Collisionless Bulk Electron Heating in Resonant Low-Voltage Capacitively Coupled Plasmas

Abstract

We investigate collisionless power absorption in resonant, low$-$pressure capacitively coupled plasmas (CCPs). In these radio-frequency (RF) discharges, the sheath capacitance almost exactly balances the plasma inductance, driving the total RF discharge voltage down to just a few volts. However, plasma persists not only in this ultra$-$low$-$voltage regime; it also generates ions that strike the electrodes with kinetic energies substantially exceeding the amplitude of the applied RF voltage. This counterintuitive behavior arises from the presence of a pronounced electrostatic potential well of approximately 40 V within the plasma bulk, which confines electrons while simultaneously accelerating ions toward the electrodes. We show that, under these resonant conditions, collisionless electron heating exhibits a fundamentally different behavior from the conventional paradigm of stochastic sheath heating mediated by electron$-$sheath interactions. Instead, the predominant energy transfer mechanism is bulk electron heating in RF electric fields via a primarily collisionless process that emerges from the synergistic action of: (i) a strongly amplified RF electric field within the plasma bulk, (ii) electron oscillatory motion (bouncing) within the plasma potential well, and (iii) electron scattering resulting from collisions with neutral atoms. Collectively, these phenomena give rise to a pronounced high$-$energy tail in the electron energy distribution function and thereby lead to a substantial enhancement of the ionization rates. As the gas pressure rises, the resonance is disrupted. At the same time, the region of maximum power absorption moves from the plasma core toward the edges and the sheath, which is accompanied by the disappearance of the high$-$energy electron population and a corresponding decrease in ionization rates