The breakdown process of capacitively coupled plasma (CCP) in the presence of a matching network is rarely studied, even though it is the indispensable part of the most laboratory and industrial devices of CCP. Based on the method of Verboncoeur, the solution method of the general “L”-type match circuit coupled with a particle-in-cell/Monte Carlo code is deduced self-consistently. Based on this method, the electrical breakdown process of CCP is studied. Both the plasma parameters and the electric parameters of the matching network during the breakdown are given and analyzed. In the pre-breakdown phase, the entire circuit can be considered as a linear system. However, the formation of the sheath during breakdown significantly enhanced the capacitance of the discharge chamber, which changed the electric signal amplitude of the external circuit. With the stabilization of plasma, the equivalent capacitance of CCP increases, which continues to change the electrical signal until the steady-state is reached. Accompanied by plasma stabilization is the appearance of high-order harmonics of discharge current caused by the gradually oscillating CCP capacitance. The breakdown characteristics can be obviously affected by the capacitance of the matching network. In the case of a breakdown zone, some breakdowns with special characteristics can be obtained by choosing the different capacitors. These works might be a reference for understanding the interaction between the plasma and the external circuit during the breakdown process and how to modulate the gas breakdown by controlling the external circuit.

1.
M. A.
Lieberman
and
A. J.
Lichtenberg
,
Principles of Plasma Discharges and Materials Processing
, 2nd ed. (
Wiley-Interscience
,
Hoboken
,
2005
).
2.
F.
Schmidt
,
T.
Mussenbrock
, and
J.
Trieschmann
, “
Consistent simulation of capacitive radio-frequency discharges and external matching networks
,”
Plasma Sources Sci. Technol.
27
,
105017
(
2018
).
3.
J. S.
Townsend
,
Electricity in Gases
(
Clarendon Press
,
1915
).
4.
D.
Vender
,
H.
Smith
, and
R.
Boswell
, “
Simulations of multipactor-assisted breakdown in radio frequency plasmas
,”
J. Appl. Phys.
80
,
4292
4298
(
1996
).
5.
H.
Wu
,
Y.
Zhou
,
J.
Gao
,
Y.
Peng
,
Z.
Wang
, and
W.
Jiang
, “
Electrical breakdown in dual-frequency capacitively coupled plasma: A collective simulation
,”
Plasma Sources Sci. Technol.
30
,
065029
(
2021
).
6.
X.-Y.
Wang
,
J.-R.
Liu
,
Y.-X.
Liu
,
Z.
Donkó
,
Q.-Z.
Zhang
,
K.
Zhao
,
J.
Schulze
, and
Y.-N.
Wang
, “
Comprehensive understanding of the ignition process of a pulsed capacitively coupled radio frequency discharge: The effect of power-off duration
,”
Plasma Sources Sci. Technol.
30
,
075011
(
2021
).
7.
V.
Lisovsky
and
V.
Yegorenkov
, “
Low-pressure gas breakdown in combined fields
,”
J. Phys. D: Appl. Phys.
27
,
2340
(
1994
).
8.
M.
Sato
and
M.
Shoji
, “
Breakdown characteristics of rf argon capacitive discharge
,”
Jpn. J. Appl. Phys.
36
,
5729
(
1997
).
9.
V.
Lisovskiy
and
V.
Yegorenkov
, “
Rf breakdown of low-pressure gas and a novel method for determination of electron-drift velocities in gases
,”
J. Phys. D: Appl. Phys.
31
,
3349
(
1998
).
10.
V. A.
Lisovskiy
and
V. D.
Yegorenkov
, “
Electron-drift velocity determination in CF4 and SF6 in a strong electric field from breakdown curves of low-pressure RF discharge
,”
J. Phys. D: Appl. Phys.
32
,
2645
(
1999
).
11.
H.
Smith
,
C.
Charles
, and
R.
Boswell
, “
Breakdown behavior in radio-frequency argon discharges
,”
Phys. Plasmas
10
,
875
881
(
2003
).
