Fluid simulation of the phase-shift effect in Ar/CF4 capacitively coupled plasmas

Abstract

A two-dimensional self-consistent fluid model combined with the full set of Maxwell equations is employed to investigate an Ar/CF4 capacitively coupled plasma, focusing on the phase-shift effect on the plasma characteristics at various frequencies and gas mixture ratios. When the discharge is sustained by a single frequency at 13.56 MHz in an Ar/CF4 mixture with a ratio of 0.9/0.1, no obvious difference is detected between the electron densities obtained in the so-called electrostatic model (with only the static electric fields taken into account) and the electromagnetic model (which includes the electromagnetic effects). However, as the frequency increases to 60 and 100 MHz, the difference becomes distinct, due to the significant influence of the electromagnetic effects.The phase-shift effect on the plasma radial uniformity has also been investigated in a dual frequency discharge, i.e. when the top driven source is switched on with a phase difference φ ranging from 0 to π, in the frequency range 13.56–100 MHz. At low concentration of CF4 (10%), Ar+ ions are the major positive ions in the entire range of frequencies. When the frequency is low, i.e. 13.56 MHz, the Ar+ density exhibits an off-axis peak at φ = 0 due to the edge effect, and a better uniformity caused by the phase-shift modulation is obtained at φ = π. At 60 MHz, the Ar+ density varies from edge-peaked at φ = 0 to uniform (i.e. at φ = 0.53π), and finally at φ = π, a broad maximum is observed at the centre due to the standing-wave effect. As the frequency increases to 100 MHz, the best radial uniformity is reached at 0.25π, and the maximum moves again towards the radial wall in the reverse-phase case (φ = π) due to the dominant skin effect.When the frequency is fixed at 100 MHz, the phase-shift control shows a different behaviour at a high concentration of CF4. For instance, the density profiles shift from edge-high over uniform to centre-high, as the CF4 content increases from 10% to 90%, which indicates that the skin effect is suppressed by the high electronegativity of the Ar/CF4 = 0.1/0.9 mixture. Moreover, the ratio of the total negative ion density to electron density decreases with increasing frequency, and it increases with CF4 content. In addition, ions become the major positive ions in the discharge with 90% CF4.