第四讲-激子与发光课件.ppt

课程内容l绪论l经典传播l带间吸收l激子l发光l半导体量子阱、自由电子、分子材料l发光中心12第四讲 ExcitonsThe concept of excitonsFree excitonsFree excitons at high densityFrenkel excitons3The concept of excitonsIn semiconductors and insulators:photon absorption electrons in the conduction band and holes in the valence band.Exciton:bound electron hole pair by Coulomb interactionObserved in semiconductors;large radius;delocalized states;move freely;binding energy 0.01 eV Observed in insulators and molecular crystals;smaller radius;localized states;less mobile and hoping;binding energy 0.1-1 eV.Stable excitons will only be formed if the attractive energy kBT(0.026eV at room temperature)Free excitons are stable at cryogenic temperature.Tight bound excitons are stable at room temperature.Two types of excitons:4Wannier 激子（自由激子）Frenkel 激子（束缚激子）:The concept of excitonsFree excitonsFree excitons at high densityFrenkel excitons5第四讲 ExcitonsBinding energy and radius of free excitonsFree excitons:weakly bound electron-hole pair;a hydrogenic system Applying the Bohr model to the exciton,considering dielectric constant r of the medium and the reduced mass of electron and hole.The energy of the nth level relative to the ionization limit RH is the Rydberg constant of the hydrogen atom(13.6 eV).RX:exciton Rydberg constant.The radius of the electron-hole orbit:aH is the Bohr radius of the hydrogen atom(5.29 10-11m)and ax is the exciton Bohr radius.ground state with n=1 has the largest binding energy and smallest radius.n1:less strong binding energy and larger radius.Biding energy tends to decrease and ax to increase as r increase.6Rx tends to increase and ax to decrease as Eg increases.Causes:r tends to decrease and to increase as the band gap increases.In insulators with band gaps greater than about 5 eV,ax becomes comparable to the unit cell size,and the Wannier model is no longer valid.narrow gap semiconductors:RH is so small that exciton effects is hard to observe.(Eg=1-3eV,free excitons behavior is best observed)7Exciton absorptionFree excitons are typically observed in direct gap semiconductors.(hard to observe in the absorption spectra of indirect semiconductor)The group velocity of an electron or hole in a band is given by:At the Brillouim zone centre of direct semiconductor:k=0 and zero gradient.Eectron-hole pairs created by direct transition and have the same velocities.Therefore,strong excitons occur in the spectral region close to the fundamental band gap.Band edge absorption spectrum for a direct gap semiconductor with excitonic effects included.The dashed line shows the expected absorption when the excitonic effects are ignored.Free excitons can only be observed in very pure samples.Impurities:screening the Coulomb interaction in the exciton and thereby strongly reduce the binding forces;generating electric field and tend to ionize excitons.8Exciton creation:electron-hole pairs and same velocities.The energy of exciton absorption is:Experimental data for free excitons in GaAs Exciton absorption of ultra pure GaAs at 1.2 K.hydrogen-like energy spectrum of the exciton in the vicinity of the band gap.E1=1.5149 eV,E2=1.5180 eV,E3=1.5187 eV The experimental Rx=4.2 meV is in good agreement with the calculated value.9Eg=l.5191 eV,agree with other measurements.The concept of excitonsFree excitonsFree excitons at high densityFrenkel excitons10第四讲 ExcitonsMort density Nmott:the density at which the exciton-exciton distance is equal to the exciton diameter:High density is achievable with a focussed laser beam.11uThe exciton density can be controlled by tuning the laser powerLow density,the exciton-exciton interactions are negligible;the exciton wave functions begin to overlap at high density and the interaction will become significant.12Density Effects:1.electron-hole plasmaweakening and broadening of the exciton absorption line is observed(absorption saturation,nonlinear effects).2.Biexcitons(exciton molecules)equivalent process to the formation of an H2 molecule;new feature line can be found.3.electron-hole droplets4.Bose-Einstein condensation(Stotal=0 or 1)Broad feature line at lower energy than the free excitonThe concept of excitonsFree excitonsFree excitons at high densityFrenkel excitons13第四讲 ExcitonsFrenkel excitons occurring in large band gap materials with small dielectric constants and large effective masses.small radii and large binding energies,0.1 eV to several eV,stable at room temperature.propagating through the crystal by hopping.Localized on the atom site,may therefore be considered as excited states of the individual atoms or molecules,especially