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

The temperature dependence of three-phonon processes in solids is discussed in terms of the exponent m in relations of the type τ∝T^-m where the value m is given by m=-Tτ^-1dτdT. 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.