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

Wen, De-Qi; Kawamura, E.; Lieberman, M. A.; Lichtenberg, A. J.; Wang, You-Nian

doi:10.1063/1.4993798

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

Abstract

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 nearmore »« less

Authors:

Wen, De-Qi ^[1]; Kawamura, E. ^[2]; Lieberman, M. A. ^[2]; Lichtenberg, A. J. ^[2];

^[3]

Dalian Univ. of Technology, Dalian (China). School of Physics; Univ. of California, Berkeley, CA (United States). Dept. of Electrical Engineering and Computer Science
Univ. of California, Berkeley, CA (United States). Dept. of Electrical Engineering and Computer Science
Dalian Univ. of Technology, Dalian (China). School of Physics

Publication Date:: 2017-08-24

Research Org.:: Univ. of Michigan, Ann Arbor, MI (United States)

Sponsoring Org.:: USDOE Office of Science (SC), Fusion Energy Sciences (FES)

OSTI Identifier:: 1474308

Alternate Identifier(s):: OSTI ID: 1376737

Grant/Contract Number:: SC0001939

Resource Type:: Accepted Manuscript

Journal Name:: Physics of Plasmas

Additional Journal Information:: Journal Volume: 24; Journal Issue: 8; 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

Citation Formats


                    Wen, De-Qi, Kawamura, E., Lieberman, M. A., Lichtenberg, A. J., and Wang, You-Nian. A nonlinear electromagnetics model of an asymmetrically-driven, low pressure capacitive discharge.  United States: N. p., 2017. 
Web.  https://doi.org/10.1063/1.4993798.

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                    Wen, De-Qi, Kawamura, E., Lieberman, M. A., Lichtenberg, A. J., & Wang, You-Nian. A nonlinear electromagnetics model of an asymmetrically-driven, low pressure capacitive discharge.  United States.  https://doi.org/10.1063/1.4993798

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                    Wen, De-Qi, Kawamura, E., Lieberman, M. A., Lichtenberg, A. J., and Wang, You-Nian. Thu .  
"A nonlinear electromagnetics model of an asymmetrically-driven, low pressure capacitive discharge".  United States.  https://doi.org/10.1063/1.4993798.  https://www.osti.gov/servlets/purl/1474308.

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@article{osti_1474308,

  title        = {A nonlinear electromagnetics model of an asymmetrically-driven, low pressure capacitive discharge},

  author       = {Wen, De-Qi and Kawamura, E. and Lieberman, M. A. and Lichtenberg, A. J. and Wang, You-Nian},

  abstractNote = {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.},

  doi          = {10.1063/1.4993798},

  journal      = {Physics of Plasmas},

  number       = 8,

  volume       = 24,

  place        = {United States},

  year         = {2017},

  month        = {8}

}

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Works referencing / citing this record:

Symmetry breaking in high frequency, symmetric capacitively coupled plasmas
journal, September 2018

Kawamura, E.; Lieberman, M. A.; Lichtenberg, A. J.
Physics of Plasmas, Vol. 25, Issue 9
DOI: 10.1063/1.5048947

Two-dimensional particle-in-cell simulations of standing waves and wave-induced hysteresis in asymmetric capacitive discharges
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Wen, De-Qi; Kawamura, E.; Lieberman, M. A.
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Experimental investigation of standing wave effect in dual-frequency capacitively coupled argon discharges: role of a low-frequency source
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Zhao, Kai; Liu, Yong-Xin; Kawamura, E.
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Observation of Nonlinear Standing Waves Excited by Plasma-Series-Resonance-Enhanced Harmonics in Capacitive Discharges
journal, May 2019

Zhao, Kai; Wen, De-Qi; Liu, Yong-Xin
Physical Review Letters, Vol. 122, Issue 18
DOI: 10.1103/physrevlett.122.185002

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

Abstract

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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

Inductive Heating and E to H Transitions in Capacitive Discharges journal, November 2005

Ion flux nonuniformities in large-area high-frequency capacitive discharges journal, July 2003

Linear electromagnetic excitation of an asymmetric low pressure capacitive discharge with unequal sheath widths journal, January 2016

A nonlinear global model of a dual frequency capacitive discharge journal, August 2006

Simulations of electromagnetic effects in high-frequency capacitively coupled discharges using the Darwin approximation journal, February 2013

Effect of electromagnetic waves and higher harmonics in capacitively coupled plasma phenomena journal, November 2013

Nonlinearity of the radio‐frequency sheath journal, April 1996

A voltage uniformity study in large-area reactors for RF plasma deposition journal, May 1997

Relationship between center-peaked plasma density profiles and harmonic electromagnetic waves in very high frequency capacitively coupled plasma reactors journal, January 2014

Symmetry breaking in high frequency, symmetric capacitively coupled plasmas journal, September 2018

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

Observation of Nonlinear Standing Waves Excited by Plasma-Series-Resonance-Enhanced Harmonics in Capacitive Discharges journal, May 2019

On the physics of a large CCP discharge
journal, March 2016

Fast 2D fluid-analytical simulation of ion energy distributions and electromagnetic effects in multi-frequency capacitive discharges
journal, December 2014

Self-consistent simulation of very high frequency capacitively coupled plasmas
journal, May 2008

Effect of the resonant growth of harmonics on the electron density in capacitively coupled plasma
journal, November 2009

