Thermal Conductivity of Germanium and Silicon at Low Temperatures

Measurements are reported of the thermal conductivity, $K$, of high-purity $n$- and $p$-type germanium, and of a single crystal of $n$-type silicon at temperatures between 2 and 150°K. These confirm that in silicon and in annealed germanium the thermal conductivity is limited only by boundary scattering at temperatures below about $\frac{\theta }{100}$, where $\theta$ is the Debye characteristic temperature; while at temperatures above $\frac{\theta }{10}$, $K\propto T^{-n}$ where $n\simeq 1.3$ for germanium and $n\simeq 1.0$ for silicon. In the range of temperature just above the conductivity maximum, that is, from $\frac{\theta }{20}$ to $\frac{\theta }{10}$, no particularly rapid rate of change of $K$ with $T$ is observed, in contrast with the behavior found in pure dielectric crystals and bismuth. These features are discussed.