Electron–phonon interaction in P-, As-, and Sb-doped germanium in the intermediate concentration region

Abstract

The electron–phonon scattering, in the analysis of low temperature thermal conductivity of n-type germanium, is studied in the intermediate donor concentration region. At low concentrations, below metal–insulator transition, the donor electrons are bound to the impurity atoms, and at high concentrations they are free in conduction band. The properties in the intermediate concentration are explained by Mikoshiba's "inhomogeneity model". According to this model, the electrons are in a mixed state both in non-metallic and metallic state. The electron concentrations in the non-metallic and metallic regions are calculated for each sample and the theory of both bound electron–phonon scattering and free electron–phonon scattering are applied. This theory of mixed electron–phonon scattering explains the thermal conductivity results of P-, As-, and Sb-doped germanium samples between 1 and 20 K for intermediate donor concentrations from 1.1 × 1017 to 5.6 × 1017 cm−3. The values of density-of-states effective mass are kept constant (= 0.22) without variation with temperature. The values of shear and dilatation-deformation potential constants are obtained from our calculations. The values of shear-deformation potential for the electrons in the bound region are found to be between 14 and 16 eV, while the values of dilatation-deformation potential are between 1 and 3.5 eV for the electrons in the conduction band and these values are in agreement with the experimentally measured values.