Magnetic probe diagnostics of nonlinear standing waves and bulk ohmic electron power absorption in capacitive discharges

Zhao, Kai; Liu, Yongxin; Zhang, Quanzhi; Economou, Demetre J.; Wang, Younian

doi:10.1088/2058-6272/ac1cce

Title: Magnetic probe diagnostics of nonlinear standing waves and bulk ohmic electron power absorption in capacitive discharges

Journal Article · Tue Sep 21 00:00:00 EDT 2021 · Plasma Science and Technology

DOI:https://doi.org/10.1088/2058-6272/ac1cce· OSTI ID:1979462

^[1]; Liu, Yongxin ^[1]; Zhang, Quanzhi ^[1]; Economou, Demetre J. ^[2]; Wang, Younian ^[1]

Dalian University of Technology (China)
University of Houston, TX (United States)

It is recognized that standing wave effects appearing in large-area, very-high-frequency capacitively coupled plasma (CCP) reactors cause center-high plasma non-uniformity. Using a high-frequency magnetic probe, we present a direct experimental diagnostic of the nonlinear standing waves and bulk ohmic electron power absorption dynamics in low pressure CCP discharges for different driving frequencies of 13.56, 30, and 60 MHz. The design, principle, calibration, and validation of the probe are described in detail. Spatial structures of the harmonics of the magnetic field, determined by the magnetic probe, were used to calculate the distributions of the harmonic current and the corresponding ohmic electron power deposition, providing insights into the behavior of nonlinear harmonics. At a low driving frequency, i.e. 13.56 MHz, no remarkable nonlinear standing waves were identified and the bulk ohmic electron power absorption was observed to be negligible. Here, the harmonic magnetic field/current was found to increase dramatically with the driving frequency, due to decreased sheath reactance and more remarkable nonlinear standing waves at a higher driving frequency, leading to the enhancements of the ohmic heating and the plasma density in the bulk, specifically at the electrode center. At a high driving frequency, i.e. 60 MHz, the high-order harmonic current density and the corresponding ohmic electron power absorption exhibited a similar node structure, with the main peak on axis, and one or more minor peaks between the electrode center and the edge, contributing to the center-high profile of the plasma density.

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

Sponsoring Organization:: USDOE Office of Science (SC), Fusion Energy Sciences (FES); National Natural Science Foundation of China (NSFC); China Postdoctoral Science Foundation; Fundamental Research Funds for the Central Universities; National Science Foundation (NSF)

Grant/Contract Number:: SC0001939; 12005035; 11935005; 2020M670741; 2021T140085; DUT20LAB201; PHY-1500518

OSTI ID:: 1979462

Journal Information:: Plasma Science and Technology, Vol. 23, Issue 11; ISSN 1009-0630

Publisher:: IOPScienceCopyright Statement

Country of Publication:: United States

Language:: English

References (76)

