Low-Temperature Transverse Resistivity of Saturation-Stressed Degenerately Dopedn-Type Germanium

Upper and lower bounds to the transverse resistivity due to ionized impurity scattering in saturation-stressed degenerately doped $n$-type germanium (single conduction-band valley occupied at $T=0\mathrm{}$ °K) have been calculated for Brooks-Herring scattering. The bounds are obtained by solving exactly the Boltzmann equation including the mass anisotropy for two different scattering rates which either overestimate or underestimate the Brooks-Herring scattering rate. The use of Kohler's variational principle also yields an upper bound to the resistivity, which is found to be approximately 20% higher than the lower bound previously obtained, but is smaller than the experimental results of Katz. The calculation is approximately corrected for the inaccuracies of the Born approximation together with contributions from multiple scattering and dressing effects. The final results are in excellent agreement with experiment.