Balance-equation analysis of linear and nonlinear electronic transport in quasi-two-dimensional quantum-well superlattices

A non-Boltzmann balance-equation approach to linear and nonlinear dc steady-state electronic transport in a type-I superlattice (which is composed of infinitely many periodically arranged finite-width quantum wells) is developed in the presence of an electric field parallel to the superlattice planes. The method is based on a separation of the parallel motion of the center of mass from the relative motion of the electron system. The Coulomb interactions between intralayer and interlayer carriers are naturally built in via the electron density-density correlation function of the superlattice system. The force and energy balance equations obtained are applied to the calculation of the Ohmic mobilities limited by remote and background impurity scatterings and by acoustic and polar optical-phonon scatterings in GaAs-${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As superlattices. The nonlinear mobility and electron temperature are numerically calculated as functions of drift velocity, including all the above-mentioned scattering mechanisms and the full effect of carrier-carrier Coulomb interaction within the framework of the random-phase approximation. The dependence of transport on the geometrical parameters of the superlattice is discussed.