Critical evaluation of analytical models for stochastic heating in dual-frequency capacitive discharges

Abstract

Dual-frequency capacitive discharges are widespread in the semiconductor industry and are used, for example, in etching of semiconductor materials to manufacture microchips. In low-pressure dual radio-frequency capacitive discharges, stochastic heating is an important phenomenon. 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 for the case of dual-frequency capacitive discharges. In this work, we investigate the dependence of stochastic heating on various discharge parameters with the help of particle-in-cell (PIC) simulation. The dual-frequency analytical models are in fair agreement with PIC results for values of the low-frequency current density amplitude Jlf (or dimensionless control parameter Hlf ∼ 5) typical of many modern experiments. However, for higher values of Jlf (or higher Hlf), new physical phenomena (like field reversal, reflection of ions, etc) appear and the simulation results deviate from existing dual-frequency analytical models. On the other hand, for lower Jlf (or lower Hlf) again the simulation results deviate from analytical models. So this research work produces a relatively extensive set of simulation data that may be used to validate theories over a wide range of parameters.