Electric field nonlinearity in very high frequency capacitive discharges at constant electron plasma frequency Sharma, Sarveshwar; Sirse, Nishant; Kuley, Animesh Plasma Sources Science and Technology, Vol. 29, Issue 4 https://doi.org/10.1088/1361-6595/ab74b5	journal	March 2020
Design and calibration of high-frequency magnetic probes for the SUNIST spherical tokamak Liu, Yangqing; Tan, Yi; Pan, Ou Review of Scientific Instruments, Vol. 85, Issue 11 https://doi.org/10.1063/1.4886423	journal	November 2014
High sensitivity, inductively coupled miniature magnetic probe array for detailed measurement of time varying magnetic field profiles in plasma flows Black, D. C.; Mayo, R. M. Review of Scientific Instruments, Vol. 67, Issue 4 https://doi.org/10.1063/1.1146882	journal	April 1996
Fast 2D fluid-analytical simulation of ion energy distributions and electromagnetic effects in multi-frequency capacitive discharges Kawamura, E.; Lieberman, M. A.; Graves, D. B. Plasma Sources Science and Technology, Vol. 23, Issue 6 https://doi.org/10.1088/0963-0252/23/6/064003	journal	December 2014
Self-consistent simulation of very high frequency capacitively coupled plasmas Rauf, Shahid; Bera, Kallol; Collins, Ken Plasma Sources Science and Technology, Vol. 17, Issue 3 https://doi.org/10.1088/0963-0252/17/3/035003	journal	May 2008
Collisionless electron heating in an inductively coupled discharge Turner, M. M. Physical Review Letters, Vol. 71, Issue 12 https://doi.org/10.1103/PhysRevLett.71.1844	journal	September 1993
Spatio-temporal analysis of the electron power absorption in electropositive capacitive RF plasmas based on moments of the Boltzmann equation Schulze, J.; Donkó, Z.; Lafleur, T. Plasma Sources Science and Technology, Vol. 27, Issue 5 https://doi.org/10.1088/1361-6595/aabebc	journal	May 2018
Magnetic fluctuation probe design and capacitive pickup rejection Franck, Christian M.; Grulke, Olaf; Klinger, Thomas Review of Scientific Instruments, Vol. 73, Issue 11 https://doi.org/10.1063/1.1512341	journal	November 2002
Magnetic field probes for use in radio frequency plasma Reilly, Michael P.; Lewis, William; Miley, George H. Review of Scientific Instruments, Vol. 80, Issue 5 https://doi.org/10.1063/1.3136907	journal	May 2009
Effect of low-frequency power on dual-frequency capacitively coupled plasmas Yuan, Q. H.; Xin, Y.; Yin, G. Q. Journal of Physics D: Applied Physics, Vol. 41, Issue 20 https://doi.org/10.1088/0022-3727/41/20/205209	journal	September 2008
Electric field filamentation and higher harmonic generation in very high frequency capacitive discharges Sharma, Sarveshwar; Sirse, N.; Sen, A. Journal of Physics D: Applied Physics, Vol. 52, Issue 36 https://doi.org/10.1088/1361-6463/ab2959	journal	July 2019
Characterization of the E to H transition in a pulsed inductively coupled plasma discharge with internal coil geometry: bi-stability and hysteresis Cunge, Gilles; Crowley, Brendan; Vender, David Plasma Sources Science and Technology, Vol. 8, Issue 4 https://doi.org/10.1088/0963-0252/8/4/309	journal	October 1999
Power dynamics in a low pressure capacitively coupled plasma discharge Rauf, Shahid; Bera, Kallol; Collins, Ken Plasma Sources Science and Technology, Vol. 19, Issue 1 https://doi.org/10.1088/0963-0252/19/1/015014	journal	December 2009
Plasma acceleration processes in an ablative pulsed plasma thruster Koizumi, Hiroyuki; Noji, Ryosuke; Komurasaki, Kimiya Physics of Plasmas, Vol. 14, Issue 3 https://doi.org/10.1063/1.2710454	journal	March 2007
An upgrade of the magnetic diagnostic system of the DIII-D tokamak for non-axisymmetric measurements King, J. D.; Strait, E. J.; Boivin, R. L. Review of Scientific Instruments, Vol. 85, Issue 8 https://doi.org/10.1063/1.4891817	journal	August 2014
