Phonon-Electron Scattering inn-Type Ge at Low Temperatures

The role of phonon-electron interaction in the thermal transport properties of $n$-type Ge crystals has been investigated for different situations provided by the large variation of the donor electron concentration from 6.1×${10}^{15}$ to 2.5×${10}^{18}$ ${\mathrm{cm}}^{-3\mathrm{}}$. Assuming the additivity of the reciprocal relaxation times and incorporating the electron-phonon scattering relaxation time in the expression for the combined relaxation time, Callaway's theory has been used to calculate the phonon conductivity of the different Sb- and As-doped Ge crystals in the temperature range 1-150°K. If one takes into account the temperature dependence of the reduced Fermi potential and the density-of-states effective mass, Ziman's scattering can explain the phonon conductivity of the samples for which the donor electron concentration is higher than ${10}^{17}$ ${\mathrm{cm}}^{-3\mathrm{}}$ and impurity levels merge with the conduction band. The large decrease in the phonon conductivity with increasing donor electron concentration is explained in terms of the increase in the deformation potential. A plot of the deformation-potential constant against the electron concentration shows a linear relationship. Carruthers's scattering, for which phonons are scattered as a result of virtual transitions of the donor electrons between the ground state and the threefold degenerate first excited state, is found to be more appropriate for those samples for which the donor electron concentration is less than ${10}^{17}$ ${\mathrm{cm}}^{-3\mathrm{}}$. Values of the shear deformation potential as obtained from the phonon conductivity data are found to lie between 17.83 and 27.91 eV. Carruthers' scattering is also appropriate for the compensated samples, which confirms Fritzsche's suggestion that for materials with sufficiently high donor concentration, compensation by acceptors may bring the donor levels from the conduction band to a position in the energy gap.