Macroparticles in beam-plasma systems
The macroparticle (MP) contamination is the most important technological problem of vacuum arc deposition of coatings. The results of theoretical study of MP charging and dynamics in the near-substrate sheath are presented. The charge and dynamics of MP are governed by local parameters of ion and...
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irk-123456789-1154482017-04-05T03:02:20Z Macroparticles in beam-plasma systems Bizyukov, A.A. Girka, I.O. Romashchenko, E.V. Chibisov, O.D. Iter and fusion reactor aspects The macroparticle (MP) contamination is the most important technological problem of vacuum arc deposition of coatings. The results of theoretical study of MP charging and dynamics in the near-substrate sheath are presented. The charge and dynamics of MP are governed by local parameters of ion and secondary electron emission fluxes in the sheath. It is shown that the maximum possible velocity of repelled MP increases with increasing substrate bias voltage. The effect of substrate biasing is seen to be larger for MPs emitted at small angles to the cathode plane of arc evaporator. Наиболее важной технологической проблемой вакуумно-дугового осаждения покрытий является загрязне- ние макрочастицами (МЧ). Представлены результаты теоретического исследования зарядки и динамики МЧ в слое у подложки. Заряд и динамика МЧ определяются локальными параметрами ионных и электронных вторично-эмиссионных потоков в слое. Показано, что максимально возможная скорость отраженной МЧ возрастает с увеличением потенциала подложки. Эффект смещения потенциала подложки больше для МЧ, которые эмитируют под малыми углами к плоскости катода вакуумного испарителя. Найбільш важливою технологічною проблемою вакуумно-дугового осадження покриттів є забруднення ма- крочастинками (МЧ). Представлено результати теоретичного дослідження зарядки та динаміки МЧ у шарі біля підкладки. Заряд і динаміка МЧ визначаються локальними параметрами іонних та електронних вторин- но-емісійних потоків у шарі. Показано, що максимально можлива швидкість відбитої МЧ зростає зі збіль- шенням потенціалу підкладки. Ефект зсуву потенціалу підкладки більший для МЧ, які емітують під малими кутами к площині катоду вакуумного випарника. 2016 Article Macroparticles in beam-plasma systems / A.A. Bizyukov, I.О. Girka, E.V. Romashchenko, O.D. Chibisov // Вопросы атомной науки и техники. — 2016. — № 6. — С. 187-190. — Бібліогр.: 24 назв. — англ. 1562-6016 PACS: 52.40.Hf http://dspace.nbuv.gov.ua/handle/123456789/115448 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Iter and fusion reactor aspects Iter and fusion reactor aspects |
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Iter and fusion reactor aspects Iter and fusion reactor aspects Bizyukov, A.A. Girka, I.O. Romashchenko, E.V. Chibisov, O.D. Macroparticles in beam-plasma systems Вопросы атомной науки и техники |
| description |
The macroparticle (MP) contamination is the most important technological problem of vacuum arc deposition of
coatings. The results of theoretical study of MP charging and dynamics in the near-substrate sheath are presented.
