Balance equations in nonlinear electronic transport for electron-phonon-impurity systems in the presence of crossed electric and magnetic fields

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Abstract
A nonlinear theory for steady state electronic transport is suggested for electron-phonon-impurity systems in the presence of both an electric field and a crossed magnetic field. An electron temperature Te is introduced without preassumption of any kind of equilibrium-type distribution function. Thus the formulation based on it should be applicable for both high and low carrier density in both classical and quantum limits in a magnetic field. A force-balance equation and an energy-balance equation are derived in steady state for determining Te and current density. It is shown that the well known formula for transverse resistivity and Hall coefficient apply equally well for the nonlinear case if the electrons move in a single, isotropic and parabolic band. For moderate magnetic fields at about room lattice temperature, the longitudinal and transverse conductivity are calculated as functions of drift velocity assuming non-polar optical phonon scattering. The cooling effect of a magnetic field is also studied.