Analysis of the Lattice Thermal Conductivity of Germanium

The lattice thermal conductivity of germanium has been analyzed on the basis of the Callaway model in the temperature range 2-1100 ^∘{}K. At high temperatures four-phonon processes are seen to play an important role in the determination of the thermal resistivity of germanium. In order to take account of the nonlinear behavior of the dispersion relations of the crystal lattice, the phonon wave vector is assumed to be certain simple but different functions of the phonon frequency for longitudinal and transverse branches. Three-phonon processes having different temperature dependences in the various temperature ranges have been used in the calculations. Very good agreement with the experimental results has been obtained.