Thermal Conductivity of Ge-Si Alloys at High Temperatures

Abstract

The thermal conductivity of several Ge-Si alloys was determined in the temperature range 300\ifmmode^\circ\else\textdegree\fi{} to 1200\ifmmode^\circ\else\textdegree\fi{} K. A strikingly large decrease in the lattice thermal conductivity in the entire temperature range was found upon alloying. The temperature dependence and magnitude of the thermal conductivity can be obtained from current theory if it is modified to permit the dependence of anharmonic scattering on alloy composition. Justification for this dependence is given in terms of second order processes involving simultaneous two-phonon point defect scattering and three-phonon anharmonic scattering. The low-thermal conductivity, the high-thermal stability, and the low mass of the Ge-Si alloys makes these materials very useful for high-temperature thermoelectric power generation. A couple made up of heavily doped $n$- and $p$-type Ge-Si alloys, operated over a temperature range 300\ifmmode^\circ\else\textdegree\fi{}-1140\ifmmode^\circ\else\textdegree\fi{}K, had an energy conversion efficiency of 10%.