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 θ100, where θ is the Debye characteristic temperature; while at temperatures above θ10, K∝T^-n where n1.3 for germanium and n1.0 for silicon. In the range of temperature just above the conductivity maximum, that is, from θ20 to θ10, 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.