Improved volume-averaged model for steady and pulsed-power electronegative discharges

Abstract

An improved volume-averaged global model is developed for a cylindrical (radius R, length L) electronegative (EN) plasma that is applicable over a wide range of electron densities, electronegativities, and pressures. It is applied to steady and pulsed-power oxygen discharges. The model incorporates effective volume and surface loss factors for positive ions, negative ions, and electrons combining three electronegative discharge regimes: a two-region regime with a parabolic EN core surrounded by an electropositive edge, a one-region parabolic EN plasma, and a one-region flat-topped EN plasma, spanning the plasma parameters and gas pressures of interest for low pressure processing (below a few hundred millitorr). Pressure-dependent effective volume and surface loss factors are also used for the neutral species. A set of reaction rate coefficients, updated from previous model calculations, is developed for oxygen for the species O2, O2(Δg1), O, O2+, O+, and O−, based on the latest published cross-section sets and measurements. The model solutions yield all of the quantities above together with such important processing quantities such as the neutral/ion flux ratio ΓO∕Γi, with the discharge aspect ratio 2R∕L and pulsed-power period and duty ratio (pulse on-time/pulse period) as parameters. The steady discharge results are compared to an experiment, giving good agreement. For steady discharges, increasing 2R∕L from 1 to 6 leads to a factor of 0.45 reduction in ΓO∕Γi. For pulsed discharges with a fixed duty ratio, ΓO∕Γi is found to have a minimum with respect to pulse period. A 25% duty ratio pulse reduces ΓO∕Γi by a factor of 0.75 compared to the steady-state case.