Fluid simulation of the phase-shift effect in hydrogen capacitively coupled plasmas: I. Transient behaviour of electrodynamics and power deposition

Abstract

A two-dimensional self-consistent fluid model coupled with the full set of Maxwell equations is established to investigate the phase-shift effect on the transient behaviour of electrodynamics and power deposition in a hydrogen capacitively coupled plasma. The effect has been examined at 13.56 MHz and 100 MHz, respectively, because of the different phase-shift modulation when the electromagnetic effects are dominant. The results indicate that the spatiotemporal distributions of the plasma characteristics obtained for various phase-shift cases are obviously different both in shape and especially in absolute values. Indeed, when the phase difference varies from 0 to π, there is an increase in the electron flux, thus the power deposition becomes more pronounced. At the frequency of 13.56 MHz, the axial electron flux in the bulk plasma becomes uniform along the z-axis, and the radial electron flux exhibits two peaks within one period at the reverse-phase case, whereas the oscillation is less pronounced at the in-phase case. Furthermore, in the very high frequency discharge, the radial electron flux is alternately positive and negative with four peaks during one period, and the ionization mainly occurs in the sheath region, due to the prominent power deposition there at a phase difference equal to π.