1、4H 和 6HSiC的介电常数讲解Dielectric functions of bulk 4H and 6H SiC and spectroscopicellipsometry studies of thin SiC films on SiStefan Zollner, J. G. Chen, Erika Duda, T. Wetteroth, S. R. Wilson et al.Citation: J. Appl. Phys. 85, 8353 (1999); doi: 10.1063/1.370682View online: http:/dx.doi.org/10.1063/1.370
2、682View Table of Contents: http:/jap.aip.org/resource/1/JAPIAU/v85/i12Published by the American Institute of Physics.Related ArticlesStrain control of orbital polarization and correlated metal-insulator transition in La2CoMnO6 from first principles Appl. Phys. Lett. 99, 202110 (2011)The role of plas
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6、PHYSICSVOLUME85,NUMBER1215JUNE1999Dielectricfunctionsofbulk4Hand6HSiCandspectroscopicellipsometrystudiesofthinSiClmsonSiStefanZollner,a)J.G.Chen,andErikaDudaMotorolaSPS,CenterforIntegratedSystemsDevelopment,ProcessandMaterialsCharacterizationLaboratory,MDM360,2200WestBroadwayRoad,Mesa,Arizona85202T.
7、WetterothandS.R.WilsonMotorolaSPS,MaterialsTechnologyLaboratory,2100EastElliotRoad,Tempe,Arizona85284JamesN.HilkerJ.A.WoollamCo.,Inc.,645MStreet,Suite102,Lincoln,Nebraska68508Received16February1998;acceptedforpublication1March1999Spectroscopicrotating-analyzerellipsometryemployingacompensatorandopti
8、caltransmissionwereusedtomeasurethedielectricfunctionsofbulk4Hand6HSiCfrom0.72to6.6eVforlightpropagatingnearlyparalleltothehexagonalaxis.Themeasurementsbelowthebandgapshowthepresenceofathinsurfacelayer,whichwasmodeledasSiO2.Thedataaresimilartoresultsforcubic3Cand6HSiCfromtheliterature,butdifferences
9、arenotable,particularlyabove4eV.At5.56eV,weobserveacriticalpointin4HSiC,whichisassignedtodirectinterbandtransitionsalongtheUMLaxisinthehexagonalBrillouinzoneaftercomparisonwithbandstructurecalculations.Noevidencefordirecttransitionsbelow6.5eVwasfoundin6HSiC.Weapplyourresultstotheanalysisofa4HSiClmon
10、insulatorSiCOIproducedbyhigh-dosehydrogenimplantationanddirectwaferbondingonSi.Forcomparison,wealsostudieda1mthickepitaxiallayerof3CSiConSi,wheretheinterferenceoscillationsareinuencedbysurfaceandinterfaceroughness.1999AmericanInstituteofPhysics.S0021-89799902312-9I.INTRODUCTIONII.BULK4HAND6HSiCA.Sam
11、plesSiChassuperiorpropertiesforapplicationsinhigh-power,high-frequency,andhigh-temperatureelectronics,mostlybecauseofitslargebandgap.1SiCoccursinmanypolytypes,suchas2Hwurtzite,hexagonal,3Czincblende,cubic,4H,6H,15R,etc.,whicharedistinguishedbythestackingsequenceofthefundamentalwurtziteandzincblendec
12、rystalarrangements.2Earlyopticalwork36onSiCfocusedonthe3Cand6Hpolytypessinceonlysmallspecimensofotherpolytypescouldbeproduced,but50mmwafersof4Hand6HSiCarenowavailablecommercially.ItisalsopossibletoformaSiConinsulatorSiCOIstructurebyhigh-dosehydrogenimplantationanddirectwaferbond-ingtoaSisubstrate.7D
13、evicesimulationsshowthat4Histhepreferredpolytypeformetalsemiconductoreldeffecttran-sistorsMESFETs.8Thisworkdescribesadetailedstudyofthedielectricfunctionsof4Hand6HSiCforlightpropa-gatingalongthehexagonalaxis,i.e.,theordinarydielectricfunctionforanelectromagneticwavewithitselectriceldvectorperpendicu
