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Graphite-Graphene Semiconductor Junctions and Magneto-Dielectric Coupling in Schottky Diodes

Permanent Link: http://ufdc.ufl.edu/UFE0041457/00001

Material Information

Title: Graphite-Graphene Semiconductor Junctions and Magneto-Dielectric Coupling in Schottky Diodes
Physical Description: 1 online resource (189 p.)
Language: english
Creator: Tongay, Sefaattin
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: carbon, condensed, device, electronic, gallium, gan, graphene, graphite, hemts, hightemperature, intercalation, magnetization, magnetodielectric, mesfet, mosfet, optical, quantum, schottky, semiconductors, silicon
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: The goal of this dissertation is to incorporate graphite and graphene into today's semiconductor technology as a Schottky barrier diodes (metal / semiconductor junctions) that are widely used in metal semiconductor field effect transistors (MESFETs), high electron mobility transistors (HEMTs), high temperature and frequency devices, solar cells and sensors/detectors. The first part of the dissertation aims to give the reader a general idea about the physics at the metal-semiconductor junctions and essential theory background. The second chapter of the dissertation questions effects of temperature and magnetic field on the diode characteristics of Schottky junctions. In this chapter, we present observation of negative magnetocapacitance on GaAs:Si/Au junctions and fully equipped with the theory, we present a phenomenological explanation for the observed effect. In the third chapter, we for the first time introduce multi-layer-graphene as a metal (semimetal) electrode to form Schottky barriers on various technologically significant semiconductors such as Si, GaAs, SiC and GaN. Multi-layer-graphene/ semiconductor junctions not only display good current-voltage (I-V) and capacitance-voltage (C-V) characteristics but also are significant since the Schottky barrier height and characteristics are mainly governed by the interaction and bond formation at few layers on the metal and semiconductor interface. This automatically implies that the presented results also hold for graphene/semiconductor junctions. Chapter 4, takes the Schottky formation at the multi-layer-graphene(graphene)/ semiconductor junction to another level and aims to change the Fermi level of the metal electrode by intercalation with Bromine and tune the barrier height. Observed results are significant in MESFET technology since different barrier height are desired depending on the application. The remainder of the dissertation, focuses on the properties of graphite and graphene to have more understanding about the content presented in the previous chapters. Chapter 5, gives a brief theory background about graphite and graphene while chapter 6 and chapter 7 discuss electrical properties of graphite at high temperatures where it starts to decouple from each graphene layer and acts as bi-layer graphene and with bromine intercation where there is $c$-axis lattice constant expansion and each graphene plane becomes more isolated. Chapter 8, gives a detailed description about epitaxial graphene growth in SiC by joule annealing technique, and we end the chapter with future directions.
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 Sefaattin Tongay.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Hebard, Arthur F.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041457:00001

Permanent Link: http://ufdc.ufl.edu/UFE0041457/00001

Material Information

Title: Graphite-Graphene Semiconductor Junctions and Magneto-Dielectric Coupling in Schottky Diodes
Physical Description: 1 online resource (189 p.)
Language: english
Creator: Tongay, Sefaattin
Publisher: University of Florida
Place of Publication: Gainesville, Fla.
Publication Date: 2010

Subjects

Subjects / Keywords: carbon, condensed, device, electronic, gallium, gan, graphene, graphite, hemts, hightemperature, intercalation, magnetization, magnetodielectric, mesfet, mosfet, optical, quantum, schottky, semiconductors, silicon
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: The goal of this dissertation is to incorporate graphite and graphene into today's semiconductor technology as a Schottky barrier diodes (metal / semiconductor junctions) that are widely used in metal semiconductor field effect transistors (MESFETs), high electron mobility transistors (HEMTs), high temperature and frequency devices, solar cells and sensors/detectors. The first part of the dissertation aims to give the reader a general idea about the physics at the metal-semiconductor junctions and essential theory background. The second chapter of the dissertation questions effects of temperature and magnetic field on the diode characteristics of Schottky junctions. In this chapter, we present observation of negative magnetocapacitance on GaAs:Si/Au junctions and fully equipped with the theory, we present a phenomenological explanation for the observed effect. In the third chapter, we for the first time introduce multi-layer-graphene as a metal (semimetal) electrode to form Schottky barriers on various technologically significant semiconductors such as Si, GaAs, SiC and GaN. Multi-layer-graphene/ semiconductor junctions not only display good current-voltage (I-V) and capacitance-voltage (C-V) characteristics but also are significant since the Schottky barrier height and characteristics are mainly governed by the interaction and bond formation at few layers on the metal and semiconductor interface. This automatically implies that the presented results also hold for graphene/semiconductor junctions. Chapter 4, takes the Schottky formation at the multi-layer-graphene(graphene)/ semiconductor junction to another level and aims to change the Fermi level of the metal electrode by intercalation with Bromine and tune the barrier height. Observed results are significant in MESFET technology since different barrier height are desired depending on the application. The remainder of the dissertation, focuses on the properties of graphite and graphene to have more understanding about the content presented in the previous chapters. Chapter 5, gives a brief theory background about graphite and graphene while chapter 6 and chapter 7 discuss electrical properties of graphite at high temperatures where it starts to decouple from each graphene layer and acts as bi-layer graphene and with bromine intercation where there is $c$-axis lattice constant expansion and each graphene plane becomes more isolated. Chapter 8, gives a detailed description about epitaxial graphene growth in SiC by joule annealing technique, and we end the chapter with future directions.
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 Sefaattin Tongay.
Thesis: Thesis (Ph.D.)--University of Florida, 2010.
Local: Adviser: Hebard, Arthur F.

Record Information

Source Institution: UFRGP
Rights Management: Applicable rights reserved.
Classification: lcc - LD1780 2010
System ID: UFE0041457:00001


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GRAPHITE-GRAPHENESEMICONDUCTORJUNCTIONSANDMAGNETO-DIELECTRICCOUPLINGINSCHOTTKYDIODESBySEFAATTINTONGAYADISSERTATIONPRESENTEDTOTHEGRADUATESCHOOLOFTHEUNIVERSITYOFFLORIDAINPARTIALFULFILLMENTOFTHEREQUIREMENTSFORTHEDEGREEOFDOCTOROFPHILOSOPHYUNIVERSITYOFFLORIDA2010

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c2010SefaattinTongay 2

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TomyfamilyandNoone 3

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ACKNOWLEDGMENTS Firstofall,itisapleasuretothankthosewhomadethisdissertationpossible.Ihaveusedmanylaboratories,collaboratedwithalotofgroupsandmorethanhundredspeoplepassedtheirexperiencetomebygivingtheirvaluabletime.IamalmostsurethatIwillunintentionallyforgetcouplenames,Iliketobeupfrontaboutitandapologizealready.Foremost,IliketoexpressmygratitudetomyadvisorProf.Dr.A.F.Hebard(Art)foreverythinghehasdoneformeinandoutofthedepartment.Hehasnotonlybeenanamazingadvisorbutalsoafathergure,afriend,acollaborator.IfeelincrediblyluckytotouchhislifeandbepartofitduringmystayhereinUniversityofFlorida.ItisnotpracticaltolistallthethingsthatIamthankfulabouthereinthisparagraph.Andalsoitwouldberatherlimitedandunfairtoconcise.Instead,Iliketothankhimforacceptingmeashisdoctoratestudentsinceitiswhenallthisstartedhappeningattherstplace.IalsoliketothankmysupervisorcommitteemembersDr.D.Maslov,Dr.S.Pearton,Dr.A.BiswasandDr.A.Rinzlerfortheirtime,mentoringandalltheirinputinthiswork.Itisalsopleasuretothanktoallofmycollaborators,Dr.D.Maslov(Physics),Dr.B.Gila(Mat.Sci.Eng.),Dr.D.Tanner(Physics),Dr.E.Lambers(Mat.Sci.Eng.),Dr.V.Cracuin(Mat.Sci.Eng.),Dr.J.Jones(Mat.Sci.Eng.),Dr.C.Abernathy(Mat.Sci.Eng.),Dr.XuDu(U.Rutgers),Dr.B.Appleton(Mat.Sci.Eng.andNIMET),Dr.Y.Hikita(Univ.ofTokyo),Dr.H.Hwang(Univ.ofTokyo),Dr.C.Martin(Chemistry),Dr.A.Rinzler(Physics),Dr.A.Biswas(Physics),Dr.H.P.Chang(Quan.Theo.Proj.),Dr.D.Norton(Mat.Sci.Eng.),Dr.C.Stanton(Physics),Dr.I.Kravchenko(OakRidgeNationallab.),Dr.E.Durgun(MIT),Dr.T.Yildirim(NIST),Dr.V.Basov(UCSD),Dr.N.Newman(Univ.Arizona),S.Trickley(Physics).Iamindebtedtomymanyofmycolleaguesanddoctoratefriendstosupportmeandworkwithmeonvariousprojects;HridisPal,R.Das,P.Mickel,S.Ghoshsi,G.B.Singh,L.Kemper,T.Dhakal,H.H.Jeen,S.Selcuk,R.Misra,M.Lemaitrebutespecially 4

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tomystudentsT.Schumann,X.Miao,K.BerkeandA.Doniusforbeingamazingstudents,collaboratorandfriends.Ialsoliketothanktoallformer,presentandfuturemembersoftheHebard'slaboratorybutespeciallytoDr.S.Selcuk.Iliketothanktoallphysicsfaculty,graduatestudents,undergraduatestudents,allmyfriendsfrompasttofuture,myofceneighborC.Stambaugh,SzoltMarcetfortalkingthroughourofcewallandthinningitdownlast4yearstoheareachotherclearly.Inexperimentalsciencemostofthemagichappensbehindthecloseddoorsandfarbeyondthefancy'working'machinesbutinthetechnicaldetails.Iliketothanktoentiremachineshopstaff(especiallytoBill,MarkandJohn),cryogenicsstaffJohnandGreg,entireelectronicsshopstaff,JayHortonforhistechnicalinputinmyexperiments,TimNolandforhistechnicalhelp,allHPCcomputingcenterstaff,ITspecialistDavid,allcleanroomstaff(B.Lewis,A.Ogden)Lastly,IwouldliketothanktoNooneforeverything.Iliketothanktomyfamily;beloveddaughter,Elise,mymom,dad,andallmysiblings.Iamthanksfultoeveryonewhohastouchedmylifeanyhow,anytimeandanywhere. 5

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TABLEOFCONTENTS page ACKNOWLEDGMENTS .................................. 4 LISTOFTABLES ...................................... 9 LISTOFFIGURES ..................................... 10 ABSTRACT ......................................... 13 CHAPTER 1SEMICONDUCTORTHEORYANDSCHOTTKYBARRIERPHYSICS ..... 15 1.1ChargeCarriersinIntrinsicandExtrinsicSemiconductors ......... 15 1.2IntrinsicandExtrinsicSemiconductors .................... 17 1.3TheSchottkyBarrier(Metal-Semiconductor)Contacts ........... 18 1.3.1OriginoftheSchottkyBarrierFormationattheM-SInterface ... 19 1.3.2DepletionCapacitanceattheM-SInterfaceandC-VRelationship 21 1.3.3TransportAcrosstheM-SInterface:ThermionicEmission ..... 23 1.3.4Non-IdealEffectsattheM-SInterfaces ................ 25 1.3.4.1Imageforceloweringorschottkyeffect .......... 25 1.3.4.2Thermioniceldemission .................. 26 1.3.4.3Directtunneling ....................... 27 1.3.5MeasurementofSchottkyBarrierHeight ............... 27 1.3.5.1Current-voltagecharacteristics ............... 27 1.3.5.2Capacitance-voltagecharacteristics ............ 30 1.3.5.3Internalphotoemissiontechnique ............. 31 1.4OhmicContactstoSemiconductors ..................... 32 2MAGNETODIELECTRICCOUPLINGINNON-MAGNETICAU/GAAS:SISCHOTTKYDIODES ................................ 34 2.1Introduction ................................... 34 2.2ExperimentalMethods ............................. 35 2.2.1SamplePreperation .......................... 35 2.2.2Current-VoltageMeasurements .................... 36 2.2.3Capacitance-VoltageMeasurements ................. 37 2.2.4InternalPhotoemissionTechnique .................. 37 2.3ExperimentalResults ............................. 38 2.3.1ObservationofMagnetocapacitanceandMagneticFieldDependenceofC)]TJ /F3 11.955 Tf 11.95 0 Td[(VCurves ............................ 38 2.3.2PhysicalProcessesintheDepletionWidth .............. 39 2.3.3EffectofMagneticFieldontheCurrent-VoltageCharacteristics .. 42 2.4ModicationoftheAbruptJunctionApproximation(AJA) .......... 43 2.5Discussion ................................... 45 6

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2.6Summary .................................... 47 3MULTI-LAYER-GRAPHENE(MLG)BASEDSCHOTTKYDIODESFORMEDONSI,GAAS,4H-SICANDGANSUBSTRATES ................. 56 3.1Introduction ................................... 56 3.2ExperimentalDetails .............................. 59 3.3FormationofSchottkyDiodesattheMulti-Layer-Graphene/SiInterface 60 3.4FormationofSchottkyDiodesattheMulti-Layer-Graphene/GaAsInterface 63 3.5FormationofSchottkyDiodesattheMulti-Layer-Graphene/4H-SiC .... 65 3.5.1SchottkyBarrierCharacteristicsofMulti-Layer-Graphene/4H-SiCSchottkyDiodesfrom250Kupto330K ............... 66 3.5.2SchottkyBarrierCharacteristicsofMulti-Layer-Graphene/4H-SiCSchottkyDiodesfrom300Kupto1100K ............... 67 3.6FormationofSchottkyDiodesattheMulti-Layer-Graphene/GaNInterfaces 71 3.7Discussion ................................... 73 3.7.1ComparisonofI)]TJ /F5 7.97 Tf 6.59 0 Td[(VtoC)]TJ /F5 7.97 Tf 6.58 0 Td[(VandDeterminationofgraphite .... 73 3.7.2BondPolarizationTheoryandMulti-Layer-GraphenetoGrapheneLimit ................................... 75 3.8Conclusion ................................... 77 4TUNINGSCHOTTKYBARRIERHEIGHTATTHEMULTI-LAYER-GRAPHENE/SEMICONDUCTORINTERFACEBYDOPING ................. 92 4.1Introduction ................................... 92 4.2ExperimentalProcedure ............................ 93 4.3ResultsandDiscussion ............................ 95 4.3.1EffectofBromineDopingontheMLG/SemiconductorSchottkyBarrierDiodeI)]TJ /F3 11.955 Tf 11.96 0 Td[(VCharacteristics .................. 95 4.3.2EffectofBromineDopingattheMLG/SemiconductorInterface:PossibleMechanisms ......................... 96 4.3.3CharacterizationofBrIntercalatedGraphite:XRD,AESandXPSMeasurements ............................. 97 4.3.4ModicationoftheBandStructureattheInterfaceandC)]TJ /F3 11.955 Tf 13.49 0 Td[(VMeasurements ............................. 101 4.3.5ResultsonMLG/SiCJunctionsandSensingApplications ..... 103 4.4Overview .................................... 105 5BANDSTRUCTUREOFGRAPHITE ........................ 115 5.1Introduction ................................... 115 5.1.1CrystalStructureofGraphiteandGraphene ............. 116 5.1.2BandStructure:EnergySpectrumofElectrons/HolesinGraphite 119 6TRANSPORTPROPERTIESOFHIGHLYORIENTEDPYROLYTICGRAPHITE(HOPG)FROM3KUPTO1500K .......................... 126 7

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6.1Introduction ................................... 126 6.2In-PlaneTransport(ab)from1.7Kupto900K ............... 127 6.2.1ExperimentalDetails .......................... 127 6.2.2In-PlaneTransportfrom1.7Kupto300K:DrudeFormula ..... 128 6.2.3In-PlaneTransportfrom300Kupto900K .............. 130 6.3OutofPlaneTransport(c)Propertiesfrom3Kupto1500K ........ 135 6.3.1BreakdownintheClassicalModel .................. 135 6.3.2ProposedMechanismsandDiscussion ................ 136 7SUPERMETALLICCONDUCTIVITYINBROMINEINTERCALATEDGRAPHITE 150 7.1Introduction ................................... 150 7.2Experimental .................................. 152 7.2.1SamplePreparationandCharacterization .............. 152 7.2.2ElectricalMeasurements ........................ 154 7.2.3OpticalMeasurements ......................... 158 7.2.4MagnetizationMeasurements ..................... 160 7.2.5Discussion ................................ 160 8GRAPHENEANDGRAPHITEGROWTHONSICBYTHERMALANNEALING 172 8.1Introduction ................................... 172 8.2ExperimentalDetails .............................. 173 8.3MaterialCharacterization ........................... 173 REFERENCES ....................................... 180 BIOGRAPHICALSKETCH ................................ 188 8

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LISTOFTABLES Table page 3-1ExtractedSBHs,dopingdensities,andcorrespondinggraphiteworkfunctionvaluesonvariousmulti-layer-graphene/semiconductorjunctions ........ 77 5-1ValuesanddescriptionoftheparametersusedinSWMcmodel ......... 121 9

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LISTOFFIGURES Figure page 1-1Energydiagramofmetal/semiconductorjunctiondiode .............. 33 2-1I-Vcharacteristicsfromroomtemperaturedownto20Kand0to70kOe. ... 49 2-2Magnetocapacitanceeffectfrom300Kdownto20K. .............. 50 2-3Extractionofbuilt-inpotentialvalues.1=C2vsVRplotsatdifferentmagneticeldandtemperatures. ............................... 51 2-4FrequencydependenceofVbiandNDatH=0and70kOe. ........... 52 2-5CapacitanceandlossversusfrequencydataatdifferentTandH. ....... 53 2-6Thedependenceofactivationenergy,Ea,ontheappliedmagneticeldH. ... 54 2-7InternalPhoto-emissionexperimentsontheSchottkydiodes. .......... 55 3-1RoomtemperaturecurrentdensityJwithrespecttoappliedbiasVonntypemulti-layer-graphene/Si:Pjunctions. ........................ 78 3-2RichardsonactivationplotsasafunctionofT)]TJ /F8 7.97 Tf 6.59 0 Td[(1from250Kupto330Konmulti-layer-graphene/Si:P. .............................. 79 3-3Inversesquareofcapacitanceperunitareameasuredat1kHzasafunctionofreversebiasatroomtemperature:multi-layer-graphene/Si:P. ......... 79 3-4RoomtemperaturecurrentdensityJwithrespecttoappliedbiasVonntypemulti-layer-graphene/GaAs:Sijunctions. ...................... 80 3-5RichardsonactivationplotsasafunctionofT)]TJ /F8 7.97 Tf 6.59 0 Td[(1from250Kupto330Konmulti-layer-graphene/GaAs:Sijunctions. ...................... 81 3-6Inversesquareofcapacitanceperunitareameasuredat1kHzasafunctionofreversebiasatroomtemperature:multi-layer-graphene/GaAs:Si ....... 82 3-7Roomtemperaturecurrentdensity,J,withrespecttoappliedbiasVonn-type4H-SiC/multi-layer-graphenejunctions. ....................... 83 3-8Inversesquareofcapacitanceperunitareameasuredat1kHzasafunctionofreversebiasatroomtemperatureonmulti-layer-graphene/4H-SiC. ...... 84 3-9I-Vcharacteristicsofmulti-layer-graphene/4H-SiCSchottkybarriersfrom300Kupto900K. ...................................... 85 3-10I-Vcharacteristicsofmulti-layer-graphene/4H-SiCSchottkybarriersfrom300Kupto800Kinthesemilogarithicform. ....................... 86 10

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3-11I-Vcharacteristicsofmulti-layer-graphene/4H-SiCSchottkybarriersfrom300Kupto800Kinthesemilogarithicformintheforwardbias. ............ 87 3-12SemilogarithmicJ-Vcharacteristicsofmulti-layer-graphene/GaN:SiSchottkybarriersfrom5Kupto330K. ............................ 88 3-13SemilogarithmicJ-Vcharacteristicsofmulti-layer-graphene/GaN:SiSchottkybarriersfrom5Kupto330Kintheforwardbiasdirection. ............ 89 3-14RichardsonactivationplotsasafunctionofT)]TJ /F8 7.97 Tf 6.59 0 Td[(1from250Kupto330Konmulti-layer-graphene/GaN:Si. ............................ 90 3-15BondpolarizationtheorySchematics ........................ 91 4-1Schematicsofmulti-layer-graphene/n-Si(1E16cm)]TJ /F4 11.955 Tf 7.08 -4.34 Td[(3). .............. 106 4-2Currentdensity-voltagecharacteristicsmeasuredonMLG/n-Sibefore(redsquares)andafterthebromination(bluetriangles). ................ 107 4-3X-raydiffractionpatterntakenonHOPGandbrominedopedHOPGatdifferentdopingtimes. ..................................... 108 4-4AugerelectronspectroscopydatatakenonbrominatedHOPG. ......... 109 4-5X-rayphotoelectronspectroscopydatatakenonthebrominatedHOPGsample. 110 4-6Changesinthebandstructureatthemetal-semiconductorinterfacebeforeandafterthechemicaldoping. ........................... 111 4-7C)]TJ /F8 7.97 Tf 6.59 0 Td[(2vs.VRplotsofMLG/n-Si. ........................... 112 4-8Roomtemperaturecurrentdensity,J,withrespecttoappliedbias,V,onMLG/n-4H-SiCbefore(redsquares)andafterthebromination. ........... 113 4-9Plotofforwardcurrentatxedvoltage(1.85V)withrespecttothetime.Bromineisturnedon/offatspeciedtimesatthetopofthegraph. ............ 114 5-1Oneunitcellofgraphenewithtranslationalvactorsa1anda2 .......... 121 5-2CrystalstructureofgraphiteshowingconsecutivelayerswithABandA'B'atoms. ......................................... 122 5-3Oneunitcellofgraphitewithtranslationalvactorsa1anda2andc ....... 123 5-4Therstbrillouinzoneofgraphiteandexplanationofthebandstructureofthegraphite. ........................................ 124 5-5ThebandstructureofgraphitenearthehighsymmetrypointsH-K(orH'-K')ascalculatedfromSWMcmodel. .......................... 125 11

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6-1X-rayphotoelectronspectroscopydatatakenonHOPGbeforeandaftertheannealing. ....................................... 142 6-2Temperaturedependenceofin-planeresistivity(ab)inHOPGfrom1.7Kupto900K. ....................................... 143 6-3Temperaturedependenceofthescatteringrate,mobilityandcarrierdensityofgraphitefrom300Kdownto5K. ........................ 144 6-4Temperaturedependenceofthein-planeresistivityfrom1.7Kuppto900K. 145 6-5Temperaturedependenceofout-of-planeresistivity,c,inHOPGfrom3Kupto300K. ........................................ 146 6-6Temperaturedependenceofout-of-planeresistivity,c,inHOPGfrom3Kupto1500K. ....................................... 147 6-7Out-of-planeconductivity,c,versusT2inthe300Kto1500Krangeandtheoreticalttotheexperimentaldata. ....................... 148 6-8Out-of-planeconductivity,c,versusT2inthe300Kto1500Krange. ..... 149 7-1Plotsofroomtemperaturein-planeresistivity,ab,andcarrierdensity,N(b),asafunctionofbromineintercalationtime. .................... 165 7-2Tranverseresistivity,xy,asafunctionofperpendicularmagneticeldBatdifferentintercalationtimes. ............................. 166 7-3Temperaturedependenceofabandcattheindicatedintercalationtimes. .. 167 7-4Infraredreectanceandopticalconductivity,1(!),atdifferentintercalationtimes. ......................................... 168 7-5OpticalconductivityofgraphiteandBr-dopedgraphiteintheregionofthe1588cm)]TJ /F8 7.97 Tf 6.59 0 Td[(1. ......................................... 169 7-6Temperaturedependenceofmagneticsusceptibilitycattheindicatedintercalationtimes. ......................................... 170 7-7Plotof1/determinedfromoptical(bluetriangles)andtransport(redtriangles)measurements. .................................... 171 8-1Ramanspectrumtakenonpristineandannealed4H-SiCsamples. ....... 176 8-2ObservationofD,Gand2DpeaksaftersubstractionofRamanspectrumtakenonpristineandannealed4H-SiCsamples. .................... 177 8-3Temperaturedependenceofin-planeresistivityofgraphitegrownonSiC ... 178 8-4AFMimagetakenongraphiteSiCsurface ..................... 179 12

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AbstractofDissertationPresentedtotheGraduateSchooloftheUniversityofFloridainPartialFulllmentoftheRequirementsfortheDegreeofDoctorofPhilosophyGRAPHITE-GRAPHENESEMICONDUCTORJUNCTIONSANDMAGNETO-DIELECTRICCOUPLINGINSCHOTTKYDIODESBySefaattinTongayDecember2010Chair:ArthurF.HebardMajor:Physics Thegoalofthisdissertationistoincorporategraphiteandgrapheneintotoday'ssemiconductortechnologyasaSchottkybarrierdiodes(metal/semiconductorjunctions)thatarewidelyusedinmetalsemiconductoreldeffecttransistors(MESFETs),highelectronmobilitytransistors(HEMTs),hightemperatureandfrequencydevices,solarcellsandsensors/detectors.Therstpartofthedissertationaimstogivethereaderageneralideaaboutthephysicsatthemetal-semiconductorjunctionsandessentialtheorybackground. ThesecondchapterofthedissertationquestionseffectsoftemperatureandmagneticeldonthediodecharacteristicsofSchottkyjunctions.Inthischapter,wepresentobservationofnegativemagnetocapacitanceonGaAs:Si/Aujunctionsandfullyequippedwiththetheory,wepresentaphenomenologicalexplanationfortheobservedeffect. Inthethirdchapter,weforthersttimeintroducemulti-layer-grapheneasametal(semimetal)electrodetoformSchottkybarriersonvarioustechnologicallysignicantsemiconductorssuchasSi,GaAs,SiCandGaN.Multi-layer-graphene/semiconductorjunctionsnotonlydisplaygoodcurrent-voltage(I)]TJ /F3 11.955 Tf 13.28 0 Td[(V)andcapacitance-voltage(C)]TJ /F3 11.955 Tf 12.67 0 Td[(V)characteristicsbutalsoaresignicantsincetheSchottkybarrierheightandcharacteristicsaremainlygovernedbytheinteractionandbondformationatfewlayers 13

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onthemetalandsemiconductorinterface.Thisautomaticallyimpliesthatthepresentedresultsalsoholdforgraphene/semiconductorjunctions. Chapter4,takestheSchottkyformationatthemulti-layer-graphene(graphene)/semiconductorjunctiontoanotherlevelandaimstochangetheFermilevelofthemetalelectrodebyintercalationwithBromineandtunethebarrierheight.ObservedresultsaresignicantinMESFETtechnologysincedifferentbarrierheightaredesireddependingontheapplication. Theremainderofthedissertation,focusesonthepropertiesofgraphiteandgraphenetohavemoreunderstandingaboutthecontentpresentedinthepreviouschapters.Chapter5,givesabrieftheorybackgroundaboutgraphiteandgraphenewhileChapter6andChapter7discusselectricalpropertiesofgraphiteathightemperatureswhereitstartstodecouplefromeachgraphenelayerandactsasbi-layergrapheneandwithbromineintercationwherethereisc-axislatticeconstantexpansionandeachgrapheneplanebecomesmoreisolated.Chapter8,givesadetaileddescriptionaboutepitaxialgraphenegrowthinSiCbyjouleannealingtechnique,andweendthechapterwithfuturedirections. 14

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CHAPTER1SEMICONDUCTORTHEORYANDSCHOTTKYBARRIERPHYSICS 1.1ChargeCarriersinIntrinsicandExtrinsicSemiconductors Theroomtemperaturetransportpropertiesinasemiconductorarelargelydeterminedbythenumberofmajoritycarriers,electronsintheconductionbandandtheholesinthevalenceband.Therefore,thedensityofthesecarriersplaysacrucialroleinthephysicalpropertiesofthesemiconductorsusedintoday'ssemiconductortechnology.Thissectionaimstogiveanintroductorybackgroundonthecarrierstatisticsinthesemiconductorswhichwillbeusedfrequentlythroughoutthefollowingchapters. ThedensityoftheelectronsintheconductionbandcanbewrittenasproductofthethetheFermi-Diracfunctionandthedensityofquantumstatesintheconductionband n(E)=gc(E)f(E),(1) andaccordinglythedensityofholesinthevalancebandis, p(E)=gv(E)[1)]TJ /F9 11.955 Tf 11.96 0 Td[(f(E)],(1) wheref(E)isthetheFermi-Diracfunctionand,gc(E)andgv(E)arerespectivelythedensityofquantumstatesintheconductionandvalencebands.IntegratingEq. 1 (Eq. 1 )overtheconductionband(valanceband)energy,thenumberofelectrons(holes)canbewrittenas n0=Zgc(E)f(E)dE,(1) and p0=Zgv(E)[1)]TJ /F9 11.955 Tf 11.96 0 Td[(f(E)]dE,(1) 15

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Inthisdissertation,allthesemiconductorwafersused,suchasSi,GaAs,4H-SiC,6H-SiCandGaN,weren-doped,andtherefore,thethermalequilibriumelectronconcentrationintheconductionbandwillbederivedindetail.However,similarstepscanbedoneforthethermalequilibriumholeconcentrationinthevalancebandanditsderivationislefttotheinterestedreader. Byusingthedensityofstatesintheconductionbandin3-dimensionsandtheFermi-Diracfunction,theconcentrationofelectronsintheconductionbandbecomes n0=Z1Ec4(2mn)3=2 h3p E)]TJ /F3 11.955 Tf 11.95 0 Td[(Ecexp)]TJ /F4 11.955 Tf 9.29 0 Td[((E)]TJ /F3 11.955 Tf 11.96 0 Td[(EF) kT,(1) Inprinciple,thelowerandhigherlimitsofintegrationinEq. 1 runfromtheminimumoftheconductionband,Ec,uptotheallowedstatesintheconductionband.However,thisintegralistypicallytakentoinnitysincethetheFermi-Diracfunctionexponentiallydecreaseswithincreasingenergy.Moreover,thetheFermi-DiracfunctionissimpliedasanexponentialfunctionsincetheFermienergyisinthebandgapandthe(E)]TJ /F3 11.955 Tf 11.95 0 Td[(EF)termismuchlargerthanthekineticenergy,kT. Underalltheseassumptions,theintegralofEq. 1 isaGammafunction.Thesolutiontothisgivesthethermalequilibriumelectronconcentrationintheconductionbandandiswrittenas n0=Ncexp)]TJ /F4 11.955 Tf 9.3 0 Td[((Ec)]TJ /F3 11.955 Tf 11.95 0 Td[(EF) kT,(1) whereNcistheeffectivedensityofstatesfunctionintheconductionband, Nc=22mnkT h23=2,(1) Eq. 1 1 aregenerallyusedtoestimatethenumberofelectronsintheconductionbandataspecictemperatureandforaspecicsemiconductorwithagiveneffectivemass(mn),positionoftheconductionbandminimumandpositionoftheFermilevel. 16

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Asimilarsetoftwoequationsforholescanbeexpressedas p0=Nvexp)]TJ /F4 11.955 Tf 9.3 0 Td[((EF)]TJ /F3 11.955 Tf 11.95 0 Td[(Ev) kT,(1) whereNvistheeffectivedensityofstatesfunctioninthevalenceband, Nv=22mpkT h23=2,(1) 1.2IntrinsicandExtrinsicSemiconductors Theequationsderivedabove(Eq. 1 andEq. 1 )aretypicallyusedtocalculatethetotalconcentrationsofelectronsandholesintheconductionbandandthevalencebandinanysemiconductor.Whenthereisnodopinginthesemiconductor,theconcentrationofelectronsisequaltotheconcentrationofholesandiscalledtheintrinsiccarrierdensity(n0=ni=p0=pi).ThesesemiconductorsarecalledintrinsicsemiconductorsandtheirFermienergybecomestheintrinsicFermilevel,EFi.UsingEq. 1 andEq. 1 withtheintrinsicFermilevel, ni=n0=Ncexp)]TJ /F4 11.955 Tf 9.3 0 Td[((Ec)]TJ /F3 11.955 Tf 11.96 0 Td[(EFi) kT,(1) and, pi=p0=Nvexp)]TJ /F4 11.955 Tf 9.3 0 Td[((EFi)]TJ /F3 11.955 Tf 11.96 0 Td[(Ev) kT,(1) Whentheintrinsicsemiconductorisdopedwitheitherelectrondonating(donor)orholedonating(acceptor)atomswiththecontrolledamounts,theelectricpropertiesofthesemiconductorchangedrastically.Theconductivityofdopedsemiconductorscanvaryfromsemi-insulatinguptoveryconductingthusenablingawiderangeofuseforindustrialpurposes.Inthiscase,thetotalconcentrationofelectronsisnotequaltothetotalconcentrationofholes,theFermilevelofthesystemchangesfromintrinsicFermilevel(EFi)totheextrinsicFermilevelwhichisdenotedasEF.These 17

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materialsarecalledextrinsicsemiconductors.tedasEF.Thesematerialsarecalledextrinsicsemiconductors. Anintroductoryideaaboutthenatureofthedopingscanbegivenasfollows:Inasilicon(Si)crystal,alltheSiatomsarecovalentlybondedtoeachother.Whenaphosphorus(P)atomfromagroupVelementhavingvevalenceelectrons,issubstitutionallyaddedtothesystem,thePatommakesacovalentbondingintheSimatrixandthefthvalanceelectronactsasadonorelectron.Thissemiconductoriscalledann-typesemiconductor.Ontheotherhand,whendopedwithboron(B)atoms,agroupIIIelementwiththreevalanceelectrons,holedopesthesystemandthesemiconductoriscalledp-typesemiconductor. Forn-typesemiconductors,forexamplephosphorusdopedSi,theenergyrequiredtoactivatethedonorelectroninthePatomintotheconductionbandismuchlessthanthatfortheelectronsinvolvedinthevalancebondingintheSimatrix.Anenergyrequiredtoactivatedonorelectronsfromtheirdopantsintotheconductionbandisreferredastheactivationenergy(Eactivation)ortheionizationenergyandtheenergylevellocatedEdbelowtheconductionbandcreatedbythecontrolledamountsofdopantsiscalledtheshallowenergylevelandislocatedatEd. 1.3TheSchottkyBarrier(Metal-Semiconductor)Contacts Metal-Semiconductor(M-S)contacts(Schottkydiodes)areaveryimportantpartoftoday'ssemiconductorandoptoelectronicdevices.Schottkybarriersformedatthemetal-semiconductorinterfacesareverydelicatekeycomponentsofmetal-semiconductoreldeffecttransistors(MESFETs)andhighelectronmobilitytransistors(HEMTs)whicharewidelyusedinhighfrequency,andhighpowerdeviceapplications.TherstobservationofSchottkybarrierformationandrecticationacrossthemetalsemiconductorinterfacedatesbacktotheearly1900s.Whenametalcontactismadeonthesemiconductor,theappliedcurrentisfoundtopassinonedirection,butnottheother.Ametal-semiconductorinterfacewiththisrectifyingpropertyiscalledaSchottky 18

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diode.Eventhoughexcitingandrevolutionaryforitstime,reliabilityandreproducibilityissuescausedSchottkydiodestobereplacedbymorepracticalandeasytomakep)]TJ /F3 11.955 Tf 12.97 0 Td[(njunctionsinthe1950s.Afterthispoint,theprogressanddevelopmentinthematerialscienceandengineering,andvacuumscienceandtechnologyhasallowedfabricationofreliable,reproducible,andpracticalmetal-semiconductorcontacts.Today,M-Scontactsareveryimportantpartofsemiconductingdevicesespeciallyforsemiconductorssuchas,suchasSiC,GaN,GaAs,wherethereisnoestablishedoxide.Intheabsenceofanoxidelayer,eldeffectgatingviathininsulatingbarrierisnotpossibleandmetal-oxide-semiconductoreldeffecttransistors(MOSFET)cannotbemanufactured.Forsuchsemiconductorswithoutanaturaloxide,MESFETdevicecongurationisusedtoinduceanelectricaleldatthesemiconductorinterfaceacrossthedepletionwidthofSchottkydiodetherebydepletingtheinterfaceofmobilecarriers. Thissection,wewillgive(1)asimplepictureabouttheformationoftheSchottkybarrieracrosstheM-Sinterface(2)explainthecapacitiveresponseandcurrent/transportacrossthejunctionanddeviationfromtheidealityattheinterface,and(3)discusscommonlyusedSchottkybarrierheightmeasurementtechniques. 1.3.1OriginoftheSchottkyBarrierFormationattheM-SInterface Metal-semiconductorcontactsareubiquitousinsemiconductortechnologynotonlybecausetheyareunavoidable,butalsobecausetheassociated(Schottky)barrierstoelectronictransportacrossmetal-semiconductorinterfacecanbetunedbyjudiciouschoiceofmaterialsandprocessingtechniques[ 1 ].ThemostprominentcharacteristicofaSchottkybarrierisitsrectifyingcharacteristic;thebarrieractslikeadiodewithlargecurrentsowingforforwardbiasandsignicantlysmallercurrentsowingforreversebias[ 2 ].Iflowresistanceandohmic(linear)I-Vcharacteristicsaredesired,thenmaterialsand/orprocessingtechniquesarechosentoassurethattheSchottkybarrierheight(SBH)Bissmallcomparedtotemperature(B<
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heightsaremuchlargercomparedtoroomtemperature(B>>kBT)andpossessastrongnon-linearity;arectication.ASchottkybarrierisformedbetweenametalandsemiconductorinterfaceduetoamismatchoftheFermilevelsforthemajoritycarrieroneachsideofthejunction.ThetoppanelofFig. 1-1 showsthemetal-semiconductorjunctionbeforethermalequilibriumforthecaseofan-typesemiconductor.Inthegure,mandsrepresentthemetalandsemiconductorworkfunctionsrespectivelywhileistheelectronafnity. Afterthermalequilibriumisachieved[Fig. 1-1 ,bottompanel],electronsfromthesemiconductorowintothelowerlyingenergystatesonthemetalsidetomaketheFermilevel(EF)constantthroughoutthesystem,leavingpositivelychargeddonoratomsbehind.ThepositivelychargeddonoratomsonthesemiconductorsidecreateaspacechargeregionandtheassociatedSchottkybarrier.Positivelychargeddonoratomsonthesemiconductorsidecreateanelectricaleldpreventingelectronsfromowingfromthemetaltothesemiconductor,butallowingelectronstoowfromsemiconductortothemetal,hencetherectication.AftertheequilibriumisachievedtheSchottkybarrierideallywouldbegivenby(Fig. 1-1 ), B=(m)]TJ /F7 11.955 Tf 11.95 0 Td[(),(1) However,deviationsfromtheidealcasemightaltertheexpectedSchottkybarrierheightgiveninEq. 1 andtheseadditionalprocesseswillbediscussedinSection 1.3.4 Sincethebarrierseenfrommetalsideisdifferentthanthebarrierseenfromthesemiconductorside,thepotentialseenbytheelectronsonthemetalsideisreferredtoastheSchottkybarrierwhilethepotentialseenbythenon-localizedelectronsontheconductionbandofthesemiconductorsideisreferredtoasthebuilt-inpotentialbarrier(Vbi),whereVbiistheenergydifferencebetweentheconductionbandofthe 20

