Energy distribution of electron flux at electrodes in a low pressure capacitively coupled plasma

Abstract

A one-dimensional particle-in-cell (PIC) model is used to examine the energy distribution of electron flux at electrodes [labeled ge(ε,t), where ε is energy and t is time] in a low pressure 60 MHz capacitively coupled Ar discharge. The effect of gas pressure and an auxiliary DC voltage on ge(ε,t) is also investigated. It is found that the electrons only leave the plasma for a short time period during the radio-frequency (RF) cycle when the sheath collapses at the electrode. Furthermore, majority of the exiting electrons have energies below 10 eV with a distribution ge(ε,t) that is narrow in both energy and time. At relatively high pressures (≥4.67 Pa for the conditions considered), the relationship between the time-average distribution ge(ε) and electron temperature in the plasma (Te) can be easily established. Below 4.67 Pa, kinetic effects become important, making it difficult to interpret ge(ε) in terms of Te. At low pressures, ge(ε,t) is found to broaden in both energy and time except for a narrow pressure range around 1.2 Pa where the distribution narrows temporally. These low pressure kinetic phenomena are observed when the electrons can be accelerated by expanding sheaths to speeds that allow them to traverse the inter-electrode distance quickly (<1.5 RF cycles for conditions considered) and when electrons undergo few collisions during this excursion. The mean energy of exiting electrons increases with decreasing gas pressure, especially below 1.0 Pa, due to higher Te and secondary electrons retaining a larger fraction of the energy they gained during initial sheath acceleration. For the relatively small DC voltages examined (|Vdc|/Vrf ≤ 0.15), the application of a negative DC voltage on an electrode decreases the electron flux there but has a weak impact on the ge profile.