22nd International Symposium on Plasma Chemistry
July 5-10, 2015; Antwerp, Belgium
Numerical characterisation of strong magnetized inductively coupled plasmas at
low pressure in argon
S. Yang1, Y. Zhang2 and W. Jiang1
1
School of Physics, Huazhong University of Science and Technology, 430074 Wuhan, P.R. China
Research group PLASMANT, Department of Chemistry University of Antwerp, 2610 Antwerpen-Wilrijk, Belgium
2
Abstract: A one-dimensional, implicit particle-in-cell Monte Carlo collision model is used
to explore the effect of magnetic field on plasma characteristics for a single radio frequency
magnetized inductively coupled plasma using a frequency source of 13.56MHz in argon
(Ar) at low pressure of 10mTorr. Plasma densities and temperature under different
magnetic field (0.1-0.4T) are shown. It is found that the increased magnetic field can
prolong the lifetime of plasma. With the increase of magnetic field, species densities
increase firstly and then decrease. The results indicate that the increased magnetic field can
be used to prolong the lifetime of plasma, but at the cost of decreased plasma density. And
the maximum value of species densities of Ar occurs at B=0.2T in our simulation.
Keywords: magnetized inductively coupled plasma, numerical simulation, Ar discharges.
1. Introduction
As widely used in the substrate etching, thin film
growth, plasma propulsion, materials processing and
semiconductor industry, inductively coupled plasma
source (ICPs) excited by a single radio frequency is an
important low temperature plasma source [1-3]. With the
development of the technology of plasma processing,
there is an increased demand for high density plasmas
with good uniformity and other excellent properties. ICPs
are expected to continue to play the key role in the next
generation of plasma reactors. Many researches have been
reported in the literature for the development of the ICPs
[4, 5]; technological applications of ICP have been
discussed in detail [6-8]; various ICP parameters have
been measured [9-11] and theoretical models and
simulation codes developed [12-15]. Although such
experimental and theoretical studies have been devoted to
the ICP, only a few researches have addressed the
fundamental characteristics of magnetized inductively
coupled plasma (MICP) discharge in the past.
In an effort to explore MICP characteristics, Lieberman
et al [16] developed a global model for homogeneous
magnetized plasma and demonstrated the predicted
relations of electron density with magnetic field, RF
power and gas pressure. Lee et al [17] first established a
model that applying a weak magnetic field to the planar
coil RF-ICP plasma source. Their experimental results
indicated that a proper application of magnetic field can
effectively improve many discharge characteristics of the
ICP, such as heating efficiency, uniformity, plasma
potential and impedance matching. Its application to
oxide etching revealed signs of less damage to the silicon
surface with increased etch rate and selectivity [18].
Among these desirable properties of MICP, a further
exploration on plasmas at a low pressure is especially
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valuable because of the future demand on the production
of high density plasmas at very low pressure (≤ 1mTorr).
Particle-in-cell Monte Carlo collision (PIC/MCC)
model is a numerical simulation technique commonly
used to simulate low temperature plasmas [19, 20]. It can
provide valuable information for understanding plasma
discharges. In this work, a one-dimensional, implicit
PIC/MCC model has been used to research the effect of
magnetic field on the species density and temperature of a
single frequency inductively coupled plasma with a radiofrequency source interaction within them.
2. Model description
We present a one-dimensional analysis of MICP
properties between two parallel plate electrodes with a
length of 20cm and the distance of two electrodes is 8cm.
A radio-frequency source of 13.56MHz is used to drive
the discharge. The Ar gas is used at a temperature of
300K and at a low pressure of 10mTorr. The application
of external magnetic fields is varying from 0.1 to 0.4T.
We use an implicit PIC/MC method [21] and the
method has been described in detail and tested widely
before [20, 23]. In this code scheme, the field equations
are obtained from direct summation and extrapolation of
the equations of particle motion. A standard MC
procedure [22] is used, in which only electron-atom and
ion-atom collisions are considered, such as electron-Ar
and Ar+-Ar elastic collisions. Because the ionisation
degree is under 1% and Coulomb collision are negligible
[23]. Table1 shows the collision reactions of Ar in the
simulation, including elastic, inelastic, ionisation and
charge exchange processes. The cross sections for these
reactions are adopted from this reference [24]. The
simulation time-step is fixed at 2×10-11s, and the
simulations are run for 104 time-steps.
1
Table 1. Collision reactions of Ar in the simulation.
Number/description
reaction
Electron energy loss
1. Elastic
e + Ar → e + Ar
2. Inelastic
e + Ar → e + Ar*
11.5eV
3. Ionisation
e + Ar → 2e + Ar+
15.8eV
4. Elastic
Ar+ + Ar → Ar+ + Ar
5. Charge exchange
Ar+ + Ar → Ar + Ar+
Figure 1. Species densities of Ar with different magnetic
field
3. Results and discussion
Figure1 and 2 show the species densities and
temperature of Ar plasma under different magnetic field
correspondingly. It can be seen from the figures that with
the increase of the external magnetic field, the time for
plasma to reach the peak of density and temperature (i.e.,
complete ionization) is getting longer and the time
interval between two different magnetic fields is longer.
That is to say, the lifetime of plasma is longer. But we can
observe the peak value of species densities increase firstly
and then decrease with the increase of magnetic field and
the maximum value occurs at B=0.2T. The results
indicate that the increased magnetic field can be used to
prolong the lifetime of plasma, but at the cost of
decreased plasma density. Moreover, at the end of the
plasma discharges, Ar+ density does not disappear
immediately like electron density. It decreases rapidly by
two orders of magnitude and then disappears after a short
period of time. This is because the electrons are of high
energy and are easy to get wall loss. And the electrons
move much faster than the Ar+.
Figure 2. Species temperature of Ar with different
magnetic field
4. Conclusion
The effect of external magnetic field on plasma
characteristics for a single radio frequency strong
magnetized inductively coupled plasma in Ar at a low
pressure was investigated by a one-dimensional, implicit
particle-in-cell Monte Carlo collision model. The
simulation results show that the increased magnetic field
can prolong the lifetime of plasma. Species densities
increase firstly and then decrease with the increase of
magnetic field. These indicate that the increased magnetic
field can be used to prolong the lifetime of plasma, but at
the cost of decreased plasma density. And the maximum
value of species densities of Ar occurs at B=0.2T in our
simulation. We think these discharge characteristics could
have positive effects on the production.
5. Acknowledgments
This work was partially supported by the NSFC
(11405067, 11105057, 11275007) and China Postdoctoral
Science Foundation , as well as by the Belgian Federal
Science Policy Office (BELSPO).
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