  A model for charge transport in undoped, photo-excited semiconductor
superlattices, which includes the dependence of the electron-hole recombination
on the electric field and on the photo-excitation intensity through the
field-dependent recombination coefficient, is proposed and analyzed. Under dc
voltage bias and high photo-excitation intensities, there appear self-sustained
oscillations of the current due to a repeated homogeneous nucleation of a
number of charge dipole waves inside the superlattice. In contrast to the case
of a constant recombination coefficient, nucleated dipole waves can split for a
field-dependent recombination coefficient in two oppositely moving dipoles. The
key for understanding these unusual properties is that these superlattices have
a unique static electric-field domain. At the same time, their dynamical
behavior is akin to the one of an extended excitable system: an appropriate
finite disturbance of the unique stable fixed point may cause a large excursion
in phase space before returning to the stable state and trigger pulses and wave
trains. The voltage bias constraint causes new waves to be nucleated when old
ones reach the contact.
