Scattering of Phonons by Electrons in Germanium-Silicon Alloys

The theory developed by Ziman for the scattering of phonons by electrons is extended to high temperatures using the formalism of Klemens and Callaway. The theory is applied to the experimental results recently published by Dismukes et al. on the effect of doping on the thermal conductivity of Ge-Si alloys. After subtracting the electronic contribution from the measured thermal conductivity, the resulting lattice conductivity is analyzed. In describing the effect of doping, the deformation potential is the only free parameter; its value is adjusted for each sample to obtain agreement with the experimental data at 500°K, which is close to the Debye temperature. The theory then predicts the correct temperature dependence of the lattice thermal conductivity. The deformation potentials, derived in this manner, are found to be higher for $n$-type than for $p$-type material, and to increase with carrier concentration. For lightly doped $p$-type and $n$-type material, values of 1.2 and 1.6 eV were obtained, respectively, which compare well with the available literature data.