One-dimensional fluid model for an rf methane plasma of interest in deposition of diamond-like carbon layers

Abstract

A one-dimensional (1D) model for a methane rf plasma consisting of 20 species (neutrals, radicals, ions, and electrons) is presented. The equations solved are the particle balances, assuming a drift-diffusion approximation for the fluxes, and the electron energy balance equation. The self-consistent electric field is obtained from the simultaneous solution of Poisson’s equation. The electron–neutral collision rates are expressed as a function of the average electron energy. These expressions are obtained from the solution of the Boltzmann equation using the Lorentz approximation. The results presented in this article are limited to the alpha regime, hence no secondary electrons are considered. In total, 27 electron reactions (vibrational excitation, dissociation, and ionization) have been included in the model, as well as seven ion–neutral reactions and 12 neutral–neutral reactions. The 1D fluid model yields, among others, information about the densities of the different species in the plasma. It is found that in a methane plasma ${\mathrm{C}}_{\mathrm{2}}{\mathrm{H}}_{\mathrm{6}},$ ${\mathrm{C}}_{\mathrm{3}}{\mathrm{H}}_{\mathrm{8}},$ ${\mathrm{C}}_{\mathrm{2}}{\mathrm{H}}_{\mathrm{4}},$ and ${\mathrm{C}}_{\mathrm{2}}{\mathrm{H}}_{\mathrm{2}}$ are also present at high densities, together with ${\mathrm{CH}}_{\mathrm{4}}$ and ${\mathrm{H}}_{\mathrm{2}}$ (inlet gases). The main radical in the plasma is ${\mathrm{CH}}_{\mathrm{3}}.$ At low pressure (e.g., 0.14 Torr) the most important ion is found to be ${\mathrm{CH}}_5^{+},$ at higher pressure (e.g., 0.5 Torr) ${\mathrm{C}}_2{\mathrm{H}}_5^{+}$ becomes the dominant ion.