14、lartothecrystalaxisfrom0.72to6.6eVusingadeep-ultravioletUVellipsometerwithautoretarder.Weapplyour4HSiCopticalconstantstotheanalysisofaSiCOIstructureconsistingofa600nm4HSiCsuperciallmbondedtoaSisubstratewitha950nmthickSiO2layer.WealsostudiedepitaxiallygrowncubicSiConSi.Wecom-pareourdatatopreviousmeas
15、urements4,5,912anddiscussourresultsinrelationtorecentabinitiobandstructurecalculations.1115aThe4Hand6HSiCsamplesstudiedherewereobtainedcommerciallyfromCreeResearch.Forspectroscopicellip-sometry,weusedsingle-sidepolishedSi-terminatedwa-fers,35mmindiameter,and0.42mmthick.Themiscut,i.e.,theanglebetween
16、thesurfacenormalandthehexagonalaxis,wasabout8,conrmedbyx-raydiffraction.Thewaferswerenotintentionallydoped,butnitrogenimpuritiesresultedinelectronconcentrationsnear681018cm3in4HSiCand11018cm3in6HSiC,determinedbysecondaryionmassspectrometry,Fourier-transforminfraredellipsometry,andelectricalmeasureme
17、ntsbythesupplier.Thesamplesweremeasuredasreceived.Nosurfacepreparationwasper-formed.Therefore,weexpectthatthewafersarecoveredwithathinnativeoxide(SiO2).Samplesusedfortransmis-sionintensitymeasurementsweresimilar,buttwo-sidepol-ished.B.ExperimentalprocedureElectronicmail:R375958353Usingacommercialrot
18、ating-analyzerellipsometer,16wemeasuredtheellipsometricanglesandfrom0.72to6.6eV1881722nmatthreeanglesofincidence60,70,and80.Ithasoftenbeenreportedthatarotating-analyzerellipsometerwithoutcompensatorcannotaccuratelymeasuretheopticalpropertiesofbulksubstrateswithlowabsorptioncoefcients,17sinceforsuchs
19、amplesiscloseto0or.Furthermore,theycannotdeterminethesignof.Weover-1999AmericanInstituteofPhysics0021-8979/99/85(12)/8353/9/$15.00Downloaded 19 Nov 2011 to 221.2.164.23. Redistribution subject to AIP license or copyright; see http:/jap.aip.org/about/rights_and_permissions8354J.Appl.Phys.,Vol.85,No.1
20、2,15June1999Zethesedifcultiesthroughtheuseofacompensator.ForagivenpolarizerpositionPandphaseretardation0,theresultingFouriercoefcientsare18,19RppRspei0tanP2RppRpsei0tanP2a2,ppspe0tanPppRps0tanPForauniaxialcrystalwiththeopticalaxisalongthesurfacenormal,theJonesmatrixisstilldiagonal24andtheFresnelreec
21、tanceratioisgivenby20cosoeocosecosoeocose2ReRppRspei0tanPRppRpsei0tanP,b2ppspe0tanPppRps0tanPwheretheRijsaretheelementsofthenormalizedJonesma-trix.WemeasuretheseFouriercoefcientswithsixdifferentinputpolarizationstatesincludingbothpositiveandnega-tivepolarizeranglesfortwo-zoneaveragingtoreducesys-tem
22、aticerrorsateachwavelengthandthenregressthemforanaccuratedeterminationoftheRijs,fromwhichwecalcu-lateand.Theretardancesusedwere040and0.Inordertoreducerandomerrors,thepolarizerwastrackeduntilP5withtheconstraint10P80.Opticaltransmissionusingtheellipsometerinthestraight-through,single-pathgeometrywaspe