The charge and dynamics of MP are governed by local parameters of ion and secondary electron emission fluxes in
the sheath. It is shown that the maximum possible velocity of repelled MP increases with increasing substrate bias
voltage. The effect of substrate biasing is seen to be larger for MPs emitted at small angles to the cathode plane of
arc evaporator. |
| format |
Article |
| author |
Bizyukov, A.A. Girka, I.O. Romashchenko, E.V. Chibisov, O.D. |
| author_facet |
Bizyukov, A.A. Girka, I.O. Romashchenko, E.V. Chibisov, O.D. |
| author_sort |
Bizyukov, A.A. |
| title |
Macroparticles in beam-plasma systems |
| title_short |
Macroparticles in beam-plasma systems |
| title_full |
Macroparticles in beam-plasma systems |
| title_fullStr |
Macroparticles in beam-plasma systems |
| title_full_unstemmed |
Macroparticles in beam-plasma systems |
| title_sort |
macroparticles in beam-plasma systems |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2016 |
| topic_facet |
Iter and fusion reactor aspects |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/115448 |
| citation_txt |
Macroparticles in beam-plasma systems / A.A. Bizyukov, I.О. Girka, E.V. Romashchenko, O.D. Chibisov // Вопросы атомной науки и техники. — 2016. — № 6. — С. 187-190. — Бібліогр.: 24 назв. — англ. |
| series |
Вопросы атомной науки и техники |
| work_keys_str_mv |
AT bizyukovaa macroparticlesinbeamplasmasystems AT girkaio macroparticlesinbeamplasmasystems AT romashchenkoev macroparticlesinbeamplasmasystems AT chibisovod macroparticlesinbeamplasmasystems |
| first_indexed |
2025-07-08T08:47:46Z |
| last_indexed |
2025-07-08T08:47:46Z |
| _version_ |
1837067893615886336 |
| fulltext |
ISSN 1562-6016. ВАНТ. 2016. №6(106)
PROBLEMS OF ATOMIC SCIENCE AND TECHNOLOGY. 2016, № 6. Series: Plasma Physics (22), p. 187-190. 187
MACROPARTICLES IN BEAM-PLASMA SYSTEMS
A.A. Bizyukov, I.О. Girka, E.V. Romashchenko, O.D. Chibisov
V.N. Karazin Kharkiv National University, Kharkov, Ukraine
E-mail: ev.romashchenko@gmail.com
The macroparticle (MP) contamination is the most important technological problem of vacuum arc deposition of
coatings. The results of theoretical study of MP charging and dynamics in the near-substrate sheath are presented.
The charge and dynamics of MP are governed by local parameters of ion and secondary electron emission fluxes in
the sheath. It is shown that the maximum possible velocity of repelled MP increases with increasing substrate bias
voltage. The effect of substrate biasing is seen to be larger for MPs emitted at small angles to the cathode plane of
arc evaporator.
PACS: 52.40.Hf
INTRODUCTION
One of the central concepts in plasma physics is
that of the charging of macroparticle (MP) by surround-
ing plasma. The charging process in the gaseous plas-
mas has been well studied [1]. The MPs are charged by
the collection of the plasma particles flowing onto their
surfaces. Because of the high thermal velocity of the
electrons compared to the ions, MPs are negatively
charged. For beam-plasma systems, in addition to col-
lecting thermal plasma particles, MPs are subjected to
fluxes of beam particles. The presence of beams in sys-
tems produces significant effect on dynamics of charging
process. The energetic beams are not only intentionally
introduced into plasma but energetic ion beams are also
formed from a plasma by a set of extractor electrodes in
vacuum arc deposition (VAD) systems to obtain layers of
cathode material on substrate. The vacuum arc sources
generate highly ionized metal plasma with multiply
charged ions (MCIs) [2]. The mean ion charge state is
2…3 and typically higher for materials with high melting
point. The ions have supersonic velocities, correspond-
ing to ion energy in the range 20…200 eV, depending
on the source material [3]. By applying negative high-
voltage bias to the substrate, ions are extracted from the
plasma, accelerated across the sheath and deposited into
the surface [4]. A disadvantage of VAD is the emission
of macroparticles (MPs) during arcing. MPs are general-
ly molten metal droplets (sometimes solid) generated by
the action of the cathode spots [5]. The MPs occur in the
range of size from fraction to tens of microns. There is a
strong dependence of MP production on the cathode
material. The cathode erosion in the droplet phase de-
creases with increasing cathode material melting tem-
perature [6], but monotonic relationship between MP
production and melting point of the different cathode
materials could not be established. MPs and plasma
fluxes are partially separated. The plasma flux is peaked
in the direction of the normal to the cathode surface [7]
whereas most of MPs produced by a steady vacuum arc
leave the cathode at small angles to the cathode plane
[8]. However, MP flux emitted in the direction of the
normal to the cathode surface can still be large. The
peak emission angle with respect to the cathode plane
increases with decreasing MP size [6]. The incorpora-
tion of MPs into the coating degrades the quality of the
films, e.g. produces surface roughening, protuberances,
bumps and pinholes [9]. MPs may constitute a consider-
able fraction of the coatings mass. This substantially
limits the possibilities of vacuum arc plasma in coating
technologies. Thus, MP contamination is regarded as
the most important technological problem. Several
methods connected with different aspects of the MP
process have been developed to eliminate MPs, such as
magnetic filters [10], magnetically steered arc [11], sub-
strate biasing [12], and nontraditional (hot refractory
anode vacuum arc, shunting vacuum arc) [13]. Among
these methods, the substrate biasing has been considered
as a positive means in our previous study [14]. We have
proposed a model of MP transport in vacuum arc sheath,
and appreciable progress was made towards explaining
the reduction of MPs which has been approached by
substrate biasing. It is obtained that the use of substrate
bias of -300 V may be capable of repelling MPs with a
size less than 1 μm from the substrate at normal inci-
dence of MPs. In the present work, we report further
results on the accumulation of MPs on a negatively bi-
ased substrate immersed in vacuum arc plasma using
measured size and angular distributions of MPs [15]-
[16].
