Temperature Dependence of Density-of-States Effective Mass and the Electronic and Phonon Contributions to Thermal Resistance of Doped Si-Ge Alloys at High Temperatures

The electronic polar and dipolar thermal conductivity of both $n$- and $p$-type Si-Ge alloys with different carrier concentrations are calculated in the temperature range 300 to 1100°K. With carrier concentration remaining constant, the nature of the scattering mechanism is determined from the temperature dependence of the conductivity mobility. The scattering parameter being known, the temperature dependences of the reduced Fermi level and the density-of-states effective mass are determined from thermoelectric measurements on these samples by Dismukes et al. These temperature variations are taken into account in the calculation of the contribution of the electron-phonon interaction to the thermal resistance of the doped Si-Ge alloys. The thermal conductivities due to longitudinal phonons and transverse phonons are calculated separately, and there is good agreement between the calculated temperature dependences of the total phonon conductivity and the experimentally obtained values of thermal conductivity minus the electronic thermal conductivity. The dilatational deformation potential is found to increase with the increase in the carrier concentration and the reduced Fermi potential. The dipolar contribution is found to be significant only at temperatures above 700°K and for $n$-type alloys, for which the doping is comparatively low.