A-LED-book-exercises

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1、ExercisesandSolutionsofthebookLight-EmittingDiodes2ndeditionE.F.Schubert(CambridgeUniversityPress,CambridgeUK2006)1Chapter2Exercise:Minoritycarrierlifetimes.Calculatetheminoritycarrierlifetimeinp-typeGaAsatdoping1518–3–103concentrationsof10and10cmusingabimolecularrecombinati

2、oncoefficientofB=10cm/s.AssumethatonecouldfabricateGaAswithoutanyimpurities.Whatisthecarrierlifetimeinintrinsic6–3GaAswithanintrinsiccarrierconcentrationof2×10cm?15–3Solution:τn=10μsforNA=10cm18–3τn=10nsforNA=10cmτ=2500sforundopedGaAs.Discusshowthemodulationspeedofcommunicat

3、ionLEDsisaffectedbytheradiativelifetimeandthedopingconcentration.Solution:WhentheinjectioncurrentofanLEDisswitchedoffinstantaneouslyatt=0andtheradiativelifetimeisτ,thenlightemissionfromtheLEDessentiallyceasesafterthetimet=τ.ThusanLEDcannotbeswitched“on”or“off”fasterthantheti

4、meτ.Assumingthatboththeswitch-onandswitch-offtimeisτ,thenthemaximummodulationfrequencyisgivenbyf≈1/(2τ).Wehaveshownthattheradiativelifetimeτdependsstronglyonthedopingconcentration.Thusbyhighlydopingtheactiveregionofadevice,theradiativelifetimeτisshortenedandthemaximummodulat

5、ionspeedisincreased.2Exercise:Concentrationofpointdefects.AssumethattheenergyrequiredtomoveasubstitutionallatticeatomintoaninterstitialpositionisEa=1.1eV.Whatistheequilibriumconcentrationofinterstitialdefectsofasimplecubiclatticewithlatticeconstanta0=2.5Å?–3Solution:Theconce

6、ntrationoflatticeatomsofasimplecubiclatticeisgivenbyN=a0=22–36.4×10cm.TheconcentrationofinterstitialdefectsunderequilibriumconditionsatroomtemperatureisthengivenbyN=N−EkT=×4−3.defectexp(a/)2.710cmNotethatthecalculatedconcentrationofdefectsissmallwhencomparedtothetypicalconce

7、ntrationsofelectronsandholes.Ifthedefectdiscussedhereformsalevelinthegap,non-radiativerecombinationthroughthedefectlevelcanoccur.3Chapter3Exercise:Radiativeefficiency.AnalyzethetemperaturedependenceoftheradiativelifetimebasedonthevanRoosbroeck–Shockleymodelandthenon-radiativ

8、elifetimebasedontheShockley–Readmodelandpredictthetemperaturedependenceofth