Abstract
It is shown that recently observed complex chaotic behavior associated with low temperature impurity breakdown can be understood by introducing the mean energy per carrier E as an additional dynamic variable besides the carrier densities. A set of coupled nonlinear evolution equations for the carrier density and mean energy is derived by a moment expansion of the Boltzmann equation including, in particular, impact ionization. This process leads to a novel, strongly nonlinear relaxation term in the dynamic energy balance equation. The simplest, spatially homogeneous version of the model yields hysteretic or non-hysteretic static current-voltage characteristics, and spontaneous self-sustained current oscillations. It can also be used to explain the coupling of the oscillations in two spatially separated hot carrier subsystems via energy exchange.
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