陈壮锐-76-77-a38

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1、CHAPTER3TheSemiconductorinEquilibriumOrTheelectronconcentrationisgivenbyOr▇CommentTheprobabilityofastatebeingoccupiedintheconductionbandcanbequitesmall，butthethermalequilibriumvalueofelectronconcentrationcanbeareasonablevaluesincethedensityofStateslarge.ExerciseProbl

2、emEX3.1CalculatethethermalequilibriumelectronconcentrationinsiliconatT=300KforthecasewhentheFermilevelis0.25eVbelowtheconduction-bandenergy,.Thethermal-equilibriumconcentrationofholesinthevalencebandisfoundbyintegratingEquation（3.2）overtherangeofenergiesinthevalence-

3、bandenergy,orDensityofholes.(3.12)Whereisthemaximumenergyofthevalencebandandistheminimumenergyofthevalenceband.However,thefunctionapproacheszeroveryquicklyastheenergydecreases,asseeninFigure3.1d,sowemayletwecannotethat(3.13a)Forenergystatesinthevalenceband,.IF(>>kT)(

4、theFermifunctionisstillassumedtobewithinbandgap),thenwehaveaslightlydifferentformoftheBoltzmannapproximation.Equation（3.13a）canbewrittenas(3.13b)ApplyingtheboltzmannapproximationofEquation(3.12),wefindthethermal-equilibriumconcentrationofholesinthevalencebandisWheret

5、helowerofintegrationistakenasminusinfinityofthebottomofthevalenceband.Theexponentialtermdecaysfastenoughsothatthisapproximationisvalid.Equation（3.14）canbesolvedmoreeasilybyagainmakingachangeofvariableIfweletThenEquation（3.14）becomesWherethenegativesigncomesfromthedif

6、ferentialdE=.Notethatthelowerlimitofbecomes+∞whenIfwechangetheofintegration,weintroduceanotherminussign.FromEquation（3.8）Equation（3.16）becomesWemaydefineaparameterasWhichiscalledtheeffectivedensityofstatesfunctioninthevalenceband.Thethermal-equilibriumconcentrationof

7、holesinthevalencebandcanNowbewrittenasThemagnitudeofisalsoontheorderofatT=300Kformostsemiconductor.OBJECTIVECalculatetheprobabilitythatenergystateinthevalencebandatisemptyofanelectronandcalculatethethermal-equilibriumholeconcentrationinsiliconatT=350K.Assumetheenergy

8、is0.25eVabovethevalence-bandenergy.ThevalueofforsiliconatT=300Kis.第三章半导体中的平衡电子浓度可以表示为OR▇评论在传导带被占领的状态的可能性可以是相当小的，但是电子集中的热平衡价值可以是合理的价