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semiconductorandtheFermienergy.ThedopingdependenceofmakesVbiweaklydependentonthesemiconductordoping. 1.3.2DepletionCapacitanceattheM-SInterfaceandC-VRelationship Afterthermalequilibriumisachieved,positivelychargeddonoratomscreatedinthedepletionarea[Fig. 1-1 bottompanel]createanelectricaleldwithinthedepletionwidth(W).Moreover,atthermalequilibrium,electronsfromthesemiconductoraccumulateathinlayerofelectronsonthemetalside.Allthepositivelychargeddonoratomscanbepicturedasalayerofpositivechargesatx=W[Fig. 1-1 bottompanel].Withintheparallelplatecapacitorapproximation,thisgivesrisetoacapacitanceattheinterfacecalledthejunctioncapacitance.Themagnitudeoftheelectricaleld,E,inthedepletionregionofthejunctionandhencetheelectrostaticpropertiesoftheSchottkyjunctioncanbedeterminedsolvingthePoisson'sequationwhichhastheform, dE dx=(x) s,(1) wherethesand(x)aredenedaspermittivityofthesemiconductorandthespacechargevolumedensityinthedepletionarea.AsdiscussedinChapter 1.2 ,itismuchhardertoactivatetheelectronsinvolvedinthecovalentbondinginbetweenSi-Siatoms,comparedtoactivatingdonorelectronshavingactivationenergiesontheorderofroomtemperatureofless.Itisthereforegenerallyassumedthatallthedonoratomsinthedepletionareaarealreadypositivelychargedandthedensityofthechargeddonorsisconstant.Thisconstantdensityapproximationistypicallycalledastheabruptjunctionapproximation(AJA)andwithinthisapproximationthedensityofpositivelychargeddonoratomsequalstothedopingdensityofthesemiconductor(Nd).FollowingEq. 1 andAJA, E=ZeNd sdx=eNdx s+,(1) 21

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whereisaconstantoftheintegration.Sincetheelectriceldhastobezeroattheedgeofthedepletionwidthonthesemiconductorside(Wawayfromthemetal-semiconductorinterface),canbedeterminedtobe =)]TJ /F3 11.955 Tf 10.49 8.09 Td[(eNdW s,(1) UsingEq. 1 and 1 E=)]TJ /F3 11.955 Tf 10.49 8.09 Td[(eNd(W)]TJ /F3 11.955 Tf 11.96 0 Td[(x) s,(1) AccordingtoEq. 1 ,theelectricelddeterminedfromPoisson'sequationandundertheAJAapproximationvarieslinearlywiththedistancefromthemetal-semiconductorinterface.Howeversincetheelectriceldiszeroinsidethemetalcontacts,therealwaysexistanegativechargeattheinterfacemakingthetotalelectriceldzero. Ex=0=0,(1) andthepotentialdifferencefromx=0tox=W(orVbi)canbecalculatedbyintegratingtheelectricaleldandusingEq. 1 .Thepotentialdifferencereads, (x)=ZE(x)dx=Z)]TJ /F3 11.955 Tf 10.49 8.08 Td[(eNd(W)]TJ /F3 11.955 Tf 11.96 0 Td[(x) sdx,(1) (x)=)]TJ /F3 11.955 Tf 10.49 8.78 Td[(eNd(Wx)]TJ /F5 7.97 Tf 13.15 4.71 Td[(x2 2) s+,(1) Thepotentialdifferencefromx=0tox=Wwillbeequaltothebuilt-inpotentialvalue,Vbi. Vbi=j(x=W)j=eNdW2 2s,(1) anddepletionwidthreads, 22

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W=2s(Vbi)]TJ /F3 11.955 Tf 11.96 0 Td[(VR) eNd1=2,(1) wheretheVRisdenedasthepotentialappliedinbetweenthemetal(positiveside)andthesemiconductor(negativeside). Oncethermalequilibriumisachieved,chargesinthedepletionwidthareroughlyseparatedonthemetalside(negativecharges)andthesemiconductor(positivecharges)creatingajunctioncapacitance.Howeveruponapplicationofthereversebiasvoltage,VR,acrossthejunction,morepositiveandnegativechargeswillbeaccumulatedatthesemiconductorandmetalsiderespectively.Thejunctioncapacitancecanthereforebewrittenas, Cdepletion=dQ dVR,(1) andusingAJA,thechargeinthedepletionareais dQ=eNddx,(1) hence, Cdepletion=eNddx dVR=esNd 2(Vbi+VR)1=2,(1) wheretheCdepletionisthecapacitanceperunitarea. 1.3.3TransportAcrosstheM-SInterface:ThermionicEmission AftertheformationoftheSchottkybarrier,thecurrenttransportacrosstheSchottkybarrierismainlydominatedbythemajoritycarriers.WhentheSchottkybarrierheightismuchlargerthankT,theMaxwell-Boltzmanndistributionstillappliesandthermalequilibriumisnotaffected,andthisapproximationiscalledthethermionicemis-sionprocess.Inthermionicemission,thetotalcurrentdensityacrossthemetal-semiconductorinterfacehastwocurrentcomponents:(1)acurrentdensityfrommetal 23

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intothesemiconductor,Jm!s,and(2)fromsemiconductorintothemetalJs!m.Thetotalcurrentreads, Jtotal=Js!m+Jm!s,(1) Thecurrentdensityfromthesemiconductorintothemetal(Js!m)isgivenbytheintegraloftheconcentrationofelectronswithenergieslargeenoughtoovercometheSchottkybarrierforthermionicemissionintothemetal, Js!m=eZ1EF+eBxdn,(1) wherexisthevelocityinthedirectionoftheelectronictransport,BistheSchottkybarrierheightanddnistheelectrondensitygivenby, dn=gc(E)f(E)dE,(1) Inthisequation,thef(E)istheFermifunctionandthegc(E)isthedensityofstatesintheconductionband.WritingthednwiththesimilarassumptionsandsimplicationmadeinthetransitionfromEq. 1 toEq. 1 wearriveattheexpression, dn=4(2mn)3=2 h3p E)]TJ /F3 11.955 Tf 11.96 0 Td[(Ecexp)]TJ /F4 11.955 Tf 9.3 0 Td[((E)]TJ /F3 11.955 Tf 11.95 0 Td[(EF) kTdE,(1) Undertheassumptionthatalltheenergyofthefreeelectronsintheconductionbandissimplythekineticenergy,thenwehave 1 2mn2=E)]TJ /F3 11.955 Tf 11.95 0 Td[(Ec,(1) Usingequations 1 1 inEq. 1 Js!m=AT2exp)]TJ /F3 11.955 Tf 10.49 8.09 Td[(eB kTexp)]TJ /F3 11.955 Tf 10.74 8.09 Td[(eV kT,(1) 24

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whereAistheeffectiveRichardsonconstantandgivenasA=e4mk2 h3. Followingsimilarstepsforthecurrentdensityfrommetalintothesemiconductor(Jm!s), Jm!s=)]TJ /F3 11.955 Tf 9.3 0 Td[(AT2exp)]TJ /F3 11.955 Tf 10.49 8.09 Td[(eB kT,(1) andusingEq. 1 andEq. 1 inEq. 1 ,thetotalcurrentacrossthemetalsemiconductorjunctionreads Jtotal=AT2exp)]TJ /F3 11.955 Tf 10.49 8.08 Td[(eB kTexpeV kT)]TJ /F4 11.955 Tf 11.95 0 Td[(1,(1) whereVistheappliedpotential[ 2 3 ].Underthermionicemission,thetotalcurrentdensityacrossthejunctioncanbeexpressedbyEq. 1 andisfrequentlyusedinthecurrentliteraturetoextractouttheSchottkybarrier(section 1.3.5.1 ).Howeverdeviationsfromthisidealcasecanaltertheexperimentaldataandmightresultinerrorousinterpretations.Thenextsectionwilldiscusstheseadditionalprocesses. 1.3.4Non-IdealEffectsattheM-SInterfaces 1.3.4.1Imageforceloweringorschottkyeffect Anelectroninadielectricmediumatadistancefromthemetalwillcreateapositivelychargecarrieronthemetalsideatthemetal-semiconductorinterface.However,thiseffectivechargeaccumulatedatthemetalsurfacecanbeimaginedasaneffectivechargelocatedinthemetalatadistance-xfromtheinterface.Inthiscase,therewillbeaninteractioninbetweentheelectroninthedielectric(studiedsemiconductor)andaneffectivechargeinthemetal.Thiscoulombinteractioniscalledanimageforceandthechargeformedonthemetalsideisknownastheimageforcecharge.Asaresultofthisimageforce,electronsonthesemiconductorsideareattractedtopositiveimagechargesinthemetalcreatedbythoseelectrons.Thermallyactivatedelectronsovercomingthebarrieratthemetal-semiconductorinterfaceexperiencethisadditionalcoulombinteractionandeffectivelytheelectrons 25

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overcomethebarrierheighteasier,leadingtoanreduction/loweringintheSchottkybarrierheight.TheloweringoftheSchottkybarrierheightasaresultofinteractioninbetweentheimagechargeandtheelectronsiscalledeitherimageforceloweringorSchottkyeffectandcanbewrittenas[ 2 3 ], B=r eE 4s,(1) orintermsofbuilt-inpotentialanddopingdensityND[ 1 ], B=s e3VbiND 823s,(1) Themagnitudeoftheimageforceloweringtypicallyvariesfrom1meVupto50meVdependingonthesemiconductor,anddopinglevelandmosttimesitconstitutesaverysmallportionofthetotalSchottkybarrierheight. 1.3.4.2Thermioniceldemission AnothermechanismgivingacorrectiontermtothepredictedSchottkybarrierheighttakesplacemostlyatlowtemperaturesandiscalledthermioniceldemission(TFE)[ 4 ].Onheavilydopedsemiconductors,thenumberofcarrierstunnelingacrossthebarrierwithenergieslessthantheSchottkybarrierheightmightexceedthenumberofthermallyactivatedcarriersovertheSchottkybarrier.ThebalancebetweenthesharpincreaseintunnelingprobabilityacrosstheSchottkybarrier(tunnelingbarrierwidthisnarrowerforhigherelectronenergies)andthedecreaseincarrierdensitywithelectronenergy,resultsintunnelingofcarriersacrosstheSchottkybarrierdespitetheirenergiesbeingtoosmallovercomethebarrier.ThisresultsinaneffectivedecreaseoftheSchottkybarrierheight.TFEtheoryrstconsiderbyPadovani[ 4 ]alongwiththeWKBapproximation,ndsthattheTFESchottkybarrierheightloweringcanbecalculatedas, B=9 4E200Vbi1=3,(1) 26

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whereE00is E00=e~ 2ND sm,(1) 1.3.4.3Directtunneling Thethermioniceldemission(TFE)processrequiresmobileelectronsonthesemiconductorsidetobethermallyactivatedtoparticularenergieslessthanthatoftheSchottkybarrierheightandtunnelacrossthemetal-semiconductorinterface.However,asthetemperatureatwhichtheSchottkydiodeismeasured/operatingatisdecreased,eventhoughelectronswillnothaveenoughenergytogoovertheSchottkybarrierortobeexcitedtoapointwheretheycantunnel(TFE)buttheywillnaturallytunnelacrosstheSchottkybarrier.Insuchcases,theinterpretationoftheSchottkybarrierisratherdifcultandcontroversial.Directtunnelingtypicallygivesnon-idealJ)]TJ /F3 11.955 Tf 12.03 0 Td[(Vcharacteristicsthatcannotbeexplainedbythermionicemissiontheory. 1.3.5MeasurementofSchottkyBarrierHeight 1.3.5.1Current-voltagecharacteristics Thecurrentdensityacrossthemetal-semiconductorinterfacehasbeendiscussedandderivedinsubsection 1.3.3 andthetotalcurrentdensityreads, Jtotal=JsatexpeV kT)]TJ /F4 11.955 Tf 11.96 0 Td[(1,(1) whereJsatisthereversesaturationcurrentdensity Jsat=AT2exp)]TJ /F3 11.955 Tf 10.49 8.09 Td[(eB kT,(1) FollowingfromEq. 1 ,whentheappliedbiaseVismuchlargerthanthethermalenergykT(eV>>kT),thenumeral-1insidebracketcanbeignored.Inthiscase,whenthemeasuredcurrentisplottedsemilogarithmicallywithrespecttotheappliedbias,itisexpectedtobelinear.However,inrealitytheadditionalcurrentprocesses 27

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discussedinsection. 1.3.4 displaydifferentdependenciesontheappliedbias,resultinginadeviationfromlinearity.Thedeviationfromthelinearityistypicallyaccountedforbyintroductionofaparameter,,insidetheexponentialandisnormalizedto=1(linear)forcurrentcompletelyoriginatingfromthermionicemissionprocessand>1whenothernon-idealeffectscontributetothemeasuredtotalcurrent.Withtheinclusionofthisadditionalparameter,thetotalcurrentacrosstheM-Sinterfaceiswrittenas, Jtotal=JsatexpeV kT)]TJ /F4 11.955 Tf 11.95 0 Td[(1,(1) HeretheparameteriscalledtheidealityfactorandwrittenasainverseslopeoftheJ)]TJ /F3 11.955 Tf 11.95 0 Td[(Vplot. =1 kT=edln(Jtotal)=dV,(1) Theidealityfactorisameasureofdeviationfromideality(thermionicemissionprocess)andreachestovalueslargerthanonewhenothernon-linearcurrentprocessescontributetothetotalmeasuredcurrent. TheJ)]TJ /F3 11.955 Tf 12.06 0 Td[(Vmeasurementprovidesatomeasureoftheeffectivebarrierheightatthemetal-semiconductorinterfaceafterthermalequilibriumisachieved.Whenthetotalcurrentismeasuredwithrespecttodifferentappliedbiasvalues,itisexpectedtopasssignicantlymorecurrentintheforwardbiasdirection.IngeneralthemeasuredJ)]TJ /F3 11.955 Tf 12.35 0 Td[(Visexpectedtospanenoughlinearrangeinthesemi-logcurrentdensityandvoltageplotsuchthatonecanmakeanextrapolationtothey-axisanddeterminethesaturationcurrentdensity,Jsat.OnceJsatisknownSchottkybarrierheightcanbedeterminedusingEq. 1 .althoughasimpletask,extractionoftheSchottkybarrier'shasalwaysbeenopentoquestions,doubtsandcontroversiesduetotheadditionalcurrentprocessestothermionicemissionprocessanddeviationfromlinearityintheidealityfactor(>1).Nevertheless,theJ)]TJ /F3 11.955 Tf 12.05 0 Td[(Vtechniqueisknowntobeverystandardandpowerfultechniqueasameasureofthebarrierheight. 28

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EventhoughextractionofSchottkybarrierfrommeasuredJ)]TJ /F3 11.955 Tf 12.62 0 Td[(Vcharacteristicsanduseofthermionicemissionisapowerful,practicalandstandardtechnique,Eq. 1 leadstoadeviationfromthetrueSchottkybarrierheightespeciallyatmetal-semiconductorinterfaceswherethevalueofthemetalcontactareaisnotexactlyknown.Insuchcases,metalelectrodesplacedonthesemiconductordonotmake100%physicalcontactattheinterfaceandthetruevalueofthecurrentdensitycannotbedetermined.Sincethevalueofthecurrentdensity(J)ortheeffectivecurrentdensity(Jsat)cannotbedetermined,Eq. 1 iswrittenintermsofcurrentandsaturationcurrentdensityasfollows, Itotal=IsatexpeV kT)]TJ /F4 11.955 Tf 11.95 0 Td[(1,(1) and Isat=AAT2exp)]TJ /F3 11.955 Tf 10.49 8.09 Td[(eB kT,(1) here,thesaturationcurrentdensity,Isatcanbewrittenas, ln)]TJ /F3 11.955 Tf 5.48 -9.68 Td[(Isat=T2=ln(AA))]TJ /F3 11.955 Tf 11.96 0 Td[(e=kTB,(1) InEq. 1 ,theunknowncontactareaisonlypresentinthersttermoftherighthandsideoftheequation.Thereforeifoneplotsthenaturallogarithmofthesaturationcurrentatspecictemperaturesdividedbysquareoftemperature,lnIsat=T2,withrespecttotheinversetemperature,T)]TJ /F8 7.97 Tf 6.58 0 Td[(1,thedependencewillbelinearandtheslopeofthelnIsat=T2versusT)]TJ /F8 7.97 Tf 6.59 0 Td[(1yieldstheSchottkybarrierheight.ThismethodisoftenreferedasanactivationenergymeasurementandhasanadvantageovertheconventionalJ)]TJ /F3 11.955 Tf 12.31 0 Td[(VmethodsincenoassumptionoftheSchottkydiodeareaisrequired. 29

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1.3.5.2Capacitance-voltagecharacteristics ThepresenceofVbiinthedepletioncapacitanceexpression(Eq. 1 )derivedinsection 1.3.2 allowsonetocalculatethemagnitudeofthedepletioncapacitanceattheM-Sinterfaceoncedepletioncapacitanceismeasuredexperimentallyandthedielectricconstantandthedopinglevelofthesemiconductorisknown.TypicallythedepletioncapaticanceinEq. 1 iswrittenas, 1 C2=2(Vbi+VR) esND,(1) AccordingtoEq. 1 ,whenthemeasuredcapacitanceisplottedas1=C2versusVRalineardependenceshouldbeobserved.Anintersectionofthelinewiththeabscissagivesthebuilt-inpotentialvalueVbiwhiletheslopeoftheplotis2=(esNd).ThistechniqueiscommonlyreferredtoastheC-Vmeasurementtechniqueintheliteraturefordeterminingthevalueofthebuilt-inpotential(Vbi).Oncethebuilt-inpotentialknown,onecandeterminetheSchottkybarrierheightasfollows(Fig. 1-1 bottom), B=Vbi+Ec)]TJ /F3 11.955 Tf 11.96 0 Td[(EF e=Vbi+kT elnNc Nd,(1) whereNc,NdandVbiarerespectivelytheeffectivedensityofstatesfunctionintheconductionband(Eq. 1 ),thedopingdensityofthesemiconductorandthebuilt-inpotentialdeterminedfromtheC)]TJ /F3 11.955 Tf 11.96 0 Td[(Vmeasurementmethod. Eventhough,bothJ)]TJ /F3 11.955 Tf 12.82 0 Td[(VandC)]TJ /F3 11.955 Tf 12.83 0 Td[(VmeasurementsbothaimtodeterminetheSchottkybarrierheight,thesetwomethodsfundamentallydifferfromeachotherinthefollowingways.(1)J)]TJ /F3 11.955 Tf 12.51 0 Td[(VmethoddirectlymeasuresBwhiletheC)]TJ /F3 11.955 Tf 12.51 0 Td[(VmethodonlymeasuresVbi(2)WhiletheJ)]TJ /F3 11.955 Tf 12.42 0 Td[(Vmethodmimicsthetransportacrossthebarrier,theC)]TJ /F3 11.955 Tf 12.12 0 Td[(VmethodprobesthedepletionwidthratherthanstrictlytheSchottkybarrierheightandM-Sinterface.(3)SincetheJ)]TJ /F3 11.955 Tf 12.18 0 Td[(Vmethodmeasuresthecurrentacrossthebarrierheight,measuredcurrentoftenpassesthroughthelowestSchottkybarrierpatches.On 30

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theotherhand,C)]TJ /F3 11.955 Tf 12.48 0 Td[(Vmeasuresthedepletioncapacitanceattheinterfaceandgivesanaveragevalueforthebuilt-inpotential.Intheliterature,thesetwomethodsareoftenconsideredcomplementaryandC)]TJ /F3 11.955 Tf 12.03 0 Td[(VmethodgivesslightlyhighervaluescomparingtoextractionsfromtheJ)]TJ /F3 11.955 Tf 11.96 0 Td[(Vmethods. 1.3.5.3Internalphotoemissiontechnique AnothermethodtomeasuretheSchottkybarrierheightisknownastheinternalphotoemissiontechnique.Inthistechnique,monochromaticlightatdifferentphotoenergiesisdirectedatthemetalside.GenerallymetalelectrodesareselectedtobethinenoughtoinsurethatlightpenetratesintothesemiconductorwithenoughintensitytoreachtheM-SinterfaceandexcitestheelectronsfromtheFermilevelofthemetal.Whenthephotoenergyishighenough,thoseexcitedelectronsareactivatedovertheSchottkybarrierandacurrentismeasuredowingthroughthemetal-semiconductorinterface.ThiscurrentiscalledthephotoelectriccurrentandisdescribedbytheFowlerequation[ 5 ], Iphotoemission=(h)]TJ /F7 11.955 Tf 11.95 0 Td[(B)2,(1) whereisthefrequencyofthephoton.WhenthephotoelectriccurrentisplottedasI1=2photoemissionagainstthephotonenergy,extrapolationofthelineardependencetoaninterceptwiththephotonenergyaxisgivestheSchottkybarrierheight.ThelightsourceusedinthistechniquemustbeintherangeoftheSchottkybarrierheightandthebandgap. Inthismethod,thephotoelectriccurrentcreatedbyillimunationoftheSchottkybarrierisexpectedtobeverysmallandthereforeleakageandnoisecanbeanissue.Thistechniqueisgenerallyperformedinaacmodewithachoppedlightsourceandsynchronomedetectionofthephotocurrentwithalock-inamplier. 31

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1.4OhmicContactstoSemiconductors Oneofthemostimportantpartsoftheanydeviceisthecontactmadefromtheproduceddevicetotheoutsideworld.Thesecontactsareexpectedtodisplayverylowresistanceatthejunctionareaandlineardependenceofthecurrentacrossthecontactwithrespecttotheappliedbias,meaning,itshouldpasscurrentfrommetalintothesemiconductorandsemiconductorintothemetal.Thesetypeofjunctions(contacts)arecalledohmiccontactsanddisplayverysmall,zeroandnegativebarrierheightatthemetal-semiconductorinterface.Typically,thesecontactscanbemadetovarioustypesofsemiconductorbyspeciallytailoredmethodsforeachsemiconductor. Therstmethodisknownasthetraditionalohmiccontact.WhentheFermilevelofthemetalandthesemiconductorisequalorifthemetalFermilevelisslightlyhigher,anohmiccontactformsattheinterface.However,inprincipleitisratherdifculttoalignorndapropermaterialwithappropriateFermilevelvaluestoinduceohmiccontactsonthesamples. Thesecondmethodutilizestunnelbarriers.InthismethodametalcontactwithapositivebarrierattheM-Sinterfaceisformedinsuchawaythatthereishighenoughdopinginthesemiconductorsothatthereisonlyathinbarrierseparatingthemetalfromthesemiconductor.Ifthewidthofthedepletionregionatthemetal-semiconductorinterfaceisverythin,ontheorderof3nmorless,carrierscanreadilytunnelacrosssuchbarrier. Andthelastandthemostusedmethodutilizesrapidthermalannealing(RTA).Inthismethod,therelativepositionsoftheFermilevelateachsideofthecontactisnotconsidered.Instead,thismethodreliesonthefactthebarrierformedatthemetal-semiconductorinterfacecanbesignicantlyloweredbyannealing.Thefabricationoftheseohmiccontactsgenerallyinvolvesahightemperaturerapidthermalannealingsuchthattheunintentionalbarrierattheinterfaceisloweredbythermally-induced 32

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diffusionofmetalandasemiconductorattheinterface,creatingauniformtransitionfrommetalintothesemiconductorthroughthenewalloyformedattheinterface. Figure1-1. Energydiagramofmetal/semiconductorjunctiondiode 33

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CHAPTER2MAGNETODIELECTRICCOUPLINGINNON-MAGNETICAU/GAAS:SISCHOTTKYDIODES 2.1Introduction Electronictransportacrossmetal-semiconductorinterfaces,whichareubiquitousinsemiconductortechnology,ismediatedbytheformationofSchottkybarriersandassociateddepletioncapacitance.NumerousstudieshaveestablishedtherelationshipbetweentheSchottkybarrierheightandmaterialspropertiesandhaveatthesametimefullycharacterizedthedependenceofelectronictransportacrossmetal-semiconductorinterfacesontemperature,frequencyandvoltagebias/polarity[ 1 2 6 11 ].Despitedecadesofinvestigationsandtheuseofconceptssuchasmetalinducedgapstatemodels[ 6 7 ]andbondpolarizationtheory[ 1 8 ]aconsensusunderstandingofSchottkybarriershasnotbeenreached.SchottkycontactsonthesemiconductorGaAsareparticularlyinterestingduetoconsiderationssuchasalongspinlifetimeinGaAs[ 12 ],thedemonstrationofspinpolarizedcurrentinjectionfromametalintoGaAs[ 13 ]andspinextractionfromGaAsintoametal[ 14 ].AnadditionalgapinknowledgehoweverbecomesapparentwiththerealizationthattherearerelativelyfewstudiesoftheeffectofexternallyappliedmagneticeldsHontheelectricalpropertiesofSchottkybarriers. Weaddressthisdeciencybyreportingonasurprisinglylargenegativemagnetocapacitance(MC>20%)associatedwithAu/GaAs(Si)Schottkybarriersamplesfabricatedandcharacterizedbystandardtechniquesasdescribedbelow.TheMCisindependentofelddirectionandisunexpectedbecause(1)therearenomagneticimpuritiesintheAu/GaAs(Si)systemand(2)theGaAs(Si)ishomogeneousandthusnotacandidateformagnetocapacitanceinnonmagneticcompositemedia[ 15 ].Clearly,suchlargeMCeffectsinnon-magneticsemiconductorsystemsmustbeexplainedbeforethebehaviorofmetal-semiconductorinterfacesinvolvingspin-polarizedmetalsand/ordilutemagneticsemiconductors(DMS)forspintronicsapplications[ 16 ]can 34

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beunderstood.Usingacombinationofcurrent-voltage,capacitance(C)andinternalphotoemission(IPE)studies,weshowthattheMCcanbeattributedtoanovelmagnetodielectriccouplinginwhichaH-inducedincreaseinthebindingenergyoftheSidonorimpuritiesstronglyaffectsthedensityofionizedimpurities(Nd)withinthedepletionwidthoftheSchottkybarrier,andhencethepolarization.WeidentifytheionizationandcapturetransitionsbetweentheshallowimpurityEshandconductionEcbands(schematicofFig. 2-2 inset)andshowthattheapparentlargeH-inducedincreaseofthebuilt-inpotentialVbideducedfromlinear1=C2versusreverse-voltagebiasVRplotsisnotduetoachangeintheSchottkybarrierheight(SBH),butrathertoaeldinducedincreaseinthebindingenergy,Ea=Ec)]TJ /F3 11.955 Tf 12.63 0 Td[(Esh,oftheSidonorimpurities.TheincreaseinEawithrespecttoH(carrierfreezeout)hasbeenpreviouslystudiedasabulkeffectboththeoretically[ 17 ]andexperimentallyusingoptical[ 18 19 ]andHallmeasurements[ 20 21 ].MagneticeldtunabilityoftheSchottkycapacitanceduetoeld-inducedcarrierfreezeoutisaninterfaceeffectthatoffersanewdegreeoffreedominthedesignandapplicationofmagnetoelectronicdevices. 2.2ExperimentalMethods 2.2.1SamplePreperation Commerciallyavailable(SumitomoElectricEuropeLtd.)GaAswaferswithanominalSidopantdensityof31016cm)]TJ /F8 7.97 Tf 6.59 0 Td[(3wereused.Ohmiccontactsweremadebasedonmultilayerrecipesexistingintheliterature[ 22 24 ].Rapidthermalannealsinnitrogengasattemperaturesintherange400C-460Cassuredgoodohmiccontactwithlowparasiticresistancedowntotemperaturesaslowas10K.Priortoevaporatingthefront-sideAuSchottkycontact,thesampleswerethoroughlycleanedin3:1:50HNO3:HF:H2Ofor3-4minutestoremoveanynativeoxide.Schottkycontactsrangingindiameterfrom100mto1000mwereformedbythermalevaporationofAuatabasepressureof10)]TJ /F8 7.97 Tf 6.59 0 Td[(7Torr.Nineseparatesamplespreparedwithdifferentcontactswerestudied,allgivingsimilarresults.Atroomtemperature,theexperimentalvalues 35

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forNddeterminedfrom1=C2vsVmeasurements(section 1.3.5.2 andEq. 1 )werefoundtobeinthe1)]TJ /F4 11.955 Tf 11.95 0 Td[(21016cm)]TJ /F8 7.97 Tf 6.59 0 Td[(3rangeconsistentwiththeHalldataresults. 2.2.2Current-VoltageMeasurements Thecurrentvoltage(I)]TJ /F3 11.955 Tf 12.34 0 Td[(V)characteristicsofahighqualitySchottkydiodeshouldexhibitpronouncedasymmetrywithrespecttothesignofthebiasvoltageandalsobewelldescribedinforwardbiasbythermionicemission[ 1 3 ](Eq. 1 ).TheseattributesaresatisedforoursamplesasshowninFig. 2-1 abytheforwardandreversebiasI-Vcharacteristics,measuredat300Kand20K,ofthesameAu/GaAs:SiSchottkysampleonwhichacimpedancemeasurementsareperformed.WhenmeasuredcurrentisplottedaslnIversusV,intheforwardbiascurrentincreasesrapidlyasthevoltageisappliedandinthereversebiasdiodesactsmoreresistiveandgivescommonlyknownasleafplotsintoppanelofFig. 2-1 .At300KtheSchottkybarrierheight,SBH,andtheidealityfactor,,areextractedforatotalofninedifferentsamplesusingthermionicemissiontheory[ 1 3 ](Eq. 1 and 1 )andfoundtoberespectivelyintheranges0.82V>1).Thisimpliesthatthetotalmeasuredcurrentisgovernedbymanyothertransportprocessesasdiscussedinsubsection 1.3.4 .andextractionofSchottkybarrierheightatdifferentappliedmagneticeldsbecomesproblematic. 36

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2.2.3Capacitance-VoltageMeasurements Compleximpedancemeasurementsoverafrequencyrange20Hz-1MHzweremadeusinganAgilentHP4284capacitancebridge.Theoutputofthebridgecanbeinterpretedbyoneoftwodifferentmodelseachhavingtwounknowns:aresistanceRsinserieswithacapacitanceCs(seriesmodel)oraresistanceRpinparallelwithacapacitanceCp(parallelmodel).ThesimplestmodelforaSchottkydiodehoweverinvolvesatleastthreeunknowns:Rinserieswithatwo-componentcomplexcapacitanceCwhichcomprisesthecapacitanceC=RefCgofthedepletionregioninparallelwithalosstermthatrepresentsdctransport(tunneling)andaclossduetochangesinpolarization.ItisstraightforwardtoshowthatCisboundedbyCsandCp(Cs>C>Cp)andthatifCsisfoundtobeclosetoCp,thenRissmallandcanbeignored[ 11 ].ForthemeasurementsreportedherewendatmostCs=1.07Cp,thusimplyingthenarrowconstraint1.07Cp>C>Cp,andhencetheassurancethatthemeasuredCpoftheparallelmodelaccuratelyrepresentsthedepletioncapacitanceCdep.SinceRisnegligible,thenanyelddependenceofRisalsonegligible,andwecanconcludethatthemeasuredMCisassociatedwiththeSchottkydepletioncapacitanceratherthanmagnetoresistanceinthecontactsorbulkmasqueradingasmagnetocapacitance[ 25 ].Attemperatureslowerthanthe20K,arapidincreaseinRmanifestsitselfasalargedifferenceinCpandCs(Cs>>Cp),andCpisnolongeranaccuratemeasureofthedepletioncapacitance[ 11 ] 2.2.4InternalPhotoemissionTechnique AnotherdirectmeasureofSBHisinternalphotoemissiontechnique.Inthismethod,thesampleismountedinacryostatandilluminatedbyacmodulatedlightemergingfromanopticalber[ 26 ].Theinternalphotocurrentthroughthesampleissynchronouslydemodulatedandthesquarerootofthephotoyielddenedasthephotocurrentperincidentphoton,isplottedagainstphotonenergy.Alinearextrapolationtozerogivesthe 37

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minimumenergy(Eq. 1 ),SBH,necessarytoexciteelectronsfromtheFermienergyofthemetaloverthebarrier.Theresultswillbediscussedlaterinthischapter. 2.3ExperimentalResults 2.3.1ObservationofMagnetocapacitanceandMagneticFieldDependenceofC)]TJ /F3 11.955 Tf 11.95 0 Td[(VCurves InFig. 2-2 weshowasourmainresulttheeffectofmagneticeldoncapacitance.ThemagnitudeoftherelativechangeincapacitanceCdep=Cdepmeasuredatfrequencyf=1MHzandoveraeldrangeof0-70kOeisobservedtoincreaseasthetemperatureTisloweredfrom300Kto20K.Nearfreeze-outtemperatures[ 27 ]theMCgrowsrapidly,reaching-21%atH=70kOeandT=20K.Tounderstandthesedata,wegeneralizetheMott-Schottky(M-S)picture1[ 2 ]byexplicitlyincludingtheindependentvariables,f,TandH,andre-writingEq. 1 as, 1 Cdep(f,H,T)2=2(Vbi(f,H,T)+VR) esND(f,H,T),(2) W(f,H,T)2=2s(Vbi(f,H,T)+VR) eND(f,H,T)1=2,(2) wheresisthedielectricconstantofthesemiconductor,VRisthemagnitudeoftheappliedreversebiasvoltage(metalelectrodeisnegative),andNd(f,T,H)isthedensityofionizedSiimpuritieswithinthedepletionwidthW(f,T,H).IntheM-SpictureatermequaltokBT,issubtractedfromVbiinthenumerator[ 1 ].HoweverthistermistypicallymuchsmallerthanthemeasuredVbiandoftenneglected[ 2 ]asitisinourcase,sinceourmeasuredvaluesofVbinear1eVassuretheinequalityVbi>>kBTatroomtemperatureandbelow.InagreementwithEq. 2 ,alineardependenceof1=C2depwithrespecttoVRisfoundatf=1MHzfordifferentH(Fig. 2-3 ,toppanel)andatH=0fordifferentf(Fig. 2-3 ,bottompanel).Foreachdatasettherearetwoextractedparameters:theslope,fromwhichNd(f,T,H)canbecalculated(Eq. 2 ),andtheinterceptVbi(f,T,H),thebuilt-inpotential.Atroomtemperaturealmostallthedonor 38

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electronsareexcitedintotheconductionbandleavingthedonoratomsfullyionizedwithadensityN0d(T=300K)Nd.However,temperatureandmagneticeldfreeze-outtakeplaceatlowertemperatures,andNd(f,T,H)becomesafunctionofHatxedTasshowninFig. 2-4 .TherelatedchangesofVbi(f,T,H)arealsoshowninthesamegure.WenotethatNd(f,T,H)andVbi(f,T,H)extractedfromthelinearplotsofFig. 2-3 canbeusedinEq. 2 tocalculatetheMC(squaresinFig.2forT=20K)andarefoundtobeingoodself-consistentagreementforallmeasuredf,TandH.Theremainderofthischapterwillfocusonelucidatingthemagnetodielectriccouplingthatgivesrisetothepronouncedf,TandHdependenceoftheextractedM-SparametersofEq. 2 andtheassociatedMCshowninFig. 2-2 2.3.2PhysicalProcessesintheDepletionWidth Theunderlyingphysicalprocessesarerevealedinthefrequency-dependentcapacitanceandlossplotsofFig. 2-5 .Therearetwoprominentlosspeakregions:therstlow-frequencyregionextendsoverthefrequencyrange100Hzto10kHzandthesecondhigh-frequencyregion,withmorepronouncedloss,extendsfrom10kHztogreaterthanthe1MHzlimitofourcapacitancebridge.WithdecreasingTand/orincreasingH,thelossyregionsmovetolowerfrequencyasshowninthesuccessivepanelsofFig. 2-5 .Inprincipleiftheelectricaleldisslowlyvaryinginthedepletionwidthregion,onemightexpecttoseeonlyonelosspeak.However,whenthereismorethanonedielectricrelaxationprocesscontributingtothemeasuredcapacitance,multiplelosspeakscenteredatdifferentfrequencies,eachadheringtoaDebyeresponse,canbeobservedprovidingthereissufcientresolution. WendthateachlosscurveiswelldescribedbytheimaginarypartoftheubiquitousCole-Coleexpression[ 28 ]forthegeneralizeddielectricconstant, =1+0)]TJ /F7 11.955 Tf 11.95 0 Td[(1 1+(i!)(1)]TJ /F13 7.97 Tf 6.58 0 Td[(),(2) 39