12.
I.
Korolov
,
A.
Derzsi
, and
Z.
Donkó
, “
Experimental and kinetic simulation studies of radio-frequency and direct-current breakdown in synthetic air
,”
J. Phys. D: Appl. Phys.
47
,
475202
(
2014
).
13.
V. A.
Lisovskiy
,
V. A.
Derevianko
, and
V. D.
Yegorenkov
, “
DC breakdown in low-pressure CF4
,”
J. Phys. D: Appl. Phys.
48
,
475201
(
2015
).
14.
Y.
Fu
,
S.
Yang
,
X.
Zou
,
H.
Luo
, and
X.
Wang
, “
Effect of distribution of electric field on low-pressure gas breakdown
,”
Phys. Plasmas
24
,
023508
(
2017
).
15.
Y.
Fu
,
P.
Zhang
,
J. P.
Verboncoeur
, and
X.
Wang
, “
Electrical breakdown from macro to micro/nano scales: A tutorial and a review of the state of the art
,”
Plasma Res. Express
2
,
013001
(
2020
).
16.
Y.-X.
Liu
,
X.-Y.
Wang
,
Q.-Z.
Zhang
,
Z.
Donkó
,
K.
Zhao
,
J.
Schulze
, and
Y.-N.
Wang
, “
Avalanche induced rapid impedance change and electron power absorption during gas breakdown under radio-frequency excitation
,”
Plasma Sources Sci. Technol.
29
12LT03
(
2020
).
17.
Y.
Deng
,
X.
Han
,
S.
ur Rehman
, and
Y.
Liu
, “
Modeling characteristics of nonequilibrium processes during breakdown of capacitive RF argon glow discharge
,”
Phys. Plasmas
15
,
053507
(
2008
).
18.
J.
Gao
,
H.
Wu
,
S.
Yu
,
Z.
Chen
,
Z.
Wang
,
W.
Jiang
, and
Y.
Pan
, “
Computational analysis of direct current breakdown process in SF6 at low pressure
,”
J. Phys. D: Appl. Phys.
54
,
445201
(
2021
).
19.
W. S.
Lawson
, “
The pierce diode with an external circuit. I. Oscillations about nonuniform equilibria
,”
Phys. Fluids B
1
,
1483
1492
(
1989
).
20.
J. P.
Verboncoeur
,
M. V.
Alves
,
V.
Vahedi
, and
C. K.
Birdsall
, “
Simultaneous potential and circuit solution for 1D bounded plasma particle simulation codes
,”
J. Comput. Phys.
104
,
321
328
(
1993
).
21.
V.
Vahedi
and
G.
DiPeso
, “
Simultaneous potential and circuit solution for two-dimensional bounded plasma simulation codes
,”
J. Comput. Phys.
131
,
149
163
(
1997
).
22.
E.
Bultinck
,
I.
Kolev
,
A.
Bogaerts
, and
D.
Depla
, “
The importance of an external circuit in a particle-in-cell/Monte Carlo collisions model for a direct current planar magnetron
,”
J. Appl. Phys.
103
,
013309
(
2008
).
23.
M.
Jiang
,
L.
Yongdong
,
H.
Wang
,
W.
Ding
, and
C.
Liu
, “
3D PIC-MCC simulation of corona discharge in needle-plate electrode with external circuit
,”
Plasma Sources Sci. Technol.
29
,
015020
(
2020
).
24.
M. M.
Salem
,
J.-F.
Loiseau
, and
B.
Held
, “
Impedance matching for optimization of power transfer in a capacitively excited RF plasma reactor
,”
Eur. Phys. J. Appl. Phys.
3
,
91
95
(
1998
).
25.
S.
Rauf
and
M. J.
Kushner
, “
The effect of radio frequency plasma processing reactor circuitry on plasma characteristics
,”
J. Appl. Phys.
83
,
5087
5094
(
1998
).
26.
A.
Metze
,
D.
Ernie
, and
H.
