Model for current patterns in physical systems with two charge carriers

Abstract

The temporal and spatial evolution of patterns in physical systems due to electrical current flow can be described for a certain class of systems, which includes certain semiconductor and gas discharge systems, by a two-layer model in terms of the electrical current density and the electrical potential. An equation for the nonlinear layer is derived, the characteristic parameters of which can be obtained from experiments at the respective systems without inhomogeneous patterns lateral to the main current direction. The resulting equation takes into account diffusion and drift effects in the nonlinear layer. It turns out that the drift effects occur only if there is a ``net space charge.'' Two special cases are derived depending on which of the two layers gives the main contribution to the displacement current density, and the typical static and dynamic behavior is studied by numerical calculations. Furthermore, the application of the model to real devices is discussed, and a comparison is made with experimental results obtained with a dc glow-discharge system.