7th Asia-Pacific Conference on Plasma Physics, 12-17 Nov, 2023 at Port Messe Nagoya

Effects of low-frequency voltage on nonlinear standing wave excitation and iondynamics in dual-frequency asymmetric capacitive discharges

Kai Zhao1, Fang-Jie Zhou1, De-Qi Wen, Jian-Kai Liu1, Zi-Xuan Su1, Yang Zhou1, Yu-Ru Zhang1
and You-Nian Wang
1
School of Physics, Dalian University of Technology
2
Department of Computational Mathematics Science and Engineering, Michigan State University
e-mail (speaker): kaizhao@dlut.edu.cn
It is known that in very-high-frequency capacitively
coupled plasmas (VHF CCPs), the higher harmonics
generated by nonlinear sheath motion can enhance thestanding wave effect (SWE), which leads to center-peaked
plasma density profiles.[1-3] In this work, an improved
nonlinear electromagnetic transmission line model
incorporating a bulk plasma model, a numerical ion sheathmodel, and an ion Monte-Carlo collision (MCC) model isdeveloped to study the effects of low-frequency (LF)
voltage VL on the nonlinear standing wave excitation,
plasma uniformity, and ion energy and angular
distribution functions (IEDF and IADF) in dual-frequency(DF) asymmetric capacitive argon discharges at relatively
low pressure of 3 Pa. The plasma diffusion in the radialdirection and ion dynamics within the LF oscillating
sheath are self-consistently considered. The LF voltage VL
at 2 MHz varies from 0 to 700 V while the high-frequency(HF) voltage VH at 60 MHz is fixed at 100 V.
Simulation results indicate that without the addition ofLF source (i.e. VL = 0 V), there are a considerable numberof high-order harmonics with short wavelengths, leading
to significant SWE and central peak in the radial plasma
density profile. Nevertheless, the high-order harmonic
excitations tend to be weakened and merely occur aroundthe phase of the full LF sheath collapse due to a shorter
characteristic damping time of the surface waves as VL
increases (figure 1). This, combined with increased

surface wavelengths of both the driving frequency and thehigher harmonics at a higher VL, leads to suppressed
standing waves and improved plasma uniformity.
Meanwhile, the simulations show that both the low andthe high energy peaks of IEDF move towards higher
energies, and the energy peak separation width ∆E
becomes wider with the increase of VL. The IEDF at theradial center of the powered electrode exhibits a broader∆E than that at the edge. For the IADF, an increased VL
results in more ions incident on the electrode with asmaller deflection angle. Because of a thinner sheath anda higher sheath voltage at the electrode center, the peakvalue of IADF at the electrode center is greater than thatat the edge. This work has been financially supported by
the National Natural Science Foundation of China(NSFC) (Grants No. 11935005, No. 12005035, and No.
12275041), and the Fundamental Research Funds for theCentral Universities (Grant No. DUT21TD104).
References[1] M. A. Lieberman et al, Plasma Sources Sci. Technol.
24, 055011 (2015)[2] K. Zhao et al, Phys. Rev. Lett. 122, 185002 (2019)[3] F. J. Zhou et al, Plasma Sources Sci. Technol. 30,125017 (2021)

Figure 1. Simulation results of the temporal evolution of the total discharge voltage V (left column), the sheath thicknesss (middle column), and the current density Jz (right column) over one LF period at the radial center r = 0 (blue lines) andthe edge r = R1 (red lines) for different VL: 0 V (first row), 25 V (second row), 200 V (third row), and 700 V (fourth row).