluderemovalofthemono/multi-vacancies[ 197 ]and/ortriggeringedgereconstruction,therebyincreasingthedensityofreconstructededgesatgrainboundaries. 6.4.3ElectricalTransportPropertiesItisreasonabletoexpectthatmostifnotalloftheabovementionedfactorswillimprovetheelectricalpropertiesoftheHOPG.ThisexpectationisborneoutbyourelectricalmeasurementsperformedonpristineandannealedHOPGsampleswhichshowthatthein-planeroomtemperatureresistivity,300Kab,decreasesfrom22.8to4.3cm,approximatelybyafactorof5.1,asshowninFig. 6-4 .Ifforsimplicityweassumethatthecarrierdensity(n)isxed,thentheDrudemodelpredictsthatthedecreasein300Kabimpliesanoverall5timesincreaseinthemobility().AconstantnapproximationishowevernotvalidasdemonstratedbyHalleffectdatadiscussedinthenextparagraph,sincemostofthecarriersderivefromunintentionalimpuritiesin 149

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HOPGaswellasfromlocalizedstatesattheFermi-levelcausedbydefectsites/grainboundarieshavehigherchargedensitythanbulk[ 198 ].However,athightemperaturetheseedge-localizedchargeshaveanincreasedchancetobecomedelocalizedbecauseofrestoredcarbonbondingacrosstheboundaries.ThisincreasedcontributiontothenumberoffreecarriersafterannealingisalsoconsistentwiththeenhanceddiamagneticbackgroundsignalinannealedHOPGdescribedpreviouslyandshowninFig. 6-1 (a).Thetemperaturedependenceofthein-planeresistivity,ab,andout-of-planeresistivity,c,oftwoseparatesamplescutfromthesamepieceareshowninFig. 6-4 andFig. 6-5 ,respectively.Thesedatadisplaythewellknownlargeresistanceanisotropyofgraphiteandalsoconrmthat,overtheentire5300Ktemperaturerange,theresistivityofannealedHOPGissignicantlylessthanthatofpristineHOPG.Thein-planeconductivityofgraphiteisdominatedbyelectronsandholeswithcomparablecarrierdensity,neandnh,butdifferentmobilities,eandh,respectively.ByttingtheHalldata(seetheinsetofFig. 6-4 )intoEq.( 6 )derivedfromtwo-bandmodel,wecanextractoute=8350cm2/Vs(11,900cm2/Vs),h=3120cm2/Vs(6200cm2/Vs),ne=4.641018cm)]TJ /F3 7.97 Tf 6.59 0 Td[(3(4.171019cm)]TJ /F3 7.97 Tf 6.59 0 Td[(3)andnh=7.531019cm)]TJ /F3 7.97 Tf 6.59 0 Td[(3(1.261020cm)]TJ /F3 7.97 Tf 6.58 0 Td[(3)forthepristine(annealed)sample.Althoughbothneandnhincreaseafterannealing,wendthatthecompensation,(nh)]TJ /F4 11.955 Tf 13.08 0 Td[(ne)=(nh+ne),decreasesfrom0.884beforeannealingto0.503afterannealing.Thus,annealingnotonlydelocalizestrappedchargeatthechargeatdefectedsitesbutalsobringstheHOPGclosertoperfectchargecompensation,wherethenumberofelectronsequalsthatofholes.Inaddition,thedecreasein300Kabandcorrespondingincreaseineandhindicatethatannealingdecreasestheoverallresistivitybyrestoringcarbonbondsatgrainboundarieswhilesimultaneouslyremovingscatteringcenters,whichisequivalenttoannealingoutvacanciesanddefects. 150

