Galvanomagnetic Effects of Warm-Electrons in Many-Valley Semiconductors

A treatment of the non-ohmic and anisotropic effects of galvanomagnetic coefficients for warm electrons in many-valley semiconductors is presented. Kohler's variational method can be applied to solving the Boltzmann equation for warm electrons in many-valley semiconductors, with scattering by acoustical and optical lattice vibrations, and thus obtaining expressions for the galvanomagnetic coefficients in any crystallographic directions. All of the galvanomagnetic coefficients for warm electrons in n -Ge can be obtained in the form of the quadratic dependence on the electric field strength for the whole region of magnetic fields. It is thus found that everything so obtained has anisotropy effects and decreases with increasing the electric field strength except for the electrical conductivity at very strong magnetic fields. In the very strong magnetic regime the electrical conductivity, for the case of acoustical lattice scattering only, has the electric field dependence opposite to that in zero magnctic field and thereby increases with increasing the electric field strength.