Magnetoresistance of Germanium Samples between 20° and 300°K

The resistivity of "pure" germanium samples and of samples with small additions of aluminum, antimony, and indium was measured at various temperatures and at various orientations in external magnetic fields. The samples chosen had sufficiently low carrier densities to remain within the limits of classical statistics. The results were compared with those following from the theoretical investigation of a classical electron gas in combined electric and magnetic fields in an isotropic medium and in a medium possessing cubic symmetry. In the transverse orientation, the relative change of the electrical conductivity was found to be proportional to the square of the magnetic field strength at low fields. The effect tends to become linear as the field strength increases. The magnitude of the effect was found to increase with the purity of the material. In the longitudinal orientation, the change of conductivity is of the expected order of magnitude in $p$-type samples, but is much larger than the theoretical results indicate in $n$-type samples. The angular dependence of the effect is as expected. Carrier mobilities calculated from magnetoresistance measurements in pure samples agree reasonably well with those calculated from Hall effect and conductivity of single crystals. In the case of samples with additions, there is fair agreement between the values of mobilities calculated from measurements of magnetoresistance and of the Hall effect on the same samples.