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where1and0arethedielectricconstantsinthehighandlowfrequencylimits,isaconstantsmallerthanone,isarelaxationtimeand!theangularfrequency.Theanalysisofthelow-frequencypeaksisstraightforward,sincethefrequencyrangeisbroadenoughtoincludethefullpeak,therebyenablingustodetermineinastraightforwardmannerthepeakfrequencyfp=1=andacorrespondingrelaxationtimeatwhichthelossforaparticularTandHpeaksatamaximum.ForconstantHtherelaxationrate)]TJ /F8 7.97 Tf 6.58 0 Td[(1adherestoathermally-activatedArrheniusdependence,)]TJ /F8 7.97 Tf 6.59 0 Td[(1=)]TJ /F8 7.97 Tf 6.59 0 Td[(10exp()]TJ /F3 11.955 Tf 9.29 0 Td[(Ea=kBT),whereEaisanactivationenergyand)]TJ /F8 7.97 Tf 6.58 0 Td[(10aprefactor.Thesemilogarithmicplotof)]TJ /F8 7.97 Tf 6.58 0 Td[(1versus1/Tforthelow-frequencypeakshownintheinsetofFig. 2-6 (H=70kOe)manifeststypicalactivatedresponse.Theeld-dependentactivationenergiesEa(H)areextractedfromtheslopesoftheselinesandplottedinthemainpanelofFig. 2-6 againsteld(redsquares)forthelow-frequencylosspeaks. Sincetheamplitudeandshapeofthelow-frequencylosspeaksremainconstantandareshiftedonlylaterallywithtemperature/eld(Fig. 2-5 ),wecanextractsimilaractivationenergiesforthehigh-frequencypeaksbymonitoringthetemperaturedependenceofanarbitrarypoint(halfamplitude)ratherthanthepeak.Bymakingthereasonableassumptionthatthehigh-frequencypeaksalsohaveaninvariantamplitudeandshape,weextracttheactivationenergiesshownasbluecirclesinFig. 2-6 .Theerrorbarsonthesedataarelargerbecausethehighfrequencyportionsofthesepeaksaregreaterthan1MHz,andthereisconsequentlygreateruncertaintyintheparametersoftheCole-Colets. ThelosspeaksofFig. 2-5 correspondtotworelaxationprocesses,eachhavingsimilaractivationenergieswhichincreasewithmagneticeld(Fig. 2-6 ).AtH=0,Ea=6.050.20meVand5.730.13meVforthelowandhighpeaksrespectively,veryclosetothereportedvaluesof5.8meV[ 2 21 ]forSiimpuritiesinGaAs.WethereforeattributethetwoobservedlosspeakstoionizationfromEshtoEcofthedopantvalenceelectronsandcapturefromEcbacktoEsh.Theseparaterelaxationfrequenciesimply 40

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thattherateforionization,sh!c,isdifferentthantherateforcapture,c!sh.Usingdetailedbalance[ 29 ],sh!cnsh=c!shnc,wherenshandncrepresentrespectivelythedensityofcarriersinEshandEc,wecaninferc!sh>sh!c,sincensh>ncnearfreezeoutwheretheMCisdominant.Thisargumentallowsustoidentifythelowfrequencylosspeakwithionizationsh!candthehighfrequencypeakwithcapture,c!sh.Intrabandtransitionssuchashoppingarenotseenbecauseourmeasurementtemperaturesaretoohigh. IntheGaAshost,theBohrradiiofthehydrogen-likedonorelectronsarerenormalizedupwardsbythesmalleffectivemass,mGaAs=0.065me,andthelargerelativepermittivity,GaAs=13.5.Theresultingmagneticfreeze-outbringselectronsclosertothedonoratoms,thusincreasingtheCoulombenergyandEa.Therenormalizationbythehostlatticesharplyreducestheeldswellbelowthelevelsrequiredtoseeanobservableeffectforhydrogenatomsinvacuum.OurobservedchangeinEawithHisingoodqualitativeagreementinfunctionalform[ 20 ]andmagnitude[ 21 ]withpreviousexperimentsonSi-dopedGaAs. TheaboveinterpretationsuggeststhatatlowTelectronscanbefrozenoutfromtheconductionbandEctotheimpuritybanddonorsasHincreases.ThiscaptureprocessexplainstheH-induceddecreaseinNd(f,T,H)atxedfandTshowninthelowerpanelofFig. 2-4 .ItdoesnotexplainhowevertheH-dependenceofVbi(f,T,H).Usually,VbiextractedfromaM-SanalysisisusedtocalculateSBHfromtherelation[ 2 ],SBH=Vbi+(EcEF)=e.AnincreaseinVbicorrespondsbyEq. 2 toanincreaseinWandacorrespondingdecreaseinCdep.SinceEc)]TJ /F3 11.955 Tf 9.59 0 Td[(EF,whichiscalculatedtobe10meV,isasmallcorrectionwithnegligibleHdependence,themeasuredshiftinVbiof300meVfora7TchangeinH(Fig. 2-3 toppanel)impliesthatthereisacomparableshiftinSBH.SuchadependenceofSBHonHextractedfromCmeasurementsisunphysicalsince,asshownbytheschematicintheinsetofFig. 2-2 ,thecapacitance,Cbond,arisingfrombondpolarizationandtheassociateddipolelayergivingrisetoSBHatthe 41

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metal-semiconductorinterfaceisinserieswiththemuchsmallerCdepandhencecanbeignored.TheexpectedHindependencewascheckedusingIPEmeasurements[ 5 26 ]onsimilarsamplesatvarioustemperaturesandeldsupto70kOe.TheinterceptsofthelinearlyextrapolatedphotocurrentyieldontheabscissaoftheinsettothetoppanelofFig. 2-7 showasmallTdependencebutnoHdependence.ThustheH-inducedVbishifthasanotheroriginandtheM-Sequationsmustbemodied. 2.3.3EffectofMagneticFieldontheCurrent-VoltageCharacteristics Theaboveconclusionalsoappliestothemagneticelddependenceoftheforward-biasedthresholdobservedintheI)]TJ /F3 11.955 Tf 12.02 0 Td[(Vcharacteristics.InFig. 2-1 bweshowtheI)]TJ /F3 11.955 Tf 12.31 0 Td[(Vcharacteristicsatthefourindicatedtemperaturesfortwovaluesofeld,H=0Oe(solidsymbols)andH=70kOe(opensymbols).Wenotethatwhilethemagneticeldhasnegligibleeffectontheforwardbiasthresholdathightemperatures(300K),thereisasystematicincreaseintheeld-dependentincrementoftheforwardbiasthresholdasTisloweredto20K.At20Ktheidealityfactorissignicantlylargerthanunity,thusindicatingthataccurateestimatesofSBHcannotbeobtainedduetothepresenceofadditionalprocessessuchasgeneration-recombination,quantumtunnelingandthermionic-eldemission(subsection 1.3.4 ).Theobservedeld-inducedchangesinthelowtemperatureforwardbiasedthresholdsarethusmorelikelyattributedtocorrectionstoSBHderivedfromimage-loweringandthermaleldemission.TheSchottkybarrierloweringduetotheimageforces(section 1.3.4 )isgivenby, B=s e3Vbi(f,T,H)ND(f,T,H) 823s,(2) andsimilarlythechangeintheSchottkybarrierheightduetothethermioniceldemissionis, B=9 4E00(f,H,T)2Vbi(f,H,T)1=3,(2) whereE00is 42

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E00=e~ 2ND(f,H,T) sm,(2) ThesetwoprocessesbecomeimportantattemperaturesmuchlowerthantheapparentbarrierheightandgiveacorrectionthatdecreaseswhenND(f,H,T)decreases[ 1 30 ].ThuswithincreasingH,theconcomitantdecreaseinND(f,H,T)leadstoanincreaseintheeffectiveSBHandtheforwardbiasthresholdasseeninFig. 2-1 b.However,ourcalculationsshowthatthesecorrectionsareonlyresponsiblefor10-20meVincreaseinbarrierheightandthusdonotexplainthelargeshiftinbuilt-inpotentialseeninFig. 2-3 .WeconcludethattheinterpretationoflowtemperatureI)]TJ /F3 11.955 Tf 12.42 0 Td[(Vcurvesusingtraditionalthermionicemissiontheory,whichremainsanopenproblemintheliterature[ 1 ],isunreliable.Forthesereasonswefocusonacimpedancemeasurements,whichidentifythefrequencymagneticelddependentprocessesoccurringwithinthedepletionregion,andtheinternalphotoemission(IPE)measurements,whichdirectlydetermineSBH. 2.4ModicationoftheAbruptJunctionApproximation(AJA) TheM-SrelationsforCdepareusuallyderivedusingtheabruptjunctionapproximation(AJA),phenomenologicaldescription,whichassumesaconstantdensityNdofionizedimpuritieswithinthedepletionregioninwhichNd(f,T,H)=N0d(T)isconstantforallxwithinthedepletionwidth(0=x=W)andzeroelsewhere.AlthoughtheAJAisoverlysimplistic,ithasthewell-knownadvantagethatwhencombinedwithPoissonsequationtherelationshipbetween1=C2depandreversebiasvoltageVRislinear.ThislinearityoftheMott-Schottky(M-S)plotsisseeninmanyexperiments[ 1 ]includingours(Fig. 2-3 ).ThefailureoftheAJAtoincludefrequency(andeld)dependenceisanobviousdeciency.Thus,ifCdepisfrequency(magneticeld)dependentasitisinourexperiment(Fig. 2-3 ),theextractedslopesandinterceptsarebynecessityalsofrequency(magneticeld)dependent(Fig. 2-3 )andcannotbesimplyrelatedtothehightemperature(fullyionized)valuesofthebuilt-inpotentialV0biandionizedimpuritydensity 43

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N0d.Oursolutiontothisdeciency,adeciencywhichhasbeenrecognizedinpreviouswork[ 10 31 32 ]istheintroductionofamodicationoftheAJAasdiscussedbelow.AsTislowered,electronsfromtheconductionbandarecapturedandN0d(T)decreases.ToincorporatetheeffectsoffandH,wemodifytheAJAwiththeexpression, Nd(x,f,T,H)=N0d+Ncap(f,T,H)[(y)]TJ /F3 11.955 Tf 11.95 0 Td[(x)exp()]TJ /F3 11.955 Tf 9.3 0 Td[(x=L)+]+Nion(f,T,H)exp()]TJ /F3 11.955 Tf 9.29 0 Td[(x=W),(2) whereNcapandNionarefrequencydependentparametersrepresentingrespectivelytheadditionalcharge(andhencepolarization)ofthehigh-frequencycaptureandlow-frequencyionizationprocesses,istheunitstepfunction,Lisacharacteristiclengthandy,whichobeystheconstraint0
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frequencies,temperaturesandeldsispreserved.Theunderstandinggainedfromthisreformulationbecomesevidentintheredenitionoftheextractedslopesandintercepts Nd(f,T,H)=)]TJ /F3 11.955 Tf 5.48 -9.69 Td[(N0d(T)+Ncap(f,T,H)+2Nion(f,T,H),(2) Vbi(f,T,H)=)]TJ /F3 11.955 Tf 5.48 -9.69 Td[(V0bi(T))]TJ /F3 11.955 Tf 11.96 0 Td[(eNcap(f,T,H)L2(exp()]TJ /F3 11.955 Tf 9.3 0 Td[(y=L)(1+y=L))=s+VR,(2) InthehighTlimitwhereallimpuritiesareionized,Ncap!0andNion!0,Eq. 2 reducestotheconventionalfandH-independentM-Srelation,1=C2dep(T)=2)]TJ /F3 11.955 Tf 5.48 -9.68 Td[(V0bi(T)+VR=esN0D(T)andtheSchottky-Mottrelationispreserved.WithdecreasingT,V0bi(T)(andhenceSBH)increasesduetotemperaturevariationsofthebandgap[ 9 ],andthedecreaseinN0d(T)(thermalfreezeout)iscompensatedbyincreasesinNcapandNion,reectingthedominanceoff-andH-dependentprocesses. 2.5Discussion AnintuitivephysicalunderstandingoftheaboveequationsderivesfromthefactthatNdisexponentiallydependentontheratio-Ea(H)=kBT.ThusasTdecreases,orHincreaseswithacorrespondingincreaseinEa(Fig. 2-6 ),N0ddecreasesfromitshigh-temperature(100%ionization)value,andthereisaconcomitantincreaseinthenumberoftransitionsbetweentheshallowEshandconductionEcbands(arrowsintheFig. 2-3 schematic).AtxedfandHtheparametersNcapandNion,whichasmodicationstotheAJArepresenttheionizeddonorsparticipatingintheinterbandtransitions,thusincreasewithdecreasingtemperature.However,therelativeincreaseofthequantityinEq. 2 withdecreasingtemperatureisnotsufcienttocompensateforthedecreaseinN0d,therebygivingrisetoanetdecreaseinNd(f,T,H)consistentwiththedecreasedcapacitancewithdecreasingtemperature.AtxedT,theinterbandtransitionsassociatedwithNcapandNionandshowninFig. 2-5 decreasewithincreasingH(eldfreezeout)andincreasingf(polarizationcannotfollowrapidchanges),thus 45

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accountingfortheobserveddecreaseinNddescribedbyEq. 2 andshowninFig. 2-4 .Asfrequencyincreases,theresponseofthelow-frequencyionizationprocessesdiminishes.However,theresponseofthehigherfrequencycaptureprocesses,whichhavethesameactivationenergyandarethuscoupledtoionization,doesnotdiminishuntilthefrequencycomesintothishigherfrequencyrange.ThelargestdecreasesinNdandcorrespondingdecreasesinpolarization(Fig. 2-5 )thusoccurinseparatefrequencyrangeswheretheionizationandcaptureprocessesdominate. WeemphasizethatEqs. 2 and 2 representausefulphenomenologicalgeneralizationoftheoriginalM-Srelationswhichinturnarebasedontheover-simpliedphenomenologicalAJA.Importantly,forthepurposesofthisstudy,weseefromEqs. 2 and 2 thattheobservedVbidependenceonHisafunctionoftheunknownparametery,whichinthelimit,y>>L,describescaptureofcarriersincloseproximitytothemetal-semiconductorinterface(x=0)whereelectronsfromthemetalarereadilyavailableandintheoppositelimit,y<
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measurementsdirectlymeasureSBHinthedclimit,itisthislimitwherebothrelaxationprocessesoccurringwithinthedepletionwidthhavetobeincluded.WehaveshownthattheAJAapproximationaloneisnotsufcientinpredictingSBHandonehastotakeintoaccountthefrequencyandeld-dependentcorrectiontermsassociatedwiththecapture/ionizationprocessesbetweentheimpurityandvalencebands.Asfrequencyincreases,Vbialsoincreasestosignicantlyhighervaluesduetothedecreaseinthecorrectionalterms,NcapandNion,toVbi(T). Atthehighestfrequencies,beyondthe1MHzupperboundofourmeasurements,NcapandNionbothapproachzero,andthewell-knownAJAformoftheMott-Schottkyrelation(Eq. 2 )ensues.InthislimitVbiisnotaphysicallymeaningfulmeasureofSBH,sinceasshowninthischaptertheoverlysimplisticAJAdoesnottakeintoaccountthefrequencyandelddependentprocessesrevealedsoexplicitlyinFigs. 2-3 and 2-5 .Thisunderstandingisrelevantforhigherfrequencyapplications. 2.6Summary Insummary,inthischapterwehaveshownthatmagneticfreezeout[ 17 ]ofshallowbandcarriersisresponsibleforsignicantchangesinpolarizationwithinthedepletionwidthofconventionalAu/GaAsSiSchottkybarriers.MagneticfreezeoutisessentiallyabulkeffectinwhichthebindingenergiesofalltheSiimpurityatomsintheGaAshostaresimultaneouslyincreased.Accordingly,bulk-sensitiveoptical[ 18 33 ]andHalleffectmeasurements[ 20 21 ]clearlyrevealtheeffectsofmagneticfreezeout.Inthischapter,wehavedemonstratedaninterfaceeffectinwhichthesameeld-inducedchangesinthebindingenergyoftheSidonorsredenesthechargedistributionandtheassociatedelectriceld,andhencethepolarization(capacitance),inthedepletionwidthofaSchottkybarrier.Themagnetodielectriccouplingisaninterfaceeffectthatarisesfromthecorrelationofmagneticfreezeoutwithinterfacialpolarizationandisthusresponsiblefortheobservedlargenegativemagnetocapacitanceinasystemwhichdoesnothaveanymagneticimpurities.OurunequivocaldeterminationofanH-independentSchottky 47

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barrierheighttogetherwithouridenticationofthermally-activatedinterbandionizationandcaptureprocessesjustiesourmodicationoftheAJAtopreservethelinearityofthe1=C2depvsVRplots(asexperimentallyobserved)andatthesametimeimposesadependenceofNdandVbionf,TandH.Finally,theunderlyingmagnetodielectriccouplingnotonlyallowsanewexperimentaltechniqueforthetuningofthedopantcarrierdensityatthesameinterfacebymagneticeld,butshouldalsobeimportantforengineeringthehighfrequency(microwave)andmagneticeldresponseofdiodesandunderstandingthebehaviorofrelatedinterfacialstructuresincorporatingDMSandspin-polarizedmetals. 48

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Figure2-1. Current-voltagecharacteristicsshowatemperatureandelddependentforwardbiasthreshold.Thetoppanelshowstherectifying(diode)characteristicsonasemilogarithmiccurrent-voltagescaleforforward(+)andreverse(-)biasvoltagesat300K(redcircles)and20K(bluesquares).Thebottompanelshowsonalinearcurrent-voltagescaletheforwardbiasonsetsofconductionattheindicatedtemperaturesforH=0(closedsymbols)andH=70kOe(opensymbols) 49

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Figure2-2. CapacitanceofaAu/GaAs:SiSchottkyjunctiondecreaseswithincreasingappliedmagneticeldH.TherelativechangeincapacitanceCdep=Cdepbecomesincreasinglymorenegativewithincreasingeld.Thesolidcurvesrepresentdatatakenatthedecreasingtemperatures(toptobottom)indicatedinthelegend.Thesolidorangesquaresassociatedwiththe20KisothermarecalculatedusingM-SrelationwiththeM-Sparametersextractedfrom1=C2versusvoltageplots.Inset,Schematicofbandbendingwithparametersdenedinthetext.Captureprocesses(redarrow)tendtodominateneartheinterfacewhereasionizationprocessesaredistributedoverthedepletionwidthW.Thelargecapacitanceassociatedwithahighdensityofpolarizedbondsattheinterfaceisinserieswiththemuchsmallerdepletioncapacitance. 50

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Figure2-3. Linearityof1=C2vsVRplotsenabledeterminationofM-Sparameters.Dataat20Kareshownat1MHzfortheindicatedeldsH(toppanel)andatH=0fortheindicatedfrequenciesf(bottompanel).Theverticalarrowsmarkselectedextrapolatedinterceptswiththeabscissacorrespondingtothebuilt-inpotentialVbi(f,H)at20K. 51

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Figure2-4. ThefrequencydependenceofVbi(righthandaxis)forH=0(70kOe)forsolid(open)trianglesandthefrequencydependenceofND(lefthandaxis,seetext)forH=0(70kOe)forsolid(open)squares. 52

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Figure2-5. Temperatureandelddependentfrequencydispersionofthecapacitancerevealstwoseparatelossprocesses.Inthethreepanelsthefrequency-dependentcapacitance(lefthandaxis,topcurves)andloss(righthandaxis,bottomcurves)areshownasafunctionoffrequencyforeachofthethreeindicatedtemperatures.Eachgroupofcurvescontainsdataforthevedifferenteldsindicatedinthelegendofthemiddlepanel.Forxedeldsthelosspeaksshifttolowerfrequencyasthetemperatureisreduced.Thehorizontalarrowineachpanelmarkstheisothermalshifttolowerfrequencyofthelow-frequencylosspeak(ionization)astheeldisincreasedfrom0to70kOe. 53

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Figure2-6. ActivatedbindingenergyEaofSiimpuritydonatedelectronsincreaseswithincreasingeld.ThedependenceofEaonHisshownforboththelowfrequency(redsquares,ionization)andhighfrequency(bluecircles,capture)losspeaks.Eachpointisdeterminedbyxingtheeldandplottingthefrequenciesofthelosspeaksversus1=Tonasemilogarithmicplot.Theslopesoftheresultinglinearplots(insetforH=70kOe)determinetheH-dependentbindingenergies. 54

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Figure2-7. IPEdatainwhichH-independentextrapolations(dottedlines)totheabscissaattheindicatedtemperaturesimplythatthereisnodependenceoftheSchottkybarrierheightonHupto70kOe. 55

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CHAPTER3MULTI-LAYER-GRAPHENE(MLG)BASEDSCHOTTKYDIODESFORMEDONSI,GAAS,4H-SICANDGANSUBSTRATES 3.1Introduction TheSchottkybarriersformedonvarioussemiconductorsareinterestingduetotheirpotentialtechnologicalapplicationashighelectronmobilitytransistors(HEMTs)andmetal-semiconductoreldeffecttransistors(MESFETs).InMESFETs,thequalityandefciencyoftheSchottkydiodesplayamajorrole.Whenreverseorforwardbiasisappliedacrosstheinterface,Schottkybarrierinterface,thedepletionwidthisdriventoeitherdepletionoraccumulationandthe'on'and'off'stateisachieved.Thedepletioncapacitanceattheinterfaceismuchsmallercomparingtothatofp)]TJ /F3 11.955 Tf 12.87 0 Td[(njunctionsandSchottkydiodesyieldfasterresponseandaretypicallyusedinradiofrequency(RF)applications.Thesameeffectwithslowerresponsescanbeachievedinmetal-oxide-semiconductoreldeffecttransistor(MOSFET)geometries.TheMOSFETdevicegeometryisspecicallyconvenientforsemiconductorssuchasSiwherenaturaloxide(SiOx)existsandthe'on'and'off'stateisachievedbyeldeffectgatingacrossthemetal-oxide-semiconductor(MOS)anddepletingoraccumulatingthesemiconductor.However,theMOSFETgeometrybecomesproblematicformostsemiconductorswherethereisnoestablishedoxideexists(suchasGaAs,SiCandGaN).Insuchcases,SchottkydiodesandtheMESFETgeometryispreferred. Moreover,Metal-semiconductorcontactsareubiquitousinsemiconductortechnologynotonlybecausetheyareunavoidable,butalsobecausetheassociated(Schottky)barrierstoelectronictransportacrossthemetal-semiconductorinterfacescanbetunedbydifferentchoiceofmaterialsandprocessingtechniques[ 1 ].ThecharacteristicofaSchottkybarrierisitsrectifyingcharacteristic;theSchottkybarrieressentiallyactslikeadiodewithlargecurrentsowingforforwardbiasandsignicantlysmallercurrentsowingforreversebias[ 2 ]asdisplayedforAu/GaAsSchottkyjunctionsinFig. 2-1 andinChapter 2 .Iflowresistanceandohmic(linear)I)]TJ /F3 11.955 Tf 11.99 0 Td[(Vcharacteristicsare 56

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desired(section 1.4 ),thenmaterialsand/orprocessingtechniquessuchasrapidthermalannealing,arechosentoassurethattheSchottkybarrierheight(SBH)Bissmallcomparedtoroomtemperature(B<
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byselectivelydopingthecarbonbasedmaterial.Theseadvantagesofgraphiteandgraphenetogetherwiththeirthermalstabilitymakegraphite-graphene/semiconductorjunctionsparticularlyinteresting. Thischapteraddressestheuseofmulti-layer-graphene(MLG)exfoliatedfromhighlyorientedpyrolyticgraphite(HOPG)andnaturalgraphiteasthesemimetalinsemimetal/semiconductorSchottkybarriers.Wedemonstrateunexpectedlyhigh-qualityrectifyingcharacteristicsonfourdifferentn-typesemiconductorseachofwhichisuniquelysuitedtospecicapplications:namelySi,withitsrobustoxide,toeldgatedtransistors,GaAs,withitsdirectbandgap,tospintronicandopticalapplicationsandSiCandGaN,withitshighthermalconductivityandbreakdownstrength,tohighpower/frequencydevices.Advantageouslythemulti-layer-graphenecontactarerobustlyimpervioustodiffusionofimpurityatoms[ 36 ]andcanbeplacedonthesemiconductoratroomtemperature.TherelativelyweakbondingassociatedwiththeVanderWaalsinteraction,causesminimaldisturbanceatthesemiconductorsurface.SincetheSchottkybarrierheight,B,isrelatedtoaninterfacialdipolelayerassociatedwithbondpolarization[ 1 ],weinferthatbarrierpropertiesaredeterminedprimarilybytheoutermostlayerofthemulti-layer-graphenecontactwhichisasinglelayergraphene(SLG)sheet.Accordingly,ourresultsanticipatesimilarphenomenologyusingtwo-dimensional(2D)grapheneratherthanmulti-layer-graphene.OtherexamplesdemonstratingSLG-likepropertiesingraphiteincludeARPESevidencefortheprecursorinuenceofK-pointDiracfermions[ 37 ]andapronouncedtemperature-dependentupturninthetemperaturerange,300K
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next-to-nearestneighborcouplingscanbeignoredconrmsthispicturethatatthesehightemperaturesgraphitecanbedescribedasastackofgraphenebilayers[ 38 ]. 3.2ExperimentalDetails Wehaveusedcommerciallyavailablen-typeSiandGaAswith11015cm)]TJ /F8 7.97 Tf 6.59 0 Td[(3phosphorus(P)and31016cm)]TJ /F8 7.97 Tf 6.58 0 Td[(3silicon(Si)dopingdensitiesrespectively.The4H-SiCwafersarelayered,comprisinga5m-thicklayerofdopedepilayer(11016cm)]TJ /F8 7.97 Tf 6.59 0 Td[(3)depositedontoaninsulating4H-SiCsubstrate.GaNsamplesweregrownonsapphiresubstratesinmolecularbeamepitaxysystemandweredopedbySidopingdensitiesof(11016cm)]TJ /F8 7.97 Tf 6.59 0 Td[(3).TheSi:P(GaAs:Si)substratesarethoroughlycleanedtoremoveanynativeoxideand/orcontaminants. OhmiccontactsaremadeontheSi:P,GaAs:Si,4H-SiC:NandGaN:Sisubstratesusingexistingohmiccontactrecipes[ 3 39 41 ].TheseohmicrecipesassurelowresistancelinearI-V'soverthetemperaturerangesmeasured.TheI-VandC-Vmeasurementsareperformedrespectivelyusingdccurrent-source/voltage-measureinstruments(Keithley220/182)andanAgilent4284Acapacitancebridge.TheSchottkybarrierheightacrossthemulti-layer-graphene/semiconductorjunctionsismeasuredbythemethodsdiscussedinsubsections 1.3.5.1 and 1.3.5.2 / Themulti-layer-graphenecontactsaredepositedtothesemiconductorsusingthreerelatedtechniques.Intherstmethod,multi-layer-graphenecontactsaremechanicallyexfoliatedfromnaturalgraphiteorHOPGsamplesusingthermalreleasetape.Inthismethod,NittoDenkoRevalphathermalreleasetape(PartNumber3193-MS)wasplacedongraphitewith3N/mm2pressurefor5minutesinachamberkeptunder10)]TJ /F8 7.97 Tf 6.59 0 Td[(3torr.Pressureappliedonthethermalreleasetape/graphitestackingallowsustoincreasethebondingandeliminatestheairpocketsatthetape-graphiteinterface.Theefciencyofthethermalreleasetapeincreasesifthepressureisappliedundermediocrevacuumconditions.Afterthisstep,thethermalreleasetapeisexfoliatedfromgraphite,leavingmulti-layer-graphene/thermalreleasetapestacking.Desired 59

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multi-layer-graphenethicknesscanbeachievedbyconsecutivethermalreleasetapeexfoliation.Inthelaststep,multi-layer-graphene/thermalreleasetapestackingplacedontopofvarioussemiconductorsbyapplyingsimilarpressuresunderthevacuum.Semiconductor/multi-layer-graphene/thermalreleasetapestackingisannealedto125C,atthistemperaturethermalreleasetapelosesitsadhesiontomulti-layer-graphenecontactdrastically,leavingmulti-layer-graphenedepositedonsemiconductorsubstrate.Thismethodcanbetailoredforspeciccontactsizes,thicknesses.Inthesecondmethod(cleavagetechnique),eitherHOPGpowder/akesarecollectedbycutting0.5FWHMbulkHOPGusingadiamondimpregranatedwireandallowingtheakestofallontothesemiconductorsubstrateorbymechanicalexfoliationmethod[ 42 ].CleavedHOPGakesmadeacontacttosemiconductorsurfacebyVanderWaalsadherenceandoccasionally,relativelylargearea(0.5mm2multi-layer-grapheneakesattenoutwithstrongadherencetothesubstrateduetoVanderWaalsattraction.Inthelastmethod(HOPGpaintmethod),graphitepowder/akesaresonicatedinresidue-free2-butoxyethylacetateandoctylacetateandthepaintedcontactsallowedtoairdry.Allofthesesoft-landingtechniquesgivesimilarresultswhentheappliedcurrentsarenormalizedwithrespecttocontactarea.Physicalcharacteristicsmeasuredatthemulti-layer-graphene/semiconductorjunctionsarealsotestedbyusingarelativelylarge(1mm2)HOPGorpristinenaturalgraphitepieceandgentlypressingontothesubstrate(springloadedgraphitemethod). 3.3FormationofSchottkyDiodesattheMulti-Layer-Graphene/SiInterface Fig. 3-1 showsthetypicalmeasuredcurrentdensityvs.voltage(J-V)room-temperaturecharacteristicsofHOPGpaintandmulti-layer-graphenecontactsonn-typeSisubstratesplacedbythemethodsdiscussedintheprevioussection.Thesedatarepresentasubsetofmorethan10differentsamples,allgivingsimilarresultsindependentofthemethodofapplicationofthemulti-layer-grapheneelectrode.AsseenfromFig. 3-1 ,multi-layer-graphenebasedjunctionsshowgoodrecticationat 60

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roomtemperature.Forallofthejunctionstherecticationispreserveddownto20K,belowwhichthequalityoftheohmiccontactsbecomesproblematic. Whenelectrontransportacrossthemetal-semiconductorinterfaceisdominatedbythermionicemission,thesemilogarithmicJ-VcurvesusuallydisplayalinearportionintheforwardbiasregionfromwhichreliableestimatesofthebarrierheightBandtheidealityconstant,,canbeextracted.TheextractionofthoseparametersisbasedontheRichardsonequationasdiscussedinsubsection 1.3.5.1 I=Is(T)[exp(qV=kBT))]TJ /F4 11.955 Tf 11.96 0 Td[(1],(3) whereIs=AAT2exp()]TJ /F3 11.955 Tf 9.29 0 Td[(qB=kBT)isthesaturationcurrent,qBistheSBH,AisRichardsonconstant,Tistheabsolutetemperature,andVisthevoltageacrosstheohmicandmulti-layer-graphenecontacts.AtroomtemperaturetheexponentialinEq. 3 dominatesatforwardvoltagesgreaterthan3kBT=q0.1V.AsshowninFig 3-1 b,themulti-layer-graphene/Sijunctionsdisplayed2-3decadesoflinearityinthesemilogarithmicJ-Vcurve.LinearityinawidevoltagerangeimpliesthatthedominanttransportprocessisthermionicemissioninaccordwithEq. 3 .Atlowandthehighappliedvoltages,J)]TJ /F3 11.955 Tf 12.16 0 Td[(Vplotsstronglydeviatefromlinearity.Thedeviationfromlinearitycanbeattributedtotheexistencenon-idealeffectsdiscussedinsection 1.3.4 suchassuchasspace-chargelimitedemissionatlowvoltagesandseriesresistanceeffectsathighervoltages. ExtractionofanaccuratevalueforBfromEq. 3 requirestheelectricallyactiveareaA.However,randomlydistributedmulti-layer-graphenepieces/akesmakecontactatsomeportionsofthesemiconductingsubstratewhiletheyarenotinphysicalcontactwiththeotherportions.Therefore,thecontactareadeterminedunderthemicroscopedoesnotnecessarilycorrespondtotheeffectiveactiveareaandtheelectricalactivearea,A,remainsunknown.WhensemilogarithmicisothermalI-Vcurvesareplotted,ratherthantheJ-VcurvesshowninFig. 3-1 ,extrapolationfromthelinearregionsto 61

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V=0toallowsonetodeterminethesaturationcurrentvaluesatspecictemperature(Is(T)).AnalysisisfacilitatedbywritingtheequationforIs(T)intheform(Eq. 1 ), ln(Is(T)=T2)=ln(AA))]TJ /F4 11.955 Tf 11.95 0 Td[((qSBH=kBT),(3) wheretheunknownsAandSBHnowappearinseparateterms. TypicalRichardsonactivationenergyplotsofln(Is(T)=T2)versusT)]TJ /F8 7.97 Tf 6.58 0 Td[(1formulti-layer-graphene/SijunctionsareshowninFig. 3-1 overthetemperaturerange250-330K.TheeffectiveSBHsforSiarecalculatedfromtheslopesaround0.40(1)eV(Table 3-1 )withidealityfactors()spanningfrom1.1to2.0forallsamples.ValuesofgreaterthanunityaregenerallyattributedtobiasdependentSBHs,generation-recombination,thermallyassistedtunneling,andimageforcelowering[ 1 ].ThelargevaluesoftheSchottkydiodesandtheireffectsonthemeasurementofbarrierheightfromJ)]TJ /F3 11.955 Tf 9.74 0 Td[(Vcharacteristicshavebeenaddressedintheliterature[ 43 ]andwillbeanalyzedinsection 3.7 AnothermethodtomeasuretheSchottkybarrierheightisknownasC)]TJ /F3 11.955 Tf 13.31 0 Td[(Vmeasurementtechniqueasdiscussedinsec. 1.3.5.2 .AsshowninFig. 3-3 ,capacitanceatthemetal-semiconductorjunction(depletionwidth)ismeasuredusingthecapacitancebridgeandcapacitance(1kHz)-voltage(C-V)measurementsplottedintheform1=C2vs.VR.Here,VRstandsforthereversebiasvoltage.TheobservedlinearityintheC)]TJ /F3 11.955 Tf 13.3 0 Td[(Vmeasurementssuggeststhatgapstatesareabsentandthatthesurfacedensityofstatesissmall.Linearextrapolation(dottedlines)totheinterceptwiththeabsiccsaidentiesthebuilt-inpotential,Vbi,whichisrelatedtoSBHviatheexpression,B=Vbi+(Ec)]TJ /F3 11.955 Tf 12.23 0 Td[(EF),whereEcistheconductionbandedgeandEFtheFermienergy.Afterthebuilt-inpotentialisextractedout,thedopantdensitiesofeachsemiconductorcanbecalculatedfromtheslopesasidentiedinEq. 1 .ThevaluesforSBHandNDextractedfromthelineardependencesshowninFig. 3-3 arelistedinTable 3-1 .TheextractedvaluesforNDareingoodagreementwithHalldata,whilethevaluesforSBH 62

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areobservedtobehigherthanthevaluesextractedfromI-Vmeasurements.Thesediscrepancieswillbediscussedinsection 3.7 3.4FormationofSchottkyDiodesattheMulti-Layer-Graphene/GaAsInterface GaAsisaIII/Vcompoundsemiconductorwiththebandgapvalueof1.43eV.Today,GaAssubstratesandwafersaremainlyusedinmanufacturingmicrowaveintegratedcircuitsandhighpowerdevices,solarcells,laserandinfraredlightemittingdiodes.Itshighermobility(8500cm2=(V.s))comparingtothatofSi(1500cm2=(V.s)),makesGaAsverysuitableforhighfrequencydeviceapplicationsworkingatfrequenciesmuchhigherthan500GHz.Moreover,GaAsdisplaysfourordersofmagnitudelessintrinsiccarrierdensity(Eq. 1 )comparingtoSi.Duetoitssmallintrinsiccarrierdensityatroomtemperature,itsintrinsiccarrierdensitydoesn'texceedtheextrinsiccarrierdensityandtheirelectricalpropertiesisstillcontrolledexternally(viadoping).ThispropertyallowsGaAsbaseddevicestoworkattemperaturesmuchhigherthantheoperatingtemperaturesofSibaseddevices.AnotheradvantageofGaAsoverSiisconsideredtobeitsbreakdownvoltagevalues.GaAsdisplaysbreakdownvoltagevaluesthataremuchhigherthanthatofSiandissuitableforradarsystems,satellitecommunicationsystems.Lastly,itsdirectbandgapallowsbetterlightemittingcharacteristicscomparedtoindirectbandgapSiwhichalsohaspooremissionpropertiesforsolarcellapplications. Ontheotherhand,theabsenceofstable,establisheddielectriconGaAsisoneofthemajordisadvantageovercheap,easytoprocesssiliconbasedtechnology.Insuchcase,thedielectrichastobegrownbyebeamorsputteringsystems(ratherthanthermallygrownSiOxonSiwafer)andthesemethodsinducesurfacestatesattheinterface.Therefore,thesemiconductorcannotbeeasilydrivenintothedepletionandaccumulationbyapplyinganelectricaleldacrossthemetal-oxide-semiconductorinterfaceandtheMOSFETdevicegeometrybecomesunpractical.However,theaccumulationanddepletionattheinterfacecanalsobeachievedbyapplyingbiasto 63

