Simulation and experimental research of Langmuir probe operation in electro-negative plasma
The mathematical model of single cylindrical Langmuir probe describing dependence of positive ion current gathered by the probe on the basic parameters of electronegative plasma, such as probe potential, densities of electrons, positive and negative ions, relation between ion and electron temperatur...
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Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2012
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irk-123456789-1091882016-11-22T03:03:16Z Simulation and experimental research of Langmuir probe operation in electro-negative plasma Dudin, S.V. Rafalskyi, D.V. Naymark, D.A. Диагностика плазмы The mathematical model of single cylindrical Langmuir probe describing dependence of positive ion current gathered by the probe on the basic parameters of electronegative plasma, such as probe potential, densities of electrons, positive and negative ions, relation between ion and electron temperatures is built. The model is based on the theory of the radial motion of charged particles. The model covers wide parameters domain of the electronegative plasma, particularly the whole range typical for technological systems. The experimental measurements, confirming the high reliability of the model are reported. The model can be used in probe measurements of electronegative plasma parameters in laboratory and technological systems, as well as for further theories perfection of surface layers in gas-discharge plasma. Построена математическая модель работы одиночного цилиндрического зонда Ленгмюра, описывающая взаимосвязь собираемого зондом тока положительных ионов с основными параметрами электроотрицательной плазмы, такими как: потенциал зонда, плотности электронов, положительных и отрицательных ионов, отношение температур электронов и ионов. Модель основывается на теории радиального движения заряженных частиц. Она перекрывает широкую область параметров электроотрицательной плазмы, в частности, весь диапазон, характерный для технологических систем. Проведены экспериментальные измерения, подтверждающие высокую достоверность модели. Модель может быть использована при проведении зондовых исследований в электроотрицательной плазме в лабораторных и технологических системах, а также для дальнейшего совершенствования теорий приповерхностных слоев в газоразрядной плазме. Побудовано математичну модель роботи одиночного циліндричного зонда Ленгмюра, яка описує взаємозв'язок струму позитивних іонів, що збирається зондом, з основними параметрами електронегативної плазми, такими як: потенціал зонда, густина електронів, позитивних та негативних іонів, співвідношення температур електронів та іонів. Модель грунтується на теорії радіального руху заряджених частинок. Вона перекриває широку область параметрів електронегативної плазми, зокрема, весь діапазон, характерний для технологічних систем. Проведено експериментальні вимірювання, які підтверджують високу достовірність моделі. Модель може бути використана під час проведення зондових досліджень електронегативної плазми в лабораторних і технологічних системах, а також для подальшого вдосконалення теорій приповерхневих шарів в газорозрядній плазмі. 2012 Article Simulation and experimental research of Langmuir probe operation in electro-negative plasma / S.V. Dudin, D.V. Rafalskyi, D.A. Naymark // Вопросы атомной науки и техники. — 2012. — № 6. — С. 258-260. — Бібліогр.: 7 назв. — англ. 1562-6016 PACS: 52.70.Nc http://dspace.nbuv.gov.ua/handle/123456789/109188 en Вопросы атомной науки и техники Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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Диагностика плазмы Диагностика плазмы |
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Диагностика плазмы Диагностика плазмы Dudin, S.V. Rafalskyi, D.V. Naymark, D.A. Simulation and experimental research of Langmuir probe operation in electro-negative plasma Вопросы атомной науки и техники |
| description |
The mathematical model of single cylindrical Langmuir probe describing dependence of positive ion current gathered by the probe on the basic parameters of electronegative plasma, such as probe potential, densities of electrons, positive and negative ions, relation between ion and electron temperatures is built. The model is based on the theory of the radial motion of charged particles. The model covers wide parameters domain of the electronegative plasma, particularly the whole range typical for technological systems. The experimental measurements, confirming the high reliability of the model are reported. The model can be used in probe measurements of electronegative plasma parameters in laboratory and technological systems, as well as for further theories perfection of surface layers in gas-discharge plasma. |
| format |
Article |
| author |
Dudin, S.V. Rafalskyi, D.V. Naymark, D.A. |
| author_facet |
Dudin, S.V. Rafalskyi, D.V. Naymark, D.A. |
| author_sort |
Dudin, S.V. |
| title |
Simulation and experimental research of Langmuir probe operation in electro-negative plasma |
| title_short |
