  We analyze the dynamical evolution of the current and the charge density in a
superlattice for fixed external dc voltage in the regime of self-sustained
current oscillations, using a microscopic sequential tunneling model. Fronts of
accumulation and depletion layers which are generated at the emitter may
collide and annihilate, thereby leading to a variety of different scenarios. We
find complex chaotic regimes at high voltages and low contact conductivities.
