The problem of the hot-carrier distribution function in crossed electric and magnetic fields is treated for free carriers in a parabolic band. To account for the discrete structure of the energy spectrum (Landau levels), a fully quantum-mechanical treatment is employed. The master equation for the diagonal elements of the density operator is solved for three Landau levels, considering optical and acoustic deformation potential scattering. Numerical results are presented for the case of the light holes in p-type germanium. The total populations of the different Landau levels are discussed as well as the one-dimensional distribution functions in the Landau levels, and their dependencies on electric and magnetic field strengths are studied. Special attention is paid to the occurrence of a population inversion between Landau levels and to a comparison of the present approach to the classical picture of streaming motion.

• Received 5 December 1988

DOI:https://doi.org/10.1103/PhysRevB.39.6212