Two-dimensional electrical modeling of asymmetric radio-frequency discharges for geometry effect analysis. Comparison with experiments

Abstract

A self-consistent two-dimensional particle model coupled to the external circuit equations was developed in an asymmetrical configuration for the self-bias voltage calculation and the reactor design study. An intermediate modeling was performed in one and two symmetrical geometries. The one-dimensional model is used to optimize the computing time which is reduced by a factor of 10 by using some optimization techniques. It is also used to validate the charged particle and basic data choices. We have shown that the consideration of only two charged particle species (electron and H3+ positive ion) is sufficient in the present hydrogen radio-frequency discharge modeling. Computational results (i.e., power density and self-bias voltage) are in good agreement with experimental results. A strong gradient of the plasma parameters (such as electric field, potential, charged particle densities and energies) was observed in the periphery of the driven electrode. Furthermore, the present two-dimensional asymmetric model shows that the interelectrode distance increase (from 1.7 up to 3.7 cm) can lead to reducing the plasma heterogeneity due to the geometrical electric field.