Symmetry breaking in high frequency, symmetric capacitively coupled plasmas
Abstract
Two radially propagating surface wave modes, “symmetric,” in which the upper and lower axial sheath fields (E_{z}) are aligned, and “antisymmetric,” in which they are opposed, can exist in capacitively coupled plasma (CCP) discharges. For a symmetric (equal electrode areas) CCP driven symmetrically, we expected to observe only the symmetric mode. Instead, we find that when the applied rf frequency f is above or near an antisymmetric spatial resonance, both modes can exist in combination and lead to unexpected nonsymmetric equilibria. We use a fast 2D axisymmetric fluidanalytical code to study a symmetric CCP reactor at low pressure (7.5 mTorr argon) and low density (~3 × 10^{15} m^{3}) in the frequency range of f = 55 to 100 MHz which encompasses the first antisymmetric spatial resonance frequency f_{a} but is far below the first symmetric spatial resonance f_{s}. For lower frequencies such that f is well below f_{a>}, the symmetric CCP is in a stable symmetric equilibrium, as expected, but at higher frequencies such that f is near or greater than f_{a}, a nonsymmetric equilibrium appears which may be stable or unstable. In our study, we develop a nonlinear lumped circuit model of the symmetric CCP to better understand thesemore »
 Authors:

 Univ. of California, Berkeley, CA (United States). Dept. of Electrical Engineering and Computer Sciences
 Publication Date:
 Research Org.:
 Univ. of Michigan, Ann Arbor, MI (United States)
 Sponsoring Org.:
 USDOE Office of Science (SC)
 OSTI Identifier:
 1540256
 Alternate Identifier(s):
 OSTI ID: 1472211
 Grant/Contract Number:
 SC0001939
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physics of Plasmas
 Additional Journal Information:
 Journal Volume: 25; Journal Issue: 9; Journal ID: ISSN 1070664X
 Publisher:
 American Institute of Physics (AIP)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 70 PLASMA PHYSICS AND FUSION TECHNOLOGY; physics
Citation Formats
Kawamura, E., Lieberman, M. A., and Lichtenberg, A. J.. Symmetry breaking in high frequency, symmetric capacitively coupled plasmas. United States: N. p., 2018.
Web. https://doi.org/10.1063/1.5048947.
Kawamura, E., Lieberman, M. A., & Lichtenberg, A. J.. Symmetry breaking in high frequency, symmetric capacitively coupled plasmas. United States. https://doi.org/10.1063/1.5048947
Kawamura, E., Lieberman, M. A., and Lichtenberg, A. J.. Mon .
"Symmetry breaking in high frequency, symmetric capacitively coupled plasmas". United States. https://doi.org/10.1063/1.5048947. https://www.osti.gov/servlets/purl/1540256.
@article{osti_1540256,
title = {Symmetry breaking in high frequency, symmetric capacitively coupled plasmas},
author = {Kawamura, E. and Lieberman, M. A. and Lichtenberg, A. J.},
abstractNote = {Two radially propagating surface wave modes, “symmetric,” in which the upper and lower axial sheath fields (Ez) are aligned, and “antisymmetric,” in which they are opposed, can exist in capacitively coupled plasma (CCP) discharges. For a symmetric (equal electrode areas) CCP driven symmetrically, we expected to observe only the symmetric mode. Instead, we find that when the applied rf frequency f is above or near an antisymmetric spatial resonance, both modes can exist in combination and lead to unexpected nonsymmetric equilibria. We use a fast 2D axisymmetric fluidanalytical code to study a symmetric CCP reactor at low pressure (7.5 mTorr argon) and low density (~3 × 1015 m3) in the frequency range of f = 55 to 100 MHz which encompasses the first antisymmetric spatial resonance frequency fa but is far below the first symmetric spatial resonance fs. For lower frequencies such that f is well below fa>, the symmetric CCP is in a stable symmetric equilibrium, as expected, but at higher frequencies such that f is near or greater than fa, a nonsymmetric equilibrium appears which may be stable or unstable. In our study, we develop a nonlinear lumped circuit model of the symmetric CCP to better understand these unexpected results, indicating that the proximity to the antisymmetric spatial resonance allows selfexciting of the antisymmetric mode even in a symmetric system. The circuit model results agree well with the fluid simulations. A linear stability analysis of the symmetric equilibrium describes a transition with increasing frequency from stable to unstable.},
doi = {10.1063/1.5048947},
journal = {Physics of Plasmas},
number = 9,
volume = 25,
place = {United States},
year = {2018},
month = {9}
}
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