1. DISTRIBUTIONS OF MPS
The size and angular distributions of MPs have
been investigated by a number of authors [17-20] for a
range of cathode material. Tuma et al. [18] obtained that
copper MPs have a monotonically decreasing size dis-
tribution, which has a maximum for MPs of diameter in
the range 0..1 μm. Similar results for a variety of cath-
ode material have been reported by Anders et al [20].
MPs have a peaked distribution which tailed off with
increasing MP volume. Therefore, MPs with smaller
volumes dominate the number density.
MPs have a size distribution f(d) that can be de-
scribed by a power law [9]
Addf )( , (1)
where d is the MP diameter, and the parameters A and α
are material dependent. This shape of size distribution
f(d) follows from the fractal nature of cathode spot phe-
nomena.
MP size distribution f(d) can be represented by a
straight line in log-log presentation as shown in Fig. 1.
188 ISSN 1562-6016. ВАНТ. 2016. №6(106)
Fig. 1 demonstrates the MP size distribution f of Ti MP
diameter d (in μm) normalized to the area (in mm
2
) and
time deposition (in s). MP sizes for Ti range up to
40 μm in the absence of background gas and 30 μm in
the presence of nitrogen [15].
Fig. 1. MP size distribution for Ti, normalized as MP
number per area and time deposition for pressures
10
-3
Pa (solid line) and 1Pa (dashed line). Experimental
results were taken from Ref. [15]
As one can see from the Fig. 2, the MP flux is
peaked with a most probable angle below 30
0
with re-
spect to the cathode plane in vacuum as well as in the
presence of nitrogen. McClure [21] proposed theory
which explains the emission of the MPs at the small
angles to the cathode surface. The plasma expands from
the cathode spots into the vacuum. In addition to the
outward flow of ions, there is a back flow of ions accel-
erated towards the liquid cathode surface of the arc spot.
The back-streaming ions press inward on the molten
metal. The plasma pressure is stronger in center than at
the sides of the crater. Therefore, MPs are pushed to-
wards the edge of the crater leading to the observed an-
gular distribution.
Fig. 2. MP angular distribution for Ti, normalized as
MP volume per are and time deposition for different
values of pressure: 1 – 10
-3
Pa;
2 – 0.1 Pa; 3 – 1 Pa [16]
MODEL DESCRIPTION
Let us consider a negatively biased substrate, im-
mersed into vacuum arc produced plasma. Application
of high negative bias Vb to the substrate leads to posi-
tive sheath formation near the substrate. This is because
the electrons are repelled from the substrate whereas
ions are accelerated towards the substrate [22].
In our coordinate system a plama-sheath interface is
taken to be the origin, x=0, and the position of the sub-
strate is determined by the sheath thickness. The ions,
hitting the substrate, may cause an electron emission.
Because of the relatively low kinetic energy of the ions
(below 1 keV), only the potential electron emission
(PEE) is of importance in the vacuum arcs [9].
