Lattice Thermal Conductivity of Germanium-Silicon Alloy Single Crystals at Low Temperatures

Abstract

Thermal conductivity measurements are reported for five single-crystal Ge-Si specimens containing 0-7.56 at.% Si. The measurements were made under steady-state conditions and cover the temperature range 2-50\ifmmode^\circ\else\textdegree\fi{}K. The experimental results are compared to three theoretical models, those of Berman et al., Callaway, and Klemens; it is found that the data are best fit by Callaway's model. Good agreement between experimental results and theoretical models is obtained by postulating only three sources of phonon scattering in the specimens: three-phonon processes, isotopic point-defect scattering by the germanium and silicon atoms, and boundary scattering. However, evidence is presented that boundary scattering occurs not only at the external surfaces of the specimens, but also at internal surfaces associated with microscale fluctuations of composition of the type reported by Goss, Benson, and Pfann.