Sheath voltage ratio for asymmetric RF discharges

Spherical and cylindrical many-particle models are being used to simulate RF discharges in which the RF powered and the grounded electrodes have different areas. This asymmetry determines the magnitude of the self-bias voltage Va (the ion bombarding energy) at the powered electrode, which is a critical process parameter. Recent analytical models for the sheath voltage ratio including the effect of the floating potential have been developed that agree with some experimental results. One dimensional (radial) spherical shell models have also been developed, incorporating various assumptions for the sheath and the glow discharges, leading to a scaling which is in agreement with some measurements. The authors simulated the spherical model with a non uniform ionization and the results agree with the theory. The cylindrical simulation shows that the floating potential plays an important role. The simulation results will be given graphically as the sheath voltage ratio versus area ratio, and will be compared with the theory. The simulation codes are PDC1 (cylindrical) and PDS1 (spherical) which utilize particle-in-cell techniques plus Monte-Carlo simulation of electron-neutral (elastic, excitation and ionization) and ion-neutral (scattering and charge-exchange) collisions