Bloch oscillations and nonlinear transport in a one-dimensional semiconductor superlattice

We present an exact analytic result for the time-dependent and steady-state current and the distribution function in a nonlinear electric field for an electron gas in a one-dimensional superlattice miniband by employing a relaxation-time approximation for inelastic scattering. Our transparent results clearly show the condition for the onset of the Bloch oscillations, the field for the peak steady-state current, and the distinct roles played by elastic and inelastic scattering for the damped oscillations and the steady-state current. The results are consistent with a recent full microscopic numerical calculation.