Transport Equations for Semiconductors

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1、TransportEquationsforSemiconductorsProf.Dr.AnsgarJ¨ungelInstitutf¨urMathematikJohannesGutenberg-Universit¨atMainzWinter2004PreliminaryLecturesNotes(Feb.2005)Contents1Introduction32BasicSemiconductorPhysics82.1Semiconductorcrystals...........................

2、..82.2Thesemi-classicalpicture...........................212.3Thek·pmethod................................282.4Semiconductorstatistics............................333ClassicalKineticModels463.1TheLiouvilleequation.............................463.2TheVlasoveq

3、uation..............................523.3TheBoltzmannequation............................583.4ThebipolarBoltzmannmodel.........................684ClassicalFluidModels724.1Derivationofthedrift-diffusionequations...................724.2Derivationofthehydrodyna

4、micequations..................844.3Derivationofthesphericalharmonicsexpansionequations.........914.4Derivationoftheenergy-transportequations.................1034.5Relaxation-timelimits.............................1145QuantumKineticModels1195.1TheSchr¨odinge

5、requation...........................11915.2ThequantumLiouvilleequation........................1215.3ThequantumVlasovandBoltzmannequation................1255.4Openquantumsystems.............................1316QuantumFluidModels1366.1Zero-temperaturequantumh

6、ydrodynamicequations.............1366.2QuantumhydrodynamicsandtheSchr¨odingerequation...........1386.3QuantumhydrodynamicsandtheWignerequation.............1416.4Derivationofthequantumdrift-diffusionequations.............15021IntroductionThemoderncomputerandt

7、elecommunicationindustryreliesheavilyontheuseanddevel-opmentofsemiconductordevices.Thefirstsemiconductordevice(agermaniumtransistor)hasbeenbuiltin1947byBardeen,BrattainandShockley,whohavebeenawardedtheNobelprizein1956.Inthefollowingdecades,alotofdifferentdevi

8、cesforspecialappli-cationshavebeeninvented;forinstance,semiconductorlasers,solarcells,light-emittingdiodes(LED),metal-oxidesemiconductor(MOS)transistors,quantumdots,tonameonlyafew.Averyimportantfactoft