Self-consistent simulation of very high frequency capacitively coupled plasmas

Abstract

A two-dimensional plasma model that includes the full set of Maxwell equations is used to understand the physics of very high frequency capacitively coupled plasmas. The effect of radio frequency (RF) source power, inter-electrode gap and gas mixture (Ar, Ar/SF 6 , Ar/CF 4 ) on the plasma characteristics is investigated. The computational results show that the plasma spatial profile is influenced by both electrostatic and electromagnetic effects. The electrostatic power deposition is stronger at the electrode edges due to electric field enhancement at corners. Therefore, when the electrostatic effects are dominant, the plasma density peaks off-axis. Due to a standing electromagnetic wave in the chamber, the electron density peak moves to the chamber center under conditions where electromagnetic effects become strong. Inductive heating due to the radial electromagnetic electric field can also influence the plasma spatial profile. The relative importance of electromagnetic and electrostatic effects is found to be a function of the RF source power, the inter-electrode gap and the plasma electronegativity. While the electron density peaks on-axis at a low source power, inductive power deposition at higher source powers shifts the electron density peak towards the electrode edge. Electrostatic power deposition makes the plasma more uniform at smaller inter-electrode gaps. Due to a lower electron density and a larger applied RF potential, electrostatic effects become more dominant in electronegative discharges.

Control of plasma uniformity in a capacitive discharge using two very high frequency power sources

“…This behavior is due to the standing electromagnetic wave effect, and it has been well characterized in previous studies. 5,7 To elucidate, we have plotted electron electrostatic power deposition ͓P e ͑ES͔͒ and electron electromagnetic power deposition at 60 MHz ͓P e ͑60͒ ͑EM͔͒ and 180 MHz ͓P e ͑180͒ ͑EM͔͒ in Fig. 1.…”

“…Chabert et al 6 developed a transmission line model for capacitive discharges and used it to understand the plasma behavior in the capacitive ͑E͒ and inductive ͑H͒ modes of operation. Rauf et al 7 developed a two-dimensional plasma model for VHF plasmas that includes the full set of Maxwell equations. Their studies showed that the plasma spatial profile at VHF is influenced by both electrostatic and electromagnetic effects.…”

“…7 to investigate the effects of mixing of power at two VHFs on the plasma spatial characteristics. When plasmas are generated using multiple VHF sources, one can expect interaction between the sources and the plasma characteristics to be different from those due to individual frequencies.…”

Comparison of electrostatic and electromagnetic simulations for very high frequency plasmas

“…In recent years, several theoretical studies [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21] and experimental research [22][23][24][25][26][27][28][29][30] have been published on the plasma characteristics in a CCP sustained by VHF sources. Lieberman et al 6 first employed a uniform slab model to investigate the standing-wave and skin effects in VHF discharges.…”

“…Lee et al 11 focused on the coupling of the electromagnetic effects with the electrostatic edge effect in a two-dimensional axisymmetric model, and they observed the so-called stop band at higher frequencies and higher pressures. Rauf et al 12,13 developed a fluid model to simulate an argon plasma, discovering that the plasma density peaked at the chamber center under the condition where the electromagnetic effects were predominant. Furthermore, they also observed that the plasma became more uniform for a small interelectrode gap at 180 MHz.…”