Magnetoresistance and Hall Effect of Hot Electrons in Germanium and Carrier Transfer to Higher Minima

Measurements are reported of the Hall coefficient and the ratio of longitudinal over transverse magnetoresistance in $n$-type Ge up to electric field strengths of 3 and 9 kV/cm, respectively, for $\overrightarrow{\mathrm{j}}\parallel \mathrm{}\left[100\right]\mathrm{}$ at 200°K, in order to obtain quantitative information about electron transfer to higher conduction-band minima. The lattice temperature was high enough to ensure that no negative differential conductivity was present. Calculations of the galvanomagnetic properties have been performed for the case that (i) electrons are only in the normally occupied $〈111〉$ valleys, taking into account acoustical, optical, and equivalent intervalley scattering as well as scattering by ionized impurities; and (ii) electrons are transferred to the higher $〈100〉$ conduction-band minima. Only in case (ii) is reasonable agreement between theoretical and experimental results obtained, giving a mobility ratio of only about 4. This is of the same order of magnitude as the theoretical value by Paige.