Statistics and Galvanomagnetic Effects in Germanium and Silicon with Warped Energy Surfaces

A method is developed for calculating the statistical properties and galvanomagnetic effects of $p$-type Ge and Si for weak magnetic fields. The calculations involving the use of the Boltzmann transport theory are applied to the warped energy surfaces which have been determined by the cyclotron resonance experiments. Expressions are developed for the hole densities, conductivity, effective masses, intrinsic carrier concentration, and Hall coefficient as a series expansion in terms of the anisotropy parameters of the warped surfaces. Results have been obtained for the assumption that the relaxation time $\tau =l{\epsilon }^{-\lambda }$, where $l$ is a constant, $\epsilon$ is the energy of the carriers and $\lambda$ is a parameter whose numerical value depends on the scattering processes. By using the results of the calculations and existing experimental data, a speculation is made concerning the possible change with temperature of the combined effective mass of holes in germanium and the corresponding change in the band structure.