Influence of internal stress on electron-phonon interaction inn-type germanium and silicon at low temperatures

Expressions for resonance scattering of phonons by the bound donor electrons have been obtained for the first time for $n$-Ge in the presence of strains for the most general situation when, besides the usual valley-orbit splitting of the four-fold degenerate ground state into a singlet state and a triplet state, the triplet state splits into a doublet state and a singlet state due to internal static and dynamic strains present in the crystal. Similarly for $n$-Si, the most general situation is considered when the degeneracy of the donor-electron ground state is completely removed due to internal strains besides the usual valley-orbit splitting of the six-fold ground state into a singlet state and five-gold degenerate state. The expressions obtained for the resonance scattering relaxation rates of phonons by bound electrons for strained $n$-Ge are used to explain the phonon conductivity results of Sb-, P-, and As-doped Ge.