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However,thedecreaseofcasshowninFig. 6-5 cannotbeexplainedsincethedominanttransportprocessalongtheout-of-planedirectionisstillunderdebatewithaninterpretionthatremainselusive.Nevertheless,wenotethatthetemperature,wherecgivesamaximumpeak(Tmax),shiftsfrom40to42Kafterannealingbutdoesnotdisappear.ExistenceofthepeakatTmaxevenafterannealingupto2100Cimpliesthatthenon-monotonictemperaturedependence(andhenceTmax)maybeafundamentalfeatureofgraphite,orcanprobablybeassociatedwithvarioustransportmechanismssuchasstacking-fault-assistedinterlayerchargetransferprocessor/andtunnelingconductionthroughthestackingdisordersasproposed/discussedinpreviousstudies[ 4 199 ]. 6.5ConclusionInthischapter,wehavedemonstratedthattheferromagnetism(FM)ofHOPGcrystalscanbeextinguishedbyannealingunderhighvacuumconditionsathightemperature.Coincidentwiththeannealingandthedisappearanceofhystereticmagnetizationloops,thereisacrystallinesizeincrease,anincreaseindiamagnetism,adecreaseinresistivityinboththein-planeandout-of-planedirectionsandanimprovedcarriercompensation.Thoseresultssuggestthatunlessferromagnetictransitionalmetalimpuritiesarepresent,theFMoriginatessolelyfromgrainboundaries,edgedefectsand/orvacancies.AperfectchemicallypureHOPGcrystalwithoutdefectswillnotexhibitferromagneticbehavior.WeattributetheannealinginducedtransitionfromFMtodiamagnetismtoarecongurationofbrokencarbonbonds(defects)atthegrainboundaries(asconrmedbyanincreaseinoverallmobilitybyelectronictransportmeasurements)aswellastopossiblezigzagedgereconstructiontoachievemorestablebutnon-ferromagneticarmchairor/andarmchair-likecongurations.OurstudynotonlyprovidesmoreinsightintothenatureofFMinHOPGbutalsoallowsonetotunethemagnetizationpropertiesofintentionallydefectedferromagneticHOPGtoachievebetter 151

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spintransportpropertiesintermsoflongerspincoherencelengthoroverallhighermobility. 6.6FutureDirectionsInteractionbetweengrapheneandtransition-metaladatomsisexpectedtogiverisetoaseriesofinterestingphysicsphenomena,includingatunablequantumanomalousHalleffectbyexternalelectricelds[ 200 ]anddifferentmagneticpropertiesinducedbyadsorptionsofvarioustransition-metalatomsonmono-/doublevacancies[ 201 ].RecentSTMandX-raymagneticcirculardichroismstudieshavedemonstratedaninducedparamagnetismbyeitherFeandCoadatoms,whiletheNimonomersbarelyalteredthelocalmagneticpropertiesofgraphene[ 202 ].Besides,spinlifetimeundergoesasurprisinglyenhancementwithincreasingAudopingupongraphenesheetaccordingtopreviousspintransportstudies[ 203 ],therebyrequiringamorecomprehensiveunderstandingofspinrelaxationmechanismsandcouplingbetweengrapheneandAu(aswellasothertransition-metal)atoms.Takingadvantageofourhome-builthighvacuumsamplehandlingsystem,in-situtransportmeasurementscanbeperformedongraphenesheetswhiledepositingtransition-metalatoms(suchasCo,FeandPdetc)atvaryingmagneticeldsandtemperatures.Toensureapuresystemandminimizetheeffectfromdefectsanddisorder,grapheneisbettertobepreparedbymechanicalexfoliationandtransferredontoBNsubstrate.ThetransportmeasurementsshouldfocusonKondoeffect,WLeffect,anomalousHalleffect(ifthereisany)andelectron-electroninteractionstoexploretheroleofmagneticcouplingbetweengrapheneandtransition-metaladsorbates.Inaddition,asobservedinarecentstudy[ 204 ],decorationofgraphenenanosheets(orgraphenequantumdots)withTbPc2magneticmoleculesexhibitshystereticbehaviorinlow-eldmagnetoconductanceatlowtemperature,inanalogytotraditionalspin-valvedevices.However,theinteractionbetweenthosemagneticmoleculesandgraphenesheets(especiallyforlargeareaCVD-growngraphene),especiallyincluding 152

