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. doi: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}
}
Web of Science
Works referenced in this record:
Electromagnetic field nonuniformities in large area, highfrequency capacitive plasma reactors, including electrode asymmetry effects
journal, March 2006
 Sansonnens, L.; Howling, A. A.; Hollenstein, Ch
 Plasma Sources Science and Technology, Vol. 15, Issue 3
On the physics of a large CCP discharge
journal, March 2016
 Eremin, D.; Bienholz, S.; Szeremley, D.
 Plasma Sources Science and Technology, Vol. 25, Issue 2
Fast 2D fluidanalytical simulation of ion energy distributions and electromagnetic effects in multifrequency capacitive discharges
journal, December 2014
 Kawamura, E.; Lieberman, M. A.; Graves, D. B.
 Plasma Sources Science and Technology, Vol. 23, Issue 6
Selfconsistent nonlinear transmission line model of standing wave effects in a capacitive discharge
journal, May 2004
 Chabert, P.; Raimbault, J. L.; Rax, J. M.
 Physics of Plasmas, Vol. 11, Issue 5
Principles of Plasma Discharges and Materials Processing
book, January 2005
 Lieberman, Michael A.; Lichtenberg, Allan J.
Selfconsistent simulation of very high frequency capacitively coupled plasmas
journal, May 2008
 Rauf, Shahid; Bera, Kallol; Collins, Ken
 Plasma Sources Science and Technology, Vol. 17, Issue 3
Standing wave and skin effects in largearea, highfrequency capacitive discharges
journal, June 2002
 Lieberman, M. A.; Booth, J. P.; Chabert, P.
 Plasma Sources Science and Technology, Vol. 11, Issue 3
Effect of resonance in external radiofrequency circuit on very high frequency plasma discharge
journal, May 2010
 Rauf, Shahid; Chen, Zhigang; Collins, Ken
 Journal of Applied Physics, Vol. 107, Issue 9
2D fluidanalytical simulation of electromagnetic effects in low pressure, high frequency electronegative capacitive discharges
journal, April 2016
 Kawamura, E.; Lichtenberg, A. J.; Lieberman, M. A.
 Plasma Sources Science and Technology, Vol. 25, Issue 3
Modeling electromagnetic effects in capacitive discharges
journal, February 2008
 Lee, Insook; Graves, D. B.; Lieberman, M. A.
 Plasma Sources Science and Technology, Vol. 17, Issue 1
Experimental investigation of standing wave effect in dualfrequency capacitively coupled argon discharges: role of a lowfrequency source
journal, May 2018
 Zhao, Kai; Liu, YongXin; Kawamura, E.
 Plasma Sources Science and Technology, Vol. 27, Issue 5
Fast 2D hybrid fluidanalytical simulation of inductive/capacitive discharges
journal, April 2011
 Kawamura, E.; Graves, D. B.; Lieberman, M. A.
 Plasma Sources Science and Technology, Vol. 20, Issue 3
Modeling of dual frequency capacitively coupled plasma sources utilizing a fullwave Maxwell solver: II. Scaling with pressure, power and electronegativity
journal, September 2010
 Yang, Yang; Kushner, Mark J.
 Plasma Sources Science and Technology, Vol. 19, Issue 5
Modeling of dual frequency capacitively coupled plasma sources utilizing a fullwave Maxwell solver: I. Scaling with high frequency
journal, September 2010
 Yang, Yang; Kushner, Mark J.
 Plasma Sources Science and Technology, Vol. 19, Issue 5
Amorphous silicon deposition: Industrial and technical challenges
journal, July 1989
 Schmitt, J. P. M.
 Thin Solid Films, Vol. 174
Shaped electrode and lens for a uniform radiofrequency capacitive plasma
journal, January 2003
 Sansonnens, L.; Schmitt, J.
 Applied Physics Letters, Vol. 82, Issue 2
Suppression of the standing wave effect in high frequency capacitive discharges using a shaped electrode and a dielectric lens: Selfconsistent approach
journal, August 2004
 Chabert, P.; Raimbault, J. L.; Rax, J. M.
 Physics of Plasmas, Vol. 11, Issue 8
A nonlinear electromagnetics model of an asymmetricallydriven, low pressure capacitive discharge
journal, August 2017
 Wen, DeQi; Kawamura, E.; Lieberman, M. A.
 Physics of Plasmas, Vol. 24, Issue 8
Analytical solution for capacitive RF sheath
journal, January 1988
 Lieberman, M. A.
 IEEE Transactions on Plasma Science, Vol. 16, Issue 6
Ion flux nonuniformities in largearea highfrequency capacitive discharges
journal, July 2003
 Perret, A.; Chabert, P.; Booth, J. P.
 Applied Physics Letters, Vol. 83, Issue 2
Calculation of the electrode shape for suppression of the standing wave effect in large area rectangular capacitively coupled reactors
journal, March 2005
 Sansonnens, L.
 Journal of Applied Physics, Vol. 97, Issue 6
Linear electromagnetic excitation of an asymmetric low pressure capacitive discharge with unequal sheath widths
journal, January 2016
 Lieberman, M. A.; Lichtenberg, A. J.; Kawamura, E.
 Physics of Plasmas, Vol. 23, Issue 1
Effect of a dielectric layer on plasma uniformity in high frequency electronegative capacitive discharges
journal, September 2017
 Kawamura, Emi; Wen, DeQi; Lieberman, Michael A.
 Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films, Vol. 35, Issue 5
Glow discharge processing in the liquid crystal display industry
journal, August 2002
 Schmitt, Jacques; Elyaakoubi, Mustapha; Sansonnens, Laurent
 Plasma Sources Science and Technology, Vol. 11, Issue 3A
Nonlinear series resonance and standing waves in dualfrequency capacitive discharges
journal, November 2016
 Wen, DeQi; Kawamura, E.; Lieberman, M. A.
 Plasma Sources Science and Technology, Vol. 26, Issue 1
Simulations of electromagnetic effects in highfrequency capacitively coupled discharges using the Darwin approximation
journal, February 2013
 Eremin, Denis; Hemke, Torben; Brinkmann, Ralf Peter
 Journal of Physics D: Applied Physics, Vol. 46, Issue 8
Nonuniform radiofrequency plasma potential due to edge asymmetry in largearea radiofrequency reactors
journal, November 2004
 Howling, A. A.; Sansonnens, L.; Ballutaud, J.
 Journal of Applied Physics, Vol. 96, Issue 10
A Monte Carlo collision model for the particleincell method: applications to argon and oxygen discharges
journal, May 1995
 Vahedi, V.; Surendra, M.
 Computer Physics Communications, Vol. 87, Issue 12
Comparison of electrostatic and electromagnetic simulations for very high frequency plasmas
journal, November 2010
 Zhang, YuRu; Xu, Xiang; Zhao, ShuXia
 Physics of Plasmas, Vol. 17, Issue 11
Nonlinear standing wave excitation by series resonanceenhanced harmonics in low pressure capacitive discharges
journal, August 2015
 Lieberman, M. A.; Lichtenberg, A. J.; Kawamura, E.
 Plasma Sources Science and Technology, Vol. 24, Issue 5
Works referencing / citing this record:
Simulations of electromagnetic effects in largearea highfrequency capacitively coupled plasmas with symmetric electrodes: Different axial plasma density profiles
journal, February 2020
 Liu, JianKai; Zhang, YuRu; Zhao, Kai
 Physics of Plasmas, Vol. 27, Issue 2