Simulations of standing wave effect, stop band effect, and skin effect in large-area very high frequency symmetric capacitive discharges

Abstract

In this paper, Maxwell equations are coupled with a radially localized global model and an analytical sheath model to investigate the electromagnetic effects under various frequencies and electron powers in large-area very high frequency symmetric capacitive argon discharges. Simulation results indicate that both the vacuum wavelength and the sheath width decrease with frequency, leading to the reduced surface wavelength. As a result, the standing wave effect becomes pronounced, causing the fact that the radial profiles of the electron density, radio frequency voltage, and sheath width shift from uniform over center-high to multiple-node. When the frequency is close to or higher than the series resonance frequency, the surface waves cannot propagate to the radial center because of the significant radial damping. Due to the lack of power deposition near the radial center, the electron density is nearly zero there, i.e. the stop band effect. As power increases, the higher electron density leads to the decrease of the skin depth. Therefore, the importance of the skin effect gradually exceeds that of the standing wave effect, giving rise to the transition from the center-high to edge-high electron density profiles. The method proposed in this work could help to predict the plasma distribution under different discharge conditions in a few minutes, which is of significant importance in optimizing the plasma processing.