Hydrodynamic balance-equation analysis of spatiotemporal domains and negative differential conductance in a voltage-biased GaAs superlattice

We present a detailed theoretical study of superlattice miniband conduction using the time-dependent hydrodynamic balance equations recently developed for systems having an arbitrary energy dispersion. The spatiotemporal evolution of field domains and current oscillations in GaAs-based superlattices subject to a dc bias voltage are calculated by directly solving this set of equations with a realistic treatment of impurity, acoustic-phonon, and polar-optic-phonon scatterings. The current-voltage characteristics yielded by the time average of the oscillating solution of the current---different from the velocity-field relation obtained under uniform field condition and from the current-voltage relation in the negative-differential-mobility regime derived from the time-independent hydrodynamic equations---is in good agreement with the recent experimental observations. The effect of miniband width and doping concentration on the current-voltage characteristics is also investigated.