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200711()Nov.2007386JournalofInnerMongoliaUniversityVol.38No.6ArticleID:1000-1638(2007)06-0627-08Electron2PhononInteractionEffectsontheSurfaceStatesinWurtziteNitrideSemiconductorsXLIGen2xiao1,2,YANZu2wei1,2(1.DepartmentofPhysics,InnerMongoliaUniversity,Hohhot010021,China;2.CollegeofScience,InnerMongoliaAgriculturalUniversity,Hohhot010018,China)Abstract:Avariationalapproachisusedtostudythesurfacestatesofelectronsinsemi2infinitewurtzitenitridesemiconductors.TheeffectiveHamiltonianandthesurfacestatelevelsarederivedbytakingtheeffectsoftheelectron2Surface2Optical2phonon(e2SO2p)interactionandstructureanisotropyintoaccount.ThenumericalcomputationhasbeenperformedfortheenergiesoftheelectronicsurfacestatesasafunctionofthesurfacepotentialV0forwurtziteGaN,AlNandInN,respectively.Theresultsshowthattheelectron2phonon(e2p)interactionlowersthesurfacestatelevels,andthee2pinteractionenergiesinwurtziteGaNandAlNarebiggerthanthatinthecorrespondingzinc2blendeone,butforInN,thecaseiscontrary.Itisalsofoundthattheelectronicsurface2statelevelsinwurtzitestructuresarelowerthanthatinthezinc2blendematerialsforhundredsofmeVforthematerialscalculated.Theinfluenceofe2pinteractiononthesurfacestatescannotbeneglected.Keywords:surfacestate;nitridesemiconductor;electron2phononinteractionCLCnumber:O471.3Documentcode:A1IntroductionRecently,muchattentionhasbeenfocusedonË2Ígroupsemiconductorswideband2gapsuchasGaN,AlN,andInNinviewoftheirevidentdeviceapplications.Forexample,theyarethesuitablematerialsforfabricatingthehigh2brightnesselectricandoptoelectricdevicesoperatinginthegreen,blue,andultravioletspectralregions,aswellasforconstructingtheheterostructure2basedfieldeffecttransistors1,2.Nitridesemiconductorshavebothwurtziteandzinc2blendenaturalcrystallinestructures.Sincethewurtzitecrystalshaveadifferentunit2cellstructure(i.e.,fouratomsperunitcell)aswellaslowersymmetrycomparedtothezinc2blendecounterparts,thephonondynamicsandcarrier2phononinteractionsinthesematerialsmaybesubstantiallydifferentfromthosewithcubicsymmetry.ThewurtzitenitridesexhibitmanyunusualpropertiesamongtheË2Ígroupofsemiconductors.Therearemanymoredistinctphononbranches(nineopticalandthreeacousticmodes)inthewurtzitenitridesemiconductors.Overthepastyears,therewasabroadexperimentalXReceiveddate:2007-03-06Foundationitem:SupportedbytheNationalNaturalScienceFoundationofChina(No.10564003,10264003)Biography:LIGen2xiao(1979),female,anativeofTongliaoofInnerMongolia,Master.andtheoreticalstudyaboutthepropertiesofpolaron,electroniceffectivemass,interface2phonon,ande2pscatteringinthewurtzitenitridesemiconductorsandtheirternarymixedcrystals39.Thesurfacestatesofelectronsinpolarcrystalshavebeenwidelystudiedbymanyexperimentalandtheoreticalscientists.Theirenergylevels,statedensitiesandexistenceconditionshavebeenreported1013.Itisrecognizedthattheterminationofthelatticeproducestheintrinsicsurfacestates,whichcalledTammorShocklystates,andwhosewavefunctionsarelocalizedinthevicinityofthesurfaceanddecayrapidlyinsidethematerials.However,inthepreviouspapers,theauthorsstudiesthemotionofanelectronintheperiodpotentialfieldwithoutconsideringtheeffectsofe2pinteractiononthesurfacestateseventhoughitiswell2knownthattheyinfluenceconsiderablythepropertiesoftheelectronsandgiverisetopolaronstatesinpolarcrystals.Thenearly2free2electronapproximationmethodandthevariationaltheorywereusedtotreattheeffectsofe2pinteractiononintrinsicsurfacestates1419.Theresultsshowthatthee2pinteractionlowersthesurface2stateenergy.Recently,thesurface2stateenergiesofthezinc2blendenitridesemiconductorswerereported20.Manyscientistsresearchedthecharacteristicsofpolaronsinthebulkwurtzitenitridesemiconductors.Forwurtzitenitridesemiconductors,afurthertheoreticaltreatmenttothesurfacestatesofelectrons,takingboththeelectron2Surface2Optical2phonon(e2SO2p)interactionandstructureanisotropyintoaccount,isnecessary.Inthispaper,avariationalapproachisusedtostudythesurfacestatesofelectroninthewurtzitenitrides.Sincethewurtziteisananisotropystructureanditssurface2statewavefunctionsarelocalizednearthesurface,weonlytakeSO2phononcontributionsandstructureanisotropyintoaccount.ThepolaroniceffectiveHamiltonianwasobtainedbyusingaLee2Low2Pines(LLP)2likemethod15,17,18,21insection2.Insection3,wecalculatedthesurface2stateenergiesforsomesemi2infinitewurtzitenitridesemiconductors.Thenumericalcomputationresultsforseveralpracticalmaterialsaregivenanddiscussedinsection4.2EffectiveHamiltonianLetusconsiderasemi2infinitepolarnitridecrystaloccupyingthepositive2halfspacezE0,whilethenegative2halfspacebeingvacuum.Thematerialshavethetranslationalsymmetryinthesurfaceplane,andthesymmetryhasbeenbrokenalongthedirectionperpendiculartothesurface.Weassumetheanisotropicaxisasthezaxisandanelectronmovingthroughthematerialinteractingwiththelatticevibrations.Usingthenearly2free2electronapproximationtheHamiltonianofsuchane2psystemcanbewrittenas10,15,17,19H=He+Hph+He-p(1)whereHe,Hph,He-pharethepartsofanfreeelectron,phonons,ande2pinteraction,respectively.Thespecificformsofthemareasfollows:He=p22m3+p2z2m0+V(z)(2)