23、rformedontwo-sidepolished4Hand6Hon-axisSiCwaferswith0.33mmthickness.Thisarrangementallowsthemeasurementofabsorptioncoefcientsbetween2and200cm1,ifthere-fractiveindexisknown.C.DepolarizationmeasurementsThecompensatoralsoallowsdepolarizationmeasure-ments.TheStokesvector2023ofthereectedwaveisSrS0S1S2S3I
24、rIsIpI45I45II1Ir,wheretheSisaretheStokesparameters,Iristhetotalinten-sity,IsandIparetheintensitiesofthes-andp-polarizedcomponents,I45andI45aretheintensitiesforanangleofpolarizationof45relativetotheplaneofincidence,andIandIaretheintensitiesforleft-andright-polarizedlight,allforthereectedbeam.Foraniso
25、tropic,nondepo-larizingsample,theellipsometriccoefcients,andarecos2,sin2cos,andsin2sin.Forade-polarizingsample,thedegreeofpolarizationisP222.Thedepolarizationis1P,eitherexpressedasafrac-tionorasapercentage.Forbulk4Hand6HSiC,thedepo-larizationwasbelowthedetectionlimitof0.1%0.2%above5eV.Theoriginofthe
26、depolarizationinthinlmsonSiisdiscussedlaterinthisarticle.D.AnisotropyconsiderationsBecauseoftheirhexagonalcrystalstructure,4Hand6HSiCareopticallyuniaxial.AccordingtoRef.4,6HSiCispositiveuniaxial,i.e.,theextraordinaryrefractiveindexneeforlightwithanelectriceldvectoralongtheopticalaxisislargerthantheo
27、rdinaryrefractiveindexnooelectriceldperpendiculartotheopticalaxiswithneno0.05.Usingthissimpleexpressionwendthat,foranon-axis6HSiCwaferinthetransparentregion,theerrorsintroducedbyneglectingtheanisotropyarelessthan0.15for,onthesameorderofmagnitudeastheexperimentalerrors.Jungk25reachedasimilarconclusio
28、n.Theerrorfortherefractiveindexislessthan0.01,theerrorforthedielectricfunctionlessthan0.1,assumingthattheangleofincidenceislargerthan40.For4HSiC,theopticalanisotropyinthetranspar-entregionisofthesameorderofmagnitude26asfor6HSiC,thereforetheerrorsfor4HSiCaresimilartothosefor6HSiC.Forananglebetweenthe
29、surfacenormalandtheopticalaxismiscutof8,theexpressionsaremuchmorecompli-cated.However,theellipsometrysoftware16isabletosimu-latetheanisotropyeffects18numerically.Wendthattheerrorsareonthesameorderofmagnitudeasforon-axiswafers.Dependingontheorientationoftheopticalaxisrela-tivetotheplaneofincidence,th
30、eremayalsobeaconversionofp-tos-polarizedlight.18ThiseffectisonlysignicantneartheBrewsterangle,wheregoestozeroandtheanglepsdescribingtheptosconversionisabout50.However,ad-ditionalsimulationsshowthatthiseffectcanonlybeob-servedintheabsenceofsurfaceroughnessoroxideoverlay-ers.Armssurfaceroughnessofonly
31、15similartoatomicforcemicroscopyresultsofSiCsubstratesreducesthepeakinpsto1.8sincenolongergoestozeroandmakesitunobservableintheexperiment.Insummary,weexpectnosignicantanisotropyeffectsandtheerrorscausedinouranalysisbyneglectingthean-isotropyareonthesameorderofmagnitudeastheexperi-mentalerrors.ThiswasalreadyfoundbyAspnes27manyyearsago:Ourellipsometryexperimentsmeasureapproxi-matelytheprojectionofthedielectrictensorontothelineofintersectionbetweensurfaceandplaneofincidence,i.e.,theordinarydielectricfunctionforanon-axiswafer.Thisexpectationwasmetbytheexperimentalobserva-tions:Nosigni