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theSchottkybarriersformedontheGaAssubstrateintheforwardandthereversedirectionsandforthatreasonSchottkybarrierjunctionsarecrucialforsemiconductorswithoutnaturaloxideandtheMOSFETdevicegeometrycanbereplacedbyMESFET(metal-semiconductoreldeffecttransistor). InFig. 3-4 ,currentdensityvs.voltage(J-V)characteristicsofHOPGpaintandmulti-layer-graphenecontactsformedonn-typeGaAssubstratesareplottedatroomtemperature.Reproducibilityoftheresultshasbeencheckedonmorethan20sampleswithvariousmulti-layer-graphenecontactdepositiontechniquesasmentionedabove.InFig. 3-4 ,multi-layer-graphenebasedjunctionsshowgoodrecticationatroomtemperaturewithbreakdownvoltagehigherthanthatofSi/multi-layer-graphenejunctions.Forallofthejunctionstherecticationispreserveddownto20K,belowwhichthequalityoftheohmiccontactsbecomesproblematic. AsshowninFig 3-4 b,themulti-layer-graphene/GaAsjunctionsdisplayed4-5decadesoflinearityinthesemilogarithmicJ)]TJ /F3 11.955 Tf 12.7 0 Td[(Vcurves.LinearityinawidevoltagerangeimpliesthatthedominanttransportprocessisthermionicemissionandisdescribedbyEq. 3 .Asdiscussedtheinprevioussection,inprincipletheSchottkybarrierheightcanbeextractedoutbyusingEq. 3 whentheactivecontactareaisknown.Followingsimilarargumentsandprocedure(Eq. 3 ),theeffectiveSBHsarecalculatedfromtheslopestobe0.50(1)eV(Table 3-1 )withidealityfactors()spanningfrom1.1to2.0forallsamplesinthe250K-330Krange. TheSBHvaluesextractedfromtheactivationenergyplotsagreeroughlywiththevaluesextractedoutfromthecapacitancemeasurementsasshowninFig. 3-6 .AsshowninFig. 3-6 ,thecapacitance-voltage(C-V)measurementsplottedintheform1=C2vs.VRatroomtemperatureand1KHzoperatingfrequenciesdislayedlinearityintheoverallmeasuredvoltagerange.Linearextrapolation(dottedlines)totheinterceptwiththeabsiccsaidentiesthebuilt-inpotential,VbiasdescribedinChapter 2 .TheextractedSchottkybarrierheightfromC)]TJ /F3 11.955 Tf 12.12 0 Td[(Vmeasurements,B=Vbi+(Ec)]TJ /F3 11.955 Tf 12.12 0 Td[(EF),are 64

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typicallyaround0.76eV(Table 3-1 ).ThediscrepanciesinbetweentheSchottkybarrierheightsdeterminedfromI)]TJ /F3 11.955 Tf 10.19 0 Td[(VandC)]TJ /F3 11.955 Tf 10.19 0 Td[(Vmeasurementswillbediscussedinsection 3.7 3.5FormationofSchottkyDiodesattheMulti-Layer-Graphene/4H-SiC Siliconcarbide(SiC)isaindirectband-gapsemiconductorwithbandbandvaluesrangingfrom2.3eVupto3.2eVdependingonthecrystalstructure.SiCisrarelyfoundinthenatureandthereforeismostlygrownunderlaboratoryconditions.SiCcrystalsexistinmorethan250crystalliteformsbutthemostcommonlyknownonesareinthecubicform(3C-SiC),hexagonalform(4H-SiCand6H-SiC)withbandgapvaluesof2.3eV,3.2eVand3.00eVrespectively.SiCcrystalsaregenerallyn-dopedeitherwithphosphorusornitrogen.WidebandgapSiCdisplaysverysmallintrinsiccarrierdensitiesintheorderof10)]TJ /F8 7.97 Tf 6.58 0 Td[(6cm)]TJ /F8 7.97 Tf 6.59 0 Td[(3whichisalmost14-16decadessmallercomparingtothatofSi.ThesmallintrinsiccarrierdensityinSiC,isespeciallyadvantageousattemperaturesexceeding500Kwherethesiliconintrinsiccarriersdensityexceedthetypicalextrinsiccarrierconcentration.Atthoseelevatedtempetures,theintrinsiccarrierdensityofthematerialincreases(Eq. 1 )rapidlywithtemperatureandmightexceedtheextrinsicdopingdensity(asinsilicon).Attemperatureswheretheintrinsiccarrierdensityishigherorcomparabletoextrinsicdopingdensity,thedevicecannolongeroperatecontrollablyandthusmaterialswithlowerintrinsiccarrierdensityaredesired.ThelowintrinsiccarrierdensityofSiCextendsthetemperaturerangewheretheintrinsiccarrierdensityissignicantlylessthantheextrinsiccarrierdensityandthismakesSiCdesiredmaterialforhightemperatureandhighpowerapplications. AnotheradvantageofSiCishighbreakdownvoltages.SiCpossessbreakdownvoltagethatissignicantlyhigherthanthebreakdownvoltageofSiandGaAs.Ontheotherhand,athigheldsSiCstartstobreakdownassociatedtoexistenceofstackingfaultsandformationofmicropipesinthecrystalandhenceandhaslessbreakdownvoltagecomparingtoGaN.Lastly,eventhoughit'simpressivelightemittingdiode(LED)history,indirectbandgapSiCemitsmorethandecadelessintenselightcomparingto 65

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thatofdirectbandgapGaNbutisconsideredtobemuchmoreefcientcomparingtotheSibasedLEDs.Overall,SiCstandssomewhereinbetweenSi,GaAsandGaNasfarasbreakdownvoltageandthepotentialLEDapplicationsgoes. Overall,SiCisusedforSchottkydiodes,MESFETdevices,ultrafastdevicecomponentsandhightemperaturebistableswitches,thyristors,buttheMOSFETgeometryisnotpreferredduetolackofnaturaloxideformedonSiCsubstrates. 3.5.1SchottkyBarrierCharacteristicsofMulti-Layer-Graphene/4H-SiCSchottkyDiodesfrom250Kupto330K InFig. 3-7 ,roomtemperaturecurrentdensityversusvoltage(J-V)characteristicsmeasuredofthemulti-layer-graphenecontactsonthen-type4H-SiCsubstratesaredisplayed.ThedatashowninFig. 3-7 hasbeenreproducedonmorethan10differentsamplesmadebydifferenttechniquessuchasspringloadedHOPG,HOPGpaintandmicromechanicalexfoliation.Schottkydiodesformedonthe4H-SiCshowsgoodforwardandreversebiascharacteristicswithsuperiorreversebreakdowncharacteristicsontheorderof80-100V(Fig. 3-7 ).ThemeasuredJ-Vcharacteristicsshowedhighrecticationdownto20-30Kwheretheohmiccontactsstarttofailand/orseriesresistancebecomestoohighandbeginstocompromisetherectifyingbehavior.Athighertemperatures,T>200K,themulti-layer-graphene/4H-SiCjunctionsdisplayed4-5decadesoflinearityinthesemilogarithmicJ-Vcurves(Fig 3-7 b). WhenthereisawiderangeoflinearityinthemeasuredJ)]TJ /F3 11.955 Tf 12.89 0 Td[(Vcharacteristics,theSchottkybarrierheightcanbeextractedoutbyusingEq. 3 ontheconditionthattheactivecontactareaisknown.Whentheactivecontactareaisnotpreciselyknown,theactivationenergyproceduregivenbyEq. 3 canbefollowed.However,activationplotsdidnotyieldalineardependenceandtheSchottkybarrierheightandtheidealityfactorswouldnotbedeterminedfromthisapproach.UndertheassumptionthatthecontactareaisknownforSiC,anduseoftheconventionalthermionicemissiontheory(Eqs. 1 and 1 )wendthattheSchottkybarrierheightformedatthemulti-layer66

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graphene/semiconductor(SiC)interfaceisaround1.14eVandtheidealityrangesfrom1.1to2.0inthe250K-330Krangeforallsamplesmeasuredinthischapter. EventhoughtheSBHextractedfromJ)]TJ /F3 11.955 Tf 12.89 0 Td[(Vmeasurementsisaround1.15eV,theSchottkybarrierheightextractedfromC)]TJ /F3 11.955 Tf 12.5 0 Td[(Vmeasurementsismeasuredaround1.80eV(Fig. 3-8 ).Thesevaluesdifferbyupto50%andandresultsanddiscrepancieswillbediscussedinsection 3.7 3.5.2SchottkyBarrierCharacteristicsofMulti-Layer-Graphene/4H-SiCSchottkyDiodesfrom300Kupto1100K SiCsubstratesaregenerallyusedforhightemperatureelectronicdevices,duetoitsthermalstability,highthermalconductivity,andthelowintrinsiccarrierconcentration,whichisalmost14decadeslessthatthaninsiliconandmoreovertheabsenceofconventionaldielectric(insulator)onSiCforcesonetotunethe'on'and'off'statebyinducingelectriceldatthemetal-semiconductorinterface.Therefore,hightemperaturephysicalpropertiesoftheSchottkybarriersformedonSiCandohmiccontactformationarescienticallyandtechnologicallyinteresting.CurrentresearchintheliteraturefocusesontheuseofdifferentmetalssuchasNi,Al,Tiasmetalelectrode[ 44 ].However,thosemetalsareknowntodiffuseintheSiCmaterialandthereforeleadtoasignicantreductionintheSchottkybarrierheightuponannealing.However,individuallayersofgraphite,graphene,consistsofsp2hybritizedcarbonatomsthataretightlybondedwithcouplingparameterwhichisorderof3.0eVandisresistanttoheatandisnotexpectedtodiffuseinsidethematerial.Thestabilityofgrapheneandmulti-layer-grapheneandtheabsenceofdiffusioninsidetheSiCisverysuitableforhightemperatureapplications. Intheprevioussection,theSchottkybarrierformationatthemulti-layer-grapheneand4H-SiCinterfaceasbeendisplayedbyC)]TJ /F3 11.955 Tf 12.13 0 Td[(VandJ)]TJ /F3 11.955 Tf 12.13 0 Td[(Vmeasurementtechniques.Inthissection,wewillfocusontheSchottkybarriercharacteristicsofmulti-layer-graphene/4H-SiCjunctionsattemperaturesfrom300Kupto1100K.Usingmulti67

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layer-grapheneasametalisspecicallyinterestingbecause:(1)thecarbonatomsinthemulti-layer-graphenecrystalaretightlybondedtoeachotherviaplanarsp2hybridizationandarenotexpectedtoeasilydiffuseintoSiCcrystalandformohmiccontact.MostoftheohmiccontactrecipesonSiCinvolvesuseofmetalelectrodesthatformdifferentalloyswiththeSiCwhenannealeduptohighertemperatures[ 44 ].However,carbonatomsinthegraphiteorgrapheneareverytightlybondedtoeachotherandknowntobeoneofthestrongestmaterial.Duetointraplanarbondingstructure,carbonatomsarenotexpectedtodiffuseintotheSiCcrystal.Graphitedisplaysinterestinggraphenelikepropertiesattemperaturesmuchhigherthan300K[ 38 ](Chapter 6 )andofferaninterestingsystem.Atthoseelevatedtemperatures,thecouplinginbetweentheadjacentgraphenelayersbecomesnegligiblecomparingtothenearestneighborcouplingparameter0aswellas1andgraphitestartsrespondingasbi-layergraphene.Inthislimit,themulti-layer-graphenecontactservesasbi-layergraphenedepositedonSiCsubstrate. Allthemeasurementspresentedinthissectionareperformedinahomemadehighvacuumtransportmeasurementsystemwith4terminalcontactmeasurementcapabilitiesfromroomtemperatureupto1500K,underanygasambientorunderhighvacuumfrom10)]TJ /F8 7.97 Tf 6.58 0 Td[(4-10)]TJ /F8 7.97 Tf 6.59 0 Td[(7Torr.ThetemperatureofthedeviceismeasuredindependentlybyanintegratedoventhermocoupleandK-typethermocoupleplacedascloseas1mmproximitytothesample.Eachdatapointistakenafterreachingthethermalequilibriumandwaitingforanadditional10minutes.Macroscopiccontactstothesampleshavebeenmadebyusingahightemperaturesilver(orgraphitepaintcontacts)andaplatinumwire.I)]TJ /F3 11.955 Tf 12.41 0 Td[(VmeasurementsareperformedbyaKeithley2400current-voltagesourcemeter. Electrictransportacrossthemulti-layer-graphene/4H-SiCsamplesisplottedinlinear(Fig. 3-9 ),semilogarithmic(Fig. 3-10 )andintheforwardbiasdirectioninthesemilogarithmicform(Fig. 3-11 ).Actualmeasurementstookplaceupto1300K,but 68

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thedataareplottedonlyupto900Kforvisualpurposes.AsseenfromFig. 3-9 ,theSchottkybarrierpreservesitsgoodrecticationupto700K.Attemperaturesabove700K,thereversebiascurrent(reversesaturationcurrentdensity)startstoincreaserapidlyandbecomeleakier.Eventually,around900K,thejunctionstartstoirreversiblyloseitsrecticationpropertiessignicantlyanddisplayslinearI)]TJ /F3 11.955 Tf 12.04 0 Td[(Vcharacteristicsafter1100K.Thebreakdowninthereversebiascharacteristicsbecomesmoreapperantwhenthecurrent-voltageisplottedinsemilogarithmicformasinFig. 3-10 .TheincreaseinthereversebiassaturationcurrentcanbeattributedtotheleakagecurrentfrommetaltosemiconductorassociatedwiththeexcitationofelectronsovertheSchottkybarrierheight.Morespecically,intheabsenceofimageforceloweringandothernon-idealeffects(section 1.3.4 ),thereversebiascurrentisexpectedtobesaturatedtoavaluecalledasaturatedcurrentdensity.Thiscurrentisexpressedas, Js=AT2exp)]TJ /F3 11.955 Tf 9.3 0 Td[(eSBH kT,(3) FollowingfromEq. 3 ,forincreasingtemperaturesthevalueoftheJsincreasesasobservedinFig. 3-10 andeventuallybecomesconductive. Intheforwardbias,studieddiodesdisplaygoodlinearportionsintheirsemilogarithmicI-Vcurves(Fig. 3-11 ).Asthetemperatureincreases,thetotalcurrentintheforwardbiasincreasesandisconsistentwiththeincreaseintotalnumberofelectronsovercomingthebarrierheightduetotheirincreasedthermalenergies. Asasummary,themulti-layer-graphene/4H-SiCSchottkydiodesdisplaygoodrecticationupto900Khoweverabove1100KtheI-Vcharacteristicscompletelybecomeirreversiblyohmic/linear.ThelinearityintheI)]TJ /F3 11.955 Tf 12.43 0 Td[(Vcharacteristicispreservedafterthesystemiscooleddowntoroomtemperature.Followingtheannealingprocedure,theI)]TJ /F3 11.955 Tf 13.4 0 Td[(Vcharacteristicsaremeasuredoveraweekperiodatroomtemperatureandthecontactsremainedohmic.Thetransitionfromrecticationto 69

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ohmiccontactformationmightbeunderstoodbyexaminingatypicalohmiccontactformationusingNiasametalelectrodeonSiC. ThenickelmetalelectrodesonSiChaveattractedalotofinterestduetotheirlowcontactresistivity.Ontheotherhand,theohmiccontactformationattheNi/SiCinterfacestillremainscontroversial.Previouslyintheliterature,theohmiccontactformationonNi/SiCjunctionsismostlyattributedtotheformationofnickelsilicides(Ni2Si)attheNiandSiCinterface.However,nickelsilicidesformattheNiandSiCinterfaceasdeterminedfromthex-raydiffractionat600C.Atthesetemperatures,Nimetalcontactsareleakyandnon-ohmicandthetemperatureisnotenoughtoformohmiccontactsonSiC.Traditionally,Nicontactsformanohmiccontactwhenthetemperatureisrampedupto900Cwithnitrogenowinggas,whichismuchhigherthanthetemperaturerequiredtoformnickelsilicides.Thisimpliesthatthenickelsilicidesmightnotbethedeterminingfactortoformanohmiccontactattheinterface[ 44 ].Morerecently,afulldetailedsurfacedepthprolinganalysishasbeenconductedonNi/SiCatdifferentannealingtemperaturesandithasbeenfoundthat[ 44 ]nickelatomsdonotdiffuseinsidetheSiCbutinsteadSiatomsdiffuseouttoformnickelsilicidesat600Catwhichthecontactisstillnon-ohmic.Uponfurtherannealing,thecarbonatomsstarttodiffuseoutthroughthenickelandnickelsilicidelayersandaccumulateatthesurfacecreatingagraphiticlayeratthesurfaceandcarbonvacancyburiedunderthenickelsilicidelayer.TheformationofcarbonvacanciesiscrucialsincethecarbonvacancysitesactaselectrondonorsandcontributetothetransportofelectronsacrosstheNi/SiCjunctionthusreducingthebarrierheight[ 44 ]. Ontheotherhand,Schottkydiodetoohmiccontacttransitionatthemulti-layer-graphene/SiCjunctiontakesplacearound1100K(800C-900C)relativelyclosetotheohmiccontactformationatthewithnickel/SiCjunctions.Herethedepositedgraphite-graphenelayerattheinterfacemightactasaseedinglayerattheoutermostlayerofSiCanduponannealingcarbonatomsboundtosiliconinsidetheSiCcrystal 70

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mightbediffusingouttoformgraphiticlayeratthegraphene/SiCinterface,creatingcarbonvacanciesburiedunderthemulti-layer-graphene.Aspointedoutinthepreviousparagraph,carbonvacanciescanactaselectrondonorsandthereforereducethebarrierheighteventuallybecomingajunctionwithbarrierheightmuchsmallerthanthethermalenergyoftheelectrons(anohmiccontact). 3.6FormationofSchottkyDiodesattheMulti-Layer-Graphene/GaNInterfaces Galliumnitride(GaN)isabinaryIII/Vdirectbandgapcompoundsemiconductorwith3.4eVbandgapvalues.Ithaswurtzitestructureandisknowntobeaverystablematerial.It'slargebandgap,stabilityathighelectricelds(highbreakdownvoltage)andextremelylowintrinsiccarrierdensityofelectronsmakeGaNanidealmaterialforoptoelectronicdevices,HEMTs,laserdiodes,detectorsandhightemperature,highpowerdevices.MostofthoseapplicationsrequireformationofSchottkybarriersonGaNsubstratesandrelyonpropermetalchoicetoformSchottkybarrierswithlowforwardbiastrashholdandhighreversebreakdownvoltageaswellasdurabilitywithrespecttotemperature. However,intheliteraturemostofthemetalizationsonGaNrequiresputterdepositionwhichcreatessurfacestatesandsurfacedamage.Afterthesputteringprocess,theSchottkydiodetypicallydisplaysnon-idealeffectsaswellasreducedresponsetimeassociatedwiththelargeinterfacecapacitanceformedattheinterface.Theseissueshavebeenpreviouslyaddressedintheliterature[ 1 ].Interestingly,depositionofgold,PdandNimetalcontactsatcryogenictemperatureshavebeenshowntoincreasethequalityofthediodes[ 45 ]. Ontheotherhand,useofgraphiteorgrapheneasametalelectrodeonGaNsubstratesareadvantageous,sincethedepositionofthesematerialscanbeaseasyasmicromechanicalexfoliationofmulti-layer-grapheneontoGaNsubstrate,applicationofgraphitepaint,amappinggraphite-graphenegrownonnickeland/orcopperthinfoilsonGaN.Thedepositionofmulti-layer-graphene(orgraphene)takesplaceatroom 71

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temperatureanddoesnotrequireadvanceddepositiontechniquesthatcreatesurfacestatesattheM-Sinterface.Inthisstudy,theHOPGsampleshavebeensuppliedbyProfessorJ.R.Fischer(UPenn)andnaturalgraphitesamplesfromBrazilbyProfessorA.CastroNeto.Multi-layer-graphenecontactshavebeendepositedonGaNbymicromechanicalexfoliationonn-typeGaNcrystalsanduseofthermalreleasetapeasdiscussedinthischapter.GaNwafersaredopedwithsiliconandweregrownonsapphirewafersinDr.Abernathy'slaboratory. Thecurrentdensity(J-V)characteristicsacrossamulti-layer-graphene/n-typeGaNsamplesaremeasuredfrom5Kupto330KandshowninFig. 3-12 .TheforwardbiascharacteristicsaredepictedinFig. 3-13 from330Kdownto250Kandatxedvoltagetheforwardbiascurrentincreasesasthetemperatureisincreased.Theincreaseincurrentdensitywiththetemperaturecanbeexplainedusingthermionicemissiontheory,meaningasthetemperatureisincreasedtheaveragethermalenergyofelectronscrossingtheM-Sincreases,thusincreasingthepossibilityofovercomingtheSchottkybarrierandincreasingthetotalcurrentdensity.Similarly,thereversebiassaturationcurrentdensityincreaseswithtemperatureconsistentwiththeinterpretationsintheprevioussectionandEq. 1 .WenotethattheJ)]TJ /F3 11.955 Tf 13.31 0 Td[(Vcharacteristicsalsoshowarectifyingbehaviorattemperaturesaslowas5K.Eventhough,technologicallyinapplicable,recticationobservedat5Kisveryinterestingsincemostoftheconventionalohmiccontactsareknowntobefailingatlowtemperaturesandgraphitecaneasilybedrivenintotheultra-quantumregimeatlaboratoryattainablemagneticelds(3Tesla)andmetalintheultra-quantumregime/semiconductorjunctionsarephysicallyinterestingtostudy.However,thischapterstrictlyfocusesonthephysicalpropertiesofmulti-layer-graphene/GaNjunctions. Whenthecontactareaisunknown,theactivationplotsareanidealmethodtopredicttheSchottkybarrierattheM-Sinterface.Intheforwardbias,thecurrentdensitygraphsdisplayedatleast2decadesoflinearityatvarioustemperatures 72

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(Figs. 3-12 3-13 ).LinearityinawidevoltagerangeimpliesthatthedominanttransportprocessisthermionicemissionandisdescribedbyEq. 3 ,andinprincipletheSchottkybarrierheightcanbeextractedoutbyusingEq. 3 whentheactivecontactareaisknown.Whenthecontactareaisnotaccuratelyknown,theSchottkybarrierheightcanbeestimatedbyusingEq. 3 ).Inthistechnique,I)]TJ /F3 11.955 Tf 12.27 0 Td[(Vmeasurementsaretakeninatemperaturewindowtypicallyaround250Kupto330Kandtheirsaturationcurrentvaluesareplotedinln(Is(T)=T2)versusT)]TJ /F8 7.97 Tf 6.58 0 Td[(1form.TheseplotshavedisplayedlineardependenceandwehavefoundthatthetheeffectiveSchottkybarrierheightsthatarecalculatedfromtheslopeswerearound0.30eV(Table 3-1 )withidealityfactors()spanningfrom1.1to2.0forallsamplesinthe250K-330Ktemperaturerange(Fig. 3-14 ). 3.7Discussion 3.7.1ComparisonofI)]TJ /F5 7.97 Tf 6.59 0 Td[(VtoC)]TJ /F5 7.97 Tf 6.59 0 Td[(VandDeterminationofgraphite Intheprevioussections,theSchottkybarriersformedatthemulti-layer-grapheneandSi,GaAs,4H-SiCandGaNsubstratesarestudiedatvarioustemperatures.AllthediodeshavedisplayedarectifyingbehavioratroomtemperatureandtheSchottkybarrierheightformedatthemetal-semiconductorinterfaceisdeterminedfromJ)]TJ /F3 11.955 Tf 12.58 0 Td[(Vmeasurementsbyuseofthermionicemissiontheory/RichardsonequationgivenbyEq. 3 ,fromC)]TJ /F3 11.955 Tf 12.85 0 Td[(Vmeasurementsbyusingdepletioncapacitanceexpression(Eq. 1 ),andI)]TJ /F3 11.955 Tf 12.23 0 Td[(Vmeasurementsusingactivationmethod,byplottingln(Is(T)=T2)withrespecttotheT)]TJ /F8 7.97 Tf 6.58 0 Td[(1,givenbyEq. 1 .TheextractedSchottkybarrierheightsusingvarioustechniquesondifferentjunctionsarelistedinTable 3-1 .Inthistable,theSchottkybarrierheightoftheGaN/multi-layer-graphenecouldnotbedeterminedusingC)]TJ /F3 11.955 Tf 12.62 0 Td[(Vplotsduetothehighresistivityofthesamples.Insuchcases,thehighseriesresistancemasksthedataandfurtherprocessing,dataminingandreinterpretationoftherawdataisrequired(refer[ 11 ]andsection 2.2.3 ).Ontheotherhand,multi-layer-graphene-graphene/4H-SiCjunctionsdonotdisplayenoughlinearityintheactivation 73

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energyplotsandSchottkybarrierheightcannotbeaccuratelydetermined.TheSchottkybarrieratmulti-layer-graphene/SiCinterfacecanbeestimatedusingEq. 1 usingthemeasuredopticalcontactareaandtheoreticalvalueoftheRichardsonconstantbyttingtheJ)]TJ /F3 11.955 Tf 11.95 0 Td[(VcurvesinFig. 3-7 ThebarrierheightsextractedfromJ)]TJ /F3 11.955 Tf 13.09 0 Td[(VandC)]TJ /F3 11.955 Tf 13.09 0 Td[(Vmeasurementsroughlyagreewitheachother.HoweverinTable 3-1 ,thebarrierheightsobtainedfromtheC)]TJ /F3 11.955 Tf 12.98 0 Td[(VmeasurementsaresystematicallyhigherthanthebarrierheightsextractedoutfromJ)]TJ /F3 11.955 Tf 13.19 0 Td[(Vmeasurements.ThisdiscrepancybetweenthetwobarrierheightvaluescanbeattributedtointerfaceimpuritiesorthinoxidelayerandtotheSchottkybarrierinhomogeneities.Existenceofathinoxidelayeronthesemiconductorsurfaceisexpectedtoformanotherbarrierattheinterface.Electronsareexpectedtotunnelthroughthisthinbarrierandinprinciplecurrentvoltagemeasurementsareinsensitivetothethinoxidelayer.Ontheotherhand,capacitancemeasurementsaremoreseriouslyaffectedsincethinoxidelayerseparatingmetalelectrodefromthesemiconductoractsasacapacitor(Cox)inserieswiththedepletioncapacitance(Cdep)andthusmasksthevoltagedependenceoftheCdepgivingslightlyhigherSchottkybarriers.AnotherreasonforhighervaluesinbarrierheightsdeterminedbytheC)]TJ /F3 11.955 Tf 12.11 0 Td[(VmethodrelatedtoSchottkybarrierinhomogeneties.InrealitythemetalelectrodesformaSchottkydiodesonthesemiconductorsthatarelaterallyinhomoneous.ThelateralvariationoftheSchottkybarrierheightshasbeenexperimentallydisplayedonCo/GaAsjunctions[ 46 ].WhentheSchottkybarrierheightislaterallyvarying,theJ)]TJ /F3 11.955 Tf 12.45 0 Td[(VandC)]TJ /F3 11.955 Tf 12.45 0 Td[(Vtechniquesgivesdifferentanswers:J)]TJ /F3 11.955 Tf 12.5 0 Td[(VtechniqueprobesthelowSchottkybarrierpatcheswhiletheC)]TJ /F3 11.955 Tf 11.9 0 Td[(VmethodtakesanaverageoverallofthesurfacesinceitprobesthedepletionwidthandthecapacitiveresponseratherthanresistivityacrosstheM-Sinterface. Intheliterature,effectscausinggreaterthanunity,arequantitativelytakenintoaccountindeterminingtheSchottkybarrierheightbyndingtheatbandzero-electric-eldSchottkybarrierheight[ 43 ],FB.Whenthediodeisdriveninthe 74

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atbandmode;surfacestates,iftheyexist,aredepletedofchargeandtunnelingandimageforceloweringeffectsarenotpresent.Forinthe1.052.2range,theoreticalargumentssupportedbyexperimentaldatasuggestthefollowingrelation[ 43 ]tocalculateFB: BF=I)]TJ /F5 7.97 Tf 6.59 0 Td[(V)]TJ /F4 11.955 Tf 11.96 0 Td[(()]TJ /F4 11.955 Tf 11.95 0 Td[(1)(kBT=e)ln(NC=ND)(3) whereNDandNCarerespectivelythedopingdensityandtheeffectivedensityofstatesintheconductionband.Usingthisexpression,thecalculatedFBvaluesarefoundtobelargerthanI)]TJ /F5 7.97 Tf 6.59 0 Td[(VandareclosertotheSBHvaluesdeterminedbytheC-Vmeasurements(Table 3-1 ). Next,usingtheSchottky-Mottrelation,FB,I)]TJ /F5 7.97 Tf 6.59 0 Td[(V=m)]TJ /F7 11.955 Tf 12.51 0 Td[(,whichrelatesSchottkybarrierheight,SBH,tothemetalworkfunctionmandthesemiconductorelectronafnity,togetherwiththeassumptionthattheFermilevelsofthesemiconductorsarenotpinned,wecalculatethemulti-layer-graphenecontactworkfunction(graphite)tobeintherange4.40eV-4.60eV(Table 3-1 ).OurvaluesofgraphitedeterminedseparatelyonSi,GaAs,4H-SiCandGaNsubstratesareingoodagreementwiththetheoreticallyandexperimentallydeterminedvalues(rangingfrom4.4eVto4.8eV)reportedintheliterature[ 47 49 ]. 3.7.2BondPolarizationTheoryandMulti-Layer-GraphenetoGrapheneLimit AccordingtotheSchottky-Mottrelation,formedSchottkybarrierismostlysensitivetothemetalworkfunctionandthesemiconductor'selectronafnityvalue.TheSchottky-MottrelationgivesaroughideaabouttheSchottkybarrierheightandtheformationmechanismofthebarriersattheinterface.SofarSchottkybarrierheightsdeviatingfromtheSchottky-Mottrelationhavebeenreportedintheliteratureanddifferentmechanismshavebeenattributedtoexplainsuchdeviation[ 3 ].InGaAs,thedeviationismostlyattributedtotheFermi-levelpinning,whileforSiitisnon-idealeffects.DuetosomedeviationsfromtheSchottky-Mottpicture,otherphysicalmechanismshave 75

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beenproposed:(1)Metalinducedgapstates(MIGS)modeland(2)bondpolarizationtheory.Thedetailsofthesetheoriescanbefoundinotherreviewarticles[ 1 ].Intheliterature,itiscommonlyacceptedthatMIGSndsbetteragreementwiththeexperimentalvalueswhileitmakesunrealisticassumptionsandphysicallysoundbondpolarizationtheoryexplainsthephysicalmechanismwellbutcannotestimatetheSchottkybarrieronsomesystems. Accordingtothebondpolarizationtheory,theSchottkybarrierheightissomewhatrelatedtothemetalworkfunctionandsemiconductor'selectronafnityvalues.However,thistheoryemphasizeontheinteractionattherstfewlayersofthemetal-semiconductorinterfaceandformationofthebondsafterthemetaliskeptincontactwiththesemiconductor.Followedbythisbondformationattheinterface,atypicalinterfacedipolelayeriscreated.AndtheelectricaleldassociatedwiththedipolelayeristypicallyverystronganddeterminesthebarrierheightseenbytheelectronsmovingacrosstheM-Sinterface.SofarthebandpolarizationtheorysuccessfullyexplainedFermilevelpinningeffect,observedSchottkybarrierinhomogeneity[ 46 ],rstprinciplessimulationsperformedattheM-Sinterfaceandassociatedchargetransfer[ 50 51 ]. Withinthebondpolarizationtheory,themeasuredresultsonmulti-layer-graphenebasedSchottkydiodesformedonvarioussemiconductorsimplythatthesamerecticationwouldalsobeexpectedongrapheneSchottkyjunctions.Accordingtothebondpolarizationtheory,theSchottkybarrierpropertiesaredeterminedbytheveryrstfewlayersofthemetalandthesemiconductorandsincethemulti-layer-grapheneismadeoutofgrapheneintheBernalstacking,thesameeffectisalsoexpectedtobeobservedonthegraphenebasedsystems. AnotherargumentforgraphenebasedSchottkydiodesonthesimilarsemiconductorscomesfromtheSchottky-Mottmodelandthedependenceoftheworkfunctiononthenumberoflayersingrapheneandmulti-layer-graphene.Fromthedensityfunctionaltheory(DFT)calculations,theFermilevelofthegraphene/graphite/multi-layer76

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grapheneispreviouslyshowntobeveryweaklydependentonthenumbergraphenelayersinvolvedinthecrystal[ 48 ]:Forgraphenetheworkfunctionis4.46eVanditincreasesto4.51eVfor7layersofgraphene(graphenebecomesbulkgraphiteormulti-layer-graphenelikeafter4-5layers).Therefore,withintheSchottky-Mottmodel,grapheneisexpectedtodisplayrectifyingbehaviorsincetheworkfunctionofgrapheneandgraphiteisalmostidentical. 3.8Conclusion Inconclusion,wehavedemonstratedtheformationofhigh-qualitySchottkycontactsusingasoft-landingmulti-layer-graphenecontactonn-typeSi,GaAs,4H-SiCandGaNsemiconductingsubstrates.FabricationcanbeaseasyasallowingadabofHOPGpainttoairdryonanyoneoftheinvestigatedsemiconductors.Thermionicemissiontheorydescribeswellthebehaviorofthemulti-layer-graphene/Si:Pandmulti-layer-graphene/GaAs:Sijunctionsfrom250Kto330K.Weattributetheobservednon-linearityintheRichardsonplotsofthemulti-layer-graphene/4H-SiCjunctionstoinhomogeneityatthemulti-layer-graphene-semiconductorinterface.TheextractedvaluesSBHroughlyobeytheSchottky-Mottrelationwithinferredgraphiteworkfunctionsagreeingwellwithliteraturevalues.Ourresultsnotonlyprovideunexpectedinsightsintothenatureofthemulti-layer-graphene/semiconductorinterfacebutalsoanticipateapplicationswheresingle-layergrapheneisdirectlycontactedtoasemiconductorsubstrateratherthanisolatedbyaninsulatingoxide[ 42 ]orgrowndirectlyonundopedinsulatingsemiconductors[ 52 ]. Table3-1. ExtractedSBHs,dopingdensities,andcorrespondinggraphiteworkfunctionvaluesonvariousmulti-layer-graphene/semiconductorjunctions BoBFC)]TJ /F5 7.97 Tf 6.59 0 Td[(VNC)]TJ /F5 7.97 Tf 6.59 0 Td[(VDNHallDHOPG junctiontype[eV][eV][eV][cm)]TJ /F8 7.97 Tf 6.59 0 Td[(3][cm)]TJ /F8 7.97 Tf 6.59 0 Td[(3][eV] HOPG/nSi0.400.600.701.210151.010154.60 HOPG/nGaAs0.600.780.763.610163.010164.78 HOPG/n4H-SiC1.151.601.841.210161.010164.80 HOPG/nGaN0.310.43NA1.21016NA4.45 77

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Figure3-1. PlotsoftheroomtemperaturecurrentdensityJwithrespecttoappliedbiasVonntypemulti-layer-graphene/Si:PjunctionsJ)]TJ /F3 11.955 Tf 11.95 0 Td[(Vplotson(a)linearand(b)semilogarithmicaxes 78

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Figure3-2. Richardsonactivationplots(lnIs=T2)asafunctionofT)]TJ /F8 7.97 Tf 6.59 0 Td[(1from250Kupto330Konmulti-layer-graphene/Si:P Figure3-3. Inversesquareofcapacitanceperunitareameasuredat1kHzasafunctionofreversebiasatroomtemperature:multi-layer-graphene/Si:P 79

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Figure3-4. PlotsoftheroomtemperaturecurrentdensityJwithrespecttoappliedbiasVonntypemulti-layer-graphene/GaAs:SijunctionsJ)]TJ /F3 11.955 Tf 11.95 0 Td[(Vplotson(a)linearand(b)semilogarithmicaxes 80

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Figure3-5. Richardsonactivationplots(lnIs=T2)asafunctionofT)]TJ /F8 7.97 Tf 6.59 0 Td[(1from250Kupto330Konmulti-layer-graphene/GaAs:Sijunctions. 81

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Figure3-6. Inversesquareofcapacitanceperunitareameasuredat1kHzasafunctionofreversebiasatroomtemperature:multi-layer-graphene/GaAs:Si 82

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Figure3-7. Plotsoftheroomtemperaturecurrentdensity,J,withrespecttoappliedbiasVonn-type4H-SiC/multi-layer-graphenejunctionsJ)]TJ /F3 11.955 Tf 11.96 0 Td[(Vplotson(a)linearand(b)semilogarithmicaxes 83

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Figure3-8. Inversesquareofcapacitanceperunitareameasuredat1kHzasafunctionofreversebiasatroomtemperatureonmulti-layer-graphene/4H-SiC. 84

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Figure3-9. I-Vcharacteristicsofmulti-layer-graphene/4H-SiCSchottkybarriersfrom300Kupto900K. 85

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Figure3-10. I-Vcharacteristicsofmulti-layer-graphene/4H-SiCSchottkybarriersfrom300Kupto800Kinthesemilogarithicform. 86

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Figure3-11. I-Vcharacteristicsofmulti-layer-graphene/4H-SiCSchottkybarriersfrom300Kupto800Kinthesemilogarithicformintheforwardbias. 87

