Longitudinal Magnetoresistance in the Quantum Limit

A study has been made of the effect of a magnetic field on the scattering of electrons in a semiconductor with spherical energy surfaces. The theory has been applied to longitudinal magnetoresistance in the case of a very large magnetic field and low temperatures so that all conduction electrons are in the ground oscillator state. Relaxation times for phonon and ionized impurity scattering have been calculated and the corresponding mobilities for a degenerate and nondegenerate semiconductor have been derived. Contrary to the zero magnetoresistance predicted by the usual Boltzmann theory, a field-dependent magnetoresistance is found. For a nondegenerate semiconductor and in the ionized impurity scattering range a negative magnetoresistance is predicted.