Variational Calculation of the Thermal Conductivity of Germanium

Abstract

The thermal conductivity of germanium has been calculated using an anharmonic isotropic continuum model. This model has been extended so as to incorporate umklapp processes by introducing a pseudo-reciprocal-lattice translation vector of magnitude equal to the diameter of the Debye sphere, in such a way that the wave vectors of the three phonons involved are coplanar. Boundary and mass-difference scattering are also included, and the calculations, besides giving good agreement with experimental values of thermal conductivity, provide information on the relative contributions of the different scattering processes to the thermal resistivity and of the different polarization branches to the conductivity. In particular, it is shown that almost all the heat transport is by transverse phonons.