Self-consistent stochastic electron heating in radio frequency discharges

Abstract

Fermi acceleration is considered as an underlying mechanism for electron heating in rf discharges, in which the heating arises from the reflection of electrons from moving sheaths. By examining the dynamics of the electron collisions with the sheaths, the map that describes the electron motion is derived. For high‐frequency discharges (ω/2π>50 MHz), the electron motion is shown to be stochastic. By combining these dynamics with collisional effects in the bulk plasma and incorporating self‐consistent physical constraints, a self‐consistent model of the discharge is developed. The model is used to calculate physically interesting quantities, such as the electron temperature and average lifetime, and to predict the minimum pressure necessary to sustain the plasma. The distribution of electron energies is shown to be non‐Maxwellian. These results can be applied to experimentally interesting parallel‐plate rf plasma discharges to predict the operating conditions necessary for stochastic heating to occur.