Experimental Evidence of Collisionless Power Absorption in Inductively Coupled Plasmas Godyak, V. A.; Piejak, R. B.; Alexandrovich, B. M. Physical Review Letters, Vol. 80, Issue 15 https://doi.org/10.1103/PhysRevLett.80.3264	journal	April 1998
Structure of an Exploding Laser-Produced Plasma Collette, A.; Gekelman, W. Physical Review Letters, Vol. 105, Issue 19 https://doi.org/10.1103/PhysRevLett.105.195003	journal	November 2010
Design, construction, and calibration of a three-axis, high-frequency magnetic probe (B-dot probe) as a diagnostic for exploding plasmas Everson, E. T.; Pribyl, P.; Constantin, C. G. Review of Scientific Instruments, Vol. 80, Issue 11 https://doi.org/10.1063/1.3246785	journal	November 2009
Nonlinear electron resonance heating in capacitive radio frequency discharges Mussenbrock, Thomas; Brinkmann, Ralf Peter Applied Physics Letters, Vol. 88, Issue 15 https://doi.org/10.1063/1.2194824	journal	April 2006
Shaped electrode and lens for a uniform radio-frequency capacitive plasma Sansonnens, L.; Schmitt, J. Applied Physics Letters, Vol. 82, Issue 2 https://doi.org/10.1063/1.1534918	journal	January 2003
Movable magnetic probe system in the T-10 tokamak Savrukhin, P. V.; Shestakov, E. A. Review of Scientific Instruments, Vol. 83, Issue 1 https://doi.org/10.1063/1.3675577	journal	January 2012
Kinetic interpretation of resonance phenomena in low pressure capacitively coupled radio frequency plasmas Wilczek, Sebastian; Trieschmann, Jan; Eremin, Denis Physics of Plasmas, Vol. 23, Issue 6 https://doi.org/10.1063/1.4953432	journal	June 2016
Collisionless Electron Heating by Capacitive rf Sheaths Gozadinos, G.; Turner, M. M.; Vender, D. Physical Review Letters, Vol. 87, Issue 13 https://doi.org/10.1103/PhysRevLett.87.135004	journal	September 2001
Stochastic heating in single and dual frequency capacitive discharges Kawamura, E.; Lieberman, M. A.; Lichtenberg, A. J. Physics of Plasmas, Vol. 13, Issue 5 https://doi.org/10.1063/1.2203949	journal	May 2006
Experimental diagnostics of plasma radial uniformity and comparisons with computational simulations in capacitive discharges Liu, Yong-Xin; Liang, Ying-Shuang; Wen, De-Qi Plasma Sources Science and Technology, Vol. 24, Issue 2 https://doi.org/10.1088/0963-0252/24/2/025013	journal	February 2015
Anomalous Capacitive Sheath with Deep Radio-Frequency Electric-Field Penetration Kaganovich, Igor D. Physical Review Letters, Vol. 89, Issue 26 https://doi.org/10.1103/PhysRevLett.89.265006	journal	December 2002
Simulation study of stochastic heating in single-frequency capacitively coupled discharges with critical evaluation of analytical models Sharma, S.; Turner, M. M. Plasma Sources Science and Technology, Vol. 22, Issue 3 https://doi.org/10.1088/0963-0252/22/3/035014	journal	June 2013
Broadband calibration of radio-frequency magnetic induction probes Messer, S.; Blackwell, D. D.; Amatucci, W. E. Review of Scientific Instruments, Vol. 77, Issue 11 https://doi.org/10.1063/1.2387880	journal	November 2006
Influence of select discharge parameters on electric field transients triggered in collisionless very high frequency capacitive discharges Sharma, Sarveshwar; Sirse, Nishant; Sen, Abhijit Physics of Plasmas, Vol. 26, Issue 10 https://doi.org/10.1063/1.5122837	journal	October 2019
Microwave resonances of a hairpin probe in a magnetized plasma Gogna, G. S.; Karkari, S. K. Applied Physics Letters, Vol. 96, Issue 15 https://doi.org/10.1063/1.3400214	journal	April 2010
Characteristics of anomalous skin effect and evolution of power absorption regions in a cylindrical radio frequency inductively coupled plasma Ding, Z. F.; Sun, B.; Huo, W. G. Physics of Plasmas, Vol. 22, Issue 6 https://doi.org/10.1063/1.4922080	journal	June 2015