The flux of secondary electrons is accelerated away
from the substrate in the sheath electric field that accel-
erated flux of MCIs towards the substrate. To obtain
potential distribution Ф(x) within the sheath one has to
consider both particle fluxes to and from the substrate in
Poisson’s equation
N
k
ek
N
k
ik nnk
e
dx
Фd
210
2
2
, (2)
where ε0 is the permittivity constant, e is the elementary
charge, k is the ion charge state number, nik is the
individual ion densities of the k-th species, nek is the
individual densities of secondary electrons produced by
the ions of the k-th species.
The boundary conditions for integration are Ф
(0)=0; dФ/dx=0. The space charge of MPs is neglected
(i. e., we assume that the MP number density to be
small). The potential variation in the sheath can be
found numerically by integration Eq. (2).
We consider the MP with radius a as a spherical
probe immersed in counter streams of ions and electrons
where the directed particle velocity is much greater than
the MP velocity [24]. The MP charge Q is one of the
most important characteristics for the MP dynamics.
The MP charge Q is determined by the MP potential
with respect to the local sheath potential Vd
)()( xСVxQ d , (3)
where C is the capacitance of the MP. If the MP radius
is much smaller than the Debye length λD the capaci-
tance is
аaС D 00 414 , (4)
where λD=( ε0Te /n0e
2
)
1/2
.
The MP charging time is shorter than the time of
flight through the plasma sheath. We assume instanta-
neous transfer of charge onto and off the MP at any MP
position in the sheath. The steady-state potential to
which a MP is charged is determined from the balance
of particle currents to the grain ( 0dV )
0 deedeidedi VIVIVIVI , (5)
where Ii is the ion current, Ie is the current of fast sec-
ondary electrons emitted from the substrate, Ii-e is the
secondary electron current from the MP surface caused
by the impact of MCIs, Ie-e is the current of secondary
electrons emitted from the MP surface due to fast elec-
tron bombardment.
We calculate the currents Ii and Ie to the MP sur-
face by using the orbital motion limited (OML) ap-
proach.
μm/s
ISSN 1562-6016. ВАНТ. 2016. №6(106) 189
N
k iki
d
ik
N
k
iki
um
keV
jaII
1
2
2
1
2
1 , (6)
N
k ee
d
ek
N
k
eke
um
eV
jaII
1
2
2
2
2
1 , (7)
ik
N
k
k
N
k
keiei I
k
II
12
,
, (8)
eee II ,
em
e
em
e
m Exp
24.7 , (9)
where δ is the secondary electron yield [24]; jik is the
current density of the ions of the k-th species, jek is the
current density of secondary electrons produced by the
ions of the k-th species; γk is a partial PEE yield , Iik =0,
if 2keVd /mi uik
2
>1; and Ie =0, if 2eVd/meue
2
<1, mi
(me ) is the ion (electron) mass, uik is the velocity of
each ion species in the sheath, ue is the velocity of sec-
ondary electrons.
Electrostatic repulsion of MPs should occur if the
potential energy exceeds the kinetic energy
2)( 2
npot MVxU , (10)
where Upot = Q(x)Ф(x), is the potential energy of MP at
the local sheath position Vn is the velocity component
normal to the substrate (Vn=Vp sinθ, where Vp is the MP
velocity, θ is the angle with the respect to the cathode
plane).
Repulsion criterion (10) is recast as
212
0 sin)()(6 xxVaV dp . (11)
While we do not know of any detailed measurements of
both velocity Vn and radius a, the analysis of inequality
can provide an answer to the question whether MP with
given radius may be reflected from a substrate. We can
find dependence of the MP critical velocity as a func-
tion of MP position for different angles. It says that MP
with a given radius must penetrate through the sheath
region with a velocity greater than the critical velocity.
