The Bohm criterion for radio-frequency discharges: A numerical verification based on Poisson’s equation

Abstract

Recently it was shown that, by using the analysis of electrostatic waves entering the plasma–sheath edge, the direct-current (dc) Bohm criterion also holds for discharges under radio-frequency (rf) conditions. In this paper, the influence of Bohm’s criterion on the sheath characteristics for generator frequencies much higher than the ion plasma frequency has been examined by means of an analysis which is based directly on the numerical solution of the Poisson equation. The present calculations indicate that for high rf voltages the time-dependent potential profile does not always increase monotonically, even if Bohm’s criterion is fulfilled. However, as this nonmonotonic behavior does not lead to a more stringent Bohm criterion, the statement that the original dc Bohm criterion also holds in the high-frequency regime is confirmed. The calculations show further that the time-dependent sheath potential is almost completely modulated in the major part of the sheath and that the modulation drops abruptly to zero close to the plasma–sheath edge.