Simulation and experimental research of Langmuir probe operation in electro-negative plasma |
| title_full |
Simulation and experimental research of Langmuir probe operation in electro-negative plasma |
| title_fullStr |
Simulation and experimental research of Langmuir probe operation in electro-negative plasma |
| title_full_unstemmed |
Simulation and experimental research of Langmuir probe operation in electro-negative plasma |
| title_sort |
simulation and experimental research of langmuir probe operation in electro-negative plasma |
| publisher |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| publishDate |
2012 |
| topic_facet |
Диагностика плазмы |
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http://dspace.nbuv.gov.ua/handle/123456789/109188 |
| citation_txt |
Simulation and experimental research of Langmuir probe operation in electro-negative plasma / S.V. Dudin, D.V. Rafalskyi, D.A. Naymark // Вопросы атомной науки и техники. — 2012. — № 6. — С. 258-260. — Бібліогр.: 7 назв. — англ. |
| series |
Вопросы атомной науки и техники |
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2025-07-07T22:41:01Z |
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2025-07-07T22:41:01Z |
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| fulltext |
258 ISSN 1562-6016. ВАНТ. 2012. №6(82)
SIMULATION AND EXPERIMENTAL RESEARCH OF LANGMUIR PROBE
OPERATION IN ELECTRO-NEGATIVE PLASMA
S.V. Dudin1, D.V. Rafalskyi2, D.A. Naymark1
1V.N. Karasin Kharkоv National University, Kharkоv, Ukraine;
2Scientific Center of Physical Technologies, Kharkоv, Ukraine
The mathematical model of single cylindrical Langmuir probe describing dependence of positive ion current
gathered by the probe on the basic parameters of electronegative plasma, such as probe potential, densities of
electrons, positive and negative ions, relation between ion and electron temperatures is built. The model is based on
the theory of the radial motion of charged particles. The model covers wide parameters domain of the
electronegative plasma, particularly the whole range typical for technological systems. The experimental
measurements, confirming the high reliability of the model are reported. The model can be used in probe
measurements of electronegative plasma parameters in laboratory and technological systems, as well as for further
theories perfection of surface layers in gas-discharge plasma.
PACS: 52.70.Nc
INTRODUCTION
Electronegative plasma can offer useful advantages
in a variety of applications, for example charge-free
etching in the semiconductor industry [1, 2], neutral
beam injections for fusion [3, 4] or electric propulsion
in space applications [5]. One of the most attractive
methods for measuring of the electro-negative plasma
parameters is the Langmuir probe method providing
local measurement of main plasma parameters in wide
range of their change. However, the probe
measurements in electro-negative plasma have specific
peculiarities appearing due to complex composition of
the plasma. The influence of negative ions on the
positive ion branch of the current-voltage characteristics
in the case of spherical and cylindrical Langmuir probe
was considered in the Amemiya and Annaratone’s paper
[6]. However, in this paper the current-voltage
characteristics of a cylindrical probe in electronegative
plasma are presented only for one value of plasma
electronegativity parameter α = 0.9, that limits the
possibility of practical application of the simulation
results. The purpose of this paper is the development
and experimental verification of a mathematical model
of the single cylindrical Langmuir probe in
electronegative plasmas, describing dependence of the
ion current collected by the probe on the main
parameters of the plasma, such as the potential of the
probe, the density of positive and negative ions, the
ratio of the ion and electron temperatures. The model
should cover wide range of plasma parameters,
particularly, the full range characteristic for
technological systems.
1. THEORETICAL MODEL
The present paper investigates current of positive
ions to a single Langmuir probe in the form of an
infinitely extended cylinder with no edge effects. The
probe is immersed in a highly non-isothermal plasma,
where the temperature of the positive ions is much
lower than the temperatures of both the electrons and
negative ions: Ti/Te<<1 и Ti/Tn<<1. The distribution of
electrons and negative ions in the plasma is assumed to
be Maxwellian. Probe sheath is considered as
collisionless, so that all the collisions between particles
are neglected. The model is based on the solution of the
Poisson’s equation for electronegative plasma written in
cylindrical coordinates.
In order to simplify the problem solving we have
introduced the following dimensionless variables:
dimensionless potential ψ = eφ/kTe,
dimensionless coordinate x = r/λDi,
and dimensionless parameters:
dimensionless probe radius xp = rp /λDi,
dimensionless probe potential ψp = eφp /kTe,
negative ions and electrons temperature ratio γ = Tn /Te,
Debye radius for positive ions λDi = (kTe /4πe2ni0)1/2,
dimensionless positive ion current to the probe
i = Ii /(2πrpLeni0(2kTe/mi)1/2).