3. RESULTS AND DISCUSSION
The numerical calculations were carried out for ti-
tanium ions, bombarding a negatively biased titanium
substrate. The specific plasma parameters and energy of
ions have been taken as typical values from experi-
ments: the electron temperature Te =1 eV, the plasma
bulk density n=10
16
m
-3
, mean initial kinetic energy of
ions εi =54 eV, mean ion charge Z=1.98, Ie/Ii=1.3. We
consider, as an example, MP with radius 0.25 μm.
Numerical solutions of set of Eqs. (2)-(9), (11) allow
to determine MP critical velocity as a function of MP
position z for different angles.
MP critical velocities for substrate bias -100 V,
-200 V, -300 V are shown in Fig. 3. The maximum pos-
sible velocity of repelled MP is defined by a maximum
of curves. The critical velocity increases with substrate
bias voltage (see Figs. 3,a,c). It may be seen from
Fig. 3,a, for substrate bias Vb=-100 V, all MPs with
velocity 20 m/s reach the substrate. MPs moving at an-
gle θ=30
0
to the cathode plane reach the substrate at
substrate bias Vb= -100 V with velocity 20 m/s (see
Fig. 3,a), whereas they become closer to the substrate
with such velocity at Vb= -200 V (see Fig. 3,b).
Fig. 3. The dependence of the critical velocity of the MP
radius with radius 0.25 μm on its position z for differ-
ent angles and substrate biases: (a) Vb=-100 V;
(b) Vb=-200 V; (c) Vb=-300 V. The curves correspond to
θ=90
0
(solid line), θ=60
0
(dashed line);
θ=30
0
(dotted line)
MPs with radius 0.25 μm and velocity 20 m/s emit-
ted in the direction of the normal to the cathode surface
can be eliminated using substrate bias
Vb=-300V(see Fig. 3,c).
CONCLUSIONS
The numerical results of MP content in films de-
posited by a titanium vacuum arc for different substrate
bias voltage and MP flight angle with respect to the
cathode surface have been presented.
Substrate bias voltage and cathode-to-substrate ge-
ometry are the key factors that influence the density of
MPs. The effect of substrate biasing is larger for MPs
emitted at small angles to the cathode plane than for
a
b
c
190 ISSN 1562-6016. ВАНТ. 2016. №6(106)
MPs emitted in the direction of the normal to the cath-
ode surface. As most of MPs produced by a steady vac-
uum arc leave the cathode at small angles to the cathode
plane, the substrate biasing is the effective method to
reduce MP contaminations of the coatings.
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Article received 29.09.2016
МАКРОЧАСТИЦЫ В ПУЧКОВО-ПЛАЗМЕННЫХ СИСТЕМАХ
А.А. Бизюков, И.А. Гирка, Е.В. Ромащенко, А.Д. Чибисов
Наиболее важной технологической проблемой вакуумно-дугового осаждения покрытий является загрязне-
ние макрочастицами (МЧ). Представлены результаты теоретического исследования зарядки и динамики МЧ
в слое у подложки. Заряд и динамика МЧ определяются локальными параметрами ионных и электронных
вторично-эмиссионных потоков в слое. Показано, что максимально возможная скорость отраженной МЧ
возрастает с увеличением потенциала подложки. Эффект смещения потенциала подложки больше для МЧ,
которые эмитируют под малыми углами к плоскости катода вакуумного испарителя.
МАКРОЧАСТИНКИ В ПУЧКОВО-ПЛАЗМОВИХ СИСТЕМАХ
О.А. Бізюков, I.О. Гірка, О.В. Ромащенко, О.Д. Чібісов
Найбільш важливою технологічною проблемою вакуумно-дугового осадження покриттів є забруднення ма-
крочастинками (МЧ). Представлено результати теоретичного дослідження зарядки та динаміки МЧ у шарі
біля підкладки. Заряд і динаміка МЧ визначаються локальними параметрами іонних та електронних вторин-
но-емісійних потоків у шарі. Показано, що максимально можлива швидкість відбитої МЧ зростає зі збіль-
шенням потенціалу підкладки. Ефект зсуву потенціалу підкладки більший для МЧ, які емітують під малими
кутами к площині катоду вакуумного випарника.
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