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1、PHYSICALREVIEWBVOLUME60,NUMBER715AUGUST1999-IModelingofthedisordercontributiontotheband-tailparameterinsemiconductormaterialsA.IribarrenDIEESInstitutodeMaterialesyReactivos,UniversidaddeLaHabana,ZapatayG,Vedado,Plaza,CiudaddelaHabana10400,CubaR.Castro-RodrõÂgu
2、ez,V.Sosa,andJ.L.PenÄaDepartamentodeFõÂsicaAplicada,CINVESTAV-IPN,UnidadMeÂrida,ApartadoPostal73-Cordemex97310,MeÂrida,YucataÂn,Mexico~Received10June1998;revisedmanuscriptreceived23October1998!Inthispaper,wepresentaquantitativeandanalyticalformulationofthediso
3、rdercontributionstotheband-tailparametermodelinsemiconductormaterialswithUrbachexponentialbehavior,whicharisefromthein¯uenceofthebulkandgrainboundarytrapconcentrationandstrain.WebasedourcalculationontheHalperin-Laxmodelcombinedwitharecentmodelthatconsideredthe
4、tailparameterE0asthesumofinteractiveanddisordercontributions.TheresultingformulationconvergedtotheDow-Red®eldmodel,whichsupportsitsvalidity.Ourtheory,appliedtoexperimentaldata,yieldsbulk-defectandgrain-boundarytrapconcentrationsingoodagreementwithreportsformon
5、o-andpolycrystallinesemiconductors.Ourmodelcandescribewhollytheband-tailparameterofanysemiconductor.@S0163-1829~99!01924-4#I.INTRODUCTIONthelow-energyregionofluminescencespectraandabsorp-tionpro®les.Thebandtailsarecharacterizedbytheband-tailTheevaluationofthed
6、egreeofdisorderassociatedwithparameterE0~Refs.6±8!asstrains,dislocations,latticeimperfections,defects,andtheeffectofthegrainsurfaceinthecaseofpolycrystals,isanhnimportantandcurrentthemeinthestudyofsemiconductora~hn!}expSD,~1!E0materials.Theincreaseofthisdisord
7、erleadstostrongpoten-1tial¯uctuationsthatresultinanincreaseoftheband-tailwhereaistheabsorptioncoef®cient,andhnisthephotonparameterE0givenbythecontributionsofthephonon-energy.Theband-tailparameterE0dependsonthecarriercarrierandcarrier-impurityinteractionsaswell
8、astheproper2concentrationnorp,thetemperatureTandthestructuraldisorder.disorder.Dependingonthegrowthmethodandconditions,asemi-2Inapreviouspaper,E0wasdeterminedconsideringitasconduct
