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Title: A nonlinear electromagnetics model of an asymmetrically-driven, low pressure capacitive discharge

Journal Article · · Physics of Plasmas
DOI: https://doi.org/10.1063/1.4993798 · OSTI ID:1474308
 [1];  [2];  [2];  [2]; ORCiD logo [3]
  1. Dalian Univ. of Technology, Dalian (China). School of Physics; Univ. of California, Berkeley, CA (United States). Dept. of Electrical Engineering and Computer Science; University of California, Berkeley
  2. Univ. of California, Berkeley, CA (United States). Dept. of Electrical Engineering and Computer Science
  3. Dalian Univ. of Technology, Dalian (China). School of Physics

It is well-known that standing waves having radially center-high voltage profiles exist in high frequency driven capacitive discharges. Capacitive sheaths can also nonlinearly excite driving frequency harmonics near the series resonance that can be spatially near-resonant, and therefore enhance the on-axis power deposition. The powered-electrode/plasma/grounded-electrode sandwich structure of an asymmetrically excited cylindrical discharge forms a three electrode system in which both z-symmetric and z-antisymmetric radially propagating wave modes can exist. We develop a nonlinear electromagnetics model for this system with radially- and time-varying sheath widths, incorporating both symmetric and antisymmetric modes, and the plasma skin effect. Waves generated in the electrostatic wave limit are also treated. The discharge is modeled as a uniform density bulk plasma with either homogeneous or Child law sheaths at the electrodes, incorporating their nonlinear voltage versus charge relations. The model includes a finite power source resistance and a self-consistent calculation of the dc bias voltages. The resulting set of nonlinear partial differential equations is solved numerically to determine the symmetric and antisymmetric mode amplitudes and the nonlinearly-excited radially-varying harmonics. Two examples driven at lower frequency (30 MHz) or at higher frequency (60 MHz) are examined. The first case displays the excited dominant ninth harmonic near the series resonance frequency with the fundamental frequency having a weak standing wave. The higher frequency case shows a more obvious standing wave effect, enhanced by the nonlinear harmonics. Finally, the symmetric and antisymmetric modes are of similar amplitudes over the driving electrode, summing to give a larger bottom sheath.

Research Organization:
Univ. of Michigan, Ann Arbor, MI (United States)
Sponsoring Organization:
USDOE Office of Science (SC), Fusion Energy Sciences (FES) (SC-24)
Grant/Contract Number:
SC0001939
OSTI ID:
1474308
Alternate ID(s):
OSTI ID: 1376737
Journal Information:
Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 8 Vol. 24; ISSN 1070-664X
Publisher:
American Institute of Physics (AIP)Copyright Statement
Country of Publication:
United States
Language:
English

References (54)