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Figure3-12. SemilogarithmicJ-Vcharacteristicsofmulti-layer-graphene/GaN:SiSchottkybarriersfrom5Kupto330K. 88

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Figure3-13. SemilogarithmicJ-Vcharacteristicsofmulti-layer-graphene/GaN:SiSchottkybarriersfrom5Kupto330Kintheforwardbiasdirection. 89

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Figure3-14. Richardsonactivationplots(lnIs=T2)asafunctionofT)]TJ /F8 7.97 Tf 6.59 0 Td[(1from250Kupto330Konmulti-layer-graphene/GaN:Si. 90

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Figure3-15. BondpolarizationtheorySchematics 91

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CHAPTER4TUNINGSCHOTTKYBARRIERHEIGHTATTHEMULTI-LAYER-GRAPHENE/SEMICONDUCTORINTERFACEBYDOPING 4.1Introduction Schottkybarriersformedatthemetal-semiconductorinterfacesarekeycomponentsofmetal-semiconductoreldeffecttransistors(MESFET)andhighelectronmobilitytransistors(HEMTs)thatarewidelyusedinhighfrequency,highpowerdeviceapplications.ThesedevicesmostlyrelyongoodcharacteristicsofSchottkybarriersandanycontrolonthephysicalpropertiesofSchottkybarrieriscrucialforefcientoperationofthedevice.IfhigherSchottkybarrierheightisachieved,thisresultsinlargergate-breakdownvoltage,powergainandoutputresistanceandlowergateleakagecurrentandnoise.TuningofSchottkybarrierheighthasbeenachievedbyapplyingpressure[ 53 ]onthejunction,controllingthecrystalstructureandgrainsizeofmetalelectrodes[ 22 ].HoweverthesemethodsrequirespecialconditionssuchasorderofGParangepressureandcryogenicmetaldeposition. Ontheotherhand,carbonbasedmaterialshavebeenthecenterofattentionformorethan5decadesindifferentformsas0Dfullerenes,1Dcarbonnanotubes,2Dgrapheneand3Dgraphite.Although,integrationofcarbonintoexistingconventionaldevicesfacesnumerouschallenges,theiruniquephysicalpropertiesmakethemagoodcandidateforfuture'selectronicsapplications[ 35 ].Specicallygraphene;whichistwodimensionalsinglelayerofsp2bondedcarbonatomsandgraphite,manylayergraphenesheetswithBernalstacking,areofparticularinterestduetotheirexoticband-structure,excellentconductivity,highmobilityandstabilityaswellastunabilityoftheirpropertiesbytheinteractionwithambientgasesorintercalantatoms/molecules(graphiteintercalationcompounds(GICs))[ 54 ].PublisheddemonstrationofSchottkybarrierformationonvarioussemiconductorsusingmulti-layer-graphenetoreplacethemetalelectrode[ 55 ]anticipatedinaccordwithbondpolarizationtheory,thatgraphene 92

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shouldmanifestthesamebehavior,sincetheSchottkybarriercharacteristicsaremainlygovernedbytherstlayerofmulti-layer-grapheneattheinterface(subsection 3.7.2 ) Inthischapter,wewillreportthetuningofSchottkybarriersformedbetweenmulti-layer-grapheneandvarioustypesofsemiconductors(n-Siand4H-SiC)bybromineintercalatingthesemi-metalmulti-layer-grapheneelectrode.Priortobromineintercalation,SchottkybarriersdisplayedtypicalrectifyingJ-VandlinearC)]TJ /F8 7.97 Tf 6.59 0 Td[(2vs.VRcharacteristics.Thesmallcouplingbetweeneachgraphenesheetallowsustointercalatebromineinbetweentheplanesandincreasestheseparationinbetweeneachconsecutivegrapheneplanes.Astheintercalantdiffusesinbetweenthelayers,thelatticeconstantincreasesandinterlayercouplingparametersdiminish,thereforepushinggraphite/multi-layer-grapheneintographenelimit.Chargetransferinbetweencarbonatomandstrongelectronegativebromineintercalantincreasesthetotalholecarrierdensityofmulti-layer-graphene/graphite/HOPGandtheworkfunction,graphite.WithintheSchottky-Mottrelation(Eq. 1 )anincreaseingraphiteleadstoanincreaseinSchottkybarrierheightwhichisconrmedfromJ-VandC-Vmeasurements.TuningSchottkybarrierheightatthemulti-layer-graphene/semiconductorinterfacehasimportantimplicationsinHEMTsandMESFETsaswellasintegrationofcarbonbasedmaterialsintoexistingconventionalsemiconductingdevices. 4.2ExperimentalProcedure Wehaveusedcommerciallyavailablen-typeSi:P(1015-1016cm)]TJ /F8 7.97 Tf 6.59 0 Td[(3)andlayered4H-SiCwaferscompromising5mepilayer(1016cm)]TJ /F8 7.97 Tf 6.59 0 Td[(3)grownoninsulatingSiCsubstrates.PriortoSchottkydiodeformation,ohmiccontactsaremadeusingmulti-layerohmiccontactrecipesexistingintheliterature[ 3 56 ].Multilayersaredepositedbythermalevaporationand/orRFsputteringat10)]TJ /F8 7.97 Tf 6.59 0 Td[(7Torrandfollowedbyrapidthermalannealing(RTA)annealinginN2gasforvarioustimes.Ohmiccontactsdisplayedlinearandlowcontactresistancefrom300Kdownto20K. 93

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multi-layer-grapheneSchottkydiodesareformedonthesubstratesbythreedifferenttechniques:(a)mechanicalexfoliationofmulti-layer-grapheneusingthermalreleasetape(refertoChapter 3 forexperimentaldetails)(b)applicationofgraphitepaint;mixtureofresiduefree2-butoxyethylacetateandoctylacetatewithgraphitepowdercollectedfromdicingHOPGbydiamondimpregnatedwire[ 55 ]atcontrolledratesand(c)mechanicalexfoliationofnaturalgraphiteandHOPG[ 42 ].Inthelattertechnique,multi-layer-grapheneakestypicallyattenoutonthesmoothsubstratesurfaceduetotheVanderWalls(VdW)interactionbetweenthemulti-layer-grapheneandthesemiconductingsubstrate. Semi-metalmulti-layer-graphenecontactsplacedbymechanicalexfoliationorgraphitepaintmethodonthesemiconductingsubstratesarethenbromineintercalatedbydirectbrominegasexposure.Thebromineexposureisperformedatroomtemperatureinasealedchamberforvariousdurationtimes.Anadditiontothesemethods,thegraphitepaintcontactsolutioncanbemadeoutofalreadybromineintercalatedgraphitepowder.Inthismethod,thegraphitepowderisbromineintercalatedpriortomixingwithorganicsolvents(ratherthandirectbrominationofthepristinegraphitepaintcontact)and'brominatedgraphitepaint'directlyappliedtothedifferentsemiconductingsubstrates.TheJ-VcharacteristicsaremeasuredusingKeithley182/220orKeithley2400current-sourcemeterandC-VusingAgilent4284ALCcapacitancebridge.Atotalof15sampleswerepreparedbythemethodsdescribedabove,'directbromination'and'brominatedmulti-layer-grapheneakepaint'method.MeasuredI-VandC-Vcharacteristicsdidnotshowanydependenceonthetypeofmethodfollowed. Changesinthepropertiesofmulti-layer-graphene/graphite/HOPGsuchascrystalstructurechanges,atomicpercentagesandchangeinEFingraphitearemeasuredbyX-raydiffraction(XRD),Augerelectronspectroscopy(AES),X-rayphotoelectronspectroscopy(XPS)respectively.Graphitepiecesusedinthisworkdisplayedtypical)]TJ /F4 11.955 Tf 12.2 0 Td[(2XRDwith0.5degreemosaicspreadmeasuredbyx-rayomega 94

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rockingcurve(!-RC)measurementsandnocontaminationusinginAESandXPSmeasurementswasobservedpriortothebromination. 4.3ResultsandDiscussion 4.3.1EffectofBromineDopingontheMLG/SemiconductorSchottkyBarrierDiodeI)]TJ /F3 11.955 Tf 11.96 0 Td[(VCharacteristics ThetwopanelsintheFig. 4-2 displaythemeasuredcurrentdensity(J)versusappliedvoltage(V)characteristicsatthemulti-layer-graphene/n-Sijunctionbefore(redsquares)andafter(bluetriangles)thebromineexposure.TheJ-Vcharacteristicsmeasuredon15differentsamplesshowagoodrectication[ 55 ]withSchottkybarrierheightsvaluesandidealityfactors()spanningaround0.4eV-0.6eVand1.12-1.90respectively.ThebluetrianglesinFig. 4-2 correspondtoJ-Vcharacteristicsafterthe'directbromineexposure'atthesameinterface.Aonedecadedecreaseintheforwardbiascurrentdensity(JFor)andatwodecadesdecreaseinthereversebiascurrentdensity(JRev)impliesthatmulti-layer-graphene/semiconductorinterfaceandsemi-metalmulti-layer-graphenearesensitivetobromineexposure.Reportedresultsinthisworkareindependentofthemethodforformingmulti-layer-graphenejunction,brominationtechniqueaswellastypeofsemiconductorused.Similarchanges/trendsinJ-VandC-Vmeasurementsaremeasuredonsamplespreparedby'directbromineexposure'ongraphitepaint/semiconductorand'brominatedgraphitepaint'/semiconductorjunctions.Moreover,existenceofsucheffectsonotherconventionalsemiconductorssuchasGaN,4H-SiCandGaAsmeansthatbrominesensitivityofthediodesisnotspecictothetypeofsemiconductorusedbutoriginatesfromtheinteractionofbrominewithmulti-layer-graphenesemi-metalelectrodeandassociatedchangesinphysicalpropertiesofmulti-layer-grapheneandinterfacebonding/dipole.TheeffectofbrominegasonthesemiconductorsaremeasuredusingAES,andXPS.Siand4H-SiCarefoundtonon-interactingwhileGaAsstronglyinteractswithbromine. 95

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Therefore,theeffectofonmulti-layer-graphene/n-GaAsdiodesarenotreportedinthiswork. Inprinciple,Schottkybarrierheight,SBH,andidealityfactor()canbeextractedoutfromthethermionicemissionoverthebarrierheightusing, I=Is(T)[exp(qV=kBT))]TJ /F4 11.955 Tf 11.96 0 Td[(1],(4) whereIs=AAT2exp()]TJ /F3 11.955 Tf 9.29 0 Td[(qSBH=kBT)isthesaturationcurrent,qB0isthezerobiasSchottkybarrierheight,AisRichardsonconstant,Tistheabsolutetemperature,andVisthevoltageacrosstheohmicandmulti-layer-graphenecontacts.BeforeBrexposure,Schottkybarrierheightandidealityfactorsvaryinbetween0.4eV-0.6eVand1.12-1.9respectivelyon15differentmulti-layer-graphene/n-SisamplesandareroughlyinagreementwiththeSchottky-Mottmodel(Sch=graphite)]TJ /F7 11.955 Tf 12.87 0 Td[(Si)withthevaluesofgraphite=4.5eVandSi=4.01[ 2 49 57 ].Onasemilogarithmicscale,theJ-Vplotdisplaysenoughlinearregionintheforwardbias(Fig. 4-2 b)andextrapolationtotheordinateatzerobiasgivesJsasameasureofzerobiasSchottkybarrierheight(Fig. 4-2 binset).Inourmeasurements,thevalueofJsdecreasesuponbrominationonallthesamplesmeasured.Byintuition,whentheSchottkybarrierheightishigher,fewerelectronsovercomethebarrierandthiscausesoveralldecreaseinthemeasuredcurrentdensityJ.Followingthesaturationcurrentexpression,Js=AAT2exp()]TJ /F3 11.955 Tf 9.3 0 Td[(qSBH=kBT),JsandhenceJForwardandJReversedecreasesonlyifSchottkybarrierheightincreasesuponBrintercalation. 4.3.2EffectofBromineDopingattheMLG/SemiconductorInterface:PossibleMechanisms WithintheSchottky-Mottmodel(Eq. 1 ),theincreaseintheSchottkybarrierheightcanonlybeattributedtoanincreaseinworkfunctionofgraphite(graphite)oradecreaseintheelectronafnityofthesilicon(Si).Bromineishighlyreactiveandelectronegativeelementwithits[Ar]4s23d104p5electroncongurationandinteracts 96

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withothersubstratesinsuchawaythatitmakesthematerialp-typeafterthechargetransfertakesplace.Inprinciple,thischargetransferinbetweenthesemiconductorandbrominevaporleadstoanincreaseinSiratherthandecreaseinSi.Moreover,theabsenceofaninteractioninbetweenbromineandSi,and4H-SiCasdeterminedfromAESandXPSalsopreventsanychargetransfer,andachangeinSiisnotexpected.WithSixed,theincreaseinSchottkybarrierheightandmeasureddecreaseinsaturationcurrentdensitycanonlyoriginatefromanincreaseingraphite.Therefore,changeingraphitedeterminesthechangeinSchottkybarrierheightatthemulti-layer-graphenesemiconductorinterface.Toelucidatethispoint,varioustechniquesandmeasurementswillbepresentedinsubsection 4.3.3 andtheremainderofthechapter. Ontheotherhand,thebondpolarizationtheorydoesnotdirectlyassociatethemagnitudeofthemeasuredSchottkybarrierheightonlytoworkfunctionofmetalandelectronafnityofsemiconductorbutalsoincorporatesthebondinginformationattheinterfaceafterthemetalcontactisplacedonthesemiconductor.Aftertheformationofbonding,theinterfacedipolesifformedattheinterfaceandthebarrierheightismainlydominatedbythisinhomogeneousregion(chargediscontinuity).Inthiscase,thebarrierheightisstronglydependentonthebondinginformationandtheinitialbindingpropertiesofthemetalandthesemiconductorsurfaces.Uponbromineintercalation,thebondingandthebindinginformationchangesatthemulti-layer-graphenesurfaceasdemonstratedinsection 4.3.3 nadcausesSchottkybarriertochange.Andthischangeisexpectedbeanincreaseinthebarrierheightsincemulti-layer-grapheneismoreelectronegativeafterthebromineintercalationanddrawsmoreelectronsforthesemiconductorsurface. 4.3.3CharacterizationofBrIntercalatedGraphite:XRD,AESandXPSMeasure-ments Asemi-metalgraphitewithniteoverlapinbetweenconduction(EC)andvalenceband(EV)isrelativelycleanmaterialwithlowcarrierdensity(1018)]TJ /F4 11.955 Tf 12.12 0 Td[(1019cm)]TJ /F8 7.97 Tf 6.59 0 Td[(3)at300K 97

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correspondingto10)]TJ /F8 7.97 Tf 6.58 0 Td[(5to)]TJ /F4 11.955 Tf 9.3 0 Td[(10)]TJ /F8 7.97 Tf 6.59 0 Td[(4freeelectronpercarbonatom(Chapter 5 ).Moreover,alargelatticeconstantandaweakcouplinginbetweenconsecutivegraphenesheetsallowsbromineatoms/molecules[ 54 58 ]todiffuseinbetweenthelayerseasilythusenablingtheinteractioninbetweenBrandC.IntercalationofBrintographitepusheseachgraphenesheetapartresultinginvisualswellingofthegraphitesamplesinthec-axisdirection(perpendiculartographenesheets)andassociatedincreaseinc-axislatticeconstantdeterminedfromX-rayelectrondiffraction(XRD)measurements.XRDprovidesawaytostudythestructuralpropertiesofvarioussystems.WehavemeasuredtheXRDpatternofbrominatedsamplesfrom10degreesto80degreesinthe-2congurationusingCuKX-raysourceandtheXRDdatatakenonpristineHOPGandatvariousBrintercalationtimesareshowninFig. 4-3 .Thestageindexdeterminationsaremostsensitivelymadeusing(00l)reections[ 54 ].Inoursamples,wedidnotobserveanypeaksindicatingastagingphenomena;moreover,thegraphitepeaksshiftandbroadentoalower2indicatinganincreaseinlatticespacingafterthedopingprocedurerelatedtopenetrationofbrominebetweenthegraphenelayers. Duetothelowcarrierdensitypercarbon(10)]TJ /F8 7.97 Tf 6.59 0 Td[(5to)]TJ /F4 11.955 Tf 9.3 0 Td[(10)]TJ /F8 7.97 Tf 6.59 0 Td[(4freeelectronpercarbonatom),asmallinteraction(chargetransfer)inbetweenthedopant/intercalantandcarbonresultsinordersofmagnitudeincreaseinfreecarrierdensitypercarbon.Thechargetransferoccurringinbetweencarboninthegraphitematrixandintercalantbrominecanberoughlyestimatedifthenumberofbromineatomspercarbonisknown.WedeterminetheconcentrationofbromineintercalatedinsidethegraphiteusingbyAugerelectronspectroscopy(AES)andX-rayphotoelectronspectroscopy(XPS). TheAEStechnique,canbeusedtoidentifytheelementalcompositiononthesurfaceorinthebulk(byremovingmaterialfromthesurfaceusingion-beamsputtering).IntheAEStechnique,innershellelectronisexcitedbyhighenergyelectronbombardment(5keV)andfollowedbyanelectronicrelaxationandemissionofAugerelectrons.ThemostpronouncedAugerpeaksoriginatefromneighboring 98

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orbitalssuchasKLL,LMM,MNNetc.ForelementswithZfrom14to40,themostprominenttransitionisLMM.Forbromine,Augerpeaksappearat55eV(MVV)and1396eV(LMM)andforcarbonat20eVand272eV(KLL).HoweverlowenergyAugerelectronsscatteranddecayeasily,thereforetheirmagnitudesaretypicallyrathersmallornon-observable.InFig. 4-4 ,weshowAugerspectrum,asdN(E)/dEversusenergy,whereN(E)istheenergydistributionofdetectedsecondaryelectronsonabrominedopedsample.Thescanistypicallytakenon100micronby100micronarea.BromineisaweakAugersensitiveelement,forthisreasonHOPGsamplehasbeendopedforalongtimetoobservebromineAugerpeaksclearly.Sincenon-destructivedepthprolingisnotpossibleinAESasitisinXPS,sampleshavebeencleavedtoprobedifferentdepthsofthesampleandrelativebromineconcentrationhavebeenmeasuredtocheckforthesampleuniformity.BromineAugerpeakslocatedat1396eVand1442eVcorrespondstoLMMAugertransitionsanddifferentdepthsinthesamesampleshowssimilarbromineconcentrationimplyingthatthesampleisuniform.Moreover,scanstakenatdifferentpartsonthesurfaceofthesamplealsoshowssimilarconcentrationsofbromineimplyingwithin100micronby100micronresolution.1%to5%chargetransfermeasuredbyAESroughlygives10)]TJ /F8 7.97 Tf 6.59 0 Td[(2chargetransfer.LargechargetransferinbetweenBrandCstronglychangesholecarrierdensity[ 58 ],andFermilevel(EF)ofthegraphiteasconrmedbyXPSmeasurements(Fig. 4-5 b). AnothermethodformeasuringthepercentagecompositionatthesurfaceisX-rayphotoelectronspectroscopy(XPS).SurfacesensitivityandquantitativeandchemicalstateanalysiscapabilitiesofXPStechniqueallowustoanalyzethephysicalpropertiesofbrominedopedsamplesatroomtemperature.However,thedepthofthematerialsampledvariesfrom2atomiclayersupto10-20atomiclayersdependingontheelectronmeanfreepathofcreatedejectedelectronaftercoreelectronsareionizedbyradiatedx-rays.Forcarbonitistypicallyinbetweenaroundtenangstromsbutthedepthofthematerialsampledcanbevariedbychangingtheincomingxraybeamangle 99

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(hencex-raypenetrationdepth)andthisallowsustoselectivelyprobesurfaceandbulk-likeregions.Highenergyphoton(orshortwavelength)canionizeanatomandproducesanejectedfreeelectron.AccordingtoEinsteinsphotoelectriclaw,thebindingenergyoftheparticularelectrontotheatomcanbeextractedoutifthekineticenergyofejectedelectronismeasured. K.E=h)]TJ /F3 11.955 Tf 11.95 0 Td[(B.E,(4) ThebindingscaleiscalibratedtakingtheAu4flevelat83.9eV.StudiedpristinegraphitesamplesarecleavedbeforeintroductioninthetheUHVchamberforXPSmeasurements.AftertheXPSmeasurementsareperformedonpristinegraphite,thesamplesareexposedtobrominegasasdescribedabovetostudytheeffectofbrominedoping.Thestudiedsampleswereconductivebeforeandafterthebrominedopingandnochargeeffecthasbeendetected.Whentherearenochargingeffects,bindingenergiesofindividualatom/levelaredirectlymeasuredwithrespecttotheFermilevelofthestudiedsample.ThereforeanyshiftoftheparticularelementalpeakpositionnotonlygivesanideaaboutbondinginformationbutalsoshiftsintheFermilevelinthesystem.TheentireXPSspectrumof30min.bromineexposedgraphitesampleismeasuredusingamonochromatizedMgX-raysourcefrom0eVupto1100eVinaUHVchamberFig. 4-5 a.Afterpristinegraphiteisexposedtobrominevapor,bromine3dand3porbitalpeaksappearat68.5eVand181.7eVrespectivelyandfoundtobearound1%to3%.InXPSmeasurementselementalpeakssuchasC1s,aremeasuredwithrespecttotheFermilevelofthesystem.WhentheEFofthesystemchangesdrasticallyasitdoesingraphiteintercalationcompounds,thechangeintheFermilevelofthesystemmanifestsitselfasachangeintheC1selementalpeakpositionandtheserelativechangesintheC1speakpositionsprovideawaytoestimatethechangesinEF.TheC1selectronbindingenergyofpristinegraphiteistypicallyat284.5eVconsistentwiththereportedvaluesintheliterature[ 59 ]andaftertheintercalationC1s 100

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peaklowersto284.1-283.9eV(Fig. 4-5 b).However,interactionofcarbonatomswithhighlyelectronegativebrominecreatespositivelychargedcarbonatomswhichpossessahigherbindingenergy.TheexperimentallymeasureddecreaseinbindingenergyasopposedtoanincreaseaspredictedbyelectrostaticrulecanbeexplainedbyredeningtheEFofthesystemafterthebromination.Inbrominatedgraphite,theFermilevelisknowntobesignicantlylargerinmagnitudecomparedtopristinegraphiteandtheC1sbindingenergyisthusmeasuredwithrespecttothelowerEFoftheholedopedsystem.Accordingly,theincreaseintheC1sbindingenergyismorethancompensatedforbythedecreaseinEF,givinganoveralldecreaseintheC1speakpositionasobserved.Similarresultsandtrendshavebeenreportedintheliterature[ 60 61 ]fordifferentgraphiteintercalationcompounds.ThismethodthusgivesalowerlimittotheorderofmagnitudechangeofEFwhichfromFig. 4-5 bcorrespondsto0.5eV. 4.3.4ModicationoftheBandStructureattheInterfaceandC)]TJ /F3 11.955 Tf 10.04 0 Td[(VMeasurements ThedecreaseinEF,oranincreaseingraphite,changesthebandstructureatthemulti-layer-graphene/semiconductorinterfaceasshowninFig. 4-6 c-d.Beforecontactismade,theFermilevelofthesemiconductoralreadyliesabovetheFermilevelofthepristinegraphite.Afterthermalequilibriumelectronsinthesemiconductorowintothelowenergystatesinthegraphite,makingEFconstantthroughoutthesystemandcreatingpositivelychargeddonorsatomsinthedepletionwidth(W)Fig 4-6 b-d.Withinthispicture,SchottkybarrierheightequalstoSBH=graphite)]TJ /F7 11.955 Tf 12.91 0 Td[(Si(Schottky-Mottapproximation)andbromineintercalationofgraphiteincreasesthegraphite,resultinginanincreaseinSchottkybarrierheightasdisplayedinFig 4-6 d.GreaterdifferenceinbetweenFermilevelofthesiliconandbrominatedgraphiterequiresmoreelectronstoowfromthesemiconductorintothemulti-layer-graphene,thusleavingamorepositivelychargedregionandanincreaseinthechargedensitywithintheW(Fig. 4-6 b). WhileJ-VmeasurementsareexponentiallysensitivetothechangesinzerobiasSchottkybarrierheight(Eq. 4 )andleadstoadecreaseincurrentdensity(Fig. 4-2 ), 101

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associatedchangesinthechargedistribution((x))acrossthedepletionwidthregion,meaninganincreaseinthechargedensity,doesnotmanifestitself.Ontheotherhand,electricaleldassociatedwiththechargedistribution((x))intheWgivesanitecapacitanceatthemulti-layer-graphene/semiconductorjunctionandthereforeunlikeJ-V,capacitancemeasurementsemphasizeonthe(x).TotalcapacitanceattheinterfacederivesfromthesolutiontothePoisson'sequationforspecicchargedistributioninthedepletionwidthregionandiswrittenas, 1 C2=2(Vbi+VR) (eNDs)(4) andC)]TJ /F8 7.97 Tf 6.59 0 Td[(2)]TJ /F3 11.955 Tf 12.24 0 Td[(VRplotsyieldsastraightlinewithaslopeof)]TJ /F4 11.955 Tf 9.3 0 Td[(2=eNDs.Linearextrapolationtotheinterceptwiththeabsiccsacorrespondstothebuilt-inpotential(Vbi)andSchottkybarrierheightcanbeexpressedasSBH=Vbi+(Ec)]TJ /F3 11.955 Tf 12.2 0 Td[(EF),whereEcistheconductionbandenergy. Fig. 4-7 displaysmeasuredcapacitanceatthemulti-layer-graphene/n-siliconjunctionatroomtemperatureat1KHzfrequencyintheformofC)]TJ /F8 7.97 Tf 6.59 0 Td[(2)]TJ /F3 11.955 Tf 12.43 0 Td[(VR.Beforeandafterthebromineintercalation,C-VplotsarefoundtobelinearaspredictedbyEq. 4 .Theinterceptwiththeabsicca,whichisVbi,typicallyspansaround0.40-0.60eVcorrespondingtoSchottkybarrierheightsof0.54-0.74eVbeforetheintercalation(Fig. 4-7 redsquares)andincreasesto0.60-0.90eVwithSchottkybarrierheightsof0.74-1.04eVaftertheintercalation.The0.3-0.4eVincreaseintheSchottkybarrierheight(Fig. 4-7 redsquares)roughlyagreeswiththechangesingraphiteworkfunctionmeasuredbyXPS(Fig. 4-5 a-b).Theslopesofthebrominatedmulti-layer-graphene/siliconjunctionsaretypicallysmallerby2-6timescomparedtopristinemulti-layer-graphene/siliconjunctions.Thedecreaseintheslope,increaseinNDorchargedensitythedepletionwidth,W,canbeattributedtolargerdifferenceinbetweengraphiteandSiandhencemoreelectronowfromSiintothemulti-layer-graphenecreatingmorepositivelychargedregionasdiscussedabove.SolutiontoPoisson'sequationat 102

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theinterfaceforincreasedchargedensityintheWleadstoanincreaseinmeasuredcapacitanceasillustratedinFig. 4-7 inset. 4.3.5ResultsonMLG/SiCJunctionsandSensingApplications Inthissection,forcompletenessofthisdissertation,theeffectsofbromineintercalationofmulti-layer-grapheneontheSchottkybarriercharacteristicsofmulti-layer-graphene/SiCjunctionswillbepresented.SincetheJ)]TJ /F3 11.955 Tf 12.16 0 Td[(VcharacteristicsoftheSchottkydiodesareverysensitivetothebromination,changesofthemeasuredcurrentatxedforwardbiaswillbepresentedasafunctionofintercalationtimetoillustratethepossibilityofsensingapplicationsbasedonthemulti-layer-graphene(orgraphene)basedSchottkyjunctions.Resultspresentedonsensingapplicationsareparticularlyinterestingsincegrapheneisparticularlysensitivetodifferentspeciesatoms(notlimitedtobromine),andanyinteractioninbetweenthegrapheneandvariousgasesleadstoachangeintheFermilevelofthegraphene.Thereforeanyinteractiontakingplaceinbetweenvariousgases,moleculesandmacromolecules(DNAetc.)andgrapheneshoulddisplayalargechangeintheJ)]TJ /F3 11.955 Tf 12.93 0 Td[(Vcharacteristicsasaresultofchangeinbarrierheightandthenumberofionizedimpuritieswiththedepletionwidth.Combinedwithbond-polarizationtheory[ 1 ]andtheSchottky-Mottmodel,theseresultssuggestpossibilityofsensingapplicationongraphenebasedSchottkyjunctions. Changesinthedopinglevelofthegraphitewithbromination,decreaseinFermilevel(increaseingraphiteworkfunction)andassociatedincreaseofionizedimpurityconcentrationhencemodicationofthebanddiagramasshowninFig. 4-6 havebeendiscussedintheprevioussections.Schottkycharacteristicsofmulti-layer-graphene/4H-SiCdiodesalsoshowsimilarchangesuponintercalationandcanbeexplainedbythechangesintheFermilevelofgraphite,modicationofthebandstructure(Fig. 4-6 )andincreaseinthebarrierheight.Withinthispicture,thecurrentdensityisexpectedtodropdrasticallywhenthemetalelectrode(multi-layer-graphene)isbrominated.The 103

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J)]TJ /F3 11.955 Tf 12.14 0 Td[(Vcharacteristicsofmulti-layer-graphene/4H-SiCjunctionsaredisplayedinlinearandsemilogarithmicformsinFig. 4-8 BasedontheresultsshowninFig. 4-2 and 4-8 ,thecurrentmeasuredacrosstheSchottkydiodeisverysensitivetothebrominegas,meaningifthecurrentismeasuredatxedvoltagewithrespecttotimeandbrominegasisturnedonandoff,oneshouldobserveadrasticdropinthecurrentdensity.InFig. 4-9 ,1.85Vxedvoltage(forwardbias)isappliedacrossthemulti-layer-graphene/4H-SiCjunction,andthecurrentisrecordedasafunctionoftime.Asseeninthegureshortlyafterthebromineexposure,thecurrentacrossthejunctiongoesdownfrom3.5A/cm2to0.7A/cm2.Eventhoughthisparticularsamplehasshownvetimescurrentdrop,ondifferentsamplesmorethananorderofmagnitudecurrentdropshavebeenachievedatdifferentvoltagesorinreverse/forwardbiasdirections.Whenthebrominegasisreleasedinthechamber,thecurrentstartstosaturateeventually.Theeffectdescribedaboveissemi-reversible,becausewhenthebrominegasispumpedoutofthechamber,thetotalcurrentacrossthemetal/semiconductorjunctionstartstoincreasebutneverreachesitsoriginalvalues.Weattributethiseffecttooutgassingofbrominefrommulti-layer-grapheneovertime.Outgassingofvariousintercalantsofgraphitehavebeenstudiedintheliterature[ 54 ]andisbeyondthescopeofthisdissertation,howeverintercalantsareknowntoout-gasovertimeandeventuallyformingaresiduecompoundofgraphite.Therefore,theincreaseinthecurrentdensitywhenthebrominegasisturnedoffcanbeattributedtotheout-gasingofintercalantsinbetweenthegraphenelayers,andeventuallysomeoftheintercalantformsaresiduecompound.TheintercalantsformingresiduecompoundslowertheFermilevelofthesystemasdiscussedintheprevioussections,andleadtoanincreaseinthebarrierheightanddecreaseincurrentdensity.Hencethecurrentisexpectedtobelowerthantheoriginalcurrentdensityvalue(priortothebromination).Uponfurtherintercalation,thecurrentdensitystartsdecreasingfrom2.5A/cm)]TJ /F8 7.97 Tf 6.59 0 Td[(2downto0.4A/cm)]TJ /F8 7.97 Tf 6.58 0 Td[(2consistentwiththedopingpicturegivenaboveand 104

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eventuallysaturatingatanothercurrentdensityvalue(asaresultofaresiduecompoundwithdifferentstoichiometry)whenthebrominegasisturnedoffforthesecondtime. Theseresultspresentedabovehavesignicantimplicationsinsensingmolecules,gasesandmacromolecules.SincetheformationofSchottkybarrieratthemetal/semiconductorjunctionisthemostsensitivetotheinterfacestructureandthecouplelayersfromtheinterface,theseresultsareexpectedtobevalidforgraphenejunctionsaswell.Moreimportantly,sincegrapheneisverysensitivetotheenvironmentandinteractionofothermoleculesandchargetransfer,thesensingapplicationbasedontheJ)]TJ /F3 11.955 Tf 12.06 0 Td[(Vcharacteristicsatthegraphene/semiconductorjunctionsaremorelikelytoprobedifferentgasesandmolecules. 4.4Overview Inthischapter,wehavedemonstratedthattheSchottkybarriersformedatthemulti-layer-graphene/semiconductorinterfacecanbetunedbychangingtheworkfunctionofgraphitegraphitebybromineintercalation.SensitivityofSchottkydiodestobrominevaporismeasuredasandecreaseincurrentdensity(J)inJ-Vandincreaseincapacitance(C)inC-Vmeasurements.Weattributethesechangestoadecrease(increase)inFermilevel(workfunction)determinedfromtheXPSandHallmeasurements.WithintheSchottky-Mottmodelanincreaseintheworkfunctionleadstoanincreaseinthebarrierheight.Thistechniquenotonlyallowsonetotunethebarrieracrossthemulti-layer-graphene/semiconductorinterfaceusingthesametypeofmetal(inthiscase,multi-layer-graphene)byintercalationofsemi-metalmulti-layer-grapheneelectrodebutalsodecreasestheJrevandimprovesthebreakdownbias.InMESFETsandHEMTswherethecharacteristicsofSchottkybarriersarecrucial,higherbarrierheightsarepreferableduetolargergate-breakdownvoltage,powergainandoutputresistanceandlowergateleakagecurrentandnoise.Therefore,suchresultsareparticularlyimportantforsemiconductorswhichhavenoestablishednativeoridealdielectricthusgatingsemiconductorsisachievedthroughSchottky 105

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barriers.Eventhough,thisdissertationspecicallyfocusesonbromineintercalationofgraphite,anincreaseordecreaseinSchottkybarrierheightcanbeachievedusingotherdonororacceptortypeofintercalantssuchasK,Li,Ca,andI2[ 54 ].Finally,theseresultsopenanewchannelinintegrationofcarbonelectronicsintosemiconductorsaswellasapplicationssuchassensingandtuningwithdifferentmolecules,atomsandintercalants. Figure4-1. Schematicsofmulti-layer-graphene/n-Si(1E16cm)]TJ /F4 11.955 Tf 7.08 -4.34 Td[(3). 106

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Figure4-2. J-VplotsonMLG/n-Sibefore(redsquares)andafterthebromination(bluetriangles)inlinear(top)andsemilogarithmicscale(bottom)Inset:ForwardbiasJ)]TJ /F3 11.955 Tf 11.96 0 Td[(Vplots. 107

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Figure4-3. (a)X-rayphotoelectronspectrum(XPS)ofbrominatedgraphitemeasuredusingmonochromatizedMgX-raysourcefrom0eVupto1100eVinaUHVchamber(b)C1smeasuredbyXPSonpristine(blacksolidlines)andbrominatedgraphite(redandbluesolidlines). 108

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Figure4-4. Augerelectronspectrum(AES)takenonbrominatedgraphitefrom0eVupto1500eVatdifferentdepthsindicatedinthelegend.Inset:bromineAugerpeakslocatedat1396eV,1442eV,and1475eVcorrespondingtoLMMAugertransitions 109

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Figure4-5. (a)XPSdataofbrominatedHOPGsample(b)C1speakofpristine(blacksolidlines)andbrominatedHOPG(redandbluesolidlines). 110

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Figure4-6. (a)Bandstructureatthemetal-semiconductorinterfacebeforethephysicalcontactandthermalequilibrium.(b)Changeinchargedistribution((x))inthedepletionwidth(W)before(red)andafter(blue)thebromination.(c)Chargetransferandassociatedbandbending,meaningSchottkybarrierformation,attheinterfaceafterthephysicalcontactmade.(d)ChangeinFermilevelm,bandstructureandSchottkybarrierheight(SBH)afterthephysicalcontactatthebrominatedgraphite/semiconductorinterface 111

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Figure4-7. C)]TJ /F8 7.97 Tf 6.59 0 Td[(2vs.VRplotsofMLG/n-Si(1016cm)]TJ /F8 7.97 Tf 6.58 0 Td[(3)substratesat1KHzand300Kbefore(redsquares)andafterthebromination(bluetriangles).Inset:Cvs.VRplots 112

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Figure4-8. Roomtemperaturecurrentdensity,J,withrespecttoappliedbias,V,onMLG/n-4H-SiCbefore(redsquares)andafterthebromination(bluetriangles)inlinear(top)andsemilogarithmicscale(bottom) 113

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Figure4-9. Plotofforwardcurrentatxedvoltage(1.85V)withrespecttothetime.Bromineisturnedon/offatspeciedtimesatthetopofthegraph. 114

