Three-Phonon Scattering and Guthrie's Limits for Its Temperature Dependence

Abstract

It is shown that one can explain the temperature dependence of the phonon conductivity of Ge in the entire range from 2 to 1000 °K if the three-phonon relaxation rate is given by $\tau _{3\mathrm{ph}}^{}{}_{}{}^{-1\mathrm{}}\propto g\left(\omega \right)T^{m\left(T\right)\mathrm{}}{e}^{-\frac{\Theta }{\alpha T}}$. Three-phonon scattering processes are classified, after Guthrie, into two groups: class I, which involves the annihilation of carrier phonons by combination, and class II, which involves splitting of carrier phonons. At all temperatures, the values of $m\left(T\right)\mathrm{}$ for both classes of processes lie either definitely below or close to the upper limit of $m\left(T\right)\mathrm{}$ as obtained by Guthrie.