Effect of the cathode structure on micro-hollow cathode discharge
Feng He1*, Shoujie He1,2, Xiaofei Zhao1, Jiting Ouyang1
1. School of Science, Beijing Institute of Technology, Beijing 100081, People’s Republic of China
2. College of Physics Science and Technology, Hebei University, Baoding 071002, China
Abstract: Micro-hollow cathode discharges (MHCD) have been investigated by
two-dimensional particle-in-cell/Monte-Carlo collision (PIC/MCC) simulations.
The discharges were produced in a metal/dielectric/metal sandwich structures
with a cylindrical hollow cathode. The diameter of the hollow cathode is about
200 ~ 400 μm. The discharge gas is argon at 200 Torr. The discharge processes
of micro-hollow cathode with planar electrode at the edge of cavity and without
planar electrode were obtained. The distributions of the electric field and electron
density in the two different micro-hollow cathodes have been compared. The
effect of the diameter of the micro-hollow cathode was also investigated.
Keywords: MHCD, Micro-plasma, numerical simulation
*
Corresponding author. Email: [email protected]
1. Introduction
The study of Hollow cathode discharges (HCD) has
a long history in the field of gas discharges, and
HCDs are widely used in many applications
including spectral lamps, lasers et al[1]. The
conventional hollow cathode can be in various
structures, such as a pair of plane parallel plates or a
hollow cylinder. A ``hollow cathode effect" (HCE)
will be obtained in the discharge of aforesaid
structures. Generally, the HCE indicates that the
electrons oscillate between the negative glows
regions of the faced cathode surfaces[2]. During the
oscillation, the high energy electrons can ionize and
excite the gas atoms. Therefore high density plasma
and large numbers of active particles can be obtained
in HCD.
In last two decades, Micro-Plasma has attracted
many attentions[3]. Schoenbach et al propose that
reducing the dimension of hollow cathode to about
tens to hundreds of micrometers, to obtain microplasma under higher pressure. And a sandwich type
micro-HCD had developed by them[4]. After that,
various structures of MHCD were investigated by
experiments in many groups. But the hollow cathode
effect in MHCD is still not confirmed in those
experiments [3].
Because of the sub-millimeter dimensions in MHCD,
study of the discharge processes by experiment is
difficult. Computer simulation of MHCD can be a
useful tool to reveal the physics characteristics of
micro-discharge. Many researches use fluid model to
investigate the characteristics of sandwich type
MHCD[5-7]. Few results of MHCD are provided by
PIC/MCC method [8].
In this paper, the discharge evolution in sandwich
type MHCD is investigated by PIC/MCC simulation.
The effect of the cathode structure is discussed. Two
different discharge processes are obtained by
simulation.
The article is organized as follows. Section 2
describes the discharge device used in 2D PIC/MCC
simulation. The calculated results are given Section
3. And the effects of different discharge structure
have been discussed. Finally, the conclusion is
summarized in Sec. 4.
2. Structure and model of MHCD
2.2 Structure of MHCD
The MHCD device investigated in our simulation
consists of a dielectric layer covered with two metal
electrodes. A hole drills through the three material
layers. According to the characteristics of MHCD
structure, an axisymmetric coordinates system is
adopted in this work. The cross section of the
MHCD is shown in Figure 1. The region with
oblique line represents the dielectric layer with
thickness z2, and the permittivity of the dielectric
layer is 7. The cathode with thickness z1 is set at the
left side of the dielectric layer. The anode is at the
right side and the thickness is z3. The radius of the
MHCD hole d is set to 100~200μm, and the radius
of the whole region r is 400μm. The left boundary of
simulation region is z0 apart from the cathode. A
second anode is used as the right boundary. The
distance between the left and the right boundary za is
1500μm. The discharge gas is pure Ar, and the
pressure is 200Torr.
d
The initial densities of electron and Ar ions are both
1014m-3. In order to reduce the time of calculation,
particles are initialized on in the hole. The maximum
total number of macro-particles is set to 106. The
time step of Poisson solver is 10–12s. The time step
of electron and ion advancing is 10–13s and 5×10–12s
respectively.
3. RESULTS AND DISCUSSION
Firstly, we simulate the discharge process in a
micro-hollow cathode. The radius of the cathode
hole is 200μm, viz. the pD product is 8 Torr·cm. The
other parameters of the sandwich structure are given
in Table 1.
Table 1. Parameters of the sandwich structure using in the
simulation
za
paramter
Z0
Z1
Z2
Z3
μm
600
100
200
100
r
z3
Second anode
z2
anode
z1
dielectric
layer
z0
cathode
R
provide a bias voltage. Neumann boundary condition
is adopted at other boundaries.
z
Figure 1. The schematic diagram of micro-hollow
cathode discharge device
Figure 2 shows the spatial distributions of electrons
at the initial stage of the discharge. From the two
figures one can see that, most of electrons are
accumulated in the hole and will be collected by the
anode. For this structure, the discharge is ignited at
the inner edge of the anode.
In our simulation, the ionization and elastic
collisions between electrons and Ar atoms are
considered, also the elastic and charge exchange
collisions between Ar+ and Ar atoms. The cross
sections are taken from Ref.[9].
