Galvanomagnetic Effects inn-Type Germanium

Abstract

The galvanomagnetic coefficients of $n$-type Ge have been calculated theoretically and compared with previously published experimental data. Calculations have been made for material containing from ${10}^{11}$ to ${10}^{18}$ impurity centers per ${\mathrm{cm}}^3$, and comparisons were made with samples having free-carrier concentrations from 5×${10}^{13}$ to 2×${10}^{17}$ per ${\mathrm{cm}}^3$. The calculations were made primarily at 77 and 300°K, but also as functions of temperature. A solution of the Boltzmann transport equation with a collision time which was anisotropic, energy-dependent, and which depended on the impurity content was used. In the expressions Herring and Vogt's equations were used for the acoustic lattice scattering, the Brooks-Herring equation modified by Ham's calculation of the anisotropy was used for the ionized impurity scattering, and the Erginsoy formula for neutral impurity scattering was used to account for the energy-independent scattering. It is shown that even though a constant mean collision time can be used to qualitatively predict the dependence of the coefficients on the magnetic field, the quantitative agreement with experiment is considerably improved when a more realistic form of the collision time is used for the calculations. Scattering functions which take the temperature dependence of the scattering and the presence of ionized impurities into account enable quantitative predictions of the behavior of the galvanomagnetic coefficients to be made quite successfully.