Phonon-Electron Scattering in Phosphorus-Doped Germanium

The drastic reduction in the phonon conductivity of P-doped Ge samples, as observed by Mathur and Pearlman in the temperature range (1.4-5) \ifmmode^\circ\else\textdegree\fi{}K, can be explained quantitatively in terms of the scattering of phonons by electrons in bound states as well as in conduction states, depending upon the donor-electron concentration of the sample. For electron concentrations ${N}_{\mathrm{ex}}l{10}^{17}$ ${\mathrm{cm}}^{\ensuremath{-}3}$, phonons are scattered by bound donor electrons. The modified expressions of Kumar, Srivastava, and Verma for the electron-phonon---scattering relaxation rate, based on Kwok's theory, explain the phonon conductivity results very well. The adjusted values of the shear deformation potential for the best fit between theory and experiment for different P-doped Ge samples are of the order of 13.32-14.18 eV, which agrees very well with the usual experimental values of 15-19 eV. For ${N}_{\mathrm{ex}}g{10}^{17}$ ${\mathrm{cm}}^{\ensuremath{-}3}$, impurity levels merge into the conduction band and Ziman's theory of phonon scattering by conduction electrons is the relevant phonon scattering mechanism. The values of the longitudinal deformation potential for different P-doped Ge samples lie in the range - 1.5 to - 5.07 eV. Values of the density-of-states effective mass ${m}^{*}$ have been determined for different samples in the temperature range (1-5) \ifmmode^\circ\else\textdegree\fi{}K. The term $\frac{{m}^{*}}{m}$ increases with temperature and its range of variation is from 0.22 to 0.60.