Physical Origin of Non-Linear Resonant Excitation in Capacitively Coupled Plasmas
Sebastian Wilczek, Jan Trieschmann, Denis Eremin, Julian Schulze, Edmund Schüngel, Ralf Peter Brinkmann, Aranka Derzsi, Ihor Korolov, Peter Hartmann, Zoltán Donkó, Thomas Mussenbrock
NCPST 5th Radio Frequency Discharges Workshop 2015, Dublin, Ireland, June 22-23 2015
In low-pressure capacitively coupled radio frequency (RF) discharges, non-linear electron resonance heating is still not fully understood. In order to explain the exact mechanism of the excitation of higher harmonics in the RF-current a detailed kinetic description of the electron dynamics must be developed. In this work, the analysis of the spatio-temporal electron velocity distribution function using Particle-in-Cell/Monte Carlo Collisions simulations is presented. A single-frequency capacitively coupled discharge operated in argon at a pressure of 1.3 Pa is characterized. At this low pressure, the plasma sheaths accelerate energetic electron beams. These traverse through the plasma bulk almost collisionlessly and leave behind a positive space charge close to the sheath edge and, consequently, an electric field. At this position the electric field attracts cold electrons from the plasma towards the expanding sheath. For a short time interval slow bulk electrons and energetic beam electrons move into opposite directions. Subsequently, these cold bulk electrons, which can only react on the timescale of the local plasma frequency, are repelled back into the bulk during the phase of sheath expansion forming a new energetic electron beam. This cycle continues until the end of the sheath expansion. The effect then can lead to the generation of multiple electron beams during one RF period. Since the electron beams form the major part of the conduction current, this effect explains the excitation of higher harmonics in the rf-current. Furthermore, the conduction current appears only locally in space and time. As such, to ensure current continuity at any given time, it is naturally compensated by a local displacement current. In this context, the terminology of the Plasma Series Resonance (PSR) as well as the Plasma Parallel Resonance (PPR) can be understood within the frame of a kinetic picture.