Simulation study of stochastic heating in single-frequency capacitively coupled discharges with critical evaluation of analytical models

Abstract

Stochastic heating is an important phenomenon in low-pressure radio-frequency capacitive discharges. Recent theoretical work on this problem using several different approaches has produced results that are broadly in agreement insofar as scaling with the discharge parameters is concerned, but there remains some disagreement in detail concerning the absolute size of the effect. In this paper we investigate the dependence of stochastic heating on various discharge parameters by scaling these parameters with the help of particle-in-cell (PIC) simulation. The analytical models are satisfactory for intermediate current density amplitude (or control parameter H) and in agreement with PIC results. However, for higher (or higher H), new physical effects appear (such as field reversal, electron trapping, reflection of ions, etc) and the simulation results deviate from existing analytical models. In most experiments, but not all, H ∼ 5 and these effects are not observed there. On the other hand, for lower (or lower H) again the simulation results deviate from analytical models. So we have produced a relatively extensive set of simulation data that may be used to validate theories over a wide range of parameters. The dependence of stochastic heating on applied frequency is also investigated here with the help of the self-consistent PIC method.