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1、PhysicaB](]]]])]]]–]]]ContentslistsavailableatSciVerseScienceDirectPhysicaBjournalhomepage:www.elsevier.com/locate/physbAstudyofenergybandgapversustemperatureforCu2ZnSnS4thinfilmsnPrashantK.Sarswat,MichaelL.FreeDepartmentofMetallurgicalEngineering,Universi
2、tyofUtah,SaltLakeCity,Utah84112,USAarticleinfoabstractArticlehistory:ThetemperaturedependentbandgapenergyofCu2ZnSnS4thinfilmwasstudiedinthetemperatureReceived5September2011rangeof77–410K.Variousrelevantparameters,whichexplainthetemperaturevariationoftheRec
3、eivedinrevisedformfundamentalbandgap,havebeencalculatedusingempiricalandsemi-empiricalmodels.Amongstthe27September2011modelsevaluated,theVarshniandPasslermodelsshowthebestagreementwithexperimentaldatain¨Accepted28September2011themiddletemperaturerange.How
4、ever,theBose–Einsteinmodelfitsreasonablywellovertheentiretemperaturerangeevaluated.ThecalculatedfittingparametersareingoodagreementwiththeKeywords:estimatedvalueoftheDebyetemperaturecalculatedusingtheMadelung–EinsteinapproximationandPhotovoltaictheHailingme
5、thod.Copperzinctinsulfide&2011ElsevierB.V.Allrightsreserved.BandgapThinfilmsTemperature1.IntroductiontemperaturesofCZTSbasedphotovoltaicdevices,whichcanvarysignificantlydailyandseasonally.Temperaturedependenceoftheelectronicinterbandtransi-Amongstthereported
6、bandgapmodelsthreepopularmodelstioncanprovidevaluableinformationconcerningexcitonichavebeenevaluatedinthisstudy:(1)theVarshnimodel[16],effectsandelectron–phononinteractions.Research,whichdis-(2)Passlermodel¨[17]and(3)theBose–Einsteinmodel[18].Thesecussest
7、heeffectoflatticevibrationandtheresultingshiftofthemodelssuggestthatbandgapshiftinsemiconductorsasafunctionofenergylevelsforsilicon,wasreportedbyFan,decadesago[1].temperatureismainlyduetoelectron–phononinteractions.However,Sincethen,significantresearchhasb
8、eenaccomplishedtoevalu-thermalexpansionalsoplaysaminorrole,whichwasconsideredbyatetheeffectoftemperatureonvarioussemiconductorsandseveralresearchgroups.Forexample,Manoogianetal.[19–20]usedaphotovoltaicmaterials.Fore
