Mechanisms of spatial current-density instabilities in $p^+ - p^- - n - p^+ -n^{++}$ structures

Abstract

Semiconductor $p^+ - p^- - n - p^+ - n^{++}$ structures with large junction and contact areas are treated as 1 \times 2-dimensional active media, in which self-organized pattern formation can be expected. The local bistable behavior of the structures may emanate from two different mechanisms both governed by a nonlinear current feedback-loop between the electrons and holes injected from the outer layers. By considering the device to be composed of an active subsystem with negative differential resistance and a passive resistive layer with positive differential resistance an analytical approach is suggested to understand and describe the corresponding physical mechanisms in a self-consistent way. Analytical solutions of the derived model equations allow a description of homogeneous stationary states and yield explicit expressions of the current-density vs. voltage characteristics of the whole structure and its subsystems. A stability analysis of the homogeneous states with respect to two-dimensional transversal harmonic fluctuations is performed for the two cases under study. The resulting dispersion relations allow two different types of instability. While the first one is of Ridley's type which is characteristic for any spatially extended electrical system with negative differential resistance, the second type can be considered as a solid-state analogue of Turing's instability known as a generic instability mechanism which may lead, e. g., to the formation of periodic patterns.