Pattern formation in planar DC semiconductor gas discharges

Abstract

Gas discharges, being highly nonlinear, far from equilibrium systems, are susceptible to instabilities and so emerge as good models to study phenomenon like pattern formation and spatio-temporal chaos. While these phenomena have been observed experimentally, we lack a good theoretical description. The thesis attempts to elucidate the phenomenon of pattern formation in semiconductor gas discharges. The Drift-Diffusion model is studied analytically and numerically. A novel numerical technique based on the Homotopy analysis method is posited to solve the model, where the effects of gas temperature and electric current on the voltage required to sustain the discharge are studied. Reaction-diffusion type models are derived and analyzed to find a simple theoretical description of the pattern formation in the system. While the derived models fail to reproduce observations quantitatively, we discuss the problems with the derived models and describe possible solutions to achieve a more quantitatively accurate model.