Abstract
The status of our theoretical understanding of self-generated nonlinear and chaotic oscillations in semiconductors associated with impact ionization of impurity centers is reviewed from the viewpoint of hot electron transport theory. A set of hydrodynamic balance equations for the carrier density, mean momentum and energy is developed. It constitutes, together with Maxwell's equations, a macroscopic nonlinear dynamic system. We discuss various simplified versions of this model, which give rise to local or global bifurcations and hysteresis of limit cycle oscillations, a period-doubling route to chaos, mode-locking and quasiperiodicity, traveling waves, and breathing current filaments.
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