Confinement of highly energetic electron beams in low pressure capacitive discharges

Abstract

In capacitively coupled radio frequency (CCRF) discharges at low pressures the electron heating is dominated by electron interaction with the plasma sheath. Especially the beams of the highly energetic electrons (of which the energy is much higher than the ionization threshold of the background gas), accelerated by the expanding plasma sheaths, play a major role to sustain the plasma. At very low pressures when the electron mean free path is comparable or larger than the gap size, electron beams traverse through the bulk with hardly any collision and interact with the opposing sheath. At a certain combination of the driving frequency, the gap size and the gas pressure of the discharge, electron beams can hit the opposing sheath near its collapse. In this case, most of the highly energetic electrons can overcome the sheath potential and are lost to the electrodes. Additionally multiple beams can be generated during one phase of sheath expansion. In this work we present the effect of changing the driving frequency on the plasma density and the electron dynamics in an argon ccrf discharge. The effect is investigated by means of Particle-in-Cell/Monte Carlo Collisions simulations. Based on an analytical power balance model, the confinement quality and the related modulation of the energy loss per electron lost at the electrode are demonstrated. In contrast to previous assumptions, the plasma density does not follow a quadratic dependence on the driving frequency. Instead, a step-like increase at a distinct frequency is observed. In this case most of the highly energetic electrons hit the opposing sheath during its collapse.