In addition, we have introduced another
dimensionless parameter characterizing the number of
negative ions in the plasma. It is determined by the ratio
of the negative ion density nn and positive ion density ni:
α = nn /ni. In the case of large values of α it is also
convenient to use a different parameter αe = ne /ni, where
ne is electron density. The values of the parameter α
vary from 0 (the case of classical plasma), to 1 (the case
of ion-ion plasma).
Poisson's equation in dimensionless variables can
thus be written as follows:
2
2
1 1 1(1 )exp( ) exp( )pxd d i
dx x dx x
ψ ψ α ψ α ψ
γψ
⎛ ⎞
+ =− + − +⎜ ⎟⎜ ⎟−⎝ ⎠
.
The boundary conditions are defined in the
presheath, where the motion of positive ions is mainly
directed to the probe, as opposed to undisturbed plasma,
where it is mostly chaotic. The boundary radius x0 was
chosen to satisfy the conditions of quasineutrality and
kTe >> |eφ| >> kTi, kTn >> |eφ| >> kTi. Thus, we used
the following boundary conditions:
( )0 0 00
/ , , / 2 /px ix d dx xτ ψ τ ψ τ= = − = ,
where τ = eφ0/kTe is the ratio of positive ions energy at
the boundary surface to the electron temperature. Note
that such choice of the dimensionless variables has
made it possible to reduce the problem solution downto
ISSN 1562-6016. ВАНТ. 2012. №6(82) 259
finding the dependence of the current on six parameters
instead of eight in the dimensional form.
The numerical results are presented in Fig. 1 as a set
of curves representing dependency of the dimensionless
current function of the dimensionless probe potential. One
can see from these dependencies that the value of
dimensionless current drops with the rise of
dimensionless radius, that is associated with decrease of
the probe sheath thickness. It is seen that the current of
positive ions to the probe falls also with the plasma
electronegativity increase.
In Fig. 2 the comparison of radial distributions of
charged particle densities in the vicinity of the probe in
electropositive and electronegative plasmas is shown. The
plasma electronegativity increase means the negative
charge redistribution between the electrons and negative
ions, while the negative ion density decreases faster when
approaching the probe due to lower temperature. Fig. 2
shows that such a change in the structure of the probe
sheath also has a strong influence on the distribution of
the density of positive ions.
2. EXPERIMENTAL RESULTS AND
DISCUSSION
In order to create a strongly electronegative plasma
a system was used based on electrostatic grid-type
electron filter described in [7]. In this system a vacuum
chamber with 250 mm diameter is divided by the filter
grid into two regions: the region with the dense ICP
plasma, produced by 2 turn shielded inductive coil with
13,56 MHz RF power 200 W, and the region with
strongly electronegative plasma. On the opposite side
the electronegative plasma region is restricted by the
grounded extraction electrode with 250 mm diameter,
placed at 100 mm distance from the grid. The
experiments were carried out at pressure of 10-3 … 10-2
Torr with the following operating gases: Ar, O2, SF6,
mixture of Ar and SF6. The residual pressure in the
chamber did not exceed 5·10-6 Torr. In all the described
experiments single cylindrical Langmuir probes with
length of 5 mm and a diameter of 70 microns was used.
The comparison of the experimentally measured
probe current-voltage characteristics are shown in Fig. 3
for the gas mixtures of Ar and SF6 with different ratio of
the gas partial pressures. As can be seen, with the SF6
partial pressure increase the electron saturation current
of the probe trace decreases with almost constant
positive ion current. This look natural taking in to
account that SF6 is an electronegative gas, so its
concentration increase causes the growth of the negative
ion density in the plasma and subsequent decrease
electron density.
In Fig. 4 a typical experimentally measured current-
voltage characteristics of the probe are shown in
comparison to the calculation results converted to
dimensional form. Comparison of all the experimental
and theoretical data shows that the results of
measurements and calculations are in good agreement in
wide range of parameters: for different gases at different
pressures and with different degrees of the plasma
electronegativity.
