# Electron heating in capacitively coupled RF plasmas: a unified scenario

Ralf Peter Brinkmann

2016 Plasma Sources Sci. Technol. 25 014001

## Abstract

Electron heating in radio-frequency capacitively coupled plasmas (RF-CCP) is studied from first principles. The starting points are the electron equations of continuity and motion, with ionization neglected but electric and pressure forces and elastic collisions with the neutral background taken into account. Poisson's equation self-consistently calculates the electric field; the ion density is assumed as a given. Postulating that the Debye length is small compared to the sheath length scale l and the applied frequency is small compared to the electron plasma frequency, an asymptotic expansion in the smallness parameter is conducted. As has been demonstrated before (Brinkmann 2015 Plasma Sources Sci. Technol. 24 064002), this ansatz gives an expression—the smooth step model (SSM)—which yields (i) the space charge field in the unipolar region, (ii) the generalized Ohmic field in the ambipolar region, and (iii) a smooth interpolation for the rapid transition in between. Using the SSM and formulas for the electron density and the electron flux, expressions for the electric force and the electric power density are established. Integrating over the sheath and taking the phase average, a representation for the total dissipated power is found as a sum of four physically distinct contributions. All terms correspond to electron heating mechanisms which are (explicitly or implicitly) already known but were so far discussed only within mutually incompatible frameworks.