Electron heating in capacitively coupled plasmas revisited Lafleur, T.; Chabert, P.; Booth, J. P. Plasma Sources Science and Technology, Vol. 23, Issue 3 https://doi.org/10.1088/0963-0252/23/3/035010	journal	May 2014
Formation and Stability of Impurity “Snakes” in Tokamak Plasmas Delgado-Aparicio, L.; Sugiyama, L.; Granetz, R. Physical Review Letters, Vol. 110, Issue 6 https://doi.org/10.1103/PhysRevLett.110.065006	journal	February 2013
Nonlinear series resonance and standing waves in dual-frequency capacitive discharges Wen, De-Qi; Kawamura, E.; Lieberman, M. A. Plasma Sources Science and Technology, Vol. 26, Issue 1 https://doi.org/10.1088/0963-0252/26/1/015007	journal	November 2016
Anomalous Skin Effect in Bounded Plasmas Reynolds, J. A.; Blevin, H. A.; Thonemann, P. C. Physical Review Letters, Vol. 22, Issue 15 https://doi.org/10.1103/PhysRevLett.22.762	journal	April 1969
Self-excitation of the plasma series resonance in radio-frequency discharges: An analytical description Czarnetzki, U.; Mussenbrock, T.; Brinkmann, R. P. Physics of Plasmas, Vol. 13, Issue 12 https://doi.org/10.1063/1.2397043	journal	December 2006
Low power density multihole cathode very-high-frequency plasma for mixed phase Si:H thin films Jariwala, C.; Chainani, A.; Eguchi, R. Applied Physics Letters, Vol. 93, Issue 19 https://doi.org/10.1063/1.3023066	journal	November 2008
Effect of driving frequency on the electron energy distribution function and electron-sheath interaction in a low pressure capacitively coupled plasma Sharma, S.; Sirse, N.; Kaw, P. K. Physics of Plasmas, Vol. 23, Issue 11 https://doi.org/10.1063/1.4967356	journal	November 2016
Spatial and frequency dependence of plasma currents in a 300 mm capacitively coupled plasma reactor Miller, Paul A.; Barnat, Edward V.; Hebner, Gregory A. Plasma Sources Science and Technology, Vol. 15, Issue 4 https://doi.org/10.1088/0963-0252/15/4/036	journal	October 2006
Direct measurement of spatial electron density oscillations in a dual frequency capacitive plasma Karkari, S. K.; Ellingboe, A. R.; Gaman, C. Applied Physics Letters, Vol. 93, Issue 7 https://doi.org/10.1063/1.2971236	journal	August 2008
Nonlinear standing wave excitation by series resonance-enhanced harmonics in low pressure capacitive discharges Lieberman, M. A.; Lichtenberg, A. J.; Kawamura, E. Plasma Sources Science and Technology, Vol. 24, Issue 5 https://doi.org/10.1088/0963-0252/24/5/055011	journal	August 2015
Frequency dependent plasma characteristics in a capacitively coupled 300 mm wafer plasma processing chamber Hebner, Gregory A.; Barnat, Edward V.; Miller, Paul A. Plasma Sources Science and Technology, Vol. 15, Issue 4 https://doi.org/10.1088/0963-0252/15/4/035	journal	October 2006
Pressure Heating of Electrons in Capacitively Coupled rf Discharges Turner, M. M. Physical Review Letters, Vol. 75, Issue 7 https://doi.org/10.1103/PhysRevLett.75.1312	journal	August 1995
Fast magnetic fluctuation diagnostics for Alfvén eigenmode and magnetohydrodynamics studies at the Joint European Torus Heeter, R. F.; Fasoli, A. F.; Ali-Arshad, S. Review of Scientific Instruments, Vol. 71, Issue 11 https://doi.org/10.1063/1.1313797	journal	January 2000
Electromagnetic field nonuniformities in large area, high-frequency capacitive plasma reactors, including electrode asymmetry effects Sansonnens, L.; Howling, A. A.; Hollenstein, Ch Plasma Sources Science and Technology, Vol. 15, Issue 3 https://doi.org/10.1088/0963-0252/15/3/002	journal	March 2006
A sandwich-like differential B-dot based on EACVD polycrystalline diamond slice Xu, P.; Yu, Y.; Xu, L. Applied Physics Letters, Vol. 112, Issue 24 https://doi.org/10.1063/1.5026614	journal	June 2018
