Resistive model of the rf discharge including additional dc currents and electrodes

Abstract

A resistive model including additional dc currents and electrodes enables understanding and analysis of rf discharges in the low-frequency range (\ensuremath{\omega}\ensuremath{\ll}${\mathrm{\ensuremath{\omega}}}_{\mathit{p}\mathit{i}}$). A general and exact analysis based on asymptotic solutions results in analytic representations of relations between sheath voltages, bias, and rf voltage. For sinusoidal rf voltage an expansion of sheath voltages and discharge current into Fourier series, e.g., important for probe measurements, and a general relation between these series is presented. From the power balance a lower bound of a sinusoidal rf voltage is derived. The model is extended for different densities and electron temperatures along the sheath edges. Correction and error estimation show the asymptotic solution to be well suited.