Stability of generation-recombination induced dissipative structures in semiconductors

A class of generation-recombination models involving one type of carriers and several impurity levels is studied. Far from equilibrium, impact ionization can lead to bistability of the homogeneous steady state resulting inS-shaped current-voltage characteristics, and to stationary spatial structures. It is shown for large samples that kink-shaped coexistence profiles are stable, while plane depletion or accumulation layers and cylindrical current filaments are unstable under constant voltage conditions, but can be stabilized by a constant current. The unstable mode is calculated analytically for wide and for narrow depletion layers. The critical slowing-down of this mode is established explicity as a function of the external electric field; it occurs when the threshold or holding field of the switching transitions, or the coexistence field of homogeneous phases is approached. It is shown that the hysteresis cycle of the switching transitions can be shortened by sufficiently large localized fluctuations inducing the nucleation of current layers or filaments.