Effect of resonance in external radio-frequency circuit on very high frequency plasma discharge
journal, May 2010

Sheath motion in a capacitively coupled radio frequency discharge
journal, January 1991

Fast 2D hybrid fluid-analytical simulation of inductive/capacitive discharges
journal, April 2011

Modeling of Resonant Surface Wave Excitation in a Large CCP Reactor
journal, April 2017

Nonlinear electron resonance heating in capacitive radio frequency discharges
journal, April 2006

Shaped electrode and lens for a uniform radio-frequency capacitive plasma
journal, January 2003

Displacement current and multiple pulse effects in plasma source ion implantation
journal, May 1993

Nonlinear plasma dynamics in capacitive radio frequency discharges
journal, April 2007

Analytical solution for capacitive RF sheath
journal, January 1988

Calculation of the electrode shape for suppression of the standing wave effect in large area rectangular capacitively coupled reactors
journal, March 2005

Measurements and consequences of nonuniform radio frequency plasma potential due to surface asymmetry in large area radio frequency capacitive reactors
journal, July 2005

Glow discharge processing in the liquid crystal display industry
journal, August 2002

Inductive heating and E to H transitions in high frequency capacitive discharges
journal, April 2006

The effects of nonlinear series resonance on Ohmic and stochastic heating in capacitive discharges
journal, June 2008

Nonlinear series resonance and standing waves in dual-frequency capacitive discharges
journal, November 2016

Self-excitation of the plasma series resonance in radio-frequency discharges: An analytical description
journal, December 2006

Nonuniform radio-frequency plasma potential due to edge asymmetry in large-area radio-frequency reactors
journal, November 2004

Spatial and frequency dependence of plasma currents in a 300 mm capacitively coupled plasma reactor
journal, October 2006

Comparison of electrostatic and electromagnetic simulations for very high frequency plasmas
journal, November 2010

Nonlinear standing wave excitation by series resonance-enhanced harmonics in low pressure capacitive discharges
journal, August 2015

Frequency dependent plasma characteristics in a capacitively coupled 300 mm wafer plasma processing chamber
journal, October 2006

Electromagnetic field nonuniformities in large area, high-frequency capacitive plasma reactors, including electrode asymmetry effects
journal, March 2006

Self-consistent nonlinear transmission line model of standing wave effects in a capacitive discharge
journal, May 2004

Standing wave and skin effects in large-area, high-frequency capacitive discharges
journal, June 2002

Probe measurements of plasma potential nonuniformity due to edge asymmetry in large-area radio-frequency reactors: The telegraph effect
journal, June 2005

Electric fields in the sheath formed in a 300 mm, dual frequency capacitive argon discharge
journal, March 2007

Self-consistent electrodynamics of large-area high-frequency capacitive plasma discharge
journal, October 2010

2D fluid-analytical simulation of electromagnetic effects in low pressure, high frequency electronegative capacitive discharges
journal, April 2016

Improving plasma uniformity using lens-shaped electrodes in a large area very high frequency reactor
journal, May 2004

Modeling electromagnetic effects in capacitive discharges
journal, February 2008

Theoretical approach for plasma series resonance effect in geometrically symmetric dual radio frequency plasma
journal, February 2012

Modeling of dual frequency capacitively coupled plasma sources utilizing a full-wave Maxwell solver: II. Scaling with pressure, power and electronegativity
journal, September 2010

Amorphous silicon deposition: Industrial and technical challenges
journal, July 1989

Modeling of dual frequency capacitively coupled plasma sources utilizing a full-wave Maxwell solver: I. Scaling with high frequency
journal, September 2010

Enhancement of Ohmic and Stochastic Heating by Resonance Effects in Capacitive Radio Frequency Discharges: A Theoretical Approach
journal, August 2008

Measurements of time average series resonance effect in capacitively coupled radio frequency discharge plasma
journal, October 2011

Electromagnetic effects in high-frequency capacitive discharges used for plasma processing
journal, January 2007

Experimental investigations of the plasma radial uniformity in single and dual frequency capacitively coupled argon discharges
journal, December 2016

Comment on “Ion energy uniformity in high-frequency capacitive discharges” [Appl. Phys. Lett. 86, 021501 (2005)]
journal, August 2005

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

Inductive Heating and $E$ to $H$ Transitions in Capacitive Discharges
journal, November 2005

Ion flux nonuniformities in large-area high-frequency capacitive discharges
journal, July 2003

Linear electromagnetic excitation of an asymmetric low pressure capacitive discharge with unequal sheath widths
journal, January 2016

A nonlinear global model of a dual frequency capacitive discharge
journal, August 2006

Simulations of electromagnetic effects in high-frequency capacitively coupled discharges using the Darwin approximation
journal, February 2013

Effect of electromagnetic waves and higher harmonics in capacitively coupled plasma phenomena
journal, November 2013

Nonlinearity of the radio‐frequency sheath
journal, April 1996

A voltage uniformity study in large-area reactors for RF plasma deposition
journal, May 1997

Relationship between center-peaked plasma density profiles and harmonic electromagnetic waves in very high frequency capacitively coupled plasma reactors
journal, January 2014

Symmetry breaking in high frequency, symmetric capacitively coupled plasmas
journal, September 2018

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

Observation of Nonlinear Standing Waves Excited by Plasma-Series-Resonance-Enhanced Harmonics in Capacitive Discharges
journal, May 2019