Balance equations for hot-electron transport in a general energy band in crossed magnetic and electric fields.

Abstract

Semiclassical balance equations of hot-carrier magnetotransport are developed for electrons moving in an arbitrary energy band. In addition to the ensemble-averaged inverse effective-mass tensor introduced earlier in the acceleration balance equation for describing the center-of-mass (c.m.) motion of the carrier system in an electric field, we define six dimensionless \ensuremath{\gamma} coefficients to describe the c.m. motion under the influence of both an electric field and a crossed magnetic field. If E and B fields are in the principal axis diretions of a separable energy spectrum, the number of required \ensuremath{\gamma} coefficients reduces to two and the Hall coefficient is given by ${\mathit{R}}_{\mathit{H}}$=\ensuremath{\gamma}/ne (e and n are the electron charge and density). By evaluating the magnitude and sign of \ensuremath{\gamma}, we are able to obtain the Hall resistivity in linear and nonlinear transport and trace the transition of carrier conduction from electron type to hole type by changing the electron density or by changing the electron temperature. As examples, three-dimensional tight-binding systems, quantum-wire arrays, planar superlattices with a transverse magnetic field, and nonparabolic Kane bands are discussed.