The simulation results show that the probe current
can depend not only on the parameter α, but also on the
temperature of the negative ions. Fig. 5 shows the
dependence of the dimensionless saturation current of
0 10 20 30 40 50
0
10
20
30
40
i
ψp
xp = 0.1
0.5
2
α = 0
0 10 20 30 40 50
0,0
0,5
1,0
1,5
2,0
i
ψp
50
100
α = 0
25
xp = 10
0 10 20 30 40 50
0
10
20
30
i
ψp
xp = 0.1
0.5
2
α = 0.9
0 10 20 30 40 50
0,0
0,5
1,0
i
ψp
100
50
α = 0.9
25
xp = 10
Fig. 1. Dimensionless current-voltage characteristics of
Langmuir probe for different values of dimensionless
radius xp in electropositive (α = 0) and electronegative
(α = 0.9) plasma
0 10 20 30 40 50
0
1
2
3
xp = 0.25
a = 0
η e
,η
+,
η -
x
ηe
η+
0 10 20 30 40 50
0,0
0,5
1,0
1,5
η-
η e
,η
+,
η -
x
xp = 0.25
a = 0.9
ηe
η+
Fig. 2. Radial distributions of densities of charged
particles for different values of parameter α with
xp = 0.25. ηe = ne /ne0 is dimensionless electron
density, η+ = ni /ne0 is dimensionless positive ions
density, η- = nn /ne0 is dimensionless negative ions
density
-40 -20 0 20
0,0
0,1
0,2
I,
m
A
U,V
1
2
3
4
1 - 50% Ar, 50% SF6
p = 2mTorr
2 - 33% Ar, 67% SF6
p = 3mTorr
3 - 20% Ar, 80% SF6
p = 5mTorr
4 - 100% SF6
p = 8mTorr
Fig. 3. Comparison of the experimentally measured
probe current-voltage characteristics for the gas
mixture of Ar and SF6, with different concentrations of
the gases
260 ISSN 1562-6016. ВАНТ. 2012. №6(82)
positive ions to the large probe (xp = 100) on the
parameter α for different values of γ (0.1…0.9)
characterizing the negative ion temperature. A
conclusion may be derived from these dependencies that
the Bohm current density of the positive ions is reduced
with the plasma electronegativity increase and negative
ion temperature decrease.
REFERENCES
1. D.J. Economou. Fundamentals and applications of
ion–ion plasmas // Appl. Surf. Sci. 2007, v.253, p. 6672-
6680.
2. S. Samukawa, K. Sakamoto.and K. Ichiki. Generating
high-efficiency neutral beams by using negative ions in
an inductively coupled plasma source // J. Vac. Sci.
Technol. 2002, v.20, p. 1566.
3. L. Grisham and J. Kwan. Perspective on the role of
negative ions and ion–ion plasmas in heavy ion fusion
science, magnetic fusion energy, and related fields //
Nucl. Instrum.Meth. Phys. Res. 2009, v.606, p. 83.
4. L. Grisham, J.W. Kwan, S.K. Hahto, K.N. Leung and
G. Westenskow. Negative halogen ions for fusion
applications// Rev. Sci. Instrum. 2006, v.77, 03A501.
5. A. Aanesland, A. Meige and P. Chabert. Electric
propulsion using ion–ion plasmas // J. Phys.: Conf. Ser.
2009, v.162.
6. H. Amemiya, B.M. Annaratone, J.E. Allen, The
collection of positive ions by spherical and cylindrical
probes in an electronegative plasma // Plasma Sources
Sci. Technol. 1999, v.8, p. 179–190.
7. D. V. Rafalskyi. and S. V. Dudin. A new grid-type
electron filter for volume-production negative-ion
source // EPL 2012, v.97, 55001.
Article received 20.09.12
МОДЕЛИРОВАНИЕ И ЭКСПЕРИМЕНТАЛЬНОЕ ИССЛЕДОВАНИЕ РАБОТЫ ЗОНДА
ЛЕНГМЮРА В ЭЛЕКТРООТРИЦАТЕЛЬНОЙ ПЛАЗМЕ
С.В. Дудин, Д.В. Рафальский, Д.А. Наймарк
Построена математическая модель работы одиночного цилиндрического зонда Ленгмюра, описывающая
взаимосвязь собираемого зондом тока положительных ионов с основными параметрами
электроотрицательной плазмы, такими как: потенциал зонда, плотности электронов, положительных и
отрицательных ионов, отношение температур электронов и ионов. Модель основывается на теории
радиального движения заряженных частиц. Она перекрывает широкую область параметров
электроотрицательной плазмы, в частности, весь диапазон, характерный для технологических систем.
Проведены экспериментальные измерения, подтверждающие высокую достоверность модели. Модель
может быть использована при проведении зондовых исследований в электроотрицательной плазме в
лабораторных и технологических системах, а также для дальнейшего совершенствования теорий
приповерхностных слоев в газоразрядной плазме.
МОДЕЛЮВАННЯ ТА ЕКСПЕРИМЕНТАЛЬНЕ ДОСЛІДЖЕННЯ РОБОТЫ ЗОНДА ЛЕНГМЮРА
В ЕЛЕКТРОНЕГАТИВНІЙ ПЛАЗМІ
С.В. Дудин, Д.В. Рафальський, