22nd International Symposium on Plasma Chemistry
July 5-10, 2015; Antwerp, Belgium
Numerical simulation of a direct-current argon microhollow cathode discharge
Y.-X. Wu and H.-X. Wang
School of Astronautics, Beihang University, Beijing, P.R. China
Abstract: A numerical simulation has been performed of a direct-current argon plasma
discharge in a microhollow cathode. The result shows that there exists significant
discharge activity outside of the hollow region. The discharge volume and intensity
increases with the increase of current and becomes more confined with increasing pressures.
Most predictions presented in this paper are in qualitative and quantitative agreement with
experimental data for MHCD’s under similar conditions.
Keywords: MHCD, high-pressure glow discharge, current-voltage characteristic curve
1. Introduction
Microdischarges have received wide attention for a
variety of applications including photonics, environmental
applications, chemical analysis, and micropropulsion over
the past decade. A number of microdischarge geometric
configurations, such as pin electrode[1], parallel-plate
electrode[2], microhollow cathode[3], and pyramidal
electrode[4], have been intensively studied. The
microhollow
cathode
(MHC)
refers
to
a
metal/dielectric/metal sandwich structure in which a
through hole is drilled. The thickness of the sandwich
layers and the diameter of the hole is on the orders tens to
hundreds of micrometers. Reasonably low breakdown
voltages and immunity to glow-to-arc transition
instabilities can be achieved by high pressures (tens to
hundreds of Torr) that maintain the nominal pressurelength (pD) scaling characteristic of classical glow
discharges.
Microhollow cathode discharge (MHCD) exhibits a rich
variety of operational modes depending on geometry and
operating conditions. With the increase of current, the
discharge mode turns from Townsend mode to abnormal
glow in MHCD. Although some examples of
experimental diagnostic studies have been reported, the
small geometric dimensions in MHCD’s have limited
detailed quantitative experimental diagnostic studies of
their properties. In this paper, we study an argon MHCD
with an emphasis on understanding different operating
conditions of the discharge to address basic plasma
phenomena in a MHCD configuration. Necessary
physical modeling approximations required to properly
address microdischarge phenomena are discussed.
Predicted results are compared to experimental data.
by the respective energy equation. The self-consistent
electric potential is determined using the electrostatic
Poisson’s equation.
In this study, the plasma is consider to contain electrons
(e), atomic argon ions (Ar+), molecular argon ions (Ar 2 +),
electronically excited atoms (Ar*), electronically excited
molecules (Ar 2 *), and the background argon atoms (Ar).
At the surfaces all excited species and charged species are
assumed to get quenched with unity sticking coefficient.
The list of reactions considered in the study is given in
Table 1.
2. Model Description
The discharge model used in this paper is based on a
two-dimensional, self-consistent multi-species, multitemperature, continuum (fluid) description of the plasma.
The electron density and mean electron energy are
computed by solving a pair of drift-diffusion equations for
the electron density and mean electron energy. The gas
temperature and the electron temperature are determined
3. Results
The cylindrically symmetric geometry of the MHCD
used in this study is similar to that presented by Aubert et
al[9], with a hole radius of 100μm, metal foils (electrodes)
of thickness 100 μm, and a dielectric layer thickness of
50μm.
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Table 1. Reactions used in simulation.
#
Reactions
Reaction rate a)
Ref.
G1
e+Ar→e+Ar
b)
[7]
G2
e+Ar→e+Ar*
b)
[7]
G3
e+Ar→2e+Ar+
b)
[7]
G4
e+Ar*→2e+Ar+
b)
[7]
G5
e+Ar*→e+Ar
b)
[7]
G6
e+Ar+→Ar*
4.0×10-13T e -0.5 (cm3∙s-1)
[8]
G7
2e+Ar+→Ar*+e
5.0×10-27T e -4.7 (cm6∙s-1)
[8]
G8
e+Ar 2 +→Ar*+Ar
5.38×10-8T e -0.66 (cm3∙s-1)
[8]
G9
2Ar*→Ar*+Ar+e
5.0×10-10 (cm3∙s-1)
[8]
G10
2Ar 2 *→Ar 2 ++2Ar+e
5.0×10-10 (cm3∙s-1)
[8]
G11
Ar*+2Ar→Ar 2 *+Ar
1.14×10-32 (cm6∙s-1)
[8]
G12
Ar++2Ar→Ar 2 ++Ar
2.5×10-31 (cm6∙s-1)
[8]
G13
Ar 2 *→2Ar
6.0×107 (s-1)
[8]
G14
e+Ar 2 →2e+Ar 2
9.0×10-88T e 0.7exp(-3.66/T e )
(cm3∙s-1)
[8]
*
+
G15
e+Ar 2 →e+2Ar
10 (cm ∙s )
[8]
The electron temperature ,T e , is in eV.
b)
Tabulated rate coefficient as a function of mean electron temperature was
obtained by the Boltzmann equation solver “BOLSIG+”.
*
-7
3 -1
a)
1
The overall current-voltage (I-V) characteristics of the
MHCD discharge is presented in Fig.1. Two pressures of
150 and 300 Torr (pD=3 and 6 Torr∙cm) over a current
range of about 0.3~3mA are shown. The predicted I-V
characteristics are compared to the experimental data
presented in Figure. 1 of the paper by Aubert et al[9]. The
result with a constant secondary electron emission
coefficient of 0.07 fails to predict the normal regime,
thereby emphasizing the role of proper secondary electron
emission processes in the MHCD phenomena.
350
Self-pulsing I
_______________
<
300
I
150Torr (expt.) I
Normal
I _____________________________
>
250
Vd , V
I
I
150Torr
B
I
A
200
C
300Torr
150
150Torr,γ=0.07
100
0
1
2
3
I , mA
Fig. 1. Comparison of experimental and simulated
current-voltage (I-V) characteristics of the MHCD.
Quantities, as electric potential, Monomer ion Ar+ and
dimer ion Ar 2 + number density, Monomer metastable
species Ar* and dimer metastable species Ar 2 * number
density, electron temperature and gas temperature, net
volumetric generation rate of electrons, are also predicted
respectively.
4. Conclusions
In conclusion, microdischarge phenomena in an argon
microhollow cathode discharge (MHCD) is investigated
using a two-dimensional fluid computational model. For
the range of pressures (150~300 Torr) and discharge
current (0.3~3 mA) conditions studied, the MHCD
operates in a normal direct-current glow discharge mode,
with distinct sheath and bulk plasma structures. The
discharge is characterized by significant gas heating. In
general, the discharge volume and intensity increases with
an increase in the current. As the pressure is increased the
discharge gets more confined within the hollow region,
owing to an overall decrease in the magnitude of all the
transport properties. For sufficiently large currents at
relatively low pressure, a significant part of the discharge
volume lies outside the hollow structure with the plasma
occupying a region of a few hollow diameters above the
flat cathode surface plane, which is confirmed by
experimental data available in the literature.
Table 2. Operating condition for three cases discussed in this study.
Case
Pressure
(Torr)
PD
(Torr∙cm)
Current
(mA)
Voltage
(V)
A
150
3
0.52
193
B
150
3
1.39
206
C
300
6
1.40
194
The working parameters used in this study are listed in
Table 2. The computed electron number density
distribution is shown in Fig. 2. In all cases, a peak in the
electron density is observed at the centerline of the
discharge within the hollow cathode region. A second
peak appears outside the hollow for the lower pressure
cases in the normal regime. The extent of the plasma
volume outside the hollow increases with increase in
current at a constant pressure.
(B)
(A)
1.3×1019
(C)
6.5×1018
2.4×10
6.5×1019
1.3×1020
19
2.4×1020
5. References
[1] K. Terashima, L. Howard, H. Haefka, and H.J.
Guntherodt, Thin Solid Films, 281-282, 634-636 (1996).
[2] O. B. Postel and M. A. Cappelli, J. Appl. Phys., 89,
4719 (2001)
[3] R. H. Stark and K. H. Schoenback, J. Appl. Phys. 85,
2075 (1999)
[4] S.J. Park, J. Chen, C. J. Wagner, N. P. Ostrom, C. Liu,
and J. G. Eden, IEEE J. Sel. Top. Quantum Electron., 8,
139 (2002)
[5] P. Kothnur , L. Raja. J. Appl. Phys., 97, 043305
(2005).
[6] T. Deconinck, L. Raja, Plasma Process. Polym., 6, 335
(2009)
[7] G. J. M. Hagelaar, L. C. Pitchford, Plasma Sources Sci.
Technol., 14, 722 (2005)
[8] B. Lay, R. S. Moss, S. Rauf, M. J. Kushner, Plasma
Sources Sci.Technol., 12, 8 (2003)
[9] X. Aubert, G. Bauville, J. Guillon, B. Lacour, V.
Puech, A.Rousseau, Plasma Sources Sci. Technol., 16, 23
(2007)
Acknowledgment
This work was supported by the National Natural Science
Foundation of China. (Grant Nos. 11275021, 11072020,
50836007).
Fig.2 Electron number density contours in the MHCD for
cases A, B and C (contour labels in units of m−3).
2
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