Modeling of a capacitively coupled radio-frequency methane plasma: Comparison between a one-dimensional and a two-dimensional fluid model

Abstract

A comparison is made between a one-dimensional (1D) and a two-dimensional (2D) self-consistent fluid model for a methane rf plasma, used for the deposition of diamond-like carbon layers. Both fluid models consider the same species (i.e., 20 in total; neutrals, radicals, ions, and electrons) and the same electron–neutral, ion–neutral, and neutral–neutral reactions. The reaction rate coefficients of the different electron–neutral reactions depend strongly on the average electron energy, and are obtained from the simplified Boltzmann equation. All simulations are limited to the alpha regime, hence secondary electrons are not taken into account. Whereas the 1D fluid model considers only the distance between the electrodes (axial direction), the 2D fluid model takes into account the axial as well as the radial directions (i.e., distance between the electrodes and the radius of the plasma reactor, respectively). The calculation results (species densities and species fluxes towards the electrodes) obtained with the 1D and 2D fluid model are in relatively good agreement. However, the 2D fluid model can give additional information on the fluxes towards the electrodes, as a function of electrode radius. It is found that the fluxes of the plasma species towards both electrodes show a nonuniform profile, as a function of electrode radius. This will have an effect on the uniformity of the deposited layer.