Sheath voltage ratio for asymmetric rf discharges

Spherical and cylindrical many-particle models are used to simulate rf (radio frequency) discharges in which the rf powered and the grounded electrodes have different areas. This asymmetry determines the magnitude of the average plasma-to-electrode voltage Va (the ion bombarding energy) at the smaller powered electrode, which is a critical process parameter. A collisionless uniform ionization discharge model predicts that the voltage ratio Va/Vb scales as the fourth power of the electrode area ratio Ab/Aa, where Vb is the potential drop at the other electrode. However, measurements indicate a much weaker dependence of Va/Vb on the area ratio, which is also observed in our simulations. Over a limited range of area ratios it was found that the power dependence was close to one, in agreement with a local ionization discharge model. The simulation codes used are PDC1 (plasma device cylindrical one-dimensional) and PDS1 (plasma device spherical one-dimensional).