Lattice Thermal Conductivity of Disordered Semiconductor Alloys at High Temperatures

TLDR

The authors derive the high‑temperature thermal conductivity of disordered semiconductor alloys using Klemens‑Callaway theory, modeling relaxation times as ω⁴ for strain and mass defects and ω² for normal and umklapp phonon processes, and expressing conductivity in terms of lattice parameters and atomic weights. The model agrees with experimental data for Ge‑Si alloys from 300–1200 K and (Ga,In)As at 300 K (using a 2.5 umklapp/normal ratio), showing that Ge‑Si resistivity is dominated by mass‑defect scattering while (Ga,In)As resistivity is mainly due to strain scattering.

Abstract

The high-temperature thermal conductivity of a disordered semiconductor alloy is derived using the Klemens-Callaway theory. It is assumed that the reciprocal relaxation times depend on frequency $\ensuremath{\omega}$ as ${\ensuremath{\omega}}^{4}$ for strain and mass point defects and as ${\ensuremath{\omega}}^{2}$ for normal and umklapp three-phonon anharmonic processes. The thermal conductivity is expressed in terms of the lattice parameters and mean atomic weights of the alloy and its constituents. Agreement is obtained between theory and published experimental data on Ge-Si alloys at temperatures 300-1200\ifmmode^\circ\else\textdegree\fi{}K, and on (Ga,In)As alloys at 300\ifmmode^\circ\else\textdegree\fi{}K, using the value 2.5 for the ratio of umklapp to normal relaxation times. It is found that the large thermal resistivity of Ge-Si alloys is predominantly due to mass defect scattering, whereas that of (Ga,In)As alloys is mainly due to strain scattering.