  We review the statics and dynamics of electric-field domains on doped
superlattices within a discrete drift model. A complete analysis of the
construction and stability of stationary field profiles having two domains is
carried out. As a consequence we determine the intervals of doping on which
self-sustained current oscillations may appear under dc voltage bias. We have
also studied the influence of doping, boundary condition and length of the
superlattice on the self-sustained oscillations. Our study shows that there are
bistability regions where either self-sustained current oscillations or steady
states are reached depending on the initial condition. For a wide bias
interval, the self-sustained oscillations are due to the formation, motion and
recycling of electric-field domain walls inside the superlattice. There are
biases (typically in the region of bistability) for which the strength of the
high and low field domains changes periodically in time while the domain wall
remains almost pinned on a few quantum wells.
