First-principles calculation of carrier-phonon scattering inn-typeSi1−xGex

First-principles electronic structure methods are used to find the rates of inelastic intravalley and intervalley $n$-type carrier scattering in ${\text{Si}}_{1\ensuremath{-}x}{\text{Ge}}_{x}$ alloys. Scattering parameters for all relevant $\ensuremath{\Delta}$ and $L$ intra- and intervalley scattering are calculated. The short-wavelength acoustic and the optical phonon modes in the alloy are computed using the random mass approximation, with interatomic forces calculated in the virtual crystal approximation using density functional perturbation theory. Optical phonon and intervalley scattering matrix elements are calculated from these modes of the disordered alloy. It is found that alloy disorder has only a small effect on the overall inelastic intervalley scattering rate at room temperature. Intravalley acoustic scattering rates are calculated within the deformation potential approximation. The acoustic deformation potentials are found directly and the range of validity of the deformation potential approximation verified in long-wavelength frozen phonon calculations. Details of the calculation of elastic alloy scattering rates presented in an earlier paper are also given. Elastic alloy disorder scattering is found to dominate over inelastic scattering, except for almost pure silicon $(x\ensuremath{\approx}0)$ or almost pure germanium $(x\ensuremath{\approx}1)$, where acoustic phonon scattering is predominant. The $n$-type carrier mobility, calculated from the total (elastic plus inelastic) scattering rate, using the Boltzmann transport equation in the relaxation time approximation, is in excellent agreement with experiments on bulk, unstrained alloys.