Calculation of the electrode shape for suppression of the standing wave effect in large area rectangular capacitively coupled reactors journal March 2005
Self-excitation of the plasma series resonance in radio-frequency discharges: An analytical description journal December 2006
Enhancement of Ohmic and Stochastic Heating by Resonance Effects in Capacitive Radio Frequency Discharges: A Theoretical Approach journal August 2008
Frequency dependent plasma characteristics in a capacitively coupled 300 mm wafer plasma processing chamber journal October 2006
Ion flux nonuniformities in large-area high-frequency capacitive discharges journal July 2003
Shaped electrode and lens for a uniform radio-frequency capacitive plasma journal January 2003
On the physics of a large CCP discharge journal March 2016
Nonlinearity of the radio‐frequency sheath journal April 1996
Simulations of electromagnetic effects in high-frequency capacitively coupled discharges using the Darwin approximation journal February 2013
Glow discharge processing in the liquid crystal display industry journal August 2002
Modeling of dual frequency capacitively coupled plasma sources utilizing a full-wave Maxwell solver: II. Scaling with pressure, power and electronegativity journal September 2010
Comment on “Ion energy uniformity in high-frequency capacitive discharges” [Appl. Phys. Lett. 86, 021501 (2005)] journal August 2005
Probe measurements of plasma potential nonuniformity due to edge asymmetry in large-area radio-frequency reactors: The telegraph effect journal June 2005
The effects of nonlinear series resonance on Ohmic and stochastic heating in capacitive discharges journal June 2008
Linear electromagnetic excitation of an asymmetric low pressure capacitive discharge with unequal sheath widths journal January 2016
Suppression of the standing wave effect in high frequency capacitive discharges using a shaped electrode and a dielectric lens: Self-consistent approach journal August 2004
Effect of the resonant growth of harmonics on the electron density in capacitively coupled plasma journal November 2009
Electric fields in the sheath formed in a 300 mm, dual frequency capacitive argon discharge journal March 2007
Comparison of electrostatic and electromagnetic simulations for very high frequency plasmas journal November 2010
Inductive Heating and E to H Transitions in Capacitive Discharges journal November 2005
Nonlinear electron resonance heating in capacitive radio frequency discharges journal April 2006
Self-consistent nonlinear transmission line model of standing wave effects in a capacitive discharge journal May 2004
Analytical solution for capacitive RF sheath journal January 1988
Modeling electromagnetic effects in capacitive discharges journal February 2008
Standing wave and skin effects in large-area, high-frequency capacitive discharges journal June 2002
2D fluid-analytical simulation of electromagnetic effects in low pressure, high frequency electronegative capacitive discharges journal April 2016
Nonlinear standing wave excitation by series resonance-enhanced harmonics in low pressure capacitive discharges journal August 2015
Experimental investigations of the plasma radial uniformity in single and dual frequency capacitively coupled argon discharges journal December 2016
Fast 2D hybrid fluid-analytical simulation of inductive/capacitive discharges journal April 2011
Principles of Plasma Discharges and Materials Processing book January 2005
Sheath motion in a capacitively coupled radio frequency discharge journal January 1991
Nonlinear plasma dynamics in capacitive radio frequency discharges journal April 2007
Spatial and frequency dependence of plasma currents in a 300 mm capacitively coupled plasma reactor journal October 2006
Measurements and consequences of nonuniform radio frequency plasma potential due to surface asymmetry in large area radio frequency capacitive reactors
  • Sansonnens, L.; Strahm, B.; Derendinger, L.
  • Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films, Vol. 23, Issue 4 https://doi.org/10.1116/1.1868572
journal July 2005
Modeling of dual frequency capacitively coupled plasma sources utilizing a full-wave Maxwell solver: I. Scaling with high frequency journal September 2010
Nonlinear series resonance and standing waves in dual-frequency capacitive discharges journal November 2016
A voltage uniformity study in large-area reactors for RF plasma deposition journal May 1997
Self-consistent simulation of very high frequency capacitively coupled plasmas journal May 2008
Inductive heating and E to H transitions in high frequency capacitive discharges journal April 2006
Electromagnetic effects in high-frequency capacitive discharges used for plasma processing journal January 2007
Nonuniform radio-frequency plasma potential due to edge asymmetry in large-area radio-frequency reactors journal November 2004
Electromagnetic field nonuniformities in large area, high-frequency capacitive plasma reactors, including electrode asymmetry effects journal March 2006
Improving plasma uniformity using lens-shaped electrodes in a large area very high frequency reactor journal May 2004
Measurements of time average series resonance effect in capacitively coupled radio frequency discharge plasma journal October 2011
Displacement current and multiple pulse effects in plasma source ion implantation journal May 1993
Self-consistent electrodynamics of large-area high-frequency capacitive plasma discharge journal October 2010
Fast 2D fluid-analytical simulation of ion energy distributions and electromagnetic effects in multi-frequency capacitive discharges journal December 2014
A nonlinear global model of a dual frequency capacitive discharge journal August 2006
Theoretical approach for plasma series resonance effect in geometrically symmetric dual radio frequency plasma journal February 2012
Effect of resonance in external radio-frequency circuit on very high frequency plasma discharge journal May 2010
Amorphous silicon deposition: Industrial and technical challenges journal July 1989
Modeling of Resonant Surface Wave Excitation in a Large CCP Reactor journal April 2017
Effect of electromagnetic waves and higher harmonics in capacitively coupled plasma phenomena journal November 2013
Relationship between center-peaked plasma density profiles and harmonic electromagnetic waves in very high frequency capacitively coupled plasma reactors journal January 2014

Cited By (4)

Observation of Nonlinear Standing Waves Excited by Plasma-Series-Resonance-Enhanced Harmonics in Capacitive Discharges journal May 2019
Two-dimensional particle-in-cell simulations of standing waves and wave-induced hysteresis in asymmetric capacitive discharges journal November 2017
Experimental investigation of standing wave effect in dual-frequency capacitively coupled argon discharges: role of a low-frequency source journal May 2018
Symmetry breaking in high frequency, symmetric capacitively coupled plasmas journal September 2018