Interband absorption,3.1 Interband transitions 3.2 The transition rate for direct absorption 3.3 Band edge absorption in direct gap semiconductors 3.4 Band edge absorption in indirect gap semiconductors 3.5 Interband absorption above the band edge 3.6 Measurement of absorption spectra 3.7 Semiconductor photodectors,3,3.1 Interband transition,Isolated atom discrete energy level Solid band (delocalized state) For semiconductor or insulator, photon excites electron from filled valence to the empty conduction band, the transtion energy is,There is a continuous range of frequency; There is a threshold h Eg= (Ef Ei)min; Creation of an electron-hole pair; Direct and Indirect band gap.,3.1 Interband transition,In a direct band material, both the conduction band minimum and the valence band minimum occur at the zone centre where k = 0; In a indirect band gap material, the conduction band minimum does not occur at k = 0, but is usually at the zone edge or close to it.,Photon absorption,Absorption and emission of phonon,3.2 The transition rate for direct absorption,The optical absorption coefficient Wi - f transition rate,3.1 Interband transition,Where the matrix element M, the density of states g(h).,(Fermis golden rule),the matrix element M, (semiclassical approach),3.2 The transition rate for direct absorption,The electron state wave function:,Perturbation:,Dipole moment:,Light wave:,Initial:,Final:,the joint density of states,This gives:,3.3 Band edge absorption in direct gap semiconductors,Electron level in a covalent crystal made from four-valent atom such as Ge or bi- nary compounds such as GaAs. The s And p states of the atoms hybridize to form bonding and antibonding molecular orbitals, which then evolve into the con- duction and valence bands of the semi- conductor,4s24p2,Selection rules: The parity of the initial and final states must be different. j = -1, 0 or +1.(Total angular momentum must change by one unit) l = 1. ms = 0. (Spin quantum numbers never change). Electric-dipole transition: high transition rate, short radiative lifetime(10-9 10-8 s)fluorescence. Magnetic dipole or electric quadrpole: smaller transition rates and longer radiative lifetime (10-6 s upwards) the slow emission by electric dipole-forbidden is called phosphorescence.,3.3.1 The atomic physics of the interband transitions,3.3.2 The band structure of a direct gap III-V semiconductor,3.3 Band edge absorption in direct gap semiconductors,s antibonding,p bonding,S-like conduction and three p-like valence band,(heavy hole band),(light hole band),(split-off hole band),Band structure of GaAs. The dispersion of the bands is shown for two directions of the Brillouin zone centre: X and L. The point co- responds to the zone centre with a wave vector of (0,0,0), while the X and L points correspond respectively to the zone edges along the (100) and (111) directions. The valence bands are Below the Fermi level and are full of electrons.,3.3 Band edge absorption in direct gap semiconductors,3.3.3 The joint density of states,The dispersion of band (E k relationship),The energy conservation of a heavy hole or a light hole transition:,Generally,等于能量 时的状态对密度 ),(,Fig.1,3.3.4 The frequency dependence of the band edge absorption,Square of the optical absorption coefficient versus photon energy for the direct gap III-V semiconductor InAs at room temperature. The band gap can be deduced to be 0.35 eV by extrapolating the absorption to zero.,Frequency dependence approximately obeyed The coulomb attraction of excitons neglected; Impurity or defect states within gap neglected; The parabolic band approximation only valid near k = 0.,3.3.5 The Franz-Keldysh effect Two main effects on band edge absorption by application of an external electric field E:,Electro-optic effect: The electric field modulated optical constants (n,). (K-K relationship). Electroreflectance: The reflectivity can be changed due to modulated optical constants (n,).,3.3.6 Band edge absorption in a magnetic field,The electrons in magnetic field: The quantized energy (Landau levels):,(cyclotron frequency),The energies electrons and holes within the bands are given by:,Quantized motion in the (x, y) plane, free motion in the z direction. E=0 at the top of the valence band:,The interband transition creates an electron in the conduction band and a hole in valence band,Selection rule: n = n, kZ = kZ . (the momentum is negligible),The absorption spectrum with kZ=0 given by:,The transition energy:,Two consequences: The absorption edge shifts by heBZ/2; Equally spaced peaks in the spectrum.,Transmission spectrum of germanium of germanium for B=0 and B=3.6T at 300 K. The electron effective mass can be determined from the energies of minima.,Fig.2,3.4 Band edge absorption in indirect gap semiconductor,The indirect transition involve both photons and phonons (h, hq ):,This is a second-order process, the transition rate is much smaller than for direct absorption.,Comp