第三讲带间吸收

课程内容绪论带间吸收自由电子、激子、分子材料发光中心发光材料的若干应用（自学）1InterbandtransitionsThetransitionratefordirectabsorptionBandedgeabsorptionindirectgapsemiconductorsBandedgeabsorptioninindirectgapsemiconductorsInterbandabsorptionabovethebandedgeMeasurementofabsorptionspectra第三讲Interbandabsorption2InterbandtransitionsIsolatedatomsDiscreteenergiesSharplinesintheabsorptionspectrasolidEnergyband(delocalizedstate)ContinuousabsorptionbandForsemiconductororinsulator,photonexciteselectronfromfilledvalencetotheemptyconductionband,thetransitionenergyisThereisathresholdħ>Eg=(Ef—Ei)min(bandedgeabsorption)ThereisacontinuousrangeoffrequencyTheselectionrulesandthePauliexclusionprinciplemustallowthesetransitionsCreationofanelectron-holepair;3PhotonabsorptionAbsorptionandemissionofphononDirectandIndirectbandgapInadirectbandmaterial,boththeconductionbandminimumandthevalencebandminimumoccurattheBrillouinzonecentrewherek=0.(bandedgeabsorption:aphotonabsorptionprocess)Inaindirectbandgapmaterial,theconductionbandminimumdoesnotoccuratk=0,butisusuallyatthezoneedgeorclosetoit.(bandedgeabsorptionmustinvolveaphonon)4InterbandtransitionsThetransitionratefordirectabsorptionBandedgeabsorptionindirectgapsemiconductorsBandedgeabsorptioninindirectgapsemiconductorsInterbandabsorptionabovethebandedgeMeasurementofabsorptionspectra第三讲Interbandabsorption5ThetransitionratefordirectabsorptionTheopticalabsorptioncoefficientisdeterminedbythequantummechanicaltransitionrateWi->fforexcitinganelectroninaninitialquantumstateitoafinalstatefbyabsorptionofaphotonofangularfrequency.(Fermi’sgoldenrule)thematrixelementM,the

jointdensityofstatesg(ħ).Thetransitionratethusdependsontwofactors:6thematrixelementM,(semiclassicalapproach)Perturbation:Dipolemoment:Lightwave:Theelectronwavefunction:Initial:Final:Conservationofmomentumneglectthemuchsmallerphotonmomentum7Jointdensityofstatesg(ħ)Thedensityofstatesfunctiondescribesthedistributionofthestateswithinthebands.Thejointdensityofstatesaccountsforthefactthatboththeinitialandfinalelectronstatesliewithincontinuousbands.thenumberofk-statesintheincrementalvolumebetweenshellsink-spaceofradiuskandk+dk.Forelectronsinaparabolicbandwitheffectivemassm*:8InterbandtransitionsThetransitionratefordirectabsorptionBandedgeabsorptionindirectgapsemiconductorsBandedgeabsorptioninindirectgapsemiconductorsInterbandabsorptionabovethebandedgeMeasurementofabsorptionspectra第三讲Interbandabsorption9TheatomicphysicsoftheinterbandtransitionsTheenvelopewavefunctionsofuiandufareneeded.(1)Theparityoftheinitialandfinalstatesmustbedifferent.(2)m=-1,0or+1.(3)l=1

(4)ms=0Selectionrulesforatomictransition(n,l,m,ms)Transitionsthatobeytheelectric-dipoleselectionrulesarecalledallowedtransitions,whilethosewhichdonotarecalledforbiddentransitions.Dipole-allowedtransitionshavehightransitionrates,andthereforehaveshortradiativelifetimes(10-9-10-8s).Fluorescence.

Forbiddentransitions:magneticdipoleorelectricquadrupoletransitions;smallertransitionratesandlongerradiativelifetimes(>10-6s).Phosphorescence.10SchematicdiagramoftheelectronlevelsinacovalentcrystalmadefromGeorGaAs.Thetransitionsbetweenthevalencebandandtheconductionbandareelectric-dipoleallowedwithhightransitionrates.11ThebandstructureofadirectgapIII-VsemiconductorThedispersionofthebandsisshownfortwodirectionsoftheBrillouinzonecentre:XandL.Thepointcorrespondstothezonecentrewithawavevectorof(0,0,0),whiletheXandLpointscorrespondrespectivelytothezoneedgesalongthe(100)and(111)directionsshadedregion:fullofelectrons;valencebandUnshadedregion:emptyofelectrons;conductionband.BandstructureofGaAs.Brillouinzoneoffccstructure12BandstructureofadirectgapIII-VsemiconductorsuchasGaAsneark=0.Usually,weareinterestedinthetransitionsthattakeplaceacrossthebandgapforsmallkvaluesclosetozerosimplifiedfour-bandmodel.e:electronband(conductionband)hh:heavyholebandlh:lightholebandso:split-offholeband,duetospin-orbitcoupling.Allfourbandshaveparabolicdispersions.ComparedwiththedetailedbandstructureofGaAs,thesimplifiedpictureisvalidneark=0.13JointdensityofstatesConservationofenergyduringaheavyholeorlightholetransitionrequiresthat:Thedispersionofband(E—krelationship)14Thefrequencydependenceofthebandedgeabsorption=0ifħ<Egtheabsorptionincreasesas(h-Eg)1/2forphotonenergiesgreaterthanthebandgap.transitionswithlargerreducedmasseshasstrongerabsorptionSquareofversusphotonenergyexhibitsalinearrelation.Thebandgapcanbededucedtobe0.35eVbyextrapolatingtheabsorptiontozero.isverylargebecauselargeg(E)15Note:thefrequencydependence(ħ-Eg)1/2isonlyapproximatelyobeyed.Thereareanumberofreasonsforthis:ExcitoneffectsneglectedImpurityordefectstateswithingapneglectedTheparabolicbandapproximationonlyvalidneark=0.16InterbandtransitionsThetransitionratefordirectabsorptionBandedgeabsorptionindirectgapsemiconductorsBandedgeabsorptioninindirectgapsemiconductorsInterbandabsorptionabovethebandedgeMeasurementofabsorptionspectra第三讲Interbandabsorption17Indirectgapsemiconductors:SiandGe,etc.Transitionsatthebandedgeinindirectsemiconductorsmustinvolvealargechangeintheelectronwavevector,andthereforebothphotonandphononinvolved:+signcorrespondingtoabsorption,andthe-signtoemission.Indirecttransitionisasecond-orderprocess,thetransitionrateismuchsmallerthanfordirectabsorption.Eg=1.42eVEg=1.12eVAbsorptioncoefficientofindirectbandgap:differentfrequencydependence;providingaconvenientwaytodeterminewhetherthebandgapisdirectornot18Bandstructureofgermanium.TheabsorptioncoefficientofgermaniumThe1/2vsħ

straightlineextrapolatesbackto0.65eV,whichindicatesaphononofenergyof0.01eV.EgofGeis0.66eV.atailextendingdowntoabout0.60eViscausedbyabsorptionofthehigherfrequencyphononsandalsomultiphononabsorption.asħ>0.8eV,frequencydependenceapproximatelyobeys2(ħ-Egdir),whereEgdir=0.80eVisthebandgapfordirecttransitionsattheFpointofgermanium.19InterbandtransitionsThetransitionratefordirectabsorptionBandedgeabsorptionindirectgapsemiconductorsBandedgeabsorptioninindirectgapsemiconductorsInterbandabsorptionabovethebandedgeMeasurementofabsorptionspectra第三讲Interbandabsorption20Interbandabsorptionabovethebandedgeismorecomplicated,however,muchusefulinformationaboutthefullbandstructurecanbeobtainedfromanalysisoftheoverallspectrum.Egisindirectandoccursat1.1eV;bandedgeabsorptioniscompletelynegligible;TheabsorptioncoefficientinthespectralregionaroundE1=3.5eVandE2=4.3eVisextremelylarge,wheretheconductionandvalenceareapproximatelyparallelalongthe(111)and(100).(why?)Parallelbandsmeanspossibilitiesofdirecttransitionswiththesamephotonenergyformanydifferentvaluesofk.ParallelbandsLargeg(E)21InterbandtransitionsThetransitionratefordirectabsorptionBandedgeabsorptionindirectgapsemiconductorsBandedgeabsorptioninindirectgapsemiconductorsInterba