The potentials applied on the cathode and the anode
in the simulation is -500V and 0V respectively. A
potential of 10V is applied to the second anode to
0
400
600
anode
dielectric
layer
800
1000
1200
1000
1200
520ns
0
400
600
800
anode
400
dielectric
layer
The discharge process is simulated by a twodimensional PIC/MCC method [9]. Two species are
considered in simulation: electron, Ar+. The
coefficients of secondary electron emission γAr of
Ar+ on the metal layers and the dielectric layer are
0.2 and 0.05, respectively.
490ns
cathode
2.2 Simulation models and conditions
cathode
400
Figure 2. Spatial distribution of electrons in micro-hollow
cathode discharge at 490 ns and 520 ns (d=200μm, z1=100μm).
After the charge formed in space, the discharge
develops fast, as shown in figure 3. At 585 ns, the
maximum density of electron is increased from the
initial value 1014m-3 up to 7.3×1016m-3. The plasma
still locates near the anode. Then electrons move
toward to the cathode along the dielectric layer. The
-348.6
0
400
600
-181.3
8.6E+18
0
400
600
800
1000
anode
-5.9
-13
.9
1000
-492
1200
anode
dielectric
layer
2
-47
6. 1
1200
-5.9
-492
-13.9
6.0E+19
0
400
anode
1000
1200
1000
1200
2
640ns
anode
800
.9
800
400
8.1
-4 6
600
- 21
dielectric
layer
6.0E+17
600
cathode
dielectric
layer
cathode
620ns
-141.4
400
0
400
-21.9
800
cathode
620ns
600
1200
400
8.6E+16
0
400
dielectric
layer
cathode
1200
anode
dielectric
layer
cathode
4. 1
1000
400
610ns
1000
2
-48
800
800
400
610ns
600
anode
-492
3.0E+15
0
400
dielectric
layer
cathode
-5.9
1.8E+17
anode
dielectric
layer
cathode
1ns
3.8
-5
585ns
2
-237.0
400
400
-484.1
maximum density increases by 2 orders in about 50
ns. Finally the high density plasma over 1020m-3 is
formed in the cathode region.
-5.9
-492
1.9E+20
anode
640ns
dielectric
layer
cathode
400
600
800
1000
1200
Figure 3. Spatial-temporal distributions of electron density in
micro-hollow cathode discharge (d=200μm, z1=100μm).
Figure 4 is the spatial-temporal distribution of the
potential during the development of micro-hollow
cathode discharge. At the beginning of the discharge,
the electric field is uniform approximately in the
center of the hole, while the field is stronger near the
inner edges of the cathode and the electrode.
Electrons will move along the electric field at the
initial stage as shown in figure 2. When the particle
density is over 1018 m-3, an equi-potential region also
the plasma channel is formed and contract to the
cathode. The plasma channel is over 120 μm apart
from the axis of the hole. From the figures, one can
see that the discharge is close to the electrodes and
the dielectric layer. The discharge process is similar
to the DC discharge along a dielectric layer.
According to the distributions of electron density
and potential, a bright ring will be formed in the
micro-hole.
.9
-37.8
0
400
1.9E+18
0
400
-21
-29.8
600
800
1000
1200
Figure 4 The evolutions of potential distribution in microhollow cathode discharge (d=200μm, z1=100μm).
Another discharge process under different microhollow cathode parameter is also simulated. The
cathode is considered as a planar electrode with a
hole, viz. the thickness of cathode z1 is increased to
700μm and z1=0μm, the left side of the hole is also a
metal electrode. The radius of the micro-hole is
150μm. Other parameter is the same as that
described in Table 1.
Figure 5 and figure 6 is the distribution of the
electron density and the potential during the
discharge respectively. Like the evolution of
previous MHCD, the discharge is also initialed at the
edge of the anode. But as the discharge developing,
high density electron and equi-potential region are
formed near the axis of the anode hole. This region
moves towards the cathode along the axis. We
consider that a bright line will be formed in the
center of the hole.
Comparing figure 4 and figure6, one can find that
the potential distribution in the micro-hole of two
discharge structures at 1ns is similar to each other.
But a ring-type and a linear-type discharge are
formed eventually. This is mainly caused by
reducing the radius of micro-hole.
400
2.4E+19
anode
dielectric
layer
cathode
460ns
Acknowledgments
2.4E+16
0
400
600
800
1000
1200
400
anode
References
1.1E+18
0
400
600
800
1000
1200
Figure 5 The evolutions of potential distribution at d=150μm,
z1=700μm.
400
anode
cathode
dielectric
layer
2
1ns
-492
-316.7
600
.9
-13
.8
-2 9
0
400
.9
-5
.0
92
-4
This work was supported in part by the National
Science Foundation of China under Grant No.
11005009.
3.7E+20
dielectric
layer
cathode
520ns
hole. The influence of the cathode structure on the
discharge will be investigated further in future.
800
1000
1200
400
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anode
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2
-492
-13
- 31
0
400
6.7
2. 0
600
- 5.
.9
9
.8
- 29
-49
800
1000
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400
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0
400
2.0
0.8
-3 0
600
-
800
.8
29
-13.9
-4 9
-5.9
1000
1200
Figure 6 The evolutions of potential distribution at d=150μm,
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4. Conclusion
In this paper, the metal/dielectric/metal sandwich
structures with a cylindrical micro-hollow cathode
have been investigated by two-dimensional
PIC/MCC simulations. The distributions of the
electric field, electron density in two different microhollow cathodes have been obtained. The results
show that ring-type and linear-type discharge can be
formed in MHCD with different radius of the micro-
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