Standing wave and skin effects in large area, high frequency capacitive discharges

It is usually assumed that capacitive discharges are a strictly electrostatic phenomenon, so that magnetic fields are negligible unless externally applied and the only electric fields are those determined by solving Poisson's equation. These are reasonable assumptions for the relatively low frequencies (e.g., 13.56 MHz) and moderate areas (e.g. 20 cm electrode diameter) discharges that are in wide use. However, there is now interest in the use of substantially higher frequencies (e.g. 100 MHz) and larger areas (e.g. 50 cm electrode diameter). In this paper we show that it is generally not safe to neglect electromagnetic effects in these cases. We make use of a predominantly analytic model in which the capacitive discharge is modelled as a plasma loaded waveguide, with vacuum regions adjacent to the electrodes representing the sheaths. In this model, the excitation is applied at the outer periphery of the planar electrodes, and the fields propagate inwards as a surface wave. Provided the wave length of the surface wave is large compared with the electrode diameter, and skin effects in the bulk plasma are not significant, this model predicts a uniform current density directed normal to the electrode surfaces. The onset of either skin effects or finite wavelength effects introduces currents in the plasma parallel to the electrode surfaces, and under these conditions there is also non-uniform power deposition, which may be expected to produce non-uniform plasma density.