A computer simulation of the effect of dusty particles on the characteristic of RF discharges
We are carried out the computer simulation of the dust cloud dynamics in the radio frequency (RF) discharges at the microgravity conditions using PIC/MCC method for electrons and ions and hydrodynamics model for dust particles. The moving of dust particles is governed by the electrostatic force, ion...
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| Zitieren: | A computer simulation of the effect of dusty particles on the characteristic of RF discharges / O.Yu. Kravchenko, A.V. Vakulenko, T.E. Lisitchenko, G.I. Levada, Yu.A. Yastrub // Вопросы атомной науки и техники. — 2007. — № 1. — С. 154-156. — Бібліогр.: 8 назв. — англ. |
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irk-123456789-1105082017-01-09T14:24:04Z A computer simulation of the effect of dusty particles on the characteristic of RF discharges Kravchenko, O.Yu. Vakulenko, A.V. Lisitchenko, T.E. Levada, G.I. Yastrub, Yu.A. Low temperature plasma and plasma technologies We are carried out the computer simulation of the dust cloud dynamics in the radio frequency (RF) discharges at the microgravity conditions using PIC/MCC method for electrons and ions and hydrodynamics model for dust particles. The moving of dust particles is governed by the electrostatic force, ion and neutral drag forces, which are averaged over period of RF discharge. The obtained results show that dust particles form layer with sharp boundaries in the discharge chamber. Locations of the layer boundaries don't coincide with the edges of the rf-sheathes and depend on size of dust particles and ion density in discharge. Проводиться комп’ютерне моделювання динаміки пилового згустку в радіочастотних розрядах в умовах мікрогравітації. Використовується PIC/MCC метод моделювання для електронів та іонів, а також гідродинамічна модель для пилових частинок. Рух пилових частинок визначається електростатичною силою, силами тертя з іонами та нейтралами, які усереднюються по періоду радіочастотного розряду. Одержані результати показують, що пилові частинки формують шари з різкими границями в розрядній камері. Положення границь пилових шарів не співпадають з границями приелектродних шарів і залежать від розміру пилових частинок та іонної густини в розряді. Проводится компьютерное моделирование динамики пылевого сгустка в радиочастотных разрядах в условиях микрогравитации. Используется PIC/MCC метод моделирования для электронов и ионов, а также гидродинамическая модель для пылевых частиц. Движение пылевых частиц определяется электростатической силой, силами трения с ионами и нейтралами, которые усредняются по периоду радиочастотного разряда. Полученные результаты показывают, что пылевые частицы формируют слои с резкими границами в разрядной камере. Положения границ пылевых слоев не совпадают с границами приэлектродных слоев и зависят от размера пылевых частиц и плотности ионов в разряде. 2007 Article A computer simulation of the effect of dusty particles on the characteristic of RF discharges / O.Yu. Kravchenko, A.V. Vakulenko, T.E. Lisitchenko, G.I. Levada, Yu.A. Yastrub // Вопросы атомной науки и техники. — 2007. — № 1. — С. 154-156. — Бібліогр.: 8 назв. — англ. 1562-6016 PACS: 52.27.Lw http://dspace.nbuv.gov.ua/handle/123456789/110508 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Low temperature plasma and plasma technologies Low temperature plasma and plasma technologies |
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Low temperature plasma and plasma technologies Low temperature plasma and plasma technologies Kravchenko, O.Yu. Vakulenko, A.V. Lisitchenko, T.E. Levada, G.I. Yastrub, Yu.A. A computer simulation of the effect of dusty particles on the characteristic of RF discharges Вопросы атомной науки и техники |
| description |
We are carried out the computer simulation of the dust cloud dynamics in the radio frequency (RF) discharges at the microgravity conditions using PIC/MCC method for electrons and ions and hydrodynamics model for dust particles. The moving of dust particles is governed by the electrostatic force, ion and neutral drag forces, which are averaged over period of RF discharge. The obtained results show that dust particles form layer with sharp boundaries in the discharge chamber. Locations of the layer boundaries don't coincide with the edges of the rf-sheathes and depend on size of dust particles and ion density in discharge. |
| format |
Article |
| author |
Kravchenko, O.Yu. Vakulenko, A.V. Lisitchenko, T.E. Levada, G.I. Yastrub, Yu.A. |
| author_facet |
Kravchenko, O.Yu. Vakulenko, A.V. Lisitchenko, T.E. Levada, G.I. Yastrub, Yu.A. |
| author_sort |
Kravchenko, O.Yu. |
| title |
A computer simulation of the effect of dusty particles on the characteristic of RF discharges |
| title_short |
A computer simulation of the effect of dusty particles on the characteristic of RF discharges |
| title_full |
A computer simulation of the effect of dusty particles on the characteristic of RF discharges |
| title_fullStr |
A computer simulation of the effect of dusty particles on the characteristic of RF discharges |
| title_full_unstemmed |
A computer simulation of the effect of dusty particles on the characteristic of RF discharges |
| title_sort |
computer simulation of the effect of dusty particles on the characteristic of rf discharges |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2007 |
| topic_facet |
Low temperature plasma and plasma technologies |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/110508 |
| citation_txt |
A computer simulation of the effect of dusty particles on the characteristic of RF discharges / O.Yu. Kravchenko, A.V. Vakulenko, T.E. Lisitchenko, G.I. Levada, Yu.A. Yastrub // Вопросы атомной науки и техники. — 2007. — № 1. — С. 154-156. — Бібліогр.: 8 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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2025-07-08T00:41:15Z |
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2025-07-08T00:41:15Z |
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| fulltext |
154 Problems of Atomic Science and Technology. 2007, 1. Series: Plasma Physics (13), p. 154-156
A COMPUTER SIMULATION OF THE EFFECT OF DUSTY PARTICLES
ON THE CHARACTERISTIC OF RF DISCHARGES
O.Yu. Kravchenko, A.V. Vakulenko, T.E. Lisitchenko, G.I. Levada, Yu.A. Yastrub
Faculty of Radio Physics, Taras Shevchenko National Kyiv University, Kyiv, Ukraine,
e-mail: kay@univ.kiev.ua
We are carried out the computer simulation of the dust cloud dynamics in the radio frequency (RF) discharges at the
microgravity conditions using PIC/MCC method for electrons and ions and hydrodynamics model for dust particles.
