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Title: 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 ( Ez) are aligned, and “anti-symmetric,” 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 anti-symmetric spatial resonance, both modes can exist in combination and lead to unexpected non-symmetric equilibria. We use a fast 2D axisymmetric fluid-analytical 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 anti-symmetric 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 non-symmetric equilibrium appears which may be stable or unstable. In our study, we develop a nonlinear lumped circuit model of the symmetric CCP tomore » better understand these unexpected results, indicating that the proximity to the anti-symmetric spatial resonance allows self-exciting of the anti-symmetric 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.« less

Authors:
ORCiD logo [1]; ORCiD logo [1];  [1]
  1. 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 1070-664X
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. doi:10.1063/1.5048947.
Kawamura, E., Lieberman, M. A., & Lichtenberg, A. J. Symmetry breaking in high frequency, symmetric capacitively coupled plasmas. United States. doi: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. doi: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 “anti-symmetric,” 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 anti-symmetric spatial resonance, both modes can exist in combination and lead to unexpected non-symmetric equilibria. We use a fast 2D axisymmetric fluid-analytical code to study a symmetric CCP reactor at low pressure (7.5 mTorr argon) and low density (~3 × 1015 m-3) in the frequency range of f = 55 to 100 MHz which encompasses the first anti-symmetric 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 non-symmetric 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 anti-symmetric spatial resonance allows self-exciting of the anti-symmetric 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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