The effect of the driving frequency on the confinement of beam electrons and plasma density in low pressure capacitive discharges

TL;DR

This study investigates how changing the driving frequency affects plasma density and electron behavior in low-pressure capacitive discharges, revealing a step-like density increase linked to electron heating mode transitions and electron confinement changes.

Contribution

It introduces a detailed analytical model explaining the step-like plasma density increase due to electron heating mode transition and electron confinement effects in low-pressure RF plasmas.

Findings

Plasma density exhibits a step-like increase at a specific driving frequency.

Electron heating mode transitions from α-mode to a resonant mode cause the density jump.

Electron confinement quality is modulated by the heating mode, affecting plasma density.

Abstract

The effect of changing the driving frequency on the plasma density and the electron dynamics in a capacitive radio-frequency argon plasma operated at low pressures of a few Pa is investigated by Particle in Cell/Monte Carlo Collisions simulations and analytical modeling. In contrast to previous assumptions the plasma density does not follow a quadratic dependence on the driving frequency in this non-local collisionless regime. Instead, a step-like increase at a distinct driving frequency is observed. Based on the analytical power balance model, in combination with a detailed analysis of the electron kinetics, the density jump is found to be caused by an electron heating mode transition from the classical $\alpha$-mode into a low density resonant heating mode characterized by the generation of two energetic electron beams at each electrode per sheath expansion phase. These electron beams propagate through the bulk without collisions and interact with the opposing sheath. In the low density mode, the second beam is found to hit the opposing sheath during its collapse. Consequently, a high number of energetic electrons is lost at the electrodes resulting in a poor confinement of beam electrons in contrast to the classical $\alpha$-mode observed at higher driving frequencies. Based on the analytical model this modulated confinement quality and the related modulation of the energy lost per electron lost at the electrodes is demonstrated to cause the step-like change of the plasma density. The effects of a variation of the electrode gap, the neutral gas pressure, the electron sticking and secondary electron emission coefficients of the electrodes on this step-like increase of the plasma density are analyzed based on the simulation results.