Simulation of current filamentation in a dc-driven planar gas discharge-semiconductor system

摘要

We have performed a theoretical study of self-organized current filamentation in a dc-driven planar gas discharge-semiconductor system at very low currents and under cryogenic conditions. The discharge instability and the observed formation of current filaments are explained by a thermal mechanism, as proposed in our previous paper. We have found, for the first time, a stationary periodic current structure in a two-dimensional Cartesian geometry from first principles, by numerically solving the general system of continuity equations for ions and electrons, the Poisson equation for the electric field in the gas, together with the equation for gas temperature and the equation for electric field in the semiconductor. The space charge induced electric field redistribution, which usually leads to a discharge instability and is automatically included in the first three equations of the system, is practically absent at the very low currents considered, and thus it cannot be responsible for the discharge instability. This is why another mechanism of filamentation (thermal) should be considered. The calculated periodic current structure agrees with the hexagonal current pattern observed in the experiment, as well as with the periodic current structure found in the frame of the previously developed simple model. This serves as a corroboration of the fact that the thermal effect is essential for pattern formation under the conditions considered.