Energy - Interband luminescence

Luminescence5.1Light emission in solids5.2Interband luminescence5.3Photoluminescence5.4Electroluminescence

Luminescence 5.1 Light emission in solids 5.2 Interband luminescence 5.3 Photoluminescence 5.4 Electroluminescence

5.1 Light emission in solidsThe spontaneous emission rate for a two level:Thereverseprocessofabsorption-emissionEmission in solids is called luminescence.(dN)Luminescencemechanisms=-AN.dtPhotoluminescence(PL)adiativeN(t)= N(O)exp(-At) = N(O)exp(-t / tR)Electroluminescence(EL)injectelectronsA: Einstein A coefficientT=A-': radiative lifetime ofthe transition8元hv3EXCITED.:A:BLrelaxationSTATEc3The transition have large absorptionTNRTRhWcoefficientsalso have high emission probabilities and shortradiative lifetime,GROUNDUpper level is populated.STATEInnormalcircumstancestheelectronsrelaxtowithin~kpTofthebottomofexcitedstatebandinject holesTheholesfollowa similar series ofrelaxationsThus light is only emitted within a narrow energyElectrons are injected into the excited staterange.bandandrelaxtothelowestavailablelevelThephotonisemittedwhenanelectroninNon-radiative relaxation: The excited energy mayan excited statedrops down into an emptytransfer into heat by emitting phonons or bestate in the ground state band. These emptytrapped by defect.state are generated bythe injection of holes

5.1 Light emission in solids The reverse process of absorption – emission Emission in solids is called luminescence. Luminescence mechanisms: • Photoluminescence (PL) • Electroluminescence (EL) Electrons are injected into the excited state band and relax to the lowest available level. The photon is emitted when an electron in an excited state drops down into an empty state in the ground state band. These empty state are generated by the injection of holes. The spontaneous emission rate for a two level: ( ) (0) exp( ) (0) exp( / ). . R radiative N t N At N t AN dt dN = − = −   = −      A: Einstein A coefficient; R=A-1 : radiative lifetime of the transition. B c h A 3 3 8   = • The transition have large absorption coefficients also have high emission probabilities and short radiative lifetime; • Upper level is populated. In normal circumstances the electrons relax to within ~ kB T of the bottom of excited state band. The holes follow a similar series of relaxations. Thus light is only emitted within a narrow energy range. Non-radiative relaxation: The excited energy may transfer into heat by emitting phonons or be trapped by defect

5.1 Light emission in solids5.2InterbandluminescenceTotal rate:The interband luminescence correspondstoNdNNannihilationof anelectron-holepair (electron-hole recombinationdtTRTNRTRNRotal5.2.1 Direct gap materialsThe luminescent efficiency nR:1ANconduction bandNRN(1/tR+1/NR)1+TR /TNRE个If Tr<< TNR, nR ~ 1, maximum possibleamountoflightis emittedIf tr>> TR, NR ~ 0, light emission is veryelectronsinefficient.oThe efficient luminescence requires thattheradiative lifetimeshouldbemuchholesshorter than the non-radiative lifetimekThe luminescent intensity at frequency v:k=0valencebandI(hv) αc|Mg(hv)×level occupancy factors.The injected electrons and holes relax very rapidly to lowest energy states.The photons are emitted when electrons at the bottom ofthe conduction bandrecombinewithholesatthetopof thevalenceband.Thetypicalvaluesoftpis in the range 10-8- 10-9s.The transition should be dipole allowed and havelarge matrix elements and the same k vector (near k=0, thus close to ho=Eg)

5.1 Light emission in solids Total rate: . 1 1          +  = −  −   = −      total R NR R NR N N N dt dN The luminescent efficiency R: . 1 / 1 (1/ 1/ ) R NR R NR R N AN +   =  +   = If R<< NR, R  1, maximum possible amount of light is emitted. If R >> NR, R  0, light emission is very inefficient. The efficient luminescence requires that the radiative lifetime should be much shorter than the non-radiative lifetime 5.2 Interband luminescence The interband luminescence corresponds to annihilation of an electron-hole pair (electron￾hole recombination) 5.2.1 Direct gap materials The injected electrons and holes relax very rapidly to lowest energy states. The photons are emitted when electrons at the bottom of the conduction band recombine with holes at the top of the valence band. The typical values of R is in the range 10-8 – 10-9 s. The transition should be dipole allowed and have large matrix elements and the same k vector (near k=0, thus close to h=Eg ). ( ) ( ) . 2 I h  M g h level occupancy factors The luminescent intensity at frequency :

conductionbandPLGaNT=4Kelectronsphononabsorptione2W个Ehaholes3.403.453.503.553.60valence bandEnergy(eV)>kk=0ThePLwasexcitedbyabsorptionof4.9eVphotonsfroma frequency doubledcopperThe interband luminesence in an indirect gapvapour laser.The spectrum consist of amaterial is a second-order process. The t muchnarrow emission line at3.5 eV close tothemorelongerthanfordirecttransition,thereforeband gap energy,while the absorption showsthismakestheluminescenceefficiency small.Sothe usual threshold at Eg with continuousthe indirect gap materials such as silicon andabsorption for ho > Eg.germanium are generally band light emitters.5.2.2 Indirect gap materialsInanindirectmaterials,conservationofmomen-tum requires that a phonon must either beemitted orabsorbed when thephoton is emitted

The PL was excited by absorption of 4.9 eV photons from a frequency doubled copper vapour laser. The spectrum consist of a narrow emission line at 3.5 eV close to the band gap energy, while the absorption shows the usual threshold at Eg with continuous absorption for h > Eg. 5.2.2 Indirect gap materials In an indirect materials, conservation of momen￾tum requires that a phonon must either be emitted or absorbed when the photon is emitted. The interband luminesence in an indirect gap material is a second-order process. The R much more longer than for direct transition, therefore this makes the luminescence efficiency small. So the indirect gap materials such as silicon and germanium are generally band light emitters

Thetotal numberdensity Neof electrons:5.3PhotoluminescenceN.=g.(E)f.(E)dE,5.3.1 Excitation andrelaxationThedensity of statein conductionband:Eelectrons1conductionband2m(E-E.)2gc(E)2元2h?EFermi-DiracdistributionfortheelectronshvhVLF.0f.(E)=exik,Tholesvalenceband(The system is in a situation of quasi-equilik=oDensity of statesbrium, thus is no unique Fermi energy. E= 0(b)(a)corresponds tothebottom ofthe conductionbandorthetopofthevalenceband)(a) Schematic diagram of the processes occurringE-mdE,Nduring PL in a direct gap semiconductor afterXh?k,TTexcitation at frequency VL. The electrons and holesrapidlyrelaxtothebottomoftheirbandsbyphononThe total number density Nof holes:emission (~10-13 s)before recombining by emittingaE-2mphoton (~ 10-9s). (b) Density of states and levelE2dEN.=expoccupancies for the electrons andholesafter opticalhk,Texcitation.Thedistributionfunctionsshown bytheN.=N,shading apply to the classical limit where Boltzmannstatistics are valid.These two Eqs can be used to calcuulate E,Ey

5.3 Photoluminescence 5.3.1 Excitation and relaxation ( a) Schematic diagram of the processes occurring during PL in a direct gap semiconductor after excitation at frequency L. The electrons and holes rapidly relax to the bottom of their bands by phonon emission (~10-13 s) before recombining by emitting a photon ( ~ 10-9s). (b) Density of states and level occupancies for the electrons and holes after optical excitation. The distribution functions shown by the shading apply to the classical limit where Boltzmann statistics are valid. The total number density Ne of electrons: N g (E) f (E)dE, Eg e  c e  = The density of state in conduction band: ( ) . 2 2 1 ( ) 2 1 2 3 2 2 g e C E E m g E −          =   Fermi-Dirac distribution for the electrons: 1 ( ) exp 1 −       +        − = k T E E f E B C F e (The system is in a situation of quasi- equili￾brium, thus is no unique Fermi energy. E= 0 corresponds to the bottom of the conduction band or the top of the valence band) exp 1 , 2 2 1 1 2 1 2 3 0 2 2 dE k T E E E m N B C e F e −         +        −          =   The total number density Ne of holes: exp 1 . 2 2 1 1 2 1 2 3 0 2 2 dE k T E E E m N B V h F h −         +        −          =   Ne = Nh These two Eqs can be used to calcuulate , . V F C EF E