Complex Ginzburg-Landau equation for nonlinear travelling waves in extrinsic semiconductors

We study the nonlinear state of a travelling-wave instability occurring close to the onset of impact ionization in extrinsic semiconductors. Our investigations are based on a complex Ginzburg-Landau equation (CGLE). For a simple generation-recombination function including impact ionization and thermal recombination of the charge carriers, we find a supercritical bifurcation of stable travelling waves for most parameter values. The results are compared with a numerical solution of the basic equations of motion. Furthermore, we expect that weak turbulence phenomena should be observed in semiconductors if their specific generation-recombination kinetics leads to a CGLE with appropriate coefficients.