Temperature Dependence of Three-Phonon Processes in Solids, with Application to Si, Ge, GaAs, and InSb

Abstract

The temperature dependence of three-phonon processes in solids is discussed in terms of the exponent $m$ in relations of the type $\ensuremath{\tau}\ensuremath{\propto}{T}^{\ensuremath{-}m}$ where the value $m$ is given by $m=\ensuremath{-}\frac{T{\ensuremath{\tau}}^{\ensuremath{-}1}d\ensuremath{\tau}}{\mathrm{dT}}$. A method is given for placing bounds on the value of $m$ for three-phonon processes involving various energies of phonons at any given temperature. Application to Si, Ge, GaAs, and InSb shows considerable similarity in the temperature dependences of the three-phonon relaxation times of longitudinal and transverse phonons. This similarity is most noticeable at the higher temperatures.