凝聚态光物理学5

5Luminescence5.1Lightemissioninsolids5.2Interbandluminescence5.3Photoluminescence5.4Electroluminescence15.1LightemissioninsolidsThereverseprocessofabsorption–emissionEmissioninsolidsiscalledluminescence.Luminescencemechanisms:Photoluminescence(PL)Electroluminescence(EL)Electronsareinjectedintotheexcitedstatebandandrelaxtothelowestavailablelevel.Thephotonisemittedwhenanelectroninanexcitedstatedropsdownintoanemptystateinthegroundstateband.Theseemptystatearegeneratedbytheinjectionofholes.Thespontaneousemissionrateforatwolevel:A:EinsteinAcoefficient;R=A-1:radiativelifetimeofthetransition.

Thetransitionhavelargeabsorptioncoefficientsalsohavehighemissionprobabilitiesandshort

radiativelifetime;Upperlevelispopulated.Innormalcircumstancestheelectronsrelaxtowithin~kBTofthebottomofexcitedstateband.Theholesfollowasimilarseriesofrelaxations.Thuslightisonlyemittedwithinanarrowenergyrange.Non-radiativerelaxation:Theexcitedenergymaytransferintoheatbyemittingphononsorbetrappedbydefect.25.1LightemissioninsolidsTotalrate:TheluminescentefficiencyR:IfR<<NR,R1,maximumpossibleamountoflightisemitted.IfR>>NR,R0,lightemissionisveryinefficient.Theefficientluminescencerequiresthattheradiativelifetimeshouldbemuchshorterthanthenon-radiativelifetime5.2InterbandluminescenceTheinterbandluminescencecorrespondstoannihilationofanelectron-holepair(electron-holerecombination)5.2.1DirectgapmaterialsTheinjectedelectronsandholesrelaxveryrapidlytolowestenergystates.Thephotonsareemittedwhenelectronsatthebottomoftheconductionbandrecombinewithholesatthetopofthevalenceband.ThetypicalvaluesofRisintherange10-8–10-9s.Thetransitionshouldbedipoleallowedandhavelargematrixelementsandthesamekvector(neark=0,thusclosetoh=Eg).Theluminescentintensityatfrequency:3ThePLwasexcitedbyabsorptionof4.9eVphotonsfromafrequencydoubledcoppervapourlaser.Thespectrumconsistofanarrowemissionlineat3.5eVclosetothebandgapenergy,whiletheabsorptionshowstheusualthresholdatEgwithcontinuousabsorptionforh>Eg.5.2.2IndirectgapmaterialsInanindirectmaterials,conservationofmomen-tumrequiresthataphononmusteitherbeemittedorabsorbedwhenthephotonisemitted.Theinterbandluminesenceinanindirectgapmaterialisasecond-orderprocess.TheRmuchmorelongerthanfordirecttransition,thereforethismakestheluminescenceefficiencysmall.Sotheindirectgapmaterialssuchassiliconandgermaniumaregenerallybandlightemitters.45.3Photoluminescence5.3.1Excitationandrelaxation

(a)SchematicdiagramoftheprocessesoccurringduringPLinadirectgapsemiconductorafterexcitationatfrequencyL.Theelectronsandholesrapidlyrelaxtothebottomoftheirbandsbyphononemission(~10-13

s)beforerecombiningbyemittingaphoton(~10-9s).(b)Densityofstatesandleveloccupanciesfortheelectronsandholesafteropticalexcitation.ThedistributionfunctionsshownbytheshadingapplytotheclassicallimitwhereBoltzmannstatisticsarevalid.

ThetotalnumberdensityNeofelectrons:Thedensityofstateinconductionband:Fermi-Diracdistributionfortheelectrons:(Thesystemisinasituationofquasi-equili-brium,thusisnouniqueFermienergy.E=

0correspondstothebottomoftheconductionbandorthetopofthevalenceband)ThetotalnumberdensityNeofholes:ThesetwoEqscanbeusedtocalcuulate55.3.2LowcarrierdensitiesAtlowcarrierdensities,theoccupancyofthelevelsissmalland+1factorinfe(E)cabbeignored.Theelectronandholedistributionwillbedescribedbyclassicalsituation.FermiBoltzmanndistribution:(validatlowdensitiesandhightemperature)PLspectrumofGaAsat100K.Theexcitationsourcewasaheliumneonlaseroperatingat632.8nm(1.96eV).ThespectrumshowsasharpriseatEgduetothe(h-Eg

)1/2factorandthenfallsoffexponentiallyduetotheBoltzmannfactor.Thefullwidthathalfmaximumoftheemissionlineisverycloseto~kBTTheinsetgiveasemi-logarithmicplotofthesamedata.65.3.3DegeneracyAihighcarrierdensities,theelectronandholedistributionsaredescribedusingFermi-Diracstatistics.Thissituationiscalleddegeneracy:IntheextremelimitofT=0Electron-holerecombinationcanoccurbetweenanystatesintwobands,thereforethereisabroademissionspectrumstatingatEguptoasharpcut-offat.Asfinitetemperature,thecutoffatwillbebroadenedoveranenergyrange~kBT.Time-resolvedPLspectraofGa0.47In0.53AsatlatticetemperatureTL=10K.Thesamplewasexcitedwithlaserpolseat610nmwithanenergyof6nJandadurationof8ps.Thisgeneratedaninitialcarrierdensityof21024m-3.

75.3.4PhotoluminescencespectroscopyPhotoluminescence(PL)spectra:

Thesampleisexcitedwithalaserorlampwithphotonenergygreaterthanthebandgap.Thespectrumisobtainedbyrecordingtheemissionasafunctionofwavelength.Photoluminescenceexcitationspectroscopy(PLE):Thedetectionwavelengthisfixedandtheexcitationwavelengthisscanned.Thetechniqueallowstheabsorptionspectrumtobemeasuredbecausethesignalstrengthissimplyproportionaltothecarrierdensity,andinturnisdeterminedbyabsorptioncoefficient.Time-resolvedphotoluminescencespectroscopy:Thesampleisexcitedwithaveryshortlightpulseandtheemissionspectrumisrecordedasafunctionoftimeafterthepulsearrives.Thetime-dependenceoftheemissionspectrumgivesdirectinformationaboutthecarrierrelaxationandrecombinationmechanisms,andallowstheradiativelifetimetobemeasured.

85.4Electroluminescence

Lightemittingdiodes(LEDs)Laserdiodes(LDs)5.4.1GeneralprinciplesofelectroluminescencedevicesThemicroscopicmechanismsthatdeterminetheemissionspectrumofELareexactlythesameastheonesofPL.Theonlydifferenceisthatthecarriersareinjectedelectricallyratherthanoptically.Layerstructure(a)andcircuitdiagram(b)foratypicalELdevice.Thethinactiveregionatthejunctionofthep-andn-layerisnotshown(~1m)(~500m)(~mm)Activeregion9Themainfactorsthatdeterminethechoiceofthematerial:(1)Thesizeofthebandgap:Eg

;

kBT;Constraintsrelatingtolatticematching;theeaseofp-trpedoping.5.4.1GeneralprinciplesofelectroluminescencedevicesBandgapofselectedIII-VsemiconductorsusedformarkingLEDsandLDs.asafunctionoftheirlatticeconstant.Twogroups:i)arsenic(As)andphosphorous(P)compounds:

GaAs:870nm,AlxGa1-xAs:630-870nm(localareafibrenetworks(850nm)andLED)problem:becomeindirectasEggetslarger.GaxIn1-xAsyP1-y:920-1650nm(opticsindustry).ii)nitride(N)compound:

GaN:3.4eVatRT;InN:1.9eVatRTalloyofGaNandInN:360–650nm(2)Growthinultra-purelayersonthetopofasubstratebyepitaxy:

liquidphaseepitaxy(LPE)(m);metal-organicvapourphaseepitaxy

(MOVPE);metal-organicchemicalvapourphasedeposition(MOCVD);molecularbeamepitaxy(MBE).Widebandgapsemiconductorshaveverydeepacceptorlevels,thusisdifficultindoping.discoveringnewtechnique.10Growthinultra-purelayersonthetopofasubstratebyepitaxy.5.4.2LightemittingdiodesThediodeconsistofap-ndiodewithheavilydopedpandnregions.Banddiagramofalightemittingdiodeat(a)zerobias,and(b)forwardbiasV0Eg/e.Thebiasisappliedtodriveacurrent,shifttheEFandshrinkthedepletionregion.Thiscreatesaregionatthejunctionwherebothelectronsandholesarepresent.Lightisemittedwhentheelectronsrecombinewithholesintheregion.SemiconductorergenningFig4.1ELspectrumofaGaAsLEDatRT.Thisgivesemissioninthenear-IRaround870nm.Thefullwidthathalfmaximumoftheemissionlineis58mV,whichisabouttwicekBTat293K.115.4.3DiodelasersSuperiorperformanceinoutputefficiency,spectrumlinewidth,beamqualityandresponsespeed.FigB.2Absorption,spontaneousemissionandstimulatedemissionsbetweentwolevelsofanatominthepresenceofelectromagnetricradiationwithenergydensityu(v).Spontaneousemission:Absorptiontransition:Stimulatedemission:Steadystatecondition:RelationshipofAandBcoefficients:Derivedfromtheequilibriumcondition,canbeapplyinallothercasesaswell.Innormalconditions:N1>N2;Inlaseroscillation:N2>N1

(

populationinversion)TheprincipleofLD:Thetopofvalencebandisemptyofelectrons,whilethebottomofthecon-ductionbandisfilledwithelectrons.ThereispopulationinversionatthebandgapfrequencyEg/e.Thisgivesrisetonetopticalgain.Lasercanbeobtainedifanopticalcavity(R1>>R2)fromtheendfacesofgainmediumisprovided.125.4.3DiodelasersTheresonantlongitudinalmodecondition:

l=integer/2nTheresonantfrequency:

v=integerc/2nlThebestlaseraresinglelongitudinalmodewithemissionlinewidthsintheMHzrange.(1)Frequencyandlinewidth:(2)Gainandthresholdvalue:gaincoefficient:

Intensity:Stableoscillationconditionataround-tripinthecavity:inincreaseslinearlywiththeinjectioncurrentIin,oncethelaserisoscillatingthegainisclampedatthevalueofth,otherwisethegainwouldexceedthelosses,andthestabilityconditionwouldnothold.ForIin>Ith,theextraelectronsandholescausetheoutputpowertoincrease.(3)Outpowerandslopeefficiency::quantumefficiencydefinedthefractionofinjectedelectron-holepairsthatgeneratephotons.slopeefficiency=1,slopeefficiency=hv/e.135.4.3DiodelasersSchematicdiagramofanoxideconfinedGaAs-AlGaAsheterojunctionstripelaser.Thecurrentflowsinthe–zdirection,whilethelightpropagatesinthexdirection.Thestripeisdefinedbythegapintheinsulatingoxidelayersdepositedonthetopofthedeviceduringthefabricationprocess.TheactiveregionistheintrinsicGaAslayeratthejunctionbetweenthen-andp-typeAlGaAscladdinglayers141.

ThebandgapoftheIII-VsemiconductoralloyAlxGa1-xAsatk=0varieswithcompositionaccordingtoEg(x)=(1.420+1.087x+0.438x2)eV.Thematerialisdirectforx0.43,andindirectforlargervaluesof