for n=1exciton energy.Theoretical treatment of Frenkel excitons is more complicated.14Rare gas crystals Crystallize at cryogenic temperatures.Large band gap,Neon has the largest band gap in nature.Exciton transitions all occur in the vacuum ultraviolet spectral range Binding energies are very large.A close correspondence between the n=1 exciton energies in the crystals and the optical transitions of the isolated atoms(For Xenon 5p65p56s).The radius increases with n,delocalized,correspondence gets weaker.15Alkali halides Large direct band gaps(5.9 eV 13.7 eV)LiF has the widest band gap of any practical optical material.Eg and exciton binding energy tends to increase with decreasing anion and cation size.The excitons are localized at the negative(halogen)ions.Strong exciton effects at RT because of large binding energy(0.8eV and 1.9eV)16Principles of luminescenceInterband luminescence PhotoluminescenceElectroluminescent第五讲 Interband Luminescence17发光的定义u固体中的电子受到外界能量的激发，从基态跃迁到激发态，这是一种非平衡态。处于激发态的电子具有一定的寿命，以一定几率回落到基态，并把多余的能量以各种形式释放出来。如果以光能的形式释放，称为发光过程。u任何物体在一定温度下均有热辐射（热发光）。为了区分其它发光形式和热发光，严格的固体发光概念不包含热发光。发光现象有两个主要特征：发 光 为 固 体 吸 收 外 界 能 量 后，所 发 出 总 辐 射 超 出 热 发 射 的部分。（发光的定义，指出了与热辐射的区别）外 界 激 发 源 对 物 体 的 作 用 停 止 后，发 光 现 象 会 持 续 一 段 时间。（发光与散射、反射等现象的区别）18发光的分类依据激发方式不同，固体发光可分为以下几种形式：u光致发光：如荧光灯，PDP。u电致发光：如LED。u阴极射线发光：CRT。u高能射线或粒子（X射线，射线，粒子等）发光：如医学胸透。u化学发光：如荧光棒。u生物发光：如萤火虫。u机械发光：摩擦发光。19Light emission in solidsR=1/A，radiative lifetime of transitionInjected electron or holeRelax to the minimum energy stateThe photon is emitted when an electron in an excited state drops down into an empty state in the ground state band-Luminescence.If the upper level has a population N at time t,the radiative emission rate is given by:A:Einstein coefficient.2021Photon absorption Photon emissionutransitions which have large absorption coefficients also have high emission probabilities and short radiative lifetimes.uphotons can be absorbed to any state within the excited state band,no matter how far it is above the bottom of the band.uElectrons and holes relax rapidly to the lowest levels of excited state,and the light will therefore only be emitted within a narrow energy range from the lowest levels in the excited state band.uNormally,the absorption and emission spectra are not same.uThe luminescent intensity at frequency:The matrix element M:Fermi s golden ruleThe joint density of state g(h)the occupancy factors give the probabilities that the relevant upper level is occupied and the lower level is empty.22光致发光的效率辐射跃迁并不是激发态电子回到基态的唯一途径。另一途径：无辐射跃迁，发射声子（吸收光能转变为热）。消弱发光。设无辐射跃迁寿命为NR，同时考虑辐射跃迁和无辐射跃迁，激发态电子数变化速率：发光效率R定义为辐射跃迁速率/总跃迁速率：u 高效发光材料要求辐射跃迁寿命R远小于无辐射跃迁寿命NR。23Principles of luminescenceInterband luminescence PhotoluminescenceElectroluminescent24第五讲 Interband LuminescenceInterband luminescenceInterband luminescence:in a semiconductor,an electron that has been excited into the conduction band drops back to the valence band by the emission of a photon.Corresponding to the annihilation of an electron-hole pair(electron-hole recombination).1.Direct gap materialsThe optical transitions are dipole-allowed and have large matrix elements.radiative lifetime:10-8-10-9s;luminescent efficiency is high.injected electrons and holes relax very rapidly to the lowest energy states.electron and hole that recombine must have the same k vector,downward vertical arrow.No matter how we excite the electrons and holes in the first place,luminescence at energies close to the band gap is always obtained.25Luminescence spectrum and absorption of a GaN epilayer at 4 K.The photoluminescence(PL)was excited by absorption of 4.9 eV photons.The emission 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 Eg.The emission and absorption spectra are not the same,even though they are determined by the same matrix element.The band gap corresponds to the threshold for optical absorption,but to the energy of the optical emission.262.Indirect gap materialsRequiring emitting both a phonon and a photon during the transition.a second-order process,with a small transition probability.longer radiative lifetime,smaller luminescent efficiency.The indirect gap materials such as silicon and germanium are generally bad light emitters.27Principles of luminescenceInterband luminescence PhotoluminescenceElectroluminescent28第五讲 Interband LuminescenceuPhotoluminescence in a direct gap semiconductor:interband luminescence excited by a photon with energy greater than Eg.Excitation and relaxationPhotons absorption from an excitation source(laser or lamp),electrons(in conduction band)and holes(in valence band)are created.hvLEgThe electrons and holes rapidly relax to the bottom of their bands by phonon emission(10-13s)before recombining by emitting a photon(10-9s).occupancy factors shown by the shading can be calculated by applying statistical physics to the electron and hole distributions.