  A standard drift-diffusion model of space charge wave propagation in
semiconductors has been studied numerically and analytically under dc voltage
bias. For sufficiently long samples, appropriate contact resistivity and
applied voltage - such that the sample is biased in a regime of negative
differential resistance - we find chaos in the propagation of nonlinear fronts
(charge monopoles of alternating sign) of electric field. The chaos is always
low-dimensional, but has a complex spatial structure; this behavior can be
interpreted using a finite dimensional asymptotic model in which the front
(charge monopole) positions and the electrical current are the only dynamical
variables.
