A general method is described for calculating the conductivity, Hall conductivity, and low-field magnetoconductivity in the case of elastic scattering within valleys and is applied to ionized impurity scattering in $n$-type Ge and Si. Two equalities between the galvanomagnetic coefficients, previously proved approximately, are shown to be exact under certain circumstances. It is found, in agreement with Korenblit, that formulas given by Herring and Vogt for the galvanomagnetic coefficients are fairly accurate, provided that accurate values are used for the relaxation times ${\tau }_{\perp }$ and ${\tau }_{\parallel }$. The reason for the success of Herring and Vogt's formulas, even in the case of very anisotropic scattering, is examined and more refined formulas are given. The validity of the "symmetry relations" between magnetoresistance coefficients is discussed with reference to $n$-type Ge.

• Received 17 July 1964

DOI:https://doi.org/10.1103/PhysRev.138.A1706