Oskam
, “
Application of the physics of plasma sheaths to the modeling of rf plasma reactors
,”
J. Appl. Phys.
60
,
3081
3087
(
1986
).
27.
M.
Lieberman
,
A.
Lichtenberg
,
E.
Kawamura
,
T.
Mussenbrock
, and
R. P.
Brinkmann
, “
The effects of nonlinear series resonance on ohmic and stochastic heating in capacitive discharges
,”
Phys. Plasmas
15
,
063505
(
2008
).
28.
T.
Mussenbrock
,
R.
Brinkmann
,
M.
Lieberman
,
A.
Lichtenberg
, and
E.
Kawamura
, “
Enhancement of ohmic and stochastic heating by resonance effects in capacitive radio frequency discharges: A theoretical approach
,”
Phys. Rev. Lett.
101
,
085004
(
2008
).
29.
F.
Schmidt
,
J.
Trieschmann
,
T.
Gergs
, and
T.
Mussenbrock
, “
A generic method for equipping arbitrary RF discharge simulation frameworks with external lumped element circuits
,”
J. Appl. Phys.
125
,
173106
(
2019
).
30.
M. J.
Kushner
, “
Hybrid modelling of low temperature plasmas for fundamental investigations and equipment design
,”
J. Phys. D: Appl. Phys.
42
,
194013
(
2009
).
31.
C.
Qu
,
S. J.
Lanham
,
S. C.
Shannon
,
S. K.
Nam
, and
M. J.
Kushner
, “
Power matching to pulsed inductively coupled plasmas
,”
J. Appl. Phys.
127
,
133302
(
2020
).
32.
Y.
Yamazawa
,
M.
Nakaya
,
M.
Iwata
, and
A.
Shimizu
, “
Control of the harmonics generation in a capacitively coupled plasma reactor
,”
Jpn. J. Appl. Phys.
46
,
7453
(
2007
).
33.
N.
Sirse
,
M.
Jeon
,
G.
Yeom
, and
A.
Ellingboe
, “
Temporal evolution of electron density in a low pressure pulsed two-frequency (60 MHz/2 MHz) capacitively coupled plasma discharge
,”
Plasma Sources Sci. Technol.
23
,
065046
(
2014
).
34.
Y.
Yamazawa
, “
Electrode impedance effect in dual-frequency capacitively coupled plasma
,”
Plasma Sources Sci. Technol.
24
,
034015
(
2015
).
35.
K. H.
Baek
,
E.
Lee
,
M.
Klick
, and
R.
Rothe
, “
Comprehensive understanding of chamber conditioning effects on plasma characteristics in an advanced capacitively coupled plasma etcher
,”
J. Vac. Sci. Technol. A
35
,
021304
(
2017
).
36.
A.
Al Bastami
,
A.
Jurkov
,
P.
Gould
,
M.
Hsing
,
M.
Schmidt
,
J.-I.
Ha
, and
D. J.
Perreault
, “
Dynamic matching system for radio-frequency plasma generation
,”
IEEE Trans. Power Electron.
33
,
1940
1951
(
2018
).
37.
K.
Hernandez
,
L. J.
Overzet
, and
M. J.
Goeckner
, “
Electron dynamics during the reignition of pulsed capacitively-coupled radio-frequency discharges
,”
J. Vac. Sci. Technol. B
38
,
034005
(
2020
).
38.
K.
Hernandez
,
A.
Press
,
M. J.
Goeckner
, and
L. J.
Overzet
, “
Optical emission intensity overshoot and electron heating mechanisms during the re-ignition of pulsed capacitively coupled ar plasmas
,”
J. Vac. Sci. Technol. B
39
,
024003
(
2021
).
39.
B. G.
Heil
,
U.
Czarnetzki
,
R. P.
Brinkmann
, and
T.
Mussenbrock
, “
On the possibility of making a geometrically symmetric RF-CCP discharge electrically asymmetric
,”
J. Phys. D: Appl. Phys.
41
,
165202
(
2008
).
40.
T.
Lafleur
,
P.-A.
