Spatio-temporal patterns in a semiconductor-gas-discharge system: stability analysis and full numerical solutions

A system of gas discharge and semiconductor layer forms spatial and temporal patterns spontaneously when a DC voltage is applied. The system is modeled here with a simple glow discharge model for positive ions, electrons and electric field, and the semiconductor is approximated as a linear conductor. This model in previous work has reproduced the diagram for the phase transition from homogeneous stationary to homogeneous oscillating states semi-quantitatively. In the present work, the formation of spatial patterns is investigated, both through linear stability analysis and through numerical simulations of the initial-value problem. The two methods show very good agreement. They show the onset of spatio-temporal patterns for high semiconductor resistance in agreement with experiments. The parameter dependence of temporal or spatio-temporal pattern formation is discussed in detail