We analyze the bifurcation of traveling waves in a standard model of electr
ical conduction in extrinsic semiconductors. In scaled variables the corres
ponding traveling wave problem is a singularly perturbed nonlinear three-di
mensional o.d.e. system. The relevant bifurcation parameters are the wave s
peed s and the total current j. By means of geometric singular perturbation
theory it suffices to analyze a two-dimensional reduced problem. Depending
on the relative size of s and a dimensionless small parameter beta differe
nt types of traveling waves exist. For 0 less than or equal to s much less
than beta the only waves are fronts corresponding to heteroclinic orbits. F
or beta much less than s similar fronts - but with left and right states re
versed - exist. The transition between these regimes occurs for s = O(beta)
in a complicated global bifurcation involving a Hopf bifurcation, bifurcat
ion of multiple periodic orbits, and heteroclinic and homoclinic bifurcatio
ns. We present a consistent bifurcation diagram which is confirmed by numer
ical computations. (C) 2000 Elsevier Science B.V. All rights reserved.