Delattre
,
E.
Johnson
, and
J.-P.
Booth
, “
Separate control of the ion flux and ion energy in capacitively coupled radio-frequency discharges using voltage waveform tailoring
,”
Appl. Phys. Lett.
101
,
124104
(
2012
).
41.
J.
Franek
,
S.
Brandt
,
B.
Berger
,
M.
Liese
,
M.
Barthel
,
E.
Schüngel
, and
J.
Schulze
, “
Power supply and impedance matching to drive technological radio-frequency plasmas with customized voltage waveforms
,”
Rev. Sci. Instrum.
86
,
053504
(
2015
).
42.
F.
Schmidt
,
J.
Schulze
,
E.
Johnson
,
J.-P.
Booth
,
D.
Keil
,
D. M.
French
,
J.
Trieschmann
, and
T.
Mussenbrock
, “
Multi frequency matching for voltage waveform tailoring
,”
Plasma Sources Sci. Technol.
27
,
095012
(
2018
).
43.
J.
Wang
,
S.
Diné
,
J.-P.
Booth
, and
E. V.
Johnson
, “
Experimental demonstration of multifrequency impedance matching for tailored voltage waveform plasmas
,”
J. Vac. Sci. Technol. A
37
,
021303
(
2019
).
44.
P.
Boyle
,
A.
Ellingboe
, and
M.
Turner
, “
Electrostatic modelling of dual frequency RF plasma discharges
,”
Plasma Sources Sci. Technol.
13
,
493
(
2004
).
45.
E.
Schüngel
,
D.
Eremin
,
J.
Schulze
,
T.
Mussenbrock
, and
U.
Czarnetzki
, “
The electrical asymmetry effect in geometrically asymmetric capacitive radio frequency plasmas
,”
J. Appl. Phys.
112
,
053302
(
2012
).
46.
Q.-Z.
Zhang
,
S.-X.
Zhao
,
W.
Jiang
, and
Y.-N.
Wang
, “
Separate control between geometrical and electrical asymmetry effects in capacitively coupled plasmas
,”
J. Phys. D: Appl. Phys.
45
,
305203
(
2012
).
47.
I.
Korolov
,
Z.
Donkó
,
U.
Czarnetzki
, and
J.
Schulze
, “
The effect of the driving frequencies on the electrical asymmetry of dual-frequency capacitively coupled plasmas
,”
J. Phys. D: Appl. Phys.
45
,
465205
(
2012
).
48.
Z.
Donkó
,
J.
Schulze
,
B.
Heil
, and
U.
Czarnetzki
, “
PIC simulations of the separate control of ion flux and energy in CCRF discharges via the electrical asymmetry effect
,”
J. Phys. D: Appl. Phys.
42
,
025205
(
2009
).
49.
J.
Schulze
,
E.
Schüngel
, and
U.
Czarnetzki
, “
The electrical asymmetry effect in capacitively coupled radio frequency discharges–measurements of dc self bias, ion energy and ion flux
,”
J. Phys. D: Appl. Phys.
42
,
092005
(
2009
).
50.
J.
Schulze
,
E.
Schüngel
,
U.
Czarnetzki
, and
Z.
Donkó
, “
Optimization of the electrical asymmetry effect in dual-frequency capacitively coupled radio frequency discharges: Experiment, simulation, and model
,”
J. Appl. Phys.
106
,
063307
(
2009
).
51.
J.
Gao
,
S.
Yu
,
H.
Wu
,
Y.
Wang
,
Z.
Wang
,
Y.
Pan
,
W.
Jiang
, and
Y.
Zhang
, “
Self-consistent simulation of the impedance matching network for single frequency capacitively coupled plasma
,”
J. Phys. D: Appl. Phys.
55
,
165201
(
2022
).
52.
A. L.
Garner
,
G.
Meng
,
Y.
Fu
,
A. M.
Loveless
,
R. S.
Brayfield
, and
A. M.
Darr
, “
Transitions between electron emission and gas breakdown mechanisms across length and pressure scales
,”
J. Appl. Phys.
128
,
210903
(
2020
).