Hysteresis and the E-to-H transition in radiofrequency inductive discharges Turner, M. M.; Lieberman, M. A. Plasma Sources Science and Technology, Vol. 8, Issue 2 https://doi.org/10.1088/0963-0252/8/2/312	journal	January 1999
Helicons in Unbounded Plasmas Stenzel, R. L.; Urrutia, J. M. Physical Review Letters, Vol. 114, Issue 20 https://doi.org/10.1103/PhysRevLett.114.205005	journal	May 2015
Low-frequency, high-density, inductively coupled plasma sources: Operation and applications Xu, S.; Ostrikov, K. N.; Li, Y. Physics of Plasmas, Vol. 8, Issue 5 https://doi.org/10.1063/1.1343887	journal	May 2001
Self-consistent nonlinear transmission line model of standing wave effects in a capacitive discharge Chabert, P.; Raimbault, J. L.; Rax, J. M. Physics of Plasmas, Vol. 11, Issue 5 https://doi.org/10.1063/1.1688334	journal	May 2004
Electron heating mode transition observed in a very high frequency capacitive discharge Abdel-Fattah, E.; Sugai, H. Applied Physics Letters, Vol. 83, Issue 8 https://doi.org/10.1063/1.1604941	journal	August 2003
Standing wave and skin effects in large-area, high-frequency capacitive discharges Lieberman, M. A.; Booth, J. P.; Chabert, P. Plasma Sources Science and Technology, Vol. 11, Issue 3 https://doi.org/10.1088/0963-0252/11/3/310	journal	June 2002
Negative Power Absorption in Inductively Coupled Plasma Godyak, V. A.; Kolobov, V. I. Physical Review Letters, Vol. 79, Issue 23 https://doi.org/10.1103/PhysRevLett.79.4589	journal	December 1997
A new B-dot probe circuit for magnetic diagnostics of radio frequency discharges Zhao, Kai; Liu, Yong-Xin; Wen, De-Qi Review of Scientific Instruments, Vol. 89, Issue 10 https://doi.org/10.1063/1.5041814	journal	October 2018
Modeling electromagnetic effects in capacitive discharges Lee, Insook; Graves, D. B.; Lieberman, M. A. Plasma Sources Science and Technology, Vol. 17, Issue 1 https://doi.org/10.1088/0963-0252/17/1/015018	journal	February 2008
Experimental investigation of standing wave effect in dual-frequency capacitively coupled argon discharges: role of a low-frequency source Zhao, Kai; Liu, Yong-Xin; Kawamura, E. Plasma Sources Science and Technology, Vol. 27, Issue 5 https://doi.org/10.1088/1361-6595/aac242	journal	May 2018
RF discharge diagnostics: Some problems and their resolution Godyak, Valery Journal of Applied Physics, Vol. 129, Issue 4 https://doi.org/10.1063/5.0024258	journal	January 2021
The anomalous skin effect in gas discharge plasmas Kolobov, V. I.; Economou, D. J. Plasma Sources Science and Technology, Vol. 6, Issue 2 https://doi.org/10.1088/0963-0252/6/2/003	journal	May 1997
Measurement of spatial and temporal evolution of electromagnetic fields in a 100 MHz plasma source using B dot and double dipole probes Lane, Barton; Campbell, Colin; Sawada, Ikuo Journal of Vacuum Science & Technology A: Vacuum, Surfaces, and Films, Vol. 34, Issue 3 https://doi.org/10.1116/1.4943586	journal	May 2016
Enhancement of Ohmic and Stochastic Heating by Resonance Effects in Capacitive Radio Frequency Discharges: A Theoretical Approach Mussenbrock, T.; Brinkmann, R. P.; Lieberman, M. A. Physical Review Letters, Vol. 101, Issue 8 https://doi.org/10.1103/PhysRevLett.101.085004	journal	August 2008
Electromagnetic effects in high-frequency capacitive discharges used for plasma processing Chabert, P. Journal of Physics D: Applied Physics, Vol. 40, Issue 3 https://doi.org/10.1088/0022-3727/40/3/R01	journal	January 2007
Experimental investigations of the plasma radial uniformity in single and dual frequency capacitively coupled argon discharges Zhao, Kai; Liu, Yong-Xin; Gao, Fei Physics of Plasmas, Vol. 23, Issue 12 https://doi.org/10.1063/1.4971782	journal	December 2016