The moving of dust particles is governed by the electrostatic force, ion and neutral drag forces, which are averaged over
period of RF discharge. The obtained results show that dust particles form layer with sharp boundaries in the discharge
chamber. Locations of the layer boundaries don't coincide with the edges of the rf-sheathes and depend on size of dust
particles and ion density in discharge.
PACS: 52.27.Lw
1. INTRODUCTION
Physics of dusty plasma are considered now as one of
the important branches of science and technology. First of
all an active research on particle formation and behavior
has been induced by contamination phenomena of
industrial plasma reactors used for etching, sputtering,
and plasma enhanced chemical-vapor deposition. Many
experimental efforts have deal with the detection and
dynamics dust particles in capacitive coupled radio
frequency discharges, since they widely used as sources
of reactive species for surface treatment. Such particles
are trapped in the plasma bulk, forming dust clouds and
voids [1], [2], and significantly affect the discharge
behavior. In particular, dust particles change electron and
ion velocity distribution functions and influence on
ionization processes and flows of plasma particles toward
the electrodes. The numerical simulations of the dust
particles dynamics in RF discharges was carried out
earlier in the frame of hydrodynamic model [3], which is
not correct for discharges of the low pressure. However,
many modern plasma reactors operate at low gas pressure
and the mean free path of charged particles becomes
comparable with or exceeds the thickness of electrode
sheaths. The influence of dust particles on radio
frequency discharge in the kinetic approach was
investigated only for the case of static dust particles [4],
[5]. In this paper we are carried out the computer
simulation of the dust cloud dynamics in the radio
frequency discharges at the microgravity conditions using
PIC/MC method for electrons and ions and
hydrodynamics model for dust particles.
2. MODEL
We use hydrodynamics approach to describe the dust
particles motion
( )
0,d d dn n v
t x
∂ ∂
+ =
∂ ∂
(1)
21 1 .
2
d d
d
d
v v
F
t x m
∂ ∂
+ =
∂ ∂
(2)
The potential of the electric field ϕ is described by
Poisson equation
[ ]
2
2
0
,i e d d
e n n q n
x
ϕ
ε
∂
= − − +
∂
(3)
where , ,d d dn v q are a density, drift velocity and charge
of a dust particle, ,i en n are averaged for a discharge
period an ion and electron densities correspondingly.
The change of the dust charge is described by equation
.d d
d e i
q q
v I I
t x
∂ ∂
+ = +
∂ ∂
, (4)
where eI is the electron and iI is the ion current to the
dust particle. The total force acting on the dust particles is
a sum of the electrostatic E dF q E= , the ion drag iF and
the neutral drag nF forces. The ion drag force is
calculated using OLM approach [6] and consists of the
collection c
iF and orbit o
iF components. The former is a
result of momentum transfer from all ions collected by the
grain
2 ,c
i c i s i iF b n v m vπ= (5)
where ( )1/ 221 2 /c d d d i ib r eq r m v= − . The orbit force is
caused by the momentum transfer from the Coulomb
scattering of ion-dust, then it be given by
2 2
04 ,o
i i i iF n m v bπ= Γ ( 6)
where 0b and Γ are impact parameters for deflection to
/ 2π angle and the Coulomb logarithm correspondingly.
Ion and electron densities, the ion drift velocity; ion and
electron currents to a dust particle are calculated using the
PIC/MCC method.
