Current layers and filaments in a semiconductor model with an impact ionization induced instability

Dissipative structures associated with an instability in a semiconductor far from equilibrium are studied. A generation-recombination mechanism, which effects anS-shaped current-voltage characteristics, is coupled to diffusion and drift of the electrons. The spectrum of linear recombination-diffusion modes is computed for the homogeneous steady state with negative differential conductivity. The obtained soft mode instability gives rise to the bifurcation of a family of transversally modulated inhomogeneous steady states and longitudinal travelling waves. The inhomogeneous steady states are calculated from the full nonlinear transport equations for plane and cylindrical geometries. They correspond to oscillatory and solitary concentration profiles, including depletion and accumulation layers and cylindrical filaments. Conditions for the formation of kink-shaped coexistence profiles are established in terms of equal area rules. The current-voltage characteristics are extended to include inhomogeneous current states. Nonequilibrium phase transitions between various branches of these characteristics are associated with switching through filamentation.