Dynamic model of the radio-frequency plasma sheath in a highly asymmetric discharge cell

A self-consistent fluid model for the radio-frequency sheath at the powered electrode of a highly asymmetric discharge cell is developed and solved. The model assumes time-independent ion motion and inertialess electrons. The voltage on the powered electrode, assumed to be sinusoidal, is shared between the powered sheath and a series resistance that represents the remainder of the discharge. The model includes ion collisions, sheath conduction currents, and secondary electron emission from the electrode surface. Model results are compared with previous sheath models and with experiment. Current wave forms predicted by the model closely resemble the nonsinusoidal current wave forms measured in highly asymmetric cells. The model accurately predicts the shape of sheath voltage wave forms, but not their de components. The magnitudes and phases of sheath impedances predicted by the model agree with experimental measurements performed in argon discharges at pressures of 4.0-133 Pa.