Modeling electromagnetic effects in capacitive discharges

We present a self-consistent two-dimensional axisymmetric model and simulation strategy to predict radial plasma uniformity in large-area high-frequency (up to 200 MHz) capacitive discharges of argon gas in the pressure range 2-150 mTorr. The model couples Maxwell equations, fluid plasma equations and a sheath model with stochastic heating effects taken into account, solving the equations using the finite element method. Electromagnetic effects (e.g. standing wave and skin effects) as well as the electrostatic edge effect are captured in the simulation, in good agreement with recent experiments. The model highlights differences between the edge effect and the skin effect, both of which can cause strong plasma production near the radial reactor edge. At higher frequencies and high pressures, we observe the 'stop band' where waves are highly damped as they propagate from the discharge edge into the center. We determine the transition from global-to-local power deposition as the pressure varies. An electrode asymmetry with a grounded reactor radial edge is found to suppress undesirable edge effects. For radial plasma uniformity, it is essential to consider the balancing of the standing wave effect (maximal at the reactor center) with the skin effect (maximal near the radial reactor edge), together with their coupling to the edge effect, which can be obtained by a choice of robust reactor design geometry and driving frequency, over the range of process parameter operating windows to be used.