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CHAPTER5BANDSTRUCTUREOFGRAPHITE 5.1Introduction Graphiteisthemoststablecarbonallotrope.Carbonatomsingraphitecrystalmakethreebonds(sp2hybridization)tothenearestneighborcarbonatoms,justlikeinmanyotherformssuchascarbonnanotubes(CNTs),grapheneandC60fullerene.Althoughgraphitesharesthesameelementandthesame/similarbondingtype,itselectricaltransportpropertiesdifferdrasticallyfromtheotherstablecarbonbasedstructures.Graphiteisclassiedasasemimetalwithniteoverlapinbetweentheconductionandvalancebandswithmajorityholesandelectronsbothcontributingtothetotalcurrent.Justlikeothertypicalsemimetalmaterialssuchasbismuth(Bi),Antimony(Sb)andgermaniumtelleride(GeTe),semimetalsdisplayverylowdensityofcarrierswithFermileveltypicallylowerthanroomtemperature(25.8meV).Inadditiontotheseproperties,graphitehasalowcyctrotronmass(mc)andisaverycleanmaterialwithhighimpurityscatteringtimes(imp).Graphitecanalsobedrivenintotheultra-quantumregimeatlaboratoryattainablemagneticeldsandtemperaturesbecauseofitslowcarrierdensityandlightcyctrotronmass.Moreover,graphiteconsistsofindividuallystackedgrapheneplanesthatareweaklycoupledinBernal(ABABAB)stacking.Sincetheadjacentlayersofgrapheneareveryweaklycoupled,itdisplayshighanisotropyintheelectricalresistivity,witharesistivityratesc/ab104.Electronictransportinlayeredmetalsshowsdifferentbehaviorofthein-plane(ab)andout-of-plane(c)resistivities:whiletemperaturedependenceinab(inplane)ismetalliclike,thatofc(out-of-plane)iseithernon-monotonicorinsulatinglike.Thisresistivitybehaviorisobservedindifferenttypesofgraphite,suchaskishgraphite,highlyorientedpyrolyticgraphite(HOPG),naturalgraphite[ 62 ],andothervariousmetalssuchaslayeredperovskiteSr2RuO4[ 63 ],hightemperaturesuperconductors[ 64 ]andorganicmetals[ 64 ]. 115

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Theexoticpropertiesofgraphitehaveattractedalotofattentionintheliteratureinlastvedecadesandavastamouthofworkhasbeendone.Duringthatperiod,thefocushasbeenshiftedtootherallotropesofcarbon:fullerenes[ 65 ]in80s-90s,CNTs[ 66 68 ]in90s-00sandrecentlygraphene[ 42 ].Therearemanyquestionsleftopenorunanswered.However,inthelastdecaderesearchongraphitehasintensiedafterthediscoveryofsinglelayeratomicsheet,graphene,anddiscoveryofDiracfermions[ 37 ],ferromagnetism[ 69 70 ],quantumhalleffect[ 71 ],intrinsicsuperconductivity[ 72 ],elddrivenmetal-insulatortransition[ 73 74 ]. Thischapterofthisdissertationaimstogivethereaderanintroductoryideaaboutthetheorybackgroundingraphitethatwillbeusedintheotherchaptersinthedissertation.Aninterestedreaderisencouragedtoreferothersourcesandreferencesinthischapterfordetailedbandtheoryofgraphite. 5.1.1CrystalStructureofGraphiteandGraphene Graphiteconsistsofmanygraphenelayersinwhichthecarbonatomsarearrangedinahexagonal(honeycomb)networkwithineachlayer.Inanidealgraphite,theselayersaregenerallystackedintheABABsequencewhichisoftenreferredasbernalstacking.Thisresultsinahexagonalunitcellwithlatticedimensionsofc=6.73Aanda=2.47A.Theunitcellconsistsof4carbonatoms,aslabeledbyA,A',BandB'inFig. 5-2 .TheBernalstackingisknownasstableandmostcommontypeofthegraphitephaseintheliterature.Inrealitylaboratorygrownhighlyorientedpyrolyticgraphite,naturallyfoundgraphite(naturalgraphite)andkishgraphitesamplesdisplayotherminorphases.AnotherorderedandstablegraphitephaseisknowntoberhombohedralgraphitewithABCABCstacking(rhombohedralstacking).Duetoitsrhombohedralstacking,itbelongstodifferentspacegroup.Moreover,rhombohedralgraphitephasehasthesamelatticeconstantsasforBernalphasewithslightlylargergraphenetographeneseparation.Changesinthestackingorderdonotalterverystrongnearestneighborcarbon-carbonbondingwhileitisdifferentby2-5%fortheext-to-nearestneightbor 116

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couplingalongthethec-axis.ThebindingenergypercarbonatomorthetotalenergyofthesetwophasesdifferslightlyandnaturefavorsBernalstackingoverrhombohedralstacking.Inpercentageterms,bernalphaseconsistsmostofthepristinegraphite(97%)whiletheremainderisinrhombohedralphase(2.5%)andAAAstacking(0.5%).Theseminorityphasescalledasstackingfaultsintheliteratureanditseffectsonthetransportpropertiesandthebandstructureremainlargelyunknown[ 75 ]. Otherthanthosephaseschanges,graphiteisknowntobeoneofthemosthighlyanisotropicmaterialknowntoman.Thehighanisotropymeasuredingraphitelargelycomesfromthefactthatthein-planeinteratomicdistance(nearestneighborC-Cdistance)is1.42Awhiletheinterplanardistanceis3.37A.Withineachcarbonplane,graphene,carbonisarrangedinhexagonallyandtheunitcellisdescribedby2carbonatomsinarhombunitcell.Theunitcellin-planelatticeconstantisa=2.47A.However,majorgraphitephaseBernalphaseisstackedinABABfashionandintheunitcellofgraphitethereare4atomswithc=6.73A.TheresultantunitcellandthetranslationalvectorsofgrapheneandgraphiteareshowninFigs. 5-1 and 5-3 respectively. Thetranslationvectorsofgraphene,namelya1anda2(Fig. 5-1 ),canbewritteninorthonormalcoordinatesasfollows, ~a1=ap 3=2,)]TJ /F4 11.955 Tf 9.3 0 Td[(1=2,0~a2=ap 3=2,1=2,0~a3=(0,0,1),(5) whereaisthedistanceinbetweenneighestneighborC-Cdistance,1.42A,andcisthelatticeconstantintheout-of-planedirection,6.72A.UsingthetranslationvectorsgiveninEq. 5 ,thedirectvector(Dn)andthereciprocalvectors(Rn)readas, ~Dn=(n1~a1+n2~a2+n3~a3)~Dn=ap 3=2(n1+n2),a=2(n1+n2),cn3,(5) and 117

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~Rn=m1~b1+m3~b2+m3~b3,(5) Here~b1,2,3arethereciprocallatticebasisvectorsderivedfromthetranslationvectors~a1,2,3by ~b1=2 a1 p 3,)]TJ /F4 11.955 Tf 9.3 0 Td[(1,0~b2=2 a1 p 3,1,0~b3=2 c(0,0,1),(5) ThereforethereciprocallatticealsosharesthesamesymmetryasdirectlatticeandtherstBrillouinzonecanbedescribedasinFig. 5-4 Eachcarboningraphiteorinindividualgraphenesheetsmakesthreenearestneightborbondingsorsp2hybridization.Thereforethereoffourvalanceelectronsareinvolvedinthebondswhilethelastvalenceelectronparticipatesinthebonding.Thefourcarbonatomsintheunitcellofgraphiteinvolvestotal16valanceelectronsthatcorrespondto16bondingofwhich8ofthemarebondingandtheother8areanti-bondingenergystates.Ontheotherhand,totalnumberofvalanceelectronsintheunitcellofgraphitethatareinvolvedinthebondingaddupto12.Thoseelectronscreate6bondingand6anti-bondingenergylevelsandtheyareroughlyseparatedby5.1eVanddonotcrosstheFermilevel.The3valenceelectrons(ineachcarbonatom)involvedinthebonding,donotcontributetotheelectronicpropertiesofthegraphite.Theother4valenceelectronsintheunitcellthatareparticipatingtotheformationofbondsareontheotherhandgives4energylevelsandthosebondingandanti-bondingstatesliearoundtheFermilevelofthesystem.Itistherefore,thevalenceelectronsinvolvedinthebondingwhichcontributetomostofthetransportpropertiesofgraphite.Theupperandlowerbandsoverlapby30meValongtheBrillouinzoneboundaries(throughHKH,H'K'H'symmetrypoints)(Fig. 5-4 )creatingitssignaturesemi-metallicproperties:Bothelectronsandholescontributingtothetransportwithorderofsimilarmobilities(4000cm2/V.sforholesand6000cm2/V.sforelectrons)andeffectivemasses(0.3m0forelectronsand0.5m0forholes). 118

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5.1.2BandStructure:EnergySpectrumofElectrons/HolesinGraphite TheelectronicpropertiesofgraphitearewellexplainedbySlonzewski,WeissandMcClure(SWMc)theory.Thedetailsofthetheorydemandseparationdiscussionandarebeyondthescopeofthischapter.However,theinterestedreaderisencouragedtoreadSWMc'soriginalarticlegivenbyreference[ 76 77 ].Nevertheless,thephysicalparametersusedinthetheoryandthelaterinthedissertationaswellassomepreliminarystepsmightbenecessarytounderstandthephysicsbehindgraphite. TheSWMctheoryusesatotalof7differentparametersdescribingtheinteractioninbetweencarbonatomsinthegraphitematrixanddeterminesthedependenceoftheenergyspectrumonthewavevectorbyusingthecrystalsymmetryasatool.Therefore,SWMctheoryisconsideredasaphenomenologicaltreatmenttopredictbandstructureofthegraphite.TheparametersusedintheSWMcmodelarelistedinTable 5-1 Undertheassumptionthatthe3parameteriszero,thesecularequationforthehamiltonianofthesystemcanbesolvedexactly.Heretheassumption(3=0),reducesfourthorderequationstosecondorderequationsandallowsonetoobtainthefourbranchesofthespectrumas, 1=1 2)]TJ /F7 11.955 Tf 5.48 -9.68 Td[(01+03"1 4)]TJ /F7 11.955 Tf 5.48 -9.68 Td[(01)]TJ /F7 11.955 Tf 11.96 0 Td[(032+2k21)]TJ /F7 11.955 Tf 13.15 8.08 Td[(4 0)]TJ /F11 11.955 Tf 6.78 16.85 Td[(2#1=2,(5) and 2=1 2)]TJ /F7 11.955 Tf 5.48 -9.68 Td[(01+03"1 4)]TJ /F7 11.955 Tf 5.48 -9.68 Td[(01)]TJ /F7 11.955 Tf 11.96 0 Td[(032+2k21+4 0)]TJ /F11 11.955 Tf 6.78 16.85 Td[(2#1=2,(5) Here,+2and+1correspondtothemajorityandminorityelectronswhile)]TJ /F8 7.97 Tf 0 -7.98 Td[(1and)]TJ /F8 7.97 Tf 0 -7.98 Td[(2correspondtomajorityandminorityholes.TheresultantbanddiagramissketchedneartheHKhighsymmetrypointsinFig. 5-5 .Inthediagram,the4energybandsarelabeledasE1,E2anddoublydegenerate(alongthezoneedges)E3bands.E1banddisplayedinFig. 5-5 isanemptybandwhileE2bandbarelycrossestheFermilevel 119

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attheHpointoftheBrillouinzonecreatingminorityholes.Thisbanddisplaysalmostlinearspectrumatthishighsymmetrypointandthedirac-likepropertiessometimesobservedinpristinegraphiteareattributedtotheseminoritycarriers[ 37 ].ThedoublydegenerateE3bandispartiallyoccupiedinbetweenH-KsymmetrypointsandgivesrisetomajorityelectronandholepocketsasdisplayedinFig. 5-5 andintheH-KzoneboundaryintheBrillouinzone(Fig. 5-4 ).Readeriskindlyremindedthatthisbandstructureiscalculatedwithinsomeapproximationsandthe3couplingparameterdescribedinTable. 5-1 issettozeroforexactsolutiontothesecularequation.ThismildapproximationdenestheFermisurfaceascylindricalandthecylindricalsymmetryautomaticallybreaksdownfornon-zero3couplings.Fornon-zero3,theholeandelectronpocketsalongtheHKH(orH'K'H')symmetrypointsstarttouchingfrom4differentpoints(forminglegs).Thiseffectistypicallycalledasatrigonalwarpingofgraphiteandtheeffectofthiscouplingparameteronthebandstructureofgraphitehasbeenstudiedintheliterature.Theinterestedreaderisadvisedtoreviewthecentralideasandthereferencestherein[ 78 79 ]. Forthecompletenessofthischapter,itisimportanttodiscussthelimitwhen2or2and1istakenaszero.WhenthecouplinginbetweentwoBatomsfromthenearestequivalentlayers(2)istakenzero,theenergyspectumcanalsobecalculatedbytightbindingapproximation[ 80 ]consistentwiththeSWMcpredictionandexpressedas, =1 2)]TJ /F2 11.955 Tf 9.43 0 Td[()]TJ /F8 7.97 Tf 6.77 4.33 Td[(221 4+2k21=2,(5) Inthislimitwhereallthecouplingparametersii=2andhigheraresettozero,graphiteinteractsonlywiththeadjacentgraphenelayerandthisregimeiscalledbi-layergraphiteregime.Here,whenthe1parameterissettozeroaswelleachgraphenelayerareisolatedfromeachotherandtheenergyspectrumreducestotheDiracspectrumgivenby=k. 120

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Table5-1. ValuesanddescriptionoftheparametersusedinSWMcmodel CouplingparametersDescriptionValues 0Interactioninbetweenthenearestneighborcarbonatomsinaplane3.2eV 1InteractioninbetweentwonearestAcarbonatomsnexttotheconsecutivelayer0.4eV 2InteractioninbetweentwocarbonatomsBfromnearestequivalent(notconsecutive)layers(determinesFermilevelofthesystem)0.02eV 3InteractioninbetweencarbonatomAwiththeatomBintheneighboringlayer0.3eV 4InteractioninbetweenatomAinonelayertothenearestatomAintheneighborlayer0.1eV 5InteractioninbetweenatomAinonelayertothenearestatomAinthenearestequivalentlayer0.01eV 6orDifferenceincrystallineexperiencedbyinequivalentcarbonsitesinlayerplanes.0.01eV Figure5-1. Oneunitcellofgraphenewithtranslationalvactorsa1anda2 121

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Figure5-2. CrystalstructureofgraphiteshowingconsecutivelayerswithABandA'B'atoms. 122

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Figure5-3. Oneunitcellofgraphitewithtranslationalvactorsa1anda2andc 123

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Figure5-4. Therstbrillouinzoneofgraphite.ElectronandholepocketsarecylindricallypositionedalongtheHKHandH'K'H'highsymmetrypointswithniteoverlapwhichiscomparableto2=0.02eV 124

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Figure5-5. ThebandstructureofgraphitenearthehighsymmetrypointsH-K(orH'-K')ascalculatedfromSWMcmodel. 125

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CHAPTER6TRANSPORTPROPERTIESOFHIGHLYORIENTEDPYROLYTICGRAPHITE(HOPG)FROM3KUPTO1500K 6.1Introduction Thefamilyofcarbonallotropesincludesfullerenes,carbonnanotubes,graphene,graphite,anddiamond.Acombinationofchemicalsimplicityanddiversephysicalproperties,characteristicforthesematerials,makescarbon-basedelectronicsapromisingeldofresearchandapplication.Surprisingly,themostcommonmemberofthisfamily,graphite,hasbeenveryactiveeldofresearchinthelastdecadeafterobservationofdiracfermions[ 37 ],ferromagnetism[ 69 70 ],quantumhalleffect[ 71 ],intrinsicsuperconductivity[ 72 ],elddrivenmetal-insulatortransition[ 73 74 ].Theserecentndingsobservedontraditionaland'wellknown'materialgraphiteraisedmanyquestionsandarestillunderdebadeandyettobeexplainedbothexperimentallyandtheoretically.Nevertheless,thesendingsallimpliedthatphysicsofgraphiteisnotassimpleasitwasthoughtandthereareinfactmoreunknownaspectstoitratherthanknown. Thetransportpropertiesofgraphitehavebeenmeasuredmorethanvedecadesfromlowtemperaturesuptoroomtemperatureonvariousqualityandtypesofgraphiteincludingkish,naturalandpyrolyticgraphite.Thequalityofthelaboratorygrowngraphitewasverypoortill70sandafter80shighlyorientedpyrolyticgraphitewithverylittleimpuritycontentaswellasveryminusculemosaicspreadbecameavailable.PriortosuccessfulHOPGgrowth,samplessizeswereverysmallandthusreliableexperimentalresultsonout-ofplaneresistivitypropertieswerenotpossible.Moreover,theresistivitypropertieswerealsodependentonthepartofthenatural/kish/pyrolyticgraphitethatthesampleswerecutfrom.Despitethosefundamentaldifferencesintheirresistivityproperties,thein-planetransportpropertiesofvarioustypesofgraphitehaveshownsomethingincommon:metallictemperaturedependencefrom1.7Kuptoroomtemperature.ThemetallictemperaturedependenceofabexplainedwithintheDrude 126

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likepicturederivesfromthecompetitioninbetweentemperaturedependenceofnumberfreecarriersandthescatteringtimes.However,thetransportpropertiesofgraphiteattemperatureshigherthantheFermilevelofthesystemhavenotbeenstudied.ThisnotonlyoffersafruitfulphysicalregimesincemostmetalsevaporatebeforethetemperaturescomparabletotheirFermilevelvalues(orderofcoupleeV)arereachedbutalsoisnecessarytounderstandpropertiesofgraphitesincegraphite(orgraphene)-semiconductorjunctionsoperateevenathightemperaturesandisoftechnologicalimportance. Thischapterofthedissertation,aimstoexplainthein-planetransportproperties(ab)ofhighlyorientedpyrolyticgraphite(HOPG)from1.7Kupto900Kandout-ofplanetransportproperties(c)from1.7Kupto1300K.Alltheexperimentalresultspresentedinthisdissertationbelongtotheauthorofthisdissertation,howeveralltheinterpretationandtheoreticalexplanationsareresultofcollaborationwithProf.Dr.D.Maslov,Dr.D.GutmananddoctoratestudentH.K.Pal[ 38 ]. 6.2In-PlaneTransport(ab)from1.7Kupto900K 6.2.1ExperimentalDetails ThesamplesmeasuredinthischapteraresuppliedfromDr.Fischer(UPenn)andallHOPGsampleswereidentiedtohave0.5degreemosaicspreaddeterminedbyX-rayrockingcurvemeasurements.AlltheHOPGsamplesdisplayedhighanisotropy(c/ab)reachingupto103-104withtypicalgraphiteroomtemperatureresistivityvalues(c30mcmandab30cm).Thesampleshavebeencutinproperdimensionsusingdiamondimpregnatedwire.Afterthedicing,sampleshasbeencleavedbyconventionalmicrocleavagemethod[ 42 ]untilsmoothandcleansurfacesareexposed.Theelectronicpropertieshavebeenmeasuredfrom1.7Kupto300Kinaphysicalpropertymeasurementsystem(PPMS)atzeromagneticeldinfourterminalcontactcongurationusingLR-70016HzACresistancebridge.Thecontactsaremadetothesampleeitherusinghightemperaturesilverpaintorhome-madegraphitepaint.The 127

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resultspresentedinthischapterareindependentofthetypeofthepaintused.Thehightemperaturemeasurementsaredoneinahomemadevacuumovenunderhighvacuum(10)]TJ /F8 7.97 Tf 6.58 0 Td[(6Torr)orinanitrogenowinggas.Theroomtemperatureresistivitywasmeasuredtobe300Kab32cmbeforeandafterannealing,consistentwiththeexistingliteraturevalues.Since300Kabremainsatthesamevaluebeforeandafterannealing,weconcludethatadsorption/desorptionofimpuritiesordopingdoesnotoccurupto900K.Inadditiontothisobservation,X-rayphotoelectronspectroscopy(XPS,Fig. 6-1 a)andAugerelectronspectroscopy(AES,Fig. 6-1 b)wereperformedondifferentsamplesandcontaminationwasnotobserved.TheXPSandAESspectradisplayedrespectivelyacharacteristicC1speakat284.6eVandaCaugerpeakat271.8eV.TheshapeandpositionoftheXPSC1speakwasunalteredindicatingthatCremainedinthesamechemicalstate(Section 4.3.3 ).ThesampletemperaturehasbeenrecordedusingcernoxandplatinumthermocoupleinPPMSandK-typethermocoupleinthevacuumovenatacloseproximitytothesample(1mm).Typicaltemperaturedependenceofthein-planeresistivityofHOPGisdisplayedinFig. 6-2 Reproducibilityoftheresultswascheckedbysuperimposingthetemperature-dependentresistivitiesoftwoseparatesamples(Fig. 6-2 blackandreddatapoints).Reproducibilityofthemeasurementswasalsocheckedbysweepingthetemperatureupanddownintherange1.7KT900Kandnosignicanttemperaturelaggingeffectwasobserved. 6.2.2In-PlaneTransportfrom1.7Kupto300K:DrudeFormula ThetemperaturedependenceofabinHOPGismetalliclikefrom1.7Kuptotheroomtemperature(Fig. 6-2 ).Thein-planeresistivityshowsnosignicanttemperaturedependenceattemperatureslowerthan6K.Atthistemperaturerange,totalresistivityisduetotheimpurityscatteringandthetotalscatteringtimeisexpectedtobetemperatureindependent(total=imp).Above6K,in-planeresistivityincreaseswithtemperatureandshowsasignofsaturationaroundroomtemperature.In-plane 128

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transportmechanisminpristinegraphiteisessentiallygovernedbytheclassicaltheory(Drudeformula)xx=ne2 m,whichiscompetitioninbetweentemperaturedependentmobility()andcarrierconcentration(n).Thetemperaturedependenceofmobility,scatteringtimeandcarrierconcentrationhavebeenpreviouslyexactedoutfromthemeasuredxxandxyinthelowmagneticeldregion(0.2Tesla)[ 73 ]andthetemperaturedependenceoftheseparametersareshowninFig. 6-3 .BlackandreddatapointscorrespondtomajorityelectronandholecarrierswhilethebluedatapointsrepresenttheminorityholecarrierswithDirac-likespectrum(Chapter 5 ).Electron-phononscatteringdecreasesdrasticallybelow70Kandthemobilityisexpectedtoincreasebyfactorof5timeswhileitislesstemperaturedependentattemperatureshigherthan70K.Asmentionedabove,theminorityholeband(bluedatapointsinFig. 6-3 )hasDirac-likefeaturesandhencehasmuchlargermobilitiescomparingtothemobilityofmajoritybandcarriers(blackandreddatapoints)butpossessthesametemperaturedependenceduetothenatureoftheelectron-phononscattering.Afterdiscussingthetemperaturedependenceofthescatteringtimes,thetemperaturedependenceofthecarrierconcentrationisnecessarytounderstandthetemperaturevariationofabusingtheDrudeformula.Inprinciple,inaregularmetalwheretheFermilevelisontheorderofcoupleeVs,thecarrierconcentrationisnotexpectedtobetemperaturedependentatthosetemperatures.However,thelowFermienergy(300K)ingraphitemakesthecarrierconcentrationastrongfunctionoftemperatureasseeninFig. 6-3 .Carrierconcentrationincreaseswiththetemperatureby4-5timesfrom5Kupto70Kanditbecomeslesstemperaturedependentabove.Thecombinationoftemperaturedependenceofthemobilityandnumberdensity,givesaslowlyvaryingresistivityinbetween70K-300Krangewhileitdecreasesdrasticallybelow70KasobservedinFig. 6-2 andbecomestemperatureindependentbelow6K. 129

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6.2.3In-PlaneTransportfrom300Kupto900K Thein-planetransportpropertiesofHOPGinthe1.7K-300KrangecanbeexplainedwithinthesimpleDrudeformula.However,attemperaturesmuchhigherthanroomtemperature,twostrikingdifferencesinthematerialfundamentalpropertiesappear:(1)temperaturesbecomecomparabletoorlargerthantheFermilevelofthegraphiteandthistemperaturerangeidentiesanewtransportregimeand(2)allthehigherordercouplingparametersotherthan0and1becomenegligiblesincetheirenergiesarelessthan300K.Whengraphenelayersareinteractingbyonly0and1couplingparameters,graphitecanbepicturedasbi-layergraphite(BLGT).Thebandoverlapinbetweentheconductionandthevalancebandcomesfromthegamma2coupling(Chapter 5 )andinthislimit,meaningwhen2couplingisnegligible,graphitebecomeszerobandgapsemiconductorwithzerooverlapbetweenconductionandvalencebands.Priortransportmeasurementsofgraphitewereperformedatorbelow300K,whereitbehavesasacompensatedsemi-metalwithniteFermienergy.Thereis,however,averyinterestingbuthithertounexploredregimeoftemperatures,EF.T.14060K.Thisregimecanbeviewedasacriticalregionofthetransitionfromasemi-metalwithnitebandoverlaptoasemiconductorwithnitebandgap.Ifslantedhopping(3)isalsoneglected,BLGTisdescribedbyasimple(andhistoricallytherst)Wallacemodelofgraphite[ 80 ],whichcontainsonlytwohoppings:0and1.Theenergyspectruminthismodelconsistsoftwoelectronandtwoholebranches, "k=1)]TJ /F2 11.955 Tf 9.43 0 Td[(q 21)]TJ /F8 7.97 Tf 6.78 3.45 Td[(2+20jSj2k,(6) where)-463(=cos(kzc=2),cisthec-axislatticeconstantandSkisstructurefactorforhoppingbetweeninequivalent(AandB)atoms. Whenallthehigherordercouplingsareignored,but0,1,theFermienergyofthesystemreducestozeroanddensityofstates,1=v20c,becomesindependentoftemperature.Ontheotherhand,theFermifunctionscaleslinearlywithtemperature 130

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whenEF=0eVandtheredensityofcarriers,n=Rf()d,alsoscaleslinearly.UsingtheDrudeformula,thein-planeconductivityscalesas(uptoO("=1)terms), ab=(4ln2=))]TJ /F3 11.955 Tf 5.48 -9.69 Td[(e2=cT.(6) WhenthetemperatureishigherthantheFermienergyofthesystem,1=scaleslinearlywithtemperatureandtheconductivitysaturates.ThecomputedvaluesofresistivityfromthissimplemodelaregiveninFig. 6-4 withbluedashedlines. Theexperimentalresultsforab(T)arepresentedinFig. 6-4 aspoints.NotethatthetendencytosaturationpronouncedatT300Kissupersededbyarapidincreasewhichcontinuesunabateduptothehighesttemperaturemeasured.ThedashedlineintheFig. 6-4 showsthetheoreticalpredictionforab(T),calculatedfor1==1=0+Tandforarealisticenergyspectrumofcarriers.Whilethismodeldescribestheexperimentatlowtemperatures,itfailscompletelyforT>300K.Aslowincreaseinthetheoreticalcurve,whichamountsonlyfora12%increaseofabfrom300to900K,isduetocorrectionsoforderT=1toEq.( 6 ). Beforeproceedingwithadiscussionofsuchmechanisms,itisinstructivetodevelopamoreintuitivepictureoftransportinBLGT.Tothisend,wereplacetheWallacespectrumbyamassive(Galilean)formobtainedbyexpandingEq. 6 inkjjp k2x+k2yandkeepingonlythedegeneratebranchesofelectronsandholes: "k=k2jj=2mjj(kz),(6) wheremjj(kz)=)]TJ /F7 11.955 Tf 19.61 0 Td[(1=v20isthekz-dependentmassofthein-planemotion.Evaluatingthein-planeconductivityas ab(T)=4e2Zd3k)]TJ /F2 11.955 Tf 5.48 -9.68 Td[()]TJ /F7 11.955 Tf 9.3 0 Td[(@f0k=@"kv2jj("k,T)=(2)3(6) withspectrum( 6 ),=const,andf0k=1=(exp("k=T)+1),wereproduceEq.( 6 ). 131

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Typicalmomentacontributingtoabarekz1=candkjjkTp 2mjjT,wheremjjmjj(kz=0)=1=v20.AlthoughexpansioninkjjbreaksdownneartheHpoints(kz==c),where)]TJ /F1 11.955 Tf 10.1 0 Td[(vanishesandthespectrumisDirac-like,thecontributionofDiracfermionstoabissmallinproportiontothevolumeoftheBrillouinzonetheyoccupy. Therefore,atypicalcarrier(inzeromagneticeld)inBLGTismassiveratherthanDirac-likeandtheisoenergeticsurfacesarecorrugatedcylinderscenteredneartheKpoints.Asinthecaseofbi-layergraphene[ 78 81 82 ],3hopping(responsiblefortrigonalwarpingoftheisoenergeticsurfaces)leadstoalinear-in-kjjtermintheenergyspectrum,whichissmallerthanthequadratictermforenergies>123=2030K.Sincewearenotinterestedhereinspecialeffectsarisingsolelyfromtrigonalwarping,meaninglongitudinalmagnetoresistance,thistermcanbesafelyneglected. AsdiscussedinChapter 5 ,graphitecontainsfouratomsinaunitcellandwiththreedegreesoffreedomthatresultsintotaltwelvemodesinwhich3ofareacousticandtheremainingninemodesareopticalphononmodes.Thephononspectrumconsistsoftwogroupsofmodes:hardandsoft[ 83 ].Thecharacteristicenergyscaleofhardmodes,whicharepresentalreadyingraphene,areontheorderof0.1eV.Ontheotherhand,softmodes,withtypicalenergiesoforder10meV,arisefromweakcouplingbetweengraphenesheets.Forthetemperaturesofinterest(T>300K),allsoftmodesareintheclassicalregime,inwhichtheoccupationnumberand,thus,thescatteringratescalelinearlywithTasdiscussedabove.AlthoughhardacousticmodesarestillbelowtheirDebyetemperatures,theyarealsointheclassicalregime.Forexample,typicalin-planephononmomentainvolvedinscatteringatahard,graphene-likeacousticmodewithdispersion!A=sabqjjareqjjkjj.Thecorrespondingfrequencies!AsabkjjaresmallerthanTaslongasTmjjs2ab1K.Therefore,allsoftmodesaswellashardacousticmodesleadtolinearscalingofthescatteringrate)]TJ /F8 7.97 Tf 6.58 0 Td[(1e)]TJ /F8 7.97 Tf 6.59 0 Td[(ph=TanddonotaccountfortheexperimentalobservationinFig. 6-4 132

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Switchingbrieytoanotherscatteringmechanismelectron-electroninteractionwenoticethatalthough1=e)]TJ /F8 7.97 Tf 6.59 0 Td[(eduetothismechanismscalesasT2forT
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(iv)ab=[(4ln2)]TJ /F4 11.955 Tf 11.95 0 Td[(1)=3])]TJ /F3 11.955 Tf 5.48 -9.68 Td[(e2=cTexp(!0=T),(6) Basedonthisresult,wetab(T)by ab=1 0+T1 "+c e21 a0Texp)]TJ /F7 11.955 Tf 10.49 8.09 Td[(!0 T,(6) wherea0=2(4ln2)]TJ /F4 11.955 Tf 11.95 0 Td[(1)=30.376and"cRd3kv2jj)]TJ /F2 11.955 Tf 5.48 -9.69 Td[()]TJ /F7 11.955 Tf 9.3 0 Td[(@f0k=@"k=82. Whencalculating",weaccountforhoppingbetweennext-to-nearestplanes,describedby20.02eV.TherstterminEq.( 6 )accountsmostlyforthelow-Tbehaviorofab,whenscatteringatimpurities(1=0)andsoftphonons(T)dominatetransport.Thesecondtermisduetointervalleyscattering.Equation( 6 )containsfourttingparameters:0,,,and!0.TheresultsofthetareshowninthetoppanelofFig. 6-4 arearedsolidline.Thettingparametersare0=6.2910)]TJ /F8 7.97 Tf 6.59 0 Td[(12s,=0.09,=1.410)]TJ /F8 7.97 Tf 6.59 0 Td[(14s,and!0=0.22eV.Thevaluesof0andareinreasonableagreementwiththosefoundpreviously[ 73 ].Thefrequency!0issomewhathigherbutstillclosetothefrequencyoftheE2gmode[ 83 85 ].Arathershortnominaltimeindicatesstrongcouplingbetweenelectronsandopticalphononsingraphite. Tosummarize,wehavestudied,bothexperimentallyandtheoretically,thein-planeresistivityofHOPG.Wefoundthatitstemperaturedependenceisdeterminedbyacompetitionbetweenthenumberdensityandthescatteringrate.Atlowtemperatures,thescatteringrateincreaseslinearlywithT,leadingtoaquasi-saturationofabatT300K.Asthetemperatureincreases,scatteringoffhardopticalphononsbecomesimportant,whichleadstoanexponentialgrowthofthescatteringratewithT.ThisresultsinafurtherincreaseofabwithTandinthistemperaturerangebulkgraphitecanbeimaginedasbi-layergraphite(bi-layergraphene)sincethehigherordercouplingtermsarenegligible. 134

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6.3OutofPlaneTransport(c)Propertiesfrom3Kupto1500K Sofarinthischapter,wehavediscussedthein-planetransportpropertiesofHOPGfrom1.7Kupto900Kandwehaveattributedtheupturnintheresistivityattemperatureabove300Ktoscatteringoffhardphononscomingintotheplayandleadingtoanexponentialincreaseinthescatteringratewithtemperature.Althoughtheexperimentallyobservedtemperaturedependenceofthein-planeresistivityisratherunexpectedandtheoreticallyhardtoexplain,thetemperaturedependenceofthein-planeresistivityfrom1.7Kupto300Kwasquiteexpectedandhasalreadybeenexplainedbyclassicalmodels[ 73 ].However,thetemperaturedependenceoftheout-of-planedirectionresistivityhasalwaysbeenpuzzlingintheliteratureandnoconcretetheoryhasbeenproposedandmanymodelsarestillunderdebate. Thetemperaturedependenceoftheout-of-planeresistivity(c)ingraphiteisnon-monotonic,meaningitismetalliclikefrom1.7KuptoTmaxwhichisintherange39K-50K.AboveTmaxthedependenceisinsulatorlikeasdisplayedinFig. 6-5 .Surprisingly,similartemperaturedependenceinchasbeenexperimentallyobservedonotherlayeredmaterialswithtotallydifferentFermienergiesandphysicalpropertiesandelectricalresistivityvaluessuchaslayeredperovskiteSr2RuO4[ 63 ],hightemperaturesuperconductors[ 64 ],organicmetals[ 64 ].Thefactthateachofthesematerialspossessdifferentphysicalproperties,butarestillfortunate(orunfortunate)enoughtosharethesametemperaturedependenceintheout-of-planeresistivitypointsouttheonlythingthatthosematerialhaveincommon:weakcouplinginbetweenadjacentlayersandhighelectricalanisotropy(c=ab103)]TJ /F4 11.955 Tf 11.96 0 Td[(104). 6.3.1BreakdownintheClassicalModel Correlationinbetweenthelayerednatureofthesematerialsandthehighelectricalresistivityaddressedintheliteratureandpossiblemechanismscanbelistedbutnotlimitedto(1)stackingfaults[ 86 ](2)resistornetworkcombinationoftunnelingacrosstheplanesandstackingfaults[ 87 ](3)coherenttoincoherentcross-over(Anderson 135

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localization)[ 88 89 ].Thenecessityofthesenon-trivialmechanismsmightbequestionablebutallhavebeenproposedinattempttoexplainthenon-monotonicbehavioraswellaslargeelectricalanisotropysimultaneouslywhichclassicaltheorycannotexplain.TrivialapplicationoftheSWMcmodeltocalculatetheelectricalanisotropyonlypredictstheoutofplaneresistivityvaluestobetwoordersofmagnitudehigherthanthein-planeresistivity(c102ab).Thisdifferenceisessentiallycomesfromthedifferenteffectivemassesinthec-axisandab-planedirections.Ontheotherhand,experimentallytheanisotropyreachesto103)]TJ /F4 11.955 Tf 12.01 0 Td[(104andsuchlargeanisotropycannotbeexplainedonlybythedifferencesintheeffectivemasses.Lastly,eveniftheanisotropyisexplainedbandtheorydoesnothandlethenon-monotonictemperaturedependenceofthecwellandlacksphysicalexplanation. 6.3.2ProposedMechanismsandDiscussion Afterdiscussingthefailureoftheclassicalmodeltoaccountforthelargeanisotropyandobservedtemperaturedependenceoftheout-of-planeresistivity,wediscussthepossibilityofAndersonlocalizationorcoherenttoincoherentcrossoverpicture.Coherenttoincoherentcrossoveroccurswhenthetunnelingtimebetweenthelayersbecomeslargerthantheinelasticscatteringtimeinelas.Whentuninelas,theelectronsexperiencemanycollisionsbeforetheytunnel(incoherent).Thismodelemphasizesonthistransitionoccursroughlyaroundtheresistivitypeaktemperature(Tmax).Howeverithasbeenexperimentallyshownthatintheincoherentregime(T>Tmax)thereisnosignatureofnon-metallicconductivity[ 88 89 ]andthenon-monotonicbehaviorthiscannotbeexplained. Anotherproposedmechanismisbasedontheideathatelectronwavesarescatteredfromthestackingfaultsinthegraphite[ 86 ].AsmentionedinChapter 5 ,graphiteconsistsofbernalstackedgraphenelayers(ABAB)whileotherminorityphasessuchasrhombohedralphases(ABCstacking)andAAAstackingalsoexist.Inthis 136

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model,naturallyoccurringstackingfaultsplayanessentialroleintheout-of-planetransportdirection.Inthismodel,thevarietyofresistivityvaluesmeasuredondifferentHOPGsamplehasbeensuccessfullyexplainedwithintheSWMctheory,howeverthetemperaturedependenceofthecremainedunexplained.Lateronmanyothermodicationstothismodelhavefollowed[ 90 ]anddecentttingshavebeenobtainedbestwithunphysicalrelaxationtimes. Thenalmodelinthischapterexplainingthetemperaturedependenceofc-axisresistivityistheresistornetworkmodel[ 87 90 ].Inthismodelc-axistransporttunnelingacrossthegraphenesheetsareinparallelcombinationwiththespatiallyoccurringmetallic-liketransport.Inhere,theparallelresistormodelisanassumptionandeachprocessmentionedaboveservesasaconductionchannelsincetheconductivitiesaddtoeachotherandthetotalconductivityreads, total=T+M,(6) wheretheTandMcorrespondtoconductivityduetotunnelingacrosstheplanesandmetallicliketransport.TheMisthephononlimitedmetalliclikecontributionandcaniswrittenas M=a b+T2,(6) andTisthetunnelingcomponentttedas T=cT2+(T=0K),(6) Eventhough,parallelcombinationofthesetwotransportmechanismgiveststhedata,theextractedparametersdon'tgivephysicalinsightandthismodelalsocan'texplainthehighanisotropymeasuredinthesamples[ 87 90 ]. 137

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Tounderstandtheout-of-planeresistivitypropertiesingraphite,westartexpandingthetemperaturerangewherecismeasured.Previously,cmeasuredfrom5Kupto300Kusingphysicalpropertymeasurementsystem(PPMS)andthesemiconductinglikebehaviorobservedinTmaxT300Krangehasbeenattributedtothetunnelingprocessesinbetweengrapheneplanes.However,thesetunnelingprocesseshavedifferenttemperaturedependencedependingonthedetailsofthetunnelingmechanism,suchasresonanttunnelingassistedbyoneortwoimpurities[ 91 ],ordirecttunneling[ 91 92 ].Ontheotherhand,becauseofthelimitedtemperaturerange,itishardtoconcludeeitheroneofthesemechanismsproposedabove. Weattempttounderstandthetransportmechanismthatdominatesathightemperatures(higherthanTmax),byextendingtheresistivitymeasurementsupto1500KasshowninFig. 6-6 .InFig. 6-6 wenotethatatlowtemperatureresistivityisnottemperatureindependentandinfactbecomessemiconductinglikeattemperaturesbelowTmin.Moreover,theresistivitykeepsdecreasingasthetemperatureisincreasedwithoutsignofsaturationorresistivityupturn.Sincethetemperaturerangeisextendedfrom250K(fromTmaxto300K)to1500K(fromTmaxto1500K),onecanclearlyseeiftheresonanttunnelingpictureorothermodelscanaccountfortheobservedtemperaturedependenceintheelectricalresistivity. Werstexaminethepossibilityofresonanttunnelingassistedbyoneortwoimpuritieslocatedinbetweentwoconductingplatesthatareseparatedbyaninsulator.Thetemperaturedependenceoftheconductivityinthissystemhasbeenstudiedexperimentallyandtheoreticallyonmetal/amorphoussilicon/metaltunneljunctions[ 91 ]andthetotaltunnelingconductivityispredictedtoscaleas 1TcT2,(6) and 138

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2TcT4=3,(6) where1Tand2Trepresentfortunnelingconductivityacrossthetunnelingjunctionvia1or2localizedimpurities(resonantimpurities)respectively.Byusingthissystemasareferencesuchthatmetal/amorphoussilicon/metalisreplacedbygraphene/gap/graphene,thesetwomodelsmightbeapplicable.However,theconductivitydueto2ormorelocalizedimpuritiesinthegapisnotexpectedsincethedistancebetweenadjacentgraphenelayersis3.4Aanditishardtophysicallyincorporate2impuritiesinsuchasmallgap.Inthiscase,theconductivityisexpectedtoscaleasT2.InFig. 6-7 ,wehaveplottedtheresistivitydatainFig. 6-6 asconductivitywithrespecttoT2.Thedatashowstrikinglinearityinthe300Kupto1500Krangeimplyingthattheresonanttunnelingassistedviaoneresonantimpurityinbetweengrapheneplanes.WenoteforthereaderthatpreviouslysuchalineartwasnotpossibleduetothelimitedtemperaturerangeasshownintheinsetofFig. 6-7 andthedeviationfromthelinearitybelow300KcanbeattributedtoatransportmechanismofunknownoriginbecomingdominantattemperaturesbelowTmax.Althoughthetemperaturedependenceoftheout-of-planeresistivityathightemperaturescanbeexplainedbytheresonanttunnelingpicture(togetherwithparallelconductionchannelwhichisdominantalowtemperatures),thismodeldoesnotgiveanyinsightaboutthescatteringtimes.Nevertheless,withinthismodel,twoindependenttransportmechanismscanbeimaginedasworkingparalleltoeachotherinsuchawaythattheirconductivities(ratherthantheirresistivities)areadditivewherethetotalconductivityiswrittenastot=T+Mandthemetallicpartoftheconductivityisattributedtothetilting(mosaicspread)andassociatedpickupfromtheinplaneconductivityab. AverytraditionalbutoftenignoredmodelisthetheoryofbandstructurebyWallace[ 80 ].Withinthismodel,theconductivityinthec-axisdirectioncanbecalculated 139

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bysolvingBoltzmannequation(Eq. 6 )inthec-axisdirectionandusinggraphite'senergyspectrumgivenbyEq. 6 (orEq. 5 ), c(T)=4e2Zd3k)]TJ /F2 11.955 Tf 5.48 -9.69 Td[()]TJ /F7 11.955 Tf 9.3 0 Td[(@f0k=@"kv2c("k,T)=(2)3(6) =1 2)]TJ /F2 11.955 Tf 9.43 0 Td[()]TJ /F8 7.97 Tf 6.77 4.34 Td[(221 4+2k21=2,(6) andbytakingtheintegral,theconductivityinthec-axisdirectionscalesas[ 80 ], cT2ln1 kbT,(6) FittingpredictedconductivityformulatotheexperimentalresultsathightemperatureareshowninFig. 6-8 intheresistivityform.ItcanbeseenfromthegurethattheconventionalbandstructurepicturebyWallace[ 80 ]canalsoexplainthetemperaturedependenceofcathightemperatures.HoweverWallace'smodelneverreceivedenoughcreditforexplainingthec-axistransportpropertiessimplybecausethehightemperatureresistivitypropertieswereabsentintheliteratureandtheproperttinghasneverbeenperformedattemperaturesabove400K.Asaresultofthislackofexperimentaldata,mosttimesWallace'smodelhasbeenoverlookedandotherexotictransportmechanismshavebeenexclusivelyconsideredintheliterature.ThettingdisplayedinFig. 6-8 essentiallyimpliesthattheresonanttunnelingmodelisnottheuniquemodelcapableofexplainingthedataatthosetemperatures.ThettingtotheWallace'smodel(Eq. 6 )startstodeviatearound400KandpossiblyothertransportmechanismstartstobecomeapparentandeventuallyentirelydominatethetransportbelowTmax.IntheinsetofFig. 6 weshowthettedvaluesofthegivenasadashedlinewiththevalueof2.810)]TJ /F8 7.97 Tf 6.59 0 Td[(14secandistemperatureindependentsincethettingisdoneinthe400K-1500Krange.Toexplainthetemperaturedependenceoftheout-of-planeresistivity,werevisittheBoltzmannequationgivenbyEq. 6 140

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Inthisequation,theintegrationI,Rd3k)]TJ /F2 11.955 Tf 5.48 -9.69 Td[()]TJ /F7 11.955 Tf 9.3 0 Td[(@f0k=@"kv2c("k,T)=(2)3,canlooselybeinterpretedasthecarrierdensityn.Inthiscase,theconductivityscalesasDrudeformula,cne2=m,meaningresistivitypeakmightbeexplainedasacompetitionbetweencarrierdensitynandthescatteringtime.ThetemperaturedependenceofnumberofcarriersinHOPGgraphitehasbeenmeasuredinthe5K-300Ktemperaturerange[ 73 ]andnincreaseswithtemperature.Toaccountforthenon-monotonictemperaturedependence(Fig. 6-6 ),isexpectedtogrowfasterthanndoes. Aroughestimateofthescatteringtime,,canbeextractedbydividingtheoreticallycomputedc=(Eq. 6 )byexperimentalexpc.ThetemperaturedependenceoftheextractedoutbythismodelisgivenbybluecirclesinFig. 6-8 inset.Firstofall,thetemperaturedependenceisratherminusculeandinagreementwiththeparametersextractedfromthettingvalues.Insensitivityofthescatteringtimeessentiallydisregardsthepossibilityofexplainingthenon-monotonicbehaviorbyacompetitioninbetweennand.Nevertheless,thebandtheory[ 80 ]givesagoodtathightemperaturesandthelowtemperatureresistivitybehaviorcannotbeexplainedbythissimplepictureunlessanothertransportmechanismisenvoked. Inconclusion,inthissectionwehaveexperimentallystudiedthetransportpropertiesofHOPGintheout-of-planedirectionfrom3Kupto1500Kexperimentally.Theseresultsgiveavaluableinsightintothepossiblemechanismsgoverningthetransportathightemperatures.Wehavemainlyconsideredtheresonanttunnelingmechanismwheretheimpurityinbetweentwographenesheetsactsasaresonantimpurityandwehavefoundthatitgivesgoodtinthe300K-1500Krather,howeveritdoesn'tgiveanyvalueonthescatteringtimeaswellasthelowtemperature(metalliclikeresistivity)hastobeexplainedbyanothermechanismwithparallelconductionchannel.Similarly,Wallace'ssimplebandstructuretheoryalsoreproducesagoodtinthe400K-1500Krangeandisfreeofexotictransportmechanisms.Itgivesgoodtwithphysicaland1parameters.Ontheotherhand,duetothetemperatureindependent 141

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scatteringtimes(Fig. 6-8 insetbluecircles),thelowtemperatureresistivitycannotbeexplainedsimplyasacompetitioninbetweencarrierdensitynandscatteringtime. Figure6-1. (a)XPSspectrabeforeandafterannealing.(b)AESspectrabeforeandafterannealing.Insets:magniedcarbonpeaks. 142

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Figure6-2. Temperaturedependenceofin-planeresistivity(ab)inHOPGfrom1.7Kupto900Kmeasuredontwoseparatesamples(blackandtheredcurve). 143

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Figure6-3. Temperaturedependenceof(a))]TJ /F8 7.97 Tf 6.59 0 Td[(1(b)mobilityand(c)carrierdensity(n)from300Kdownto5K. 144

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Figure6-4. abversusTinHOPGfrom1.7Kupto900Kforwarming(blacksquares)andcooling(blackhollowtriangles).BluedashedtcorrespondstothettingfromWallace'smodel. 145

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Figure6-5. TemperaturedependenceofcinHOPGfrom3Kupto300K.ResistivitygivesapeakattemperatureTmaxasindicatedinthegure 146

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Figure6-6. TemperaturedependenceofcinHOPGfrom3Kupto1500K.Inset:ResistivityupturnobservedbelowTmax 147

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Figure6-7. cversusT2inthe300Kto1500Krangewithalineart(redline)Inset:Deviationfromlinearitybelow300Kduetounknowntransportmechanisms. 148

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Figure6-8. cversusT2inthe300Kto1500Krangewiththeoreticaltting(blackline)Inset:extractedfromexperimentandtheory(bluecircles)andttingtotheexperimentallymeasuredresistivity(redcirclesintheinset)givenbyblackstraightline. 149

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CHAPTER7SUPERMETALLICCONDUCTIVITYINBROMINEINTERCALATEDGRAPHITE 7.1Introduction AtthesimplestlevelgraphitecanbethoughtofasanorderedBernalstacking(refertosection 5.1.1 )ofweakly-coupledgraphenesheets.Delaminationordeconstructionofgraphiteintoisolatedgraphenesheetsforexperimentalcharacterizationbymechanicalmeans[ 42 ]hasnucleatedintenseexperimentalandtheoreticalinvestigationintotheelectronicpropertiesofthistwo-dimensionalcarbonallotrope.ThepresenceofDirac-likeelectronicexcitations,ananomalousintegerquantumHalleffect,andsignaturesensitivitytodifferenttypesofdisorderarebutafewofthefascinatingphenomenaemergingfromthesestudies.Bernalstackedgraphitewithaninterplanarspacingc=3.4Amanifestspropertiesthatareprecursorstotheunusualbehaviorsassociatedwithgrapheneandfew-layergraphene.ForexamplethepresenceofDiracfermionsneartheHpointintheBrillouinzonehasbeendetectedbyangle-resolvedphotoemissionspectroscopy[ 93 ]. Graphiteintercalationcompounds(GICs)havelongbeenrecognizedashavingunusualandsometimessurprisingproperties[ 54 ].Thischapterofthedissertationtakestheapproachofusingbromine(Br)atomasanintercalanttosimultaneouslydopeandseparatetheadjacentgrapheneplanesingraphiteandtherebybeginanapproachtothelimitwheretheinterplanarcouplingissufcientlyweaktoassurethattheresultingin-planeconductivitycanbeconsideredastheparallelcontributionofrelativelyindependentdopedgraphenesheets.Sincethebandstructureofgraphitegivesnearlyequalnumbersofelectronsandholes(Chapter 5.1.2 ),withadensityontheorderof10)]TJ /F8 7.97 Tf 6.59 0 Td[(4carrierspercarbonatom,[ 73 ]asmallchargetransferbetweentheintercalantandtheadjacentcarbonplanescanresultinasignicantincreaseinfreecarrierspercarbon.Wendthatrandomsiteinterplanardopingwithbrominetoconcentrations(6at%)givesrisetoapronounceddecreaseofthein-plane 150

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resistivityabtosupermetallicvaluesthataresignicantlylowerthanCuoverthetemperaturerange300K>T>1.7K.Theremainderofthischapterisfocusedondisplayinganddiscussingtheobservedchangesintheelectrical,structural,opticalandthemagnetizationpropertiesofHOPGuponbromineintercalation.HallandX-rayphotoelectronspectroscopy(XPS)measurementsconrmthattheBrdopantactslikeanacceptor,thusholedopingthegrapheneplanes.Opticalreectancemeasurementsconrmthesupermetallicin-planeconductivityandfurtherrevealadoping-inducedincreaseofmobilityandcarrierdensity.Thediamagneticsusceptibilitydecreasestowardzeroaswouldbeexpectedforisolatedgraphenesheets,[ 77 ]andthereisnoevidenceofdiamagneticscreeningthatmightbeassociatedwithsuperconductinguctuations.AtT=5Ktheinferredsheetresistancepergrapheneplaneoflessthan1issignicantlylowerthanreportedforisolatedgraphenesheetseitherbiasedbyanadjoininggate[ 42 ]ordopedwithimpurityatoms.[ 94 ] ThischapteraimstoreporttheexperimentalndingsonBrintercalatedgraphite,understandandexplainthephysicalprocesses/mechanismsassociatedwithobservationofsupermetallicity.Section 7.2.1 givestheexperimentaldetailsandmaterialandcharacterizationmeasurementssuchasX-raydiffraction(XRD),Augerelectronspectrocopy(AES),X-rayphotoelectronspectroscopy(XPS).Insection 7.2.2 ,weshowourmainnding;ultraconductivityinBrintercalatedgraphiteandwesupportthesedatawithadditionHalleffectdata.Toconvincereaderthattheenhancedconductivityisreal,wepresentopticaldatainsection 7.2.3 andthemagnetizationpropertiesinsection 7.2.4 anddiscusstheresultsinsection 7.2.5 .Inthischapter,theopticaldatapresentedinsection 7.2.3 istakenincollaborationwithDr.J.HwangandDr.D.TannerinTanner'slaboratoryandallthetheoreticalconsiderationsandinterpretationsarearesultofcollaborationwithDr.D.MaslovandhisgraduatestudentH.K.Pal. 151

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7.2Experimental 7.2.1SamplePreparationandCharacterization TheHOPGsamplesarecutfromasinglepiecehaving0.5mosaicspreadandtypicallyhavedimensionsontheorderof1mm.Priortothetransportmeasurementsandbromineintercalation,samplesarefreshlycleaved.ThesamplesareexposedtoBrgasatroomtemperatureinclosedchamberatcontrolledratesforvariousintercalationtimes.Aftereachexposuresamplesareremovedfromthechamberandmeasuredinafour-contactarrangementusingaLR70017Hzresistancebridgeattemperaturesandeldsalongthec-axisintheranges5K
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noadditionalreectionsindicatingstaging[ 54 ]or,equivalently,orderingoftheBrintercalants. Opticalreectancemeasurementsweremadeat300KusingaBruker113vFourierspectrometerovertherange40-5000cm)]TJ /F8 7.97 Tf 6.58 0 Td[(1(5-600meV)andaZeissMPM800micro-spectrophotometerover4000-40,000cm)]TJ /F8 7.97 Tf 6.58 0 Td[(1(0.5-5eV).Thelowfrequencylimitissetbythesignal-to-noiseanddiffractionlimitationsofoursmallsamples.BrLMMAugerpeaksareobservedtobelocatedat1396eV,1442eVand1476eVforBrexposuretimes30minutes.ThesampleswererepeatedlycleavedandremeasuredtoprobetheBrconcentrationatdifferentdepthsofthesample;thepeakheightsforagivensampleremainedconstanttowithin5%.TheBrconcentrationsextractedfromtheAugermeasurementsagreedwellwiththeweight-uptake/volume-expansionmeasurements. XPSspectraofbrominedopedHOPGsamplesweremeasuredwitha99%monochromatizedMgX-raysourcewithenergiesupto1100eV.Sattelitepeaksshiftedby10eVwerebarelyvisible.ElementalpercentageanalyseswerefoundtobeconsistentwithAESandweightuptakemeasurements.TheC1selectronbindingenergymeasuredrelativetotheFermilevelisobservedtobeat284.5eVforpristineandat284.0eVforthetBr=70minsample.Atrstsight,thereductionintheC1sbindingenergyby0.5eVcontradictstheacceptornatureofBr,themorepositivelychargedcarbonshould,forxedEF,haveahigherbindingenergy.However,similartrends/ndingsindonor(acceptor)typeintercalantsandassociatedincrease(decrease)inC1sbindingenergyhavebeenreportedintheliteraturefordifferentcompounds[ 60 96 ]andattributedtothechangeinEFbeforeandafterintercalation.InbrominatedHOPG,EFisnegativeandsignicantlylargerinmagnitudecomparedtopristineHOPGandtheC1sbindingenergyisthusmeasuredwithrespecttothelowerEFofthehole-dopedsystem.Accordingly,theincreaseintheC1sbindingenergyismorethancompensatedforbythedecreaseinEF,givinganoveralldecreaseintheC1speakpositionasobserved.TheXPSmethodthusgivesanotherwayofestimatingthe 153

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changeinFermilevelandimpliesa)]TJ /F4 11.955 Tf 22.58 0 Td[(0.5eVchangeinEFafterholedopingto6at%Br.(refertosection 4.3.3 ). 7.2.2ElectricalMeasurements Fig. 7-1 ashowsthedependenceofabonBrintercalationtimeatT=300K.Althoughtheinitiallineardependenceisnotunderstood,wenotethatafter70minutes,abappearstosaturateatavaluewhichisapproximatelyafactorofvelowerthantheroomtemperaturevalue(1.7cm)ofcopperindicatedbythehorizontaldashedline.OurinterpretationofhowthecarrierdensityN,thescatteringtimeandtheeffectivemassm?areaffectedbyBrintercalationisbasedonusingtheDrudemodelinwhichtheconductivityofeachcontributingbandis=Ne2=m?=Ne,wherethemobility=e=m?. InFig. 7-2 weshowtheevolutionoftheeld(B)dependenttransverseresistancexyforvariousintercalationtimestBrrangingfromtBr=0(pristineHOPG)totBr=70min.ThedataforpristineHOPGarewelltbytheexpressionforthetwo-bandmodel,[ 73 ] xy(B) exx(0)2=)]TJ /F2 11.955 Tf 5.48 -9.68 Td[()]TJ /F3 11.955 Tf 9.29 0 Td[(ne2e+nh2hB+2e2h(nh)]TJ /F3 11.955 Tf 11.96 0 Td[(ne)B3 1+e2xx(0)22e2h(nh)]TJ /F3 11.955 Tf 11.96 0 Td[(ne)2B2(7) wherexx(0)istheB=0in-planeresistivityandthesubscriptseandhreferrespectivelytotheelectronandholebands.Theparametersnh,ne,handeareobtainedbythefollowingprocedure; withintwobandmodelthetransverseresistivitycanbewrittenas, xy=)]TJ /F7 11.955 Tf 5.48 -9.68 Td[(2hRe+2eRhB+RhRe(Rh+Re)B3 (h+e)2+(Rh+Re)2B2,(7) whereRh=1=nhe,Re=1=nee,h=1=nhehande=1=neee.ByusingtheseexpressionsinEq. 7 reducesto, 154

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exy=)]TJ /F2 11.955 Tf 5.48 -9.69 Td[()]TJ /F3 11.955 Tf 9.3 0 Td[(ne2e+nh2hB+2e2h(nh)]TJ /F3 11.955 Tf 11.96 0 Td[(ne)B3 (nee+nhh)2+2e2h(nh)]TJ /F3 11.955 Tf 11.96 0 Td[(ne)2B2(7) Ingraphite,majorityelectronandholescontributetotheconductivityandthetotalresistancexxreads, )]TJ /F8 7.97 Tf 6.59 0 Td[(1xx=)]TJ /F8 7.97 Tf 6.58 0 Td[(1e+)]TJ /F8 7.97 Tf 6.59 0 Td[(1h=e(nee+nhh),(7) substitutingEq. 7 intoEq. 7 yields, xy(B) exx(0)2=)]TJ /F2 11.955 Tf 5.48 -9.68 Td[()]TJ /F3 11.955 Tf 9.3 0 Td[(ne2e+nh2hB+2e2h(nh)]TJ /F3 11.955 Tf 11.96 0 Td[(ne)B3 1+e2xx(0)22e2h(nh)]TJ /F3 11.955 Tf 11.95 0 Td[(ne)2B2=B+B3 1+B2(7) where,andaregivenby =)]TJ /F3 11.955 Tf 9.3 0 Td[(ne2e+nh2h(7) =2e2h(nh)]TJ /F3 11.955 Tf 11.96 0 Td[(ne)(7) =e2xx(0)22e2h(nh)]TJ /F3 11.955 Tf 11.96 0 Td[(ne)2(7) =e22xx(nh)]TJ /F3 11.955 Tf 11.96 0 Td[(ne)(7) FittingthetransverseresistivityintheformgiveninEq. 7 tothehallmagnetoresistivitydisplayedinFig. 7-2 resultsinsetofttingparameters,,and.Afterdeterminationofalltheparameters,onedeterminesthedeviationfromcompensationfromEq. 7 ,whichisexpressedasnh)]TJ /F3 11.955 Tf 12.47 0 Td[(ne.Similarly,rearrangingEq. 7 givesanotherimportantrelationregardingtoehgivenas, eh=r nh)]TJ /F3 11.955 Tf 11.95 0 Td[(ne=s e22xx=exx 1=2(7) 155

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Anotherequationthatisusedindeterminingnumberdensityandmobilityofeachchanneliscanbederivedfromthettingparameterasfollows, =)]TJ /F3 11.955 Tf 9.3 0 Td[(ne2e+nh2h=2e2hnh 2e)]TJ /F3 11.955 Tf 13.63 8.09 Td[(ne 2h= (nh)]TJ /F3 11.955 Tf 11.96 0 Td[(ne)nh 2e)]TJ /F3 11.955 Tf 13.63 8.09 Td[(ne 2h(7) usingnh)]TJ /F3 11.955 Tf 11.96 0 Td[(neinEq. 7 gives, = e22xxnh 2e)]TJ /F3 11.955 Tf 13.63 8.09 Td[(ne 2h(7) byarrangingthelastequationweget, nh 2e)]TJ /F3 11.955 Tf 13.63 8.09 Td[(ne 2h= e22xx2(7) TosummarizealltheequationsusedtoanalyzetheHalldata, ne+e+nhh=1 exx,(7) nh)]TJ /F3 11.955 Tf 11.96 0 Td[(ne= e22xx,(7) eh=exx 1=2,(7) nh 2e)]TJ /F3 11.955 Tf 13.63 8.09 Td[(ne 2h= e22xx2,(7) Thesefourequationinvolvefourunknowns(e,h,neandnh),andcanbesolvedexactly.Theobtainedttingparametersarenh=2.0(1)1019cm)]TJ /F8 7.97 Tf 6.59 0 Td[(3,ne=1.6(1)1019cm)]TJ /F8 7.97 Tf 6.58 0 Td[(3,h=4700(100)cm2/Vsande=6800(100)cm2/VsshowingthatourpristineHOPGisslightlyholedopedwithsimilarmobilitiesineachband. Ingraphite,Eq.( 7 )isapplicableforB&1,whenxx(B)isquadraticinB.[ 97 ]AtT=300K,B=1correspondstoB=0.3Tinpristinegraphite,so 156

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Eq.( 7 )describesmostoftheeldrangepresentedinFig. 7-2 .WithincreasingtBr,thequadraticdependenceofxx(B)occursoveradecreasingeldrange,thusrestrictingtherangeofvalidityofEq.( 7 ).Constrainedbythisrequirement,weextractasquare-rootdependenceofNontBrshowninFig. 7-1 b.AsseeninFig. 7-2 ,thelow-eldslope,whichispositivefortBr20min.decreaseswithincreasingBrconcentrationandbecomeslinearforthehighesttBr,thusindicatingthatBrisholedopingthegraphenesheetswithacarrierdensityN=nhdominatedbyholes. Thetemperature-dependentresistivitydataofpanels(a)and(b)ofFig. 7-3 showthattheresistivityscalesforab(c)decrease(increase)asTisreducedfrom300Kto5K.ThepositivecurvatureforsampleswithtBr70min.isconsistentwiththenotionthatthedopingissufcienttoguaranteeEFkBTincontrasttopristineHOPGandthelightlydopedsampleswhereEF300KandsignicantvariationofNwithTleadstoanegativecurvatureofab(T).Inprinciple,thenegativecurvatureinthetemperaturedependenceofabobservedinpristineHOPGsamplesisaresultofcompetitioninbetweenthetemperaturedependenceofscatteringtimeandnumberofcarriersN.Uponcoolingfromroomtemperaturedowntolowertemperatures,becauseofthesmallmagnitudeoftheFermienergyinHOPG,thenumberofcarriersincreasesbyafactorof4-6timesespeciallyinthe300K-70Krangeandisalmostconstantbelowthattemperature[ 73 ].Ontheotherhand,thescatteringtime,decreasesdrasticallyatlowtemperatures(1.7K-60K)sincethephononscatteringisgreatlyreducedatthesetemperatures.UsingDrudeformula,thetemperaturedependenceinthesetwoparametersresultinratherslowdecreaseinresistivityastemperatureisloweredfrom300Kdownto70KassociatedwithcompensationofincreaseinwithdecreaseinN.However,atlowertemperaturesnumberofcarriersstaystemperatureindependentasstartstoincreasefasterastemperatureisloweredfrom70Kto1.7KandthisgivestheuniquenegativecurvatureintheabinHOPG.AstheHOPGisintercalatedasdeterminedfromXPS(section 4.3.3 )andHallmeasurements(Fig. 7-1 andFig. 7-2 ), 157

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theFermilevelofthesystemincreasesorderby0.5eVandbecomesmuchhigherthantheFermienergyofpristinegraphitewhichis25meV.Inthiscase,thenumberdensityNbecomestemperatureindependent,whiletheelectricaltransportisstillphonondominantandwhenNiscompletelytemperatureindependent,abisexpectedtohaveapositivecurvature.InFig. 7-3 ,astheHOPGisintercalatedthecurvatureofthetemperaturedependenceofthein-planeresistivitychangesslowlyfromnegativetopositive.ThispicturealsogivesanindirectmeasureofFermienergyofgraphiteaftertheintercalationtakesplace.Theratioab(300K)/ab(5K)=47forthesamplewithtBr=70min.ishigherbymorethanafactorof10thanthesameratio(4.0)forpristineHOPGcanalsobeattributedtothetemperatureindependentN. Incontrasttoab,cincreaseswithincreasingtBrduetothepresenceofBrintercalantsactinglikeanegativepressurepushingtheplanesapart(schematicinsetofFig. 7-1 a),therebyresultingindecreasedinterplanartunneling.Withtheapplicationofpositivepressuretheinterplanarspacingdecreasesandthereisacorrespondingdecreaseinc.[ 87 ]Theholedopingoftheplanes(decreasingab)concomitantwithanincreasinginterplanarspacing(increasingc)leadstoananisotropyratioc=abat5Kapproaching107,afactorof1000greaterthanmeasuredforpristineHOPGatthesametemperature. 7.2.3OpticalMeasurements WithincreasingtBrthefar-infraredandmidinfraredreectanceincreasedramaticallyasshowninFig. 7-4 a.ThisincreaseinreectanceimpliesanassociatedincreaseinopticalconductivitywhichisborneoutbyaKramers-Kroniganalysis[ 98 ].WeusedaDrudeextrapolationatlowfrequenciesandapower-lawbehaviorathighfrequencies,withtheresultsshowninFig. 7-4 b.Notethattheopticalconductivitycurvesincludefrequencies(dashedlines)whereweusedtheextrapolation;thegoodagreementwiththedcconductivityinFig. 7-1 aandthegoodtstothereectanceprovidecondencethatthebehaviorisasshown.Asthedopingproceeds,thelow-frequencyconductivity 158

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increasesandthespectralweight(theareaunderthecurve)increasessignicantly(Fig. 7-4 b).ThefullwidthofthisDrude-likepeakrepresentsthecarrierscatteringrate)]TJ /F8 7.97 Tf 6.59 0 Td[(1whichatthehighestdopingisdecreasedbyafactorofverelativetothepristinesample. WealsonoteintherawreectancedataofFig. 7-4 atheappearanceofaphononmodearound1580cm)]TJ /F8 7.97 Tf 6.59 0 Td[(1.Thismode,whichappearstostrengthenanddevelopaFanolineshapewithBrintercalation,canbarelybeseenasasmallfeatureabovethelineintheconductivityspectraofFig. 7-4 b.Toshowthisfeatureinmoredetail,wehavemagniedtheappropriateregionbyafactorof1000asshowninFig. 7-5 .Theweakopticalphononnear1588cm)]TJ /F8 7.97 Tf 6.59 0 Td[(1increasesinstrengthbynearlyafactoroffourandredshiftsby3cm)]TJ /F8 7.97 Tf 6.59 0 Td[(1.Thesetrendsareconsistentwithpriorresults[ 54 99 ]whichshowthatintercalationchangesthelineshape,lowersthefrequency,andalsoleadstohigheroscillatorstrengthofthismode.Metallicbehaviorthuspersistsouttotheseenergiesinthestronglyintercalatedsamples. Fromthesumruleontheopticalconductivity,wecanrelatethelow-energyspectralweighttothecarrierdensity.Thespectralweightalsoaffectstherealpartofthedielectricfunction,1(!),whichforfreecarriersfollows1(!)=1)]TJ /F7 11.955 Tf 12.98 0 Td[(!2p=!2,where!2p=4Ne2=m?istheplasmafrequency.TheinsetofFig. 7-4 bshows1(!)plottedvs1/!2;theslopesoftheseplotsgivethecarrierdensity,whichisseentoincreasebymorethanafactorofeightwithincreasingtBr.Thatthecurvesarestraightlinesimpliesstronglythatafree-carrier(metallic)pictureofthelow-energyelectrodynamicsisanaccurateviewoftheintercalatedgraphite.ThedcresistivitiesinferredfromtheDrudettotheinfraredreectancemeasurementsareshownasbluetrianglesinFig. 7-1 a.Becausethereectancemeasurementsaremadewithoutplacingelectricalcontactsonthesample,theinferreddcconductivitiesofFig. 7-4 bgiveindependentconrmationofthesupermetallicconductivityinferredfromtransportmeasurements. 159

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7.2.4MagnetizationMeasurements Fig. 7-6 showsthatthetemperaturedependentdcdiamagneticsusceptibility(eldparalleltoc-axis)decreaseswithincreasingtBr.Ourroomtemperaturevalueforpristinegraphite,=)]TJ /F4 11.955 Tf 12.63 0 Td[(21.310)]TJ /F8 7.97 Tf 6.58 0 Td[(6emu/g,isingoodagreementwithpreviousexperiments;[ 77 ]thesusceptibilitydecreasesbyafactorofthreefortBr=90min.ThisdecreaseinwithincreasedholedopingofthegrapheneplanesisqualitativelyunderstoodbyrealizingthatastheFermienergymovesawayfromtheneutralitypoint(nh=ne)ofpristinegraphite,thecyclotronmassm?cincreasesand/1=m?cdecreases,approachingthelimitofexponentiallyweakdiamagnetismforsingle-planeDiracfermions.Importantly,thereisnosignatureofsuperconductivity,which,ifassociatedwiththegiantconductivity,wouldbecomemanifestasanincreaseindiamagnetismatsomecharacteristictemperature. 7.2.5Discussion Graphiteintercalationcompoundsinthedilutelimitarewellknowntoexhibitenhancementsofroom-temperatureconductivitywhich,withincreasingintercalantconcentration,saturatetomodestvalues10timesthepristinevalue.[ 100 ]Thesurprisingandunexpectedresultpresentedhereisthatforuniformlydispersednon-stagedBrdopantsatrelativelylowconcentrationsnear5-6at%,theconductivitycanjustiablybereferredtoassupermetallic.Tomakecomparisonstosingle-layergraphene,weconvertourabmeasurementstoresistancepersquareRgofeachcarbonplaneandseethatRgnear1000forHOPGat300Kdecreasestolessthan0.5at5KforintercalatedsampleswithtBr=70min.ToourknowledgetherearenoreportsofsuchalowRgforgraphene. Theexperimentalresultsraisemanyquestions,sincedopingintroducesdisorder,whydoestheconductivityincrease?Athighdopinglevel,mostofthecarriers(holes)comefromnegativelychargedacceptors,sowehaveasysteminwhichthenumberofcarriersisapproximatelyequaltothenumberofscatteringcenters.Ontheother 160

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hand,sincetheFermienergyshiftsdownwardandincreaseswithdoping,thescatteringcross-sectiondecreases,sowehavetwocompetingeffects.Assumingforamomentthatthescatteringcross-sectionisofthe2DclassicalRutherfordformARe2=EF,thatEFobeysthe2DscalingEF/na,wherena=nhcisthenumberdensityofacceptorsperlayer,andestimatingthemeanfreepathas`=1=naAR,wearriveatasimpleresultfortheparameterkF`,whichcharacterizespurityofamaterial:kF`1=rs,wherersistheaverageinter-carrierdistancemeasuredinBohrradii.Alreadyinpristinegraphite,rs1(Ref.[ 101 ])anditdecreasesfurtherwithdoping,sothissimplemodelpredictsthatthematerialbecomescleanerwithdoping,concomitantwithanincreaseinthe2Dconductivity,whichisproportionaltokF`. Inreality,thissimplepictureismodiedsignicantlyduetoeffectsofscreening.Toseethisinmoredetail,weconsiderthescreeningmechanismindopedgraphite.Inpristinegraphite,theFermienergyEF22.5meVisontheorderofthehoppingenergybetweenthenext-to-nearestgraphenelayers,2.UpondopingtheFermienergyincreases.Weconsidertwolimitingcases:i)2EF1andii)1EF0,where10.3eVisthenearest-layerhoppingand03.2eVisthenearest-neighborhoppinginthegrapheneplane.Intherstcase,graphiteisthebi-layerregime:[ 101 ]theenergyspectrumofholesisapproximately"k=)]TJ /F16 11.955 Tf 9.3 0 Td[(~2k2jj=2mjj(kz),wheremjj(kz)=mjjcos(kzc=2)isthekzdependentin-planemasswithmjj1=v20,v0108cm/sistheDiracvelocity,andc6.8Aisthecaxislatticeconstant.Thedensityofstates(perspinandperKpointofthegraphiteBrillouinzone)inthisregime=1=~22v20cdoesnotdependontheelectronenergy.Inthesecondcase,graphiteisinthegrapheneregime:thespectrumisDirac-like"k=)]TJ /F16 11.955 Tf 9.3 0 Td[(~v0kjjandthedensityofstates="=22~2v20cincreaseslinearlywithenergy".IntheThomas-Fermimodel,thesquareofthescreeningwavevectoris2=16e2.AlthoughincreaseswithEF,itstillremainsmuchsmallerthanthereciprocallatticeconstantfornottoohighdopings.Indeed,itiseasytoseethat2c2(c=aB)(EF=1)inthegrapheneregime,where 161

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aB=0~2=e2mjj50Aforthebackgrounddielectricconstant0=5.[ 102 ]Therefore,2c2.1forEF.1010.Accordingly,inboththebilayerandgrapheneregimesscreeningisnotsensitivetodetailsofthespectrum,allofwhichareincorporatedintothedensityofstates.Inthecontinuumlimit,withthescreeningradiuslargecomparedtothelatticeconstant,thescreenedpotentialisisotropic. TheaboveargumentsallowustomodelthepotentialofasinglechargedacceptorbyasimpleThomas-Fermiform V(q)=)]TJ /F4 11.955 Tf 30.32 8.09 Td[(4e2 q2jj+q2z+2,(7) where~qjjand~qzarethein-planeandc-axismomentumtransfersofchargecarriers.ThescatteringtimecanbethenobtainedfromtheFermiGoldenRule 1 =2 ~naZd2qjj (2)2Zdqz 2V2(q)"kjj+qjj,kz+qz)]TJ /F7 11.955 Tf 11.95 0 Td[("kjj,kz.(7) Anothersimplicationcomesfromthefactthatqjjisboundedbytwicethein-planeradiusoftheFermisurfacekFjjp nhc,whichissmallerthanfornottoohighdopings.ThisimpliesthatonecanneglectqjjinEq.( 7 ).Ontheotherhand,astypicalqz1=c,onecanneglectqzintheenergiesenteringthefunctioninEq.( 7 ).Theintegraloverqzcanbethenperformedindependentlyofthatoverqjjandyieldsaneffectivecouplingconstantforin-planescatteringV=RdqzV2(q)=2=42e4=3.IntermsofV,thescatteringratecanbewrittenas 1 =2 ~naV2D,(7) where 2D=Zd2qjj (2)2"kjj+qjj,kz)]TJ /F7 11.955 Tf 11.95 0 Td[("kjj,kz(7) istheeffectivedensityofstatespergraphenelayer.Accordingly,chargedacceptorsacteffectivelyasshort-rangescattererswhichaffectonlythein-planemotionofelectrons. 162

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Aposteriori,thisexplainswhyweignoredthedifferencebetweenthetotalandtransportscatteringtimes.Inthebi-layerregime,2D=mjj(kz)=2~2,whileinthegrapheneregime2D="=~2v20.Inbothcases,2Dc.Therefore,onecanwritedownthefollowingestimatefor1=:1 e2 ~nac Inthebi-layerregime,doesnotdependonnaand,therefore,1=increaseslinearlywithdoping.Inthegrapheneregime,doesincreasewithdoping(sothattheeffectivescatteringcross-sectiondecreases)butonlyweaklyas1=2/E1=2F/n1=4aand1=stillincreaseswithna(asn3=4a).Wesee,therefore,thattheobservednon-monotonicdependenceof1=ondopingshowninFig. 7-7 cannotbeexplainedwithinamodelofscatteringfromrandomlyplacedchargedacceptorsthatarescreenedbymobilecarriers. Adecreaseof1=withdopingmaybeattributedtopartialorderingofBrions:theabsenceofthree-dimensionalorder(staging)doesnotprecludeformationofalaminarstructure,inwhichthereisnocorrelationbetweenorderedlayersoftheintercalant.[ 103 ]Scatteringofchargecarriersbysuchlayerswillbesuppressedduetominibandformation(iftheFermienergyliesoutsidetheforbiddengaps)inexactlythesameway(partial)orderingofdonorsinmodulation-dopedsemiconductorheterostructuresisbelievedtoberesponsibleforextremelyhighcarriermobilitiesinsuchstructures.Atthehighestdopinglevelachievedinthisstudy(bulknumberdensityn=1020cm)]TJ /F8 7.97 Tf 6.59 0 Td[(3orsheetdensitypergraphenelayernc=2=3.41012cm)]TJ /F8 7.97 Tf 6.59 0 Td[(2),theaveragedistancebetweenBrintercalantsis30A.For0=5,theCoulombenergyatthisdistanceisabout0.1eV,whichisabout4timeslargerthanthethermalenergyatroomtemperature.Theoreticalandexperimentalstudiesof2DclassicalWignercrystalsonstructureless(liquid)substratesshowthattheCoulombenergyexceedsthethermalenergyatthemeltingtemperaturebyafactorof127.[ 104 ]Accordingtothiscriterion,aWignercrystalisnotexpectedtobestableabove10Kinourcase.Screeningbymobilecarriers 163

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shouldleadtoafurtherreductionofthemeltingtemperature.Nevertheless,the2Dordercanbestabilizedduetothepresenceofcrystallinesubstrate(graphenesheets).Also,afullydeveloped2Dordermaynotbeneededlong-rangecorrelationsinthepositionsofBrionsmaybeenoughtoreducetheireffectonthemobilityoffreecarriers.Adetailedanalysisofthisquestionrequiresseparateexperimentalandtheoreticalstudieswhichareoutsidethescopeofthischapter. ThemobilityofBr-intercalatedHOPGatroomtemperature,conrmedbyopticalmeasurements,is50,000cm2/Vsec,afactorof5higherthanpristineHOPG.Fromtransportdataat5Kwendh106cm2/Vsbutconsiderthiswithsomereservationsintheabsenceofconrmingopticaldata.AlthoughwehavenotreachedthelimitwheretheinterplanarcouplingissufcientlylowtoconsiderourintercalatedgraphiteasanorderedstackofisolatedgraphenesheetseachofwhichisdominatedbyDiracfermions,webelieveourresultsillustratetheemergenceofintriguingphenomenologyatthegraphite/grapheneboundaryaccessedbyintercalation. 164

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Figure7-1. Plotsoftheroomtemperaturein-planeresistivityab(a)andcarrierdensityN(b)asafunctionofBrintercalationtime.Thesolidredcircles(bluetriangles)inbothpanelsareinferredfromtransport/Hall(opticalreectance)measurements.After100minutesabisreducedbyafactorof100belowitsstartingvaluetoaresistivitythatisafactorofvebelowthatofcopper(horizontaldashedline). 165

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Figure7-2. TransverseresistancexyasafunctionofperpendicularmagneticeldBfortheindicatedintercalationtimes.Theinsetshowsthesamedataoveralargereldrange. 166

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Figure7-3. Temperaturedependenceof(a)aband(b)cattheindicatedintercalationtimes.Therighthandaxisofpanel(a)isanexpandedscaleforthetBr=70min.curve 167

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Figure7-4. Infraredreectance(a)andopticalconductivity,1(!),(b)atindicatedintercalationtimestBr.Databelow35cm)]TJ /F8 7.97 Tf 6.59 0 Td[(1inpanel(b)arefromtheDrude-Lorentzttothereectance.Inset:Realpartofthedielectricfunctionversus1/!2.Theslope,proportionaltotheplasmafrequencysquared,isameasureofthetotalcarrierdensity. 168

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Figure7-5. OpticalconductivityofgraphiteandBr-dopedgraphiteintheregionofthe1588cm)]TJ /F8 7.97 Tf 6.59 0 Td[(1phononcorrespondingtotheintercalationtimestBr(toptobottom)indicatedinthelegend. 169

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Figure7-6. Temperaturedependenceofmagneticsusceptibilitycattheindicatedintercalationtimes. 170

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Figure7-7. Plotofscatteringratesdeterminedfromoptical(bluetriangles)andtransport(redtriangles)showsnon-monotonicdependenceonbromineintercalationtimes. 171

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CHAPTER8GRAPHENEANDGRAPHITEGROWTHONSICBYTHERMALANNEALING 8.1Introduction Grapheneisanearlyidealsinglelayerofsp2bondedcarbonatomsformingahoneycomblattice.Grapheneisazerobandgapsemiconductorwithitsuniquebandstructurepropertiessuchasmasslesschargecarriers(Diracfermions)withexperimentallymeasuredmobilitiesexceeding100,000cm2V)]TJ /F8 7.97 Tf 6.59 0 Td[(1s)]TJ /F8 7.97 Tf 6.59 0 Td[(1(100timesbiggerthanSi)[ 105 ].Thebandstructureofgraphenecaneasilybederivedfromgraphite'smorecomplicatedenergyspectrum.Thecouplingparametersforgraphiteareidentiedfrom0upto6andtheirvaluesanddescriptionsaregiveninsection 5.1.2 ,Table 5-1 .Ontheotherallthosecouplingsthatexistingraphitegoestozeroexceptthenearestneighborcarboncarboncoupling(in-planecarboncarboncoupling)labelledas0,andthebi-layergraphitespectrumgivenbyEq. 5 reducesto=k.Moreover,grapheneistransparentinthevisiblerangeandthesp2natureofthebondinginbetweencarbonsmakesgrapheneachemically/thermallyrobustmaterial.Sofargraphenehasattractedalotofattentionafterbecomingexperimentallyaccessibleviamechanicalexfoliationmethod[ 42 ].However,variousallotropesofgraphenehavebeenthecenterofattentionformorethan5decadesas:0Dfullerenes,1Dcarbonnanotubes,and3Dgraphite.Recentadvancesincarbonnanotechnologyhaveresultedinthecontrollablegrowthofsinglelayergrapheneon4H-SiC,6H-SiC,variouscrystallinemetalsandmetalthinlms.Suchadvanceshaveresultedinatremendousgrowthofbothexperimentalandtheoreticalinvestigationsthathaveleadtoavarietyofpotentialapplicationsfromengineeringtofundamentalsciences. Sofarsingleormanylayergraphenehasbeengrownondifferentsubstratesbysolidstatesublimationon4H-SiCand6H-SiC[ 52 ],chemicalvapordepositiononnickelthinfoils[ 106 ]andepitaxialmethodsoncopperthinlms[ 107 ].Eventhougheachmethodhasitsownstrengths,onlygraphenegrowthonSiCbysolid 172

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statesublimationgivesthehighestqualitygraphene.Ontheotherhand,experimentaldifcultiesassociatedwithgrowthrequirementssuchasUHV,localelectroneldeffectannealingaswellassensitivegrowthconditionsaretypicallytoocomplicatedforthepossibleindustrialproposes.Ithasbeenspeculatedthat,ifSiCsamplesareannealedtohighenoughtemperaturestheUHVconditionsmightnotbenecessary.Inthispartofthedissertation,wepresentanothernewtechniquetogrowgraphiteandgrapheneon4H-SiCand6H-SiCviaajouleheatingeffect. 8.2ExperimentalDetails MostofthegraphenegrowthtechniquesonSiCinvolveannealingaverylimitedareaonSiCunderultrahighvacuumconditions(UHV)byquantumeldemissionofhighenergyelectronsfromaverysharptungstenmetaltip.Theseheatersarecommerciallyavailableandheavilyusedinscanningelectronmicroscopes(SEM).Inthistechnique[ 52 ],localpartsoftheSiCisannealeduptohightemperatureforvarioustimescales,electronenergyintensityanddifferentsoakingtemperaturestotunethenumberofgraphenelayersgrownonSiC.Inthischapter,weproposeamuchsimplerandpracticalwaytogrowgraphite(graphene)onSiCunderhighvacuumconditionsaround10)]TJ /F8 7.97 Tf 6.59 0 Td[(6)]TJ /F4 11.955 Tf 12.84 0 Td[(10)]TJ /F8 7.97 Tf 6.58 0 Td[(7TorrWeannealSiCwafersthatarealreadyinthermalcontactwithatungstenboatandwepassdirectcurrentwhichisorderof100-200Ampthroughthetungstenboatforvarioustime,atvariousmagnitudes,differentratesanddifferentcoolingratesandsoakingtemperatures.ManyparametersonthegrowthconditionsallowsustotunethenumberofgraphenelayersgrownonSiCeasierthanthepreviousmethod.Thedetailsofthegrowthparameterswillberevealedinaseparatepublication. 8.3MaterialCharacterization WehaveemployedRamanspectroscopy,Augerelectronspectroscopy(AES),X-raydiffraction(XRD)measurements,andelectricalmeasurementstovalidatethequalityofthegraphite(graphene)grownbythisjouleheatingtechniqueonSiC. 173

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InFig. 8-1 thedatainblackdatapoints(upperpanel)correspondtothebare4H-SiCRamanspectrawhileredandbluestraightlinescorrespondtothejouleannealedsamples.TheRamandatatakenonsamplegivenbyredlines(middlepanel)isannealedbypassing170Ampfor6minthroughthetungstenboatwhilethesamplegiveninblue(lowerpanel)isannealedbypassing200Ampfor3min.Thesecurrentsapproximatelycorrespondsto1900Cand2400Cfor170Aand200Aaccordingly.Comparingblack,redandbluelines,showsaclearindicationofnewadditionalpeakswhilenativeSiCpeaksstartstodisappear.ThoseadditionalpeaksareidentiedasD,Gand2Dgraphitepeaks.Therefore,200AmpsetsahighlimitinthegraphenegrowthonSiCbythismethod.Afterthetreatment,thesamplesaretypicallyobservedtobeblack,shinyandconductive.200Amp(2400C)heatsupthesampletothehightemperatureunderhighvacuumconditions,andcreatesthickblackandshinygraphiteontheSiCsurface.However,reductionofthecurrentto170AmpsignicantlyreducesthethicknesstocouplelayersandbecomeslessconductivethanthatofgraphiteontheSiC.Accordingly,theRamandatatakenonthe170Ampannealedsampledoesn'tshowcleargraphite/graphenevibrationalmodes.UponcloselookaroundthebareSiCsampleandannealedSiCsampleslookslightlydifferentwiththebackgroundhiddengraphitevibrationalmodepeaks.InFig. 8-2 thesubtractionofthebareSiCrawdatafromtheannealedSiC(200Amp3min.)fromshowsaclearD,Gand2DgrapheneRamanmodeswithGmodepositioncorrespondingtosomewhereinbetweenGraphiteandgraphene(singleand/orcouplelayergraphene). EventhoughRamanspectroscopyshowsanevidenceofgraphene,graphiteonthesurfacemanyothertechniquescanbeperformedonthesample.Electronictransport,Augerelectronspectroscopy,andX-raydiffractionmeasurementsaredoneonthesample.Fig. 8-3 showstheresistivitydatafrom300Kdownto1.7Kon200AmpannealedSiC(2400C).Theroomtemperaturein-planeresistivityismeasuredtobearound30.cmatroomtemperature(Fig. 8-3 )consistentwiththepristinehighly 174

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orientedpyrolyticgraphite(HOPG)samplewith15-30.cmin-planeresistivities.[ 38 ].InpristineHOPG,thetemperaturedependenceofthein-planeresistivityismetallicwhiletheresistivityofgraphitegrownonSiCisinsulatinglikeandstartstosaturatebelow50K.Tounderstandthetemperaturedependenceoftheresistivity,wehavefurthercharacterizedsamplesusingAEStomeasureconcentrationoftheimpuritiesandAFMtodetermineaveragegrainsizesinthegraphitethinlm.Fig. 8-4 displaystheAFMimagestakenonthesamples.Typicallmsareobservedtohaveaveragegrainsizesof25nm. Sincegraphiteisacleansemi-metal,theatroomtemperaturetheaverageelectronhasenoughenergytoovercometheenergybarrier(tunneling)barrierbetweenadjacentgrainsandthemeasuredresistivitycorrespondstoresistivityofHOPGgraphite.However,asthetemperaturelowered,tunnelingprocessesbecomemoredominantandbecomestemperatureindependentasobservedinFig. 8-3 Overall,inthischapterwehavedisplayedanewmethodtogrowgrapheneorgraphiteonSiCsubstrates.AES,Ramanspectroscopy,resistivitymeasurementsaswellasAFMimagesshowagoodqualitygraphiteat300K.Ourcurrentresearchwillbemostlyfocusedongraphenegrowthon4H-SiCand6H-SiCusingthemethoddescribedabove,aswellascarbonimplantationinSiCsubstratesanddiffusionofcarbonatomsathightemperatures.Ourpreliminarymeasurementsimplythatlowertemperatureandpressuregraphenegrowthispossible.Moreover,carbonimplantationinSi,Ge,CuandNithinlmsalsoshowencauragingresults.Experimentaldetails,andfurtherdiscussiononthistopicwillbepublishedinupcomingarticlesandcontinuationdissertations. 175

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Figure8-1. Ramanspectrumtakenonpristine4H-SiC(blackline)andannealedSiCbypassingcurrentthroughTungstenwire(170Aredlineand200Ablueline). 176

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Figure8-2. SubtractionofRamanspectrumofpristine4H-SiC(blackline)andannealed(2000Cfor3minutes)samples(redandgreenlines)andexistanceofD,G,and2Dmodes(magentaandbluelines.) 177

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Figure8-3. Temperaturedependenceofin-planeresistivityofgraphitegrownonSiC 178

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Figure8-4. AFMimagetakenongraphiteSiCsurface 179

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REFERENCES [1] Tung,R.T.Recentadvancesinschottkybarrierconcepts.Mater.Sci.Eng.R-Rep.a35,1(2001). [2] Neamen,D.A.SemiconductorPhysicsandDevices,Thirded.(McgrawHill,Boston,2003). [3] Sze,S.M.Physicsofsemiconductordevices2ndedition(JohnWileyandSons,NewYork,1981). [4] Padovani,F.A.&Stratton,R.Fieldandthermionic-eldemissioninschottkybarriers.Solid-StateElectronics9,695707(1966). [5] Fowler,R.Theanalysisofphotoelectricsensitivitycurvesforcleanmetalsatvarioustemperatures.Phys.Rev.38,45(1931). [6] Louie,S.G.&Cohen,M.L.Self-consistentpseudopotentialcalculationforametal-semiconductorinterface.Phys.Rev.Lett.35,866(1975). [7] Tersoff,J.Schottkybarrierheightsandthecontinuumofgapstates.PhysicalReviewLetters52,465(1984). [8] Fujitani,H.&Asano,S.SchottkybarriersatNiSi2/Si(111)interfaces.PhysicalReviewB42,1696LP(1990). [9] Kim,D.M.,Kim,D.H.&Lee,S.Y.Characterizationandmodelingoftemperature-dependentbarrierheightsandidealityfactorsingaasschottkydiodes.Solid-StateElectronics51,865869(2007). [10] Bauza,D.Effectofdeeptrapsonthecapacitance-voltageplotsofschottkybarrierdiodes:Applicationtothestudyofsputter-etchedTi-W/n-Sidiodes.JournalofAppliedPhysics73,1858(1993). [11] Newman,N.,Schilfgaarde,M.,Kendelwicz,T.&Williams,F.Electricalstudyofschottkybarriersonatomicallycleangaas(110)surfaces.Phys.Rev.B33,1146(1985). [12] Kikkawa,J.M.&Awschalom,D.D.Lateraldragofspincoherenceingalliumarsenide.Nature397,139(1999). [13] Hanbicki,A.T.,Jonker,B.T.,Itskos,G.&Kioseoglou,G.Efcientelectricalspininjectionfromamagneticmetal/tunnelbarriercontactintoasemiconductor.AppliedPhysicsLetters80,1240(2002). [14] Crooker,S.A.,Furis,M.,Lou,X.&Adelmann,C.Imagingspintransportinlateralferromagnet/semiconductorstructures.Science309,2191(2005). [15] Parish,M.M.&Littlewood,P.B.Magnetocapacitanceinnonmagneticcompositemedia.Phys.Rev.Lett.101,166602(2008). 180

PAGE 181

[16] Zutic,I.,Fabian,J.&Sarma,S.D.Spintronics:Fundamentalsandapplications.ReviewsofModernPhysics76,323(2004). [17] Yafet,Y.,Keyes,R.W.&Adams,E.N.Hydrogenatominastrongmagneticeld.JournalofPhysicsandChemistryofSolids1,137142(1956). [18] Armistead,C.J.,Makado,P.C.,Najda,S.P.&Stradling,R.A.Far-infraredstudiesatintermediatemagneticeldswiththeneutralshallowdonorsinGaAsandInPoftransitionsnotinvolvingthegroundstate.JournalofPhysicsC:SolidStatePhysics19,6023(1986). [19] Klarenbosch,A.V.,Klaassen,T.O.,Wenckebach,W.T.&Foxon,C.T.IdenticationandionizationenergiesoftheshallowdonormetastablestatesinGaAs:Si.J.Appl.Phys.67,6323(1990). [20] Poehler,T.O.Magneticfreezeoutandimpactionizationingaas.PhysicalReviewB4,1223LP(1971). [21] Jouault,B.,Raymond,A.&Zawadzki,W.Ionizationenergyofmagnetodonorsinpurebulkgaas.PhysicalReviewB65,245210(2002). [22] Herrero,A.M.,Gerger,A.M.,Gila,B.P.&Pearton,S.J.InterfacialdifferencesinenhancedschottkybarrierheightAu/n-GaAsdiodesdepositedat77k.AppliedSurfaceScience253,32983302(2007). [23] Kwak,J.S.,Kim,H.N.,Baik,H.K.&Lee,J.MicrostructuralandelectricalinvestigationsofPd/Ge/Ti/Auohmiccontactton-typeGaAs.JournalofAppliedPhysics80,3904(1996). [24] Lai,J.T.&Lee,J.Y.RedistributionofconstituentelementsinPd/Gecontactston-typeGaAsusingrapidthermalannealing.JournalofAppliedPhysics76,1686(1994). [25] Catalan,G.Magnetocapacitancewithoutmagnetoelectriccoupling.AppliedPhysicsLetters88,102902(2006). [26] Hikita,Y.,Kozuka,Y.,Susaki,T.&Takagi,H.CharacterizationoftheschottkybarrierinSrRuO3/Nb:SrTiO3junctions.AppliedPhysicsLetters90,143507(2007). [27] Shklovskii,B.I.&Efros,A.L.ElectronicPropertiesofDopedSemiconductors(Springer-Verlag,Berlin,1984). [28] Cole,K.S.&Cole,R.H.Dispersionandabsorptionindielectricsi.alternatingcurrentcharacteristics.TheJournalofChemicalPhysics9,341(1941). [29] Stanton,C.J.&Bailey,D.W.Rateequationsforthestudyoffemtosecondintervalleyscatteringincompoundsemiconductors.Phys.Rev.B45,8369(1991). 181

PAGE 182

[30] Rhoderick,E.H.&Williams,R.H.Metal-SemiconductorContacts,2nded.(OxfordUniversityPress,USA,1988). [31] Barbolla,J.,Dueas,S.&Bailn,L.Admittancespectroscopyinjunctions.Solid-StateElectronics35,285297(1992). [32] Fonash,S.J.Areevaluationofthemeaningofcapacitanceplotsforschottky-barrier-typediodes.JournalofAppliedPhysics54,1966(1983). [33] Klarenbosch,A.V.,Klaassen,T.O.,Wenckebach,W.T.&Foxon,C.T.IdenticationandionizationenergiesoftheshallowdonormetastablestatesinGaAs:Si.JournalofAppliedPhysics67,6323(1990). [34] Zimmerman,J.D.,Brown,E.R.&Gossard,A.C.Tunableallepitaxialsemimetal-semiconductorschottkydiodesystem:ErAsonInAlGaAs.JournalofVacuumScience&TechnologyB:MicroelectronicsandNanometerStructures23,1929(2005). [35] Neto,A.D.Theelectronicpropertiesofgraphene.ReviewsofModernPhysics81,109(2009). [36] Geim,A.K.Graphene:Statusandprospects.Science324,1530(2009). [37] Zhou,S.Y.,Gweon,G.H.,Graf,J.&Fedorov,A.V.Firstdirectobservationofdiracfermionsingraphite.NaturePhysics2,595(2006). [38] Gutman,D.B.,Tongay,S.,Pal,H.K.&Maslov,D.L.Graphiteinthebilayerregime:In-planetransport.Phys.Rev.B80,045418(2009). [39] Hao,P.H.,Wang,L.C.,Deng,F.&Lau,S.S.OnthelowresistanceAu/Ge/Pdohmiccontactton-GaAs.JournalofAppliedPhysics79,4211(1996). [40] Han,S.Y.,Shin,J.Y.,Lee,B.T.&Lee,J.L.Microstructuralinterpretationofniohmiccontactonn-type4hsic.JournalofVacuumScience&TechnologyB:MicroelectronicsandNanometerStructures20,1496(2002). [41] Wang,H.T.,Jang,S.,Anderson,T.&Chen,J.J.IncreasedschottkybarrierheightsforAuonn-andp-typeGaNusingcryogenicmetaldeposition.AppliedPhysicsLetters89,122106(2006). [42] Novoselov,K.S.,Geim,A.K.,Morozov,S.V.&Jiang,D.Electriceldeffectinatomicallythincarbonlms.Science306,666(2004). [43] Wagner,L.,Young,R.&Sugerman,A.Anoteonthecorrelationbetweentheschottky-diodebarrierheightandtheidealityfactorasdeterminedfromI-Vmeasurements.ElectronDeviceLetters,IEEE4,320(1983). 182

PAGE 183

[44] Han,S.Y.,Kim,K.H.,Kim,J.K.&Jang,H.W.OhmiccontactformationmechanismofNionn-type4H-SiC.AppliedPhysicsLetters79,1816(2001). [45] Wang,H.T.,Jang,S.,Anderson,T.&Chen,J.J.IncreasedschottkybarrierheightsforAuonn-andp-typeGaNusingcryogenicmetaldeposition.AppliedPhysicsLetters89,122106(2006). [46] Olbrich,A.,Vancea,J.,Kreupl,F.&Hoffmann,H.Potentialpinch-offeffectininhomogeneousAu/Co/GaAs(100)-schottkycontacts.AppliedPhysicsLetters70,2559(1997). [47] Suzuki,S.,Bower,C.,Kiyokura,T.&Nath,K.G.Photoemissionspectroscopyofsingle-walledcarbonnanotubebundles.JournalofElectronSpectroscopyandRelatedPhenomena114-116,225228(2001). [48] Sque,S.J.,Jones,R.&Briddon,P.R.Thetransferdopingofgraphiteandgraphene.phys.stat.sol.(a)204,3078(2007). [49] Taft,E.&Apker,L.Photoelectricemissionfrompolycrystallinegraphite.Phys.Rev.99,1831(1955). [50] Dandrea,R.G.&Duke,C.B.InterfacialatomiccompositionandschottkybarrierheightsattheAl/GaAs(001)interface.vol.11,1553(AVS,1993). [51] Fujitani,H.&Asano,S.Electronicstructureofsi/disilicideinterfaces.AppliedSurfaceScience41-42,164168(1989). [52] Berger,C.,Song,Z.,Li,T.&Li,X.Ultrathinepitaxialgraphite:2delectrongaspropertiesandaroutetowardgraphene-basednanoelectronics.J.Phys.Chem.B108,19912(2004). [53] Gworek,C.,Phatak,P.,Jonker,B.T.&Weber,E.R.PressuredependenceofCu,Ag,andFe/n-GaAsschottkybarrierheights.Phys.Rev.B64,045322(2001). [54] Dresselhaus,M.S.&Dresselhaus,G.Graphiteintercalationcompounds.AdvancesinPhysics30,189(1981). [55] Tongay,S.,Schumann,T.&Hebard,A.F.GraphitebasedschottkydiodesformedonSi,GaAs,and4H-SiCsubstrates.AppliedPhysicsLetters95,222103(2009). [56] Han,S.Y.,Shin,J.Y.,Lee,B.T.&Lee,J.L.MicrostructuralinterpretationofNiohmiccontactonn-type4H-SiC.JournalofVacuumScience&TechnologyB:MicroelectronicsandNanometerStructures20,1496(2002). [57] Karpan,V.M.,Giovannetti,G.,Khomyakov,P.A.&Talanana,M.Graphiteandgrapheneasperfectspinlters.Phys.Rev.Lett.99,176602(2007). 183

PAGE 184

[58] Tongay,S.,Hwang,J.,Tanner&Pal,D.B.Ultrasuperconductivityinbromineintercalatedgraphite.arXiv:0907.1111v11,1(2010). [59] Rousseau,B.,Szwarckopf,H.E.,Thomann,A.&Brault,P.Xrsstudiesofgraphiteandintercalatedgraphite.Appl.Phys.A,MaterialSci.andProc.77,591(2003). [60] Wertheim,G.K.,VanAttekum,P.T.T.M.&Basu,S.Electronicstructureoflithiumgraphite.SolidStateCommunications33,11271130(1980). [61] Zhang,Y.,Zhang,Z.,Li,T.,Liu,X.&Xu,B.XpsandxrdstudyofFeCl3-graphiteintercalationcompoundspreparedbyarcdischargeinaqueoussolution.Spec-trochimicaActaPartA:MolecularandBiomolecularSpectroscopy70,10601064(2008). [62] Brandt,N.B.,Chudinov,S.M.&Ponomarev,Y.G.SemimetalsIGraphiteandItsCompounds(North-Holland,Amsterdam,1988). [63] Hussey,N.E.,Mackenzie,A.P.,Cooper,J.R.&Maeno,Y.Normal-statemagnetoresistanceofSr2RuO4.Phys.Rev.B57,5505(1998). [64] Annett,J.F.,Goldenfeld,N.&Renn,S.R.PhysicalPropertiesofHighTempera-tureSuperconductorsII(WorldScientic,Singapore,1990). [65] Kroto,H.W.,Heath,J.R.,O'Brien,S.C.&Curl,R.F.C60:Buckminsterfullerene.Nature318,162(1985). [66] Radushkevich,L.&Lukyanovich,V.Tubulecarbons.Zurn.Fisc.Chim(JournalofPhysicalChemistryofRussia)26,88(1952). [67] Oberlin,A.,Endo,M.&Koyama,T.Filamentousgrowthofcarbonthroughbenzenedecomposition.JournalofCrystalGrowth32,335349(1976). [68] Iijima,S.Helicalmicrotubulesofgraphiticcarbon.Nature354,56(1991). [69] Cervenka,J.,Katsnelson,M.I.&Flipse,C.F.J.Room-temperatureferromagnetismingraphitedrivenbytwo-dimensionalnetworksofpointdefects.NatPhys5,840(2009). [70] Esquinazi,P.,Setzer,A.,Hohne,R.&Semmelhack,C.Ferromagnetisminorientedgraphitesamples.Phys.Rev.B66,024429(2002). [71] Kempa,H.,Esquinazi,P.&Kopelevich,Y.Integerquantumhalleffectingraphite.SolidStateCommunications138,118122(2006). [72] Esquinazi,P.,Garcia,N.,Barzoil,J.&Rodiger,P.Indicationsforintrinsicsuperconductivityinhighlyorientedpyrolyticgraphite.Phys.Rev.B78,134516(2008). 184

PAGE 185

[73] Du,X.,Tsai,S.,Maslov,D.L.&Hebard,A.F.Metal-insulator-likebehaviorinsemimetallicbismuthandgraphite.Phys.Rev.Lett.94,166601(2005). [74] Kopelevich,Y.,Pantoja,J.C.,daSilva,R.R.&Moehlecke,S.Universalmagnetic-eld-drivenmetal-insulator-metaltransformationsingraphiteandbismuth.Phys.Rev.B73,165128(2006). [75] Ebbesen,T.W.Carbonnanotubes:preparationandproperties(CRCPress,INC,1997). [76] Slonczewski,J.C.&Weiss,P.R.Bandstructureofgraphite.Phys.Rev.109,272(1958). [77] McClure,J.W.BandstructureofgraphiteanddeHaas-vanAlpheneffect.Phys.Rev.108,612(1957). [78] Sharma,M.P.,Johnson,L.G.&McClure,J.W.Diamagnetismofgraphite.PhysicsLettersA44,445446(1973). [79] Ushio,H.,Uda,T.&Uemura,Y.Theoryofcyclotronresonanceofgraphite.i.determinationofthedegreeofbandwarping.JournalofthePhysicalSocietyofJapan33(6),1551(1972). [80] Wallace,P.R.Thebandtheoryofgraphite.Phys.Rev.71,622(1947). [81] McCann,E.&Falko,V.I.Landau-leveldegeneracyandquantumhalleffectinagraphitebilayer.Phys.Rev.Lett.96,086805(2006). [82] Nilsson,J.,Neto,A.H.C.,Peres,N.M.R.&Guinea,F.Electron-electroninteractionsandthephasediagramofagraphenebilayer.Phys.Rev.B73,214418(2006). [83] Wirtz,L.&Rubio,A.Thephonondispersionofgraphiterevisited.SolidStateComm.131,141(2004). [84] Gonzalez,J.,Guinea,F.&Vozmediano,M.A.Marginal-fermi-liquidbehaviorfromtwo-dimensionalcoulombinteraction.Phys.Rev.B(RapidComm.)59,2474(1999). [85] Maultzsch,J.,Reich,S.,Thomsen,C.&Requardt,H.Phonondispersioningraphite.Phys.Rev.Lett.92,075501(2004). [86] Ono,S.C-axisresistivityofgraphiteinconnectionwithstackingfaults.J.Phys.Soc.Jpn.40,498(1976). [87] Uher,C.,Hockey,R.L.&Ben,E.J.Pressuredependenceofthec-axisresistivityofgraphite.Phys.Rev.B35,44834488(1986). 185

PAGE 186

[88] Ioffe,L.B.,Larkin,A.I.,Varlamov,A.A.&Yu,L.Effectofsuperconductinguctuationsonthetransverseresistanceofhigh-tcsuperconductors.Phys.Rev.B47,8936(1993). [89] Moses,P.&McKenzie,R.H.Comparisonofcoherentandweaklyincoherenttransportmodelsfortheinterlayermagnetoresistanceoflayeredfermiliquids.Phys.Rev.B60,7998(1999). [90] Matsubara,K.,Sugihara,K.&Tsuzuku,S.Electricalresistanceinthecdirectionofgraphite.Phys.Rev.B41,969(1989). [91] Xu,Y.,Ephron,D.&Beasley,M.R.Directedinelastichoppingofelectronsthroughmetal-insulator-metaltunneljunctions.Phys.Rev.B52,2843(1995). [92] Simmons,J.G.GeneralizedthermalJ-Vcharacteristicfortheelectrictunneleffect.J.Appl.Phys.35,,2655(1964). [93] Zhou,S.Y.,Gweon,G.H.,Graf,J.&Fedorov,A.V.Firstdirectobservationofdiracfermionsingraphite.NaturePhysics595,2006(2). [94] Schedin,F.,Geim,A.K.,Morozov,S.V.&Hill,E.W.Detectionofindividualgasmoleculesadsorbedongraphene.NatureMaterials6,652(2007). [95] Foley,G.M.T.,Zeller,C.,Falardeau,E.R.&Vogel,F.L.MetallicreectanceofAsF5-graphiteintercalationcompounds.SolidStateCommunications24,371(1977). [96] Yan,Z.,Zhuxia,Z.,Tianbao,L.&Xuguanga,L.XpsandxrdstudyofFeCl3graphiteintercalationcompoundspreparedbyarcdischargeinaqueoussolution.SpectrochimicaActaPartA70,1060(2008). [97] Pal,H.K.&Maslov,D.L.(unpublished)(2010). [98] Wooten,F.OpticalPropertiesofSolids(AcademicPress,SanDiego,1972). [99] Leung,S.Y.,Underhill,C.,Dresselhaus,G.&Dresselhaus,M.S.Infraredactivelatticemodesingraphitealkalimetalcompounds.SolidStateCommun.33,285(1980). [100] Dresselhaus,M.S.,Dresselhaus,D.&Fischer,J.E.Graphiteintercalationcompounds:Electronicpropertiesinthedilutelimit.Phys.Rev.B15,3180(1977). [101] Gutman,D.,Tongay,S.,Pal,H.K.&Maslov,D.L.Graphiteinthebilayerregime:In-planetransport.Phys.Rev.B80,045418(2009). [102] Venghaus,H.Infraredreectanceanddielectricpropertiesofpyrolyticgraphiteforeparcpolarization.Phys.StatusSolidi81,221(1977). [103] Shklovskii,B.I.(privatecommunication). 186

PAGE 187

[104] Chui,S.T.&Esfarjani,S.T.Finite-temperaturetwo-dimensionalwignertransition.Phys.Rev.B44,11498(1991). [105] Du,X.,Skachko,I.,Barker,A.&Andrei,E.Y.Approachingballistictransportinsuspendedgraphene.NatureNanotechnology3,491(2008). [106] Yu,Q.GraphenesegregatedonNisurfacesandtransferredtoinsulators.Appl.Phys.Lett.93,113103(2008). [107] Li,X.,Cai,W.,An,J.&Kim,S.Large-areasynthesisofhigh-qualityanduniformgraphenelmsoncopperfoils.Science324,1312(2009). 187

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BIOGRAPHICALSKETCH SefaattinTongaywasborninBerlin,Germanyin1980.HehasspentdreamychildhoodyearswithhisparentsSuzanTongayandErgunTongayandhis4sistersand1brother.HestartedhiseducationinGermanyandwenttosecondaryandhighschoolinthemostwesternpointofTurkey,Izmir.HehasstartedhiscollegedegreeinEgeUniversity,DepartmentofPhysics,theoreticalphysicsdivisionin1998andgraduatedin2002withSummaCumLaudehonorsrankingrstinclassof2002.Duringhisundergraduatestudies,hespecializedonmoleculardynamicsandab-initiocalculationsunderProf.Dr.EmineCebe'ssupervision.Afterbachelor'sdegree,hedecidedtoworkintheoreticalcondensedmatterphysicsatBilkentUniversityinTurkeywithProf.Dr.SalimCiraci.DuringMasterofSciencestudies,hehasworkedoncarbonbasedsystemsusingab-initio,moleculardynamics,andrstprinciplecalculationsasanapproach.HehasbeenawardedwithMasterofScienceandhehaswrittenhisMasterofSciencethesisonCarbonandSiliconbasednanowires.Hismajorndinginhismaster'sdegreeincludesprediction(andstudyingitsphysicalproperties)ofcarbonlinearchainsasstablecarbonallotropewhichhasbeenexperimentallysynthesizedforthersttimebyJapaneesephysicistS.Iijimain2009.Startingfrom2005,hehasstartedworkinginUniversityofFlorida,DepartmentofPhysicsasaresearchassistantinProf.Dr.A.F.Hebard'slaboratory.HehasbeendeeplyinnovatedandinspiredbyProf.Dr.A.F.HebardduringhisstayinFloridaandhehasfocusedonsemiconductors,dilutedmagneticsemiconductors,carbonbasedsystems(graphite,graphene,CNTsandC60s),andcomplexoxides.HisworkinDoctorofPhilosophystudiesincludesthediscoveryofsupermetallicityinbromineintercalatedgraphite,formationofdiodesatthemulti-layer-graphene(orgraphene)/varioussemiconductorjunctionsandsensor,diode,hightemperatureandhighfrequencyapplications,magnetocapacitanceeffectinmetal/semiconductorjunctionsandtransitionfromgraphitetobi-layergrapheneathightemperatures.Hehasbeen 188

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awardedtheprestigiousTomScottawardinDecember2009,andheiscurrentlytheauthorof13refereedjournalswithh-indexof8andoneprovisionalpatenttitled'integrationofcarbonbasedstructuresinsemiconductortechnology'. 189