半導(dǎo)體物理與器件－4的知識(shí)

CarrierGenerationAtanyT>0°K,someelectronsinthevalencebandgainsufficientenergytojumpintotheconductionband.Thisleavesbehindholes.InthermalequilibriumGth=RthEquilibriumlowlevelInjectionhighlevelinjectionn?Nd

+Dnp?ni2/Nd

+DpLowLevel:Dn<<NdHighLevel:Dn3NdCarrierRecombinationDirectRecombinationDirectBand-gapSemiconductore.g.GaAsIndirectBand-gapSemiconductore.g.Si,GeAnimpurity(e.g.,Au)isintroducedwhichprovidesa"trappinglevel"orasetofallowedstatesatenergyEtRecombinationisaccomplishedbytrappinganelectronandahole.BeforeAfterThisisanextremelyimportantresultandisbasedupontheworkofShockley,ReadandHall.ThistheoryisknownasSRHrecombination.1.The"drivingforce"orrateofrecombinationisproportionalto(pn-ni2),i.e.,thedeviationfromequilibrium.2.UisamaximumwhenEt=Ei,i.e.,trappinglevelsnearmid-bandarethemostefficientrecombinationcenters.WhenEt

?Ec

,electroncaptureismoreprobablebutholecaptureislessprobable.WhenEt

?Ec,electronemissionbacktoconductionbandishighlyprobableandrecombinationislessprobable.InN-typesemiconductor,lotsofelectronswillbearoundforcaptureandhencethelimitingfactorinrecombinationwillbetheminoritycarrier(i.e.,hole)lifetimetp.2.P-type:p??nandp??niAgain,thelimitingfactoristheminoritycarrier(inthiscase,electron)lifetime.3.Ifthetraplevelisnotatthemiddleofthebandgap(Et

1Ei),foraN-typesemiconductor,assumingthatn?nnoandni2=pnonno,4.Ifwehavethesituationinwhichpn<ni2,i.e.generationistakingplace,thenG=-URecombinationlifetimeandgenerationlifetimevs.energyleveloftherecombinationcenterNotethatbothtrandtgareminimizedwhenEt=Ei.However,ingeneral,tr

1tg.QuasiFermiLevelsUnderthermalequilibrium,Ifthereisinjection(pn>ni2)orextraction(pn<ni2),theserelationshipsarenolongervalidbecauseEfismeaningless.Wecan,however,definetwonewquantitiescalledquasiFermilevelssuchthatrelationshipsofthetypeshownabovedohold,i.e.whereEfn=electronquasiFermilevel,Efp=holequasiFermilevelExample:Generationthroughlowlevellightirradiation.n?nnobutp>>pnoIngeneral,Efn

1Efp.EfnandEfparemathematicaltools;theirvaluesarechosensothatthe"correct"carrierconcentrationaregiveninnonequilibriumsituations.NotethatthequasiFermilevelofthemajoritycarriersisessentiallyunchangedunderlowlevelinjection.ContinuityEquationWehavediscussed1.Carriertransport(driftanddiffusion)2.GenerationofcarriersandrecombinationofcarriersThemechanismwhichtiesallofthesetogetheristheconditionofcontinuityofcurrent(orconservationofcharges).Similarlyforelectrons,OnefinalequationneededtodescribedeviceoperationisthePoisson'sequation.Ingeneral,thenetchargedensityinasemiconductorisgivenby

Givenappropriateboundaryconditions,wecansolvethemforanarbitrarydevicestructure.Generally,wewillbeabletosimplifythembaseduponphysical