The PIC/MCC method described in detail in [7] for
discharges without dust particles is developed for
computer simulations of the RF discharge with dust
particles [5]. The Monte Carlo technique is used to
describe electron and ion collisions. The collisions
include elastic collisions of electrons and ions with atoms,
an ionization and excitation of atoms by electrons, the
charge exchange between ions and atoms, Coulomb
collisions of electrons and ions with dust particles, as well
as the electron and ion collection and scattering by dust
particles. In addition to a usual PIC/MCC scheme, the
weighting procedure is used also for the determination of
a macroparticle charge part, which is interacting with a
dust particle.
mailto:kay@univ.kiev.ua
155
The Coulomb cross-section for electron and ion
scattering by immobile dust particles is taken from [5].
The electron-argon collision cross-sections used in the
model are the same as those used in [8]. Due to the
significant difference in dust and ion (even more electron)
mass dust particles move hardly at all at one electron time
step. Thus in order to speed up simulation code the sub-
cycling technique was used.
3. RESULTS AND DISCUSSION
Simulations have been carried out at several different
radii of dust particles and pressure values, whereas the
other plasma parameters are kept constant. The rf
frequency and the amplitude of rf power are set
10rf MHzν = and 150rfV V= , the distance between the
electrodes is set to 0.05 m, the initial dust density is set
10 3
0 10dn m−= .
Results of calculations were shown that dust particles
are pushed out from sheaths into the plasma and are
distributed in the central part of discharged gap. The
stationary spatial distribution of dust particles is settled
after a time. Discussed below spatial profiles correspond
to time t = 0.02 s when steady state of the dust layer is
achieved in the rough.
Fig. 1a shows the dust density at three radii dr and the
neutral gas pressure p = 0.1 Torr. Values of radii have
indicated in micrometers. As shown in this figure, in all
cases dusty layers with sharp boundaries are formed and
the dust density is at maximums at these boundaries.
Width of the dust layer is decreasing with increasing dust
particle radius. This fact is caused by the increasing of the
dust particle charge and electrostatic force with the
increasing dr . The dust density distribution is uniform in
the central part of the layer in all cases depictured in the
figure.
Dust layers are modified plasma parameters. Fig. 1b
shows spatial profiles of the ion current averaged over
period of the rf discharge. We can see that it is happened
a strong perturbation of the ion current near dust densities
peaks. Namely, ion flows are directed to dust density
peaks at 6dr mµ= .
The time-averaged ion density is pictured in Fig. 2. It
is seen the decreasing of the ion density with increasing of
the dust particle radius, that is a consequence of a bigger
ion deposition on dust particles. In case with 6dr mµ=
peaks of the ion density are formed in locations of dust
density peaks. Double layers are appeared in locations of
these peaks and stimulate the ion acceleration in the
direction to peaks.
Fig. 3 shows dust density spatial distributions at three
values of a neutral gas pressure and 3dr mµ= . Values of
gas pressure in figure are indicated in torrs. Note, that the
width of dust layer is a monotonically increasing function
of the pressure. This result is a consequence of more thin
sheaths at a big pressure and the balance of forces acting
on a dust particle is reached closer to electrodes. At the
gas pressure p = 0.1 Torr the biggest dust density peaks is
formed at dust layer boundaries. As a result the big
potential jumps are appeared at these locations which
accelerate ions toward electrodes.
0 1 2 3 4 5
0
2
4
8
12
Nd, m-3*1010
X, cm
rd=0.5
rd=3
rd=6
a
0 1 2 3 4 5
-0,2
-0,1
0,0
0,1
0,2
rd=0.5
rd=3.0
rd=6.0Ji
X, cm
b
Fig.1. Dust density profiles (a) and time-averaged ion
current profiles (b) at different dust particle radii
Fig.2. Ion density profiles at different dust particle radii
156
Fig. 3. Dust density profiles at different pressure values of
the neutral gas
To conclude, the dust cloud forming have been
numerically studied in radio frequency discharge under
microgravity. It was shown that the dust particles
compression is happen in some locations of the discharge
chamber due to join action of an electrostatic, an ion drag
and a neutral drag forces. It was studied the influence of a
dust particle radius and a neutral gas pressure on plasma
parameters distributions.
REFERENCES
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G.E. Morfill, A.P. Nefedov, V.E. Fortov et al. //New
Journal of Physics. 2003, p.19.1-19.12.
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3. M.R. Akdim, W.J. Goedheer //Physical Review E.
2002, v.65, p. 015401.
4. Y. Chutov, W. Goedheer, O. Kravchenko, V. Zuz,
Yan Min // Journal Plasma and Fusion Research.
2001, v.4, p.340-348.
5. Y.I. Chutov, W.J. Goedheer // IEEE Trans. Plasma
Phys. 2003, v.31, p.606-613.
6. P.K. Shukla, A.A. Mamun. Introduction to Dusty
Plasma Physics. Bristol and Philadelphia: “IoP
Publishing Ltd.”, 2001.
7. C. K. Birdsall // IEEE Trans. Plasma Sci. 1991, v.19,
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8. V. Vahedi, G. DiPeso, C.K. Birdsall, M.A. Liberman,
T.D. Roghlien // Plasma Sources Sci. Technol. 1993,
v.2, p.261-272.
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