Redefinition of the self-bias voltage in a dielectrically shielded thin sheath RF discharge

In a geometrically asymmetric capacitively coupled discharge where the powered electrode is shielded from the plasma by a layer of dielectric material, the self-bias manifests as a nonuniform negative charging in the dielectric rather than on the blocking capacitor. In the thin sheath regime where the ion transit time across the powered sheath is on the order of or less than the Radiofrequency (RF) period, the plasma potential is observed to respond asymmetrically to extraneous impedances in the RF circuit. Consequently, the RF waveform on the plasma-facing surface of the dielectric is unknown, and the behaviour of the powered sheath is not easily predictable. Sheath circuit models become inadequate for describing this class of discharges, and a comprehensive fluid, electrical, and plasma numerical model is employed to accurately quantify this behaviour. The traditional definition of the self-bias voltage as the mean of the RF waveform is shown to be erroneous in this regime. Instead, using the maxima of the RF waveform provides a more rigorous definition given its correlation with the ion dynamics in the powered sheath. This is supported by a RF circuit model derived from the computational fluid dynamics and plasma simulations.