Spatial current-density instabilities in multilayered semiconductor structures

Semiconductor ${p}^{+}\ensuremath{-}{p}^{\ensuremath{-}}\ensuremath{-}n\ensuremath{-}{p}^{+}\ensuremath{-}{n}^{++}$ structures are considered as (1\ifmmode\times\else\texttimes\fi{}2)-dimensional active media. Such systems may exhibit several carrier injection modes associated with different nonequilibrium plasma/field patterns along the cathode-to-anode direction and numerous self-organized current-density patterns in the transversal plane. We study a peculiar field punch-through (FPT) mode by regarding the structure to be composed of two transistor subsystems coupled by a field domain. The suggested model allows one to analyze the stability properties of the uniform FPT mode with respect to transversal harmonic perturbations of the distributed variables. An analysis of the dispersion relations $\ensuremath{\zeta}(k)$ shows that depending on the material and design parameters three different types of instability may occur. The first one is of Ridley type, in which $\ensuremath{\zeta}$ first becomes positive for the lowest wave number $\stackrel{\ensuremath{\rightarrow}}{k}0.$ The second case corresponds to an analog of Turing's instability where the uniform state is destabilized by a fluctuation with a wave number $kg0$ and being different from the lowest possible k value. Third, at certain conditions both types of instability may appear simultaneously, so that a new diversity of spatiotemporal patterns can be expected due to the competition between fluctuations with different wave numbers.