第四讲-激子与发光

课程内容绪论经典传播带间吸收激子发光半导体量子阱、自由电子、分子材料发光中心12第四讲Excitons•Theconceptofexcitons•Freeexcitons•Freeexcitonsathighdensity•Frenkelexcitons3Theconceptofexcitons•Insemiconductorsandinsulators:photonabsorptionelectronsintheconductionbandandholesinthevalenceband.•Exciton:boundelectron–holepairbyCoulombinteractionObservedinsemiconductors;largeradius;delocalizedstates;movefreely;bindingenergy~0.01eVObservedininsulatorsandmolecularcrystals;smallerradius;localizedstates;lessmobileandhoping;bindingenergy~0.1-1eV.•StableexcitonswillonlybeformediftheattractiveenergykBT(0.026eVatroomtemperature)•Freeexcitonsarestableatcryogenictemperature.•Tightboundexcitonsarestableatroomtemperature.Twotypesofexcitons:4Wannier激子（自由激子）•Frenkel激子（束缚激子）:•Theconceptofexcitons•Freeexcitons•Freeexcitonsathighdensity•Frenkelexcitons5第四讲ExcitonsBindingenergyandradiusoffreeexcitons•Freeexcitons:weaklyboundelectron-holepair;ahydrogenicsystem•ApplyingtheBohrmodeltotheexciton,consideringdielectricconstantrofthemediumandthereducedmassofelectronandhole.HXXHrnRmRnRnRmEr)/(202220•TheenergyofthenthlevelrelativetotheionizationlimitRHistheRydbergconstantofthehydrogenatom(13.6eV).RX:excitonRydbergconstant.•Theradiusoftheelectron-holeorbit:0220maaananmrrHXXHrnaHistheBohrradiusofthehydrogenatom(5.2910-11m)andaxistheexcitonBohrradius.•groundstatewithn=1hasthelargestbindingenergyandsmallestradius.n1:lessstrongbindingenergyandlargerradius.•Bidingenergytendstodecreaseandaxtoincreaseasrincrease.6•RxtendstoincreaseandaxtodecreaseasEgincreases.•Causes:rtendstodecreaseandtoincreaseasthebandgapincreases.•Ininsulatorswithbandgapsgreaterthanabout5eV,axbecomescomparabletotheunitcellsize,andtheWanniermodelisnolongervalid.•narrowgapsemiconductors:RHissosmallthatexcitoneffectsishardtoobserve.(Eg=1-3eV,freeexcitonsbehaviorisbestobserved)7Excitonabsorption•Freeexcitonsaretypicallyobservedindirectgapsemiconductors.(hardtoobserveintheabsorptionspectraofindirectsemiconductor)•Thegroupvelocityofanelectronorholeinabandisgivenby:kEg1•AttheBrillouimzonecentreofdirectsemiconductor:k=0andzerogradient.Eectron-holepairscreatedbydirecttransitionandhavethesamevelocities.Therefore,strongexcitonsoccurinthespectralregionclosetothefundamentalbandgap.2nREEXgn•Bandedgeabsorptionspectrumforadirectgapsemiconductorwithexcitoniceffectsincluded.Thedashedlineshowstheexpectedabsorptionwhentheexcitoniceffectsareignored.•Freeexcitonscanonlybeobservedinverypuresamples.Impurities:screeningtheCoulombinteractionintheexcitonandtherebystronglyreducethebindingforces;generatingelectricfieldandtendtoionizeexcitons.8•Excitoncreation:electron-holepairsandsamevelocities.•Theenergyofexcitonabsorptionis:ExperimentaldataforfreeexcitonsinGaAs•ExcitonabsorptionofultrapureGaAsat1.2K.•hydrogen-likeenergyspectrumoftheexcitoninthevicinityofthebandgap.•E1=1.5149eV,E2=1.5180eV,E3=1.5187eV•TheexperimentalRx=4.2meVisingoodagreementwiththecalculatedvalue.9•Eg=l.5191eV,agreewithothermeasurements.•Theconceptofexcitons•Freeexcitons•Freeexcitonsathighdensity•Frenkelexcitons10第四讲Excitons•MortdensityNmott:thedensityatwhichtheexciton-excitondistanceisequaltotheexcitondiameter:3341nMottrN•Highdensityisachievablewithafocussedlaserbeam.11Theexcitondensitycanbecontrolledbytuningthelaserpower•Lowdensity,theexciton-excitoninteractionsarenegligible;theexcitonwavefunctionsbegintooverlapathighdensityandtheinteractionwillbecomesignificant.12DensityEffects:1.electron-holeplasmaweakeningandbroadeningoftheexcitonabsorptionlineisobserved(absorptionsaturation,nonlineareffects).2.Biexcitons(excitonmolecules)equivalentprocesstotheformationofanH2molecule;newfeaturelinecanbefound.3.electron-holedroplets4.Bose-Einsteincondensation(Stotal=0or1)Broadfeaturelineatlowerenergythanthefreeexciton•Theconceptofexcitons•Freeexcitons•Freeexcitonsathighdensity•Frenkelexcitons13第四讲ExcitonsFrenkelexcitons•occurringinlargebandgapmaterialswithsmalldielectricconstantsandlargeeffectivemasses.•smallradiiandlargebindingenergies,0.1eVtoseveraleV,stableatroomtemperature.•propagatingthroughthecrystalbyhopping.•Localizedontheatomsite,maythereforebeconsideredasexcitedstatesoftheindividualatomsormolecules,especiallyforn=1excitonenergy.•TheoreticaltreatmentofFrenkelexcitonsismorecomplicated.14Raregascrystals•Crystallizeatcryogenictemperatures.•Largebandgap,Neonhasthelargestbandgapinnature.•Excitontransitionsalloccurinthevacuumultravioletspectralrange•Bindingenergiesareverylarge.•Aclosecorrespondencebetweenthen=1excitonenergiesinthecrystalsandtheopticaltransitionsoftheisolatedatoms(ForXenon5p65p56s).•Theradiusincreaseswithn,delocalized,correspondencegetsweaker.15Alkalihalides•Largedirectbandgaps(5.9eV13.7eV)•LiFhasthewidestbandgapofanypracticalopticalmaterial.•Egandexcitonbindingenergytendstoincreasewithdecreasinganionandcationsize.•Theexcitonsarelocalizedatthenegative(halogen)ions.StrongexcitoneffectsatRTbecauseoflargebindingenergy(0.8eVand1.9eV)16•Principlesofluminescence•Interbandluminescence•Photoluminescence•Electroluminescent第五讲InterbandLum