# Quantum theory of free carrier absorption in polar semiconductors

## Abstract

A quantum mechanica treatment of the free carrier absorption by electrons in polar semiconductors has been constructed in terms of the Kane model. It takes into account overlap wavefunction factors, intermediate states in other bands, the finite optical phonon energy, and the effects of arbitrary spin orbit splitting on the electron energy and wavefunction. The scattering mechanisms considered include polar optical mode scattering, ionic scattering, piezoelectric and deformation coupled acoustic mode scattering, and electron-electron scattering. The theory, in the appropriate limits, applies to a wide range of photon energies, electron concentrations, and lattice temperatures. It relates the dominant scattering mechanism involved in the various limits to the characteristic behavior of the absorption coefficient as a function of the photon energy. In particular, the dominant scattering mechanism for small carrier concentrations is found to be polar optical mode scattering, which exhibits a λ3 dependence of the absorption coefficient times the index of refraction, (except at the lowest frequencies, where the expected λ2 dependence is obtained). Ionic, or impurity, scattering becomes important as the carrier concentration is increased, and the characteristic wavelength dependence of the electron cross section times the index of refraction varies from λ4 to λ3, and the absorption coefficient times the index of refraction from λ4 to λ2, depending on the ratio of the photon energy to the initial electron energies. Comparisons are made with the available data over a wide range of photon energies, temperatures, and electron concentrations, for the III-V compounds InSb, InAs, InP, and GaAs. © 1973.