53.
M.
Radmilović-Radjenović
and
J.
Lee
, “
Modeling of breakdown behavior in radio-frequency argon discharges with improved secondary emission model
,”
Phys. Plasmas
12
,
063501
(
2005
).
54.
B.
Horváth
,
M.
Daksha
,
I.
Korolov
,
A.
Derzsi
, and
J.
Schulze
, “
The role of electron induced secondary electron emission from SiO2 surfaces in capacitively coupled radio frequency plasmas operated at low pressures
,”
Plasma Sources Sci. Technol.
26
,
124001
(
2017
).
55.
B.
Horváth
,
J.
Schulze
,
Z.
Donkó
, and
A.
Derzsi
, “
The effect of electron induced secondary electrons on the characteristics of low-pressure capacitively coupled radio frequency plasmas
,”
J. Phys. D: Appl. Phys.
51
,
355204
(
2018
).
56.
V.
Georgieva
,
Computer Modeling of Low-Pressure Fluorocarbon-Based Discharges for Etching Purposes
(
Universiteit Antwerpen
,
Belgium
,
2006
).
57.
M. M.
Turner
,
A.
Derzsi
,
Z.
Donko
,
D.
Eremin
,
S. J.
Kelly
,
T.
Lafleur
, and
T.
Mussenbrock
, “
Simulation benchmarks for low-pressure plasmas: Capacitive discharges
,”
Phys. Plasmas
20
,
013507
(
2013
).
58.
W.
Hong-Yu
,
S.
Peng
,
J.
Wei
,
Z.
Jie
, and
X.
Bai-Song
, “
Implicit electrostatic particle-in-cell/Monte Carlo simulation for the magnetized plasma: Algorithms and application in gas-inductive breakdown
,”
Chin. Phys. B
24
,
065207
(
2015
).
59.
V.
Vahedi
,
G.
DiPeso
,
C.
Birdsall
,
M.
Lieberman
, and
T.
Rognlien
, “
Capacitive rf discharges modelled by particle-in-cell Monte Carlo simulation. I. Analysis of numerical techniques
,”
Plasma Sources Sci. Technol.
2
,
261
(
1993
).
60.
E.
Kawamura
,
C. K.
Birdsall
, and
V.
Vahedi
, “
Physical and numerical methods of speeding up particle codes and paralleling as applied to RF discharges
,”
Plasma Sources Sci. Technol.
9
,
413
(
2000
).
61.
H.-Y.
Wang
,
W.
Jiang
, and
Y.-N.
Wang
, “
Implicit and electrostatic particle-in-cell/Monte Carlo model in two-dimensional and axisymmetric geometry: I. Analysis of numerical techniques
,”
Plasma Sources Sci. Technol.
19
,
045023
(
2010
).
62.
V.
Vahedi
and
M.
Surendra
, “
A Monte Carlo collision model for the particle-in-cell method: Applications to argon and oxygen discharges
,”
Comput. Phys. Commun.
87
,
179
198
(
1995
).
63.
K.
Nanbu
,
K.
Mitsui
, and
S.
Kondo
, “
Self-consistent particle modelling of DC magnetron discharges of an O2/Ar mixture
,”
J. Phys. D: Appl. Phys.
33
,
2274
(
2000
).
64.
A.
Phelps
and
Z. L.
Petrovic
, “
Cold-cathode discharges and breakdown in argon: Surface and gas phase production of secondary electrons
,”
Plasma Sources Sci. Technol.
8
,
R21
(
1999
).
65.
A. C.
Hindmarsh
,
P. N.
Brown
,
K. E.
Grant
,
S. L.
Lee
,
R.
Serban
,
D. E.
Shumaker
, and
C. S.
Woodward
, “
Sundials: Suite of nonlinear and differential/algebraic equation solvers
,”
ACM Trans. Math. Softw. (TOMS)
31
,
363
396
(
2005
).
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