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theeffectsofspin-orbitcouplingandinteratomicchargetransfer,remainunclear.Futureworkaimstoansweringthosequestionsbyinvestigatinglowtemperaturemagneto-transportandtemperature-dependenttransportpropertiesonvariousgraphene/magnetmoleculehybridsystems.Themoleculescanbedecoratedwithvariousligandswithversatilefunctionalities.Thephasecoherencebreakingratecanbeobtainedfromweak-localizationeffecttoinvestigatetheroleofelectron-electroninteractions,electron-magneticmoleculesinteractionsandinelasticcoulombinteractionsbetweenelectronandchargedligands.Moreover,spintransportmeasurementsarealsonecessarytorevealdetailsofspinrelaxationdynamicsandthestrengthofmagneticcouplingbetweengrapheneandmagneticmolecules. 153

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Figure6-1. LowtemperaturemagneticpropertycharacterizationsisdoneinSQUID.A)TheM?vsHmeasuredat5KinpristineHOPG(blacksquares),afterannealingto2100C(redcircles),andupto2300C(bluetriangles)for5minutesinhighvacuum.B)M?vsHloopsaftersubtractingthediamagneticbackgroundsignal. 154

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Figure6-2. RamanspectraofasameHOPGsamplebefore(blackcurve)andafterannealing(redcurve)at2300C.Inset:detailedRamanspectraaroundGand2Dpeakregions. 155

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Figure6-3. XRDpatternsofpristine(blackcurve)andannealed(redcurve)HOPGsampleswithprominent(002)and(004)peaks.Inset:expandedviewofthe(004)reectionpeaksinpristineandannealedHOPGwiththesamecolordenitionasthatinthemainpanels. 156

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Figure6-4. Temperaturedependenceofin-planeresistivity,ab,from5Kto300Ktakeninasamesamplebefore(bluecircles)andafterannealing(redtriangles)atzeromagneticeld.Inset:Hallresistance(Rxy)vsmagneticeld(B)inthesamesamplebeforeandafterannealing. 157

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Figure6-5. Out-of-planeresistivityvstemperaturetakenfrompristine(bluecircles)andannealed(redtriangles)HOPGsamplesatzeromagneticeld. 158

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BIOGRAPHICALSKETCH XiaochangMiaowasborninWenzhou,P.R.Chinaintheyearof1986.Astheonly-childofherparents,CunxingMiaoandXiaofengYu,shespentherjoyfulchildhoodyearswiththem.Encouragedtoexpandthehorizonbyherparents,shelefthomeatanearlyageandstartedhercolorfulhighschoollifeinthebiggestcityofChina,Shanghai,in2001.Duringthose3years,shemadeamazingfriendsandenjoyedadiversehighschoollife,andnallygraduatedin2004withtheOutstandingHigh-SchoolGraduateAward,aprestigioushonorgrantedbytheDepartmentofEducationofShanghai.Afterthat,shewasenrolledintheDepartmentofPhysicsatUniversityofScienceTechnologyofChina(USTC)tobeginstudyinphysicsatanadvancedlevel.In2006,shejoinedtheAdvancedThin-lmLaboratoryandworkedwithDr.GuanzhongWang,whereshegottoknowtheso-called'wondermaterial'-grapheneandworkwithitforthersttime.Herworkon`FabricationandSEMcharacterizationofgraphene'wasselectedasoutstandingundergraduateresearchprojectin2007,ayearbeforegraduationfromUSTCwithaB.S.degree.In2009,ShejoinedDr.Hebard'slabinDepartmentofPhysicsatUniversityofFlorida.Herresearchmainlyfocusedonthetransportandmagneticphysicalpropertiesofgraphene/graphiteandrelateddeviceapplications,especiallyinSchottkygeometry.ShewasawardedaDoctorofPhilosophydegreein2013. 170