Galvanomagnetic Effects in Oriented Single Crystals ofn-Type Germanium

Measurements of the magnetoresistance, Hall, and planar Hall coefficients have been made on oriented single crystals of n-type germanium at 77^∘{} and 300^∘{}K. At 77^∘{}K measurements made as a function of the magnetic field strength and of the angle between the current and the magnetic field are found to be in agreement with theoretical calculations based on an energy-independent mean free time τ₀ which has the same form of anisotropy as the effective mass at the bottom of the conduction band. The value of τ₀ is determined from previously described Hall measurements and the anisotropy factor K is determined from the high-field longitudinal magnetoresistance. K decreases from about 16 to about 12 or 13 as the electron density increases from about 5.4×{}10¹³ cm^-3 to about 5.2×{}10¹⁴ cm^-3.At 300^∘{}K measurements were made for selected orientations of current and field on samples whose resistivities varied from 0.016 to 8.9 ohm-cm. The usual low-field symmetry relations are satisfied. Most of the low-field coefficients may be satisfactorily interpreted by means of relatively simple functional relationships between the mean free time τ and the energy E. Although the field dependence of the Hall coefficient cannot be quantitatively explained in this manner, the qualitative features of the various Hall curves may be understood. Above 0.1 ohm-cm, K is found to be about 17.3 independent of the relationship between τ and E. Below 0.1 ohm-cm, K falls off, reaching about 14 at 0.016 ohm-cm.The decrease in the value of K as the temperature is lowered or as the impurity concentration is increased is attributed to an increase in the scattering anisotropy as impurity scattering becomes more important. With the assumption that the mass anisotropy is constant with temperature and impurity density, the magnitude of the scattering anisotropy can be computed.