Ion energy uniformity in high-frequency capacitive discharges Perret, A.; Chabert, P.; Jolly, J. Applied Physics Letters, Vol. 86, Issue 2 https://doi.org/10.1063/1.1848183	journal	January 2005
Disparity between current and voltage driven capacitively coupled radio frequency discharges Wilczek, S.; Trieschmann, J.; Schulze, J. Plasma Sources Science and Technology, Vol. 27, Issue 12 https://doi.org/10.1088/1361-6595/aae5c1	journal	December 2018
Electron dynamics in low pressure capacitively coupled radio frequency discharges Wilczek, S.; Schulze, J.; Brinkmann, R. P. Journal of Applied Physics, Vol. 127, Issue 18 https://doi.org/10.1063/5.0003114	journal	May 2020
Experimental setup and electrical characteristics of an inductively coupled plasma Godyak, V. A.; Piejak, R. B.; Alexandrovich, B. M. Journal of Applied Physics, Vol. 85, Issue 2 https://doi.org/10.1063/1.369150	journal	January 1999
Standing Helicon Wave Induced by a Rapidly Bent Magnetic Field in Plasmas Takahashi, Kazunori; Takayama, Sho; Komuro, Atsushi Physical Review Letters, Vol. 116, Issue 13 https://doi.org/10.1103/PhysRevLett.116.135001	journal	March 2016
Ion flux nonuniformities in large-area high-frequency capacitive discharges Perret, A.; Chabert, P.; Booth, J. -P. Applied Physics Letters, Vol. 83, Issue 2 https://doi.org/10.1063/1.1592617	journal	July 2003
Observation of Nonlinear Standing Waves Excited by Plasma-Series-Resonance-Enhanced Harmonics in Capacitive Discharges Zhao, Kai; Wen, De-Qi; Liu, Yong-Xin Physical Review Letters, Vol. 122, Issue 18 https://doi.org/10.1103/PhysRevLett.122.185002	journal	May 2019
Collisionless electron heating by radio frequency bias in low gas pressure inductive discharge Lee, Hyo-Chang; Chung, Chin-Wook Applied Physics Letters, Vol. 101, Issue 24 https://doi.org/10.1063/1.4770312	journal	December 2012
Simulations of electromagnetic effects in high-frequency capacitively coupled discharges using the Darwin approximation Eremin, Denis; Hemke, Torben; Brinkmann, Ralf Peter Journal of Physics D: Applied Physics, Vol. 46, Issue 8 https://doi.org/10.1088/0022-3727/46/8/084017	journal	February 2013
Moment analysis of rf parallel-plate-discharge simulations using the particle-in-cell with Monte Carlo collisions technique Surendra, M.; Dalvie, M. Physical Review E, Vol. 48, Issue 5 https://doi.org/10.1103/PhysRevE.48.3914	journal	November 1993
Three-dimensional measurements of plasma parameters in an inductively coupled plasma processing chamber Han, Jia; Pribyl, Patrick; Gekelman, Walter Physics of Plasmas, Vol. 26, Issue 10 https://doi.org/10.1063/1.5115415	journal	October 2019
Prevention of ion flux lateral inhomogeneities in large area capacitive radio frequency plasmas via the electrical asymmetry effect Schüngel, Edmund; Mohr, Sebastian; Schulze, Julian Applied Physics Letters, Vol. 106, Issue 5 https://doi.org/10.1063/1.4907887	journal	February 2015
Measurement and identification of azimuthal current in an RF plasma thruster employing a time-varying magnetic field Sekine, H.; Koizumi, H.; Komurasaki, K. AIP Advances, Vol. 11, Issue 1 https://doi.org/10.1063/5.0029492	journal	January 2021
Relationship between center-peaked plasma density profiles and harmonic electromagnetic waves in very high frequency capacitively coupled plasma reactors Sawada, Ikuo; Ventzek, Peter L. G.; Lane, Barton Japanese Journal of Applied Physics, Vol. 53, Issue 3S2 https://doi.org/10.7567/JJAP.53.03DB01	journal	January 2014

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Title: Magnetic probe diagnostics of nonlinear standing waves and bulk ohmic electron power absorption in capacitive discharges

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