Nonelectronic scattering of longitudinal-optical phonons in bulk polar semiconductors

This paper contains a study of the processes whereby LO phonons in bulk polar semiconductors relax energy and momentum other than via interactions with free carriers. The three-phonon process responsible for determining the lifetime is described in terms of an anharmonicity parameter that is the optical-mode analog of the Gruneisen parameter. Other first-order three-phonon processes are shown to have negligible rates for relaxing momentum, and this is true of second-order three-phonon and first-order four-phonon processes. The theory of the optical-mode analog of Rayleigh scattering is given for alloy fluctuations in mixed crystals and for neutral impurities in isolation and in clusters. The momentum relaxation rate for alloy semiconductors exhibits mode dependence and can be comparable with the energy relaxation rate. It is also shown that momentum relaxation associated with clusters can be significant at average densities of ${10}^{18}$ ${\mathrm{cm}}^{\mathrm{-}3}$ and above. An interaction with isolated charged impurities analogous to the Fröhlich interaction also yields significant rates for momentum relaxation at similar densities, especially for long wavelengths. A parallel interaction is shown to occur associated with the anharmonicity induced by the polarization field surrounding the charged impurity, though this turns out to relax momentum only weakly. We conclude that in pure material the decay process is the fastest for both energy and momentum, but in heavily doped material charged impurity scattering will tend to dominate momentum relaxation. The relevance for hot-electron transport in the presence of hot phonons is pointed out.