Collisionless electron heating by capacitive radio-frequencyplasma sheaths

Abstract

Low-pressure capacitive rf plasmas can be maintained chiefly bycollisionless heating in the rf modulated sheaths adjacent to the electrodes.Theoretical models dealing with this mechanism are often based on a `hardwall' approximation where the electrons are considered to collide elasticallywith the oscillating sheath edge. The power transfer is then calculated byaveraging forward and reverse power fluxes over an rf period. There are,however, several drawbacks to this approach: the models are sensitive toassumptions regarding the incident electron distribution, transit time effectsin the sheath electric field are neglected, electron loss is not consideredand current conservation is not satisfied. In order to examine the validity ofthe theoretical models, we use a Monte Carlo approach to study electroninteractions with the model and self-consistent fields providing modificationsthat can lead to a more consistent treatment of the electron dynamics insidethe sheath. Of particular importance is the presence of a small field behindthe moving electron sheath edge which maintains quasi-neutrality between theelectron sheath position and the bulk plasma. In addition, a semi-infiniteparticle-in-cell (PIC) simulation is used to investigate in detail sheathdynamics. The errors that the `hard wall' approximation gives are calculatedand power deposition scalings with current drive, frequency and electrontemperature are provided. Our results indicate that collisionless heatingcannot be attributed to the stochastic heating mechanism based on the `hardwall' approximation and that in contrast electron inertia plays a dominantrole as far as collisionless heating is concerned.