Phonon Conductivity of Ge in the Temperature Range 2-1000 °K

Abstract

The contributions of transverse and longitudinal phonons toward thermal conductivity of undoped Ge have been investigated, both in high- as well as low-temperature regions. Four-phonon processes are also included in the determination of the combined relaxation time ${\tau }_c$ and hence the phonon conductivity. The group velocity of respective phonons in the conductivity integral is obtained on the basis of $\overrightarrow{\mathrm{q}}=\left(\frac{\omega }{\overrightarrow{\mathrm{v}}}\right)(1+\alpha {\omega }^2)$, where the parameter $\alpha$ is determined from the experimentally obtained dispersion curves for the different acoustic branches in the region $0-\frac{1}{2}{q}_{max}$ and $\frac{1}{2}{q}_{max}-q_{max}$. It is observed that the transverse phonons in general make a major contribution toward thermal conductivity in the entire temperature range.