Dielectric Enhancement of the Resistivity ofn-Type Degenerately Doped Germanium at Low Temperature

By employing Kohler's principle, an upper bound to the electrical resistivity has been calculated for unstressed $n$-type degenerately doped germanium at $T=0\mathrm{}$ °K, assuming Brooks-Herring scattering. The observed resistivity, however, is found to be 5-7 times larger than the theoretical estimate. We find that the usual corrections to Brooks-Herring scattering for semiconductors originally discussed by Moore and Ehrenreich for isotropic bands are not sufficient to account for this discrepancy. Instead, we show that the use of dielectric screening instead of that due to Thomas-Fermi leads to a significant decrease in the intervalley contribution to the screening in many-valley semiconductors with highly anisotropic band structure. When this effect is taken into consideration, we find good agreement between theory and experiment for the resistivity of arsenic-doped germanium.