(a)Schematic diagram of the processes occurring during PL in a direct gap semiconductor after excitation at frequency L.(b)Density of states and level occupancies for the electrons and holes after optical excitation.29Low carrier densities At low carrier densities,the occupancy of the levels is small and+1 factor in fe(E)can be ignored.The electron and hole distribution will be described by classical statistics.Fermi Boltzmann distribution:The luminescent intensity at frequency:Assuming that the matrix element is independent of frequency.Arising from the joint density of states Arising from the Boltzmann statistics of the electrons and holes.30uPL spectrum of GaAs at 100 K.The excitation source was a helium neon laser operating at 632.8 nm(1.96 eV).The spectrum shows a sharp rise at Eg due to the(h-Eg)1/2 factor.Then falls off exponentially due to the Boltzmann factor.The full width at half maximum of the emission line is very close to kBT 31Photoluminescence spectroscopy Photoluminescence(PL)spectra:The sample is excited with a laser or lamp with photon energy greater than the band gap.The spectrum is obtained by recording the emission as a function of wavelength.Photoluminescence excitation spectroscopy(PLE):The luminescence intensity at the peak of the emission is measured as the excitation wavelength is scanned.3233GaN:Zn:excitation and emission spectraPrinciples of luminescenceInterband luminescence PhotoluminescenceElectroluminescent34第五讲 Interband Luminescence35General principles of electroluminescent devices uElectroluminescence is the process by which luminescence is generated while an electrical current flows through an optoelectronic device.uTwo main types of devices:Light Emitting Diodes(LED)and Laser Diode(LD).Structure:epitaxial layer;p-and n-type region;active region.Mechanism:operated in forward bias;electron s and holes injection and recombination in active region.Be same as the photoluminescence and band gap determining the emission spectra(line emission at Eg with band width of kT).Commercial electroluminescent devices are therefore made from direct gap compounds.Three factors for the choice of materials:1.band gap size;2.lattice matching;3.p-type doping.36Band gap of selected III-V semiconductors vs lattice constant“lattice matching”between the epitaxial layers and the substrate:if not,the formed dislocation will degrade the optical quality.Nitride?AlxGa1-xAs:630-870nm,red and infrared LED;perfect lattice matching.GaxInl-xAsyPl-y:0.92 1.65m,as light source for optical fiber communication(operated at 1.55 and 1.3 m)GaxIn1-xN:The emission wavelength varied from 360 to 650nm,green and blue LED;Lattice matching and p-doping problems;p-type doping in wide band gap semiconductor will result in deep acceptor levels.And then the low hole density gives the layers a high resistivity,which causes ohmic heating when the current flows and hence device failure.This a common problem for most of wide gap semiconductors.37Light Emitting Diodes(LED)Heavily doping produces degenerate distributions of holes and electronsIn thermal equilibrium at zero bias,the Fermi energy must be same everywhere.depletion region formed electron and hole seperated and no light emissionAt forward bias:The depletion region shrinks;creates a region at the junction where both electrons and holes are present.The electrons recombine with the holes,emitting photons at energy Eg by interband luminescence.38Electroluminescence spectrum of a GaAs LED at room temperature.A current of 1 mA flowing through the device.Emission in the near-infrared around 870 nm.(GaAs,Eg=1.42eV)The full width at half maximum(FWHM)of the emission line is 58 meV,which is about twice kBT at 293 K.39作业：Question 4.1 1）Calculate the binding energy and radius of the n=1 and n=2 free excitons in zinc sulphide(ZnS)which has me*=0.28m0,mh*=0.5m0 and r=7.9.2)Would you expect these excitons to be stable at room temperature.3)the bandgap of ZnS is about 3.76 eV,calculated the wavelength of the photon corresponding to the n=1 exciton absorption peak.4)Excitons can absorb photons by making transitions to excited states in exactly the same way that hydrogen atoms do.Calculate the wavelength of the photon required to promote an exciton in ZnS from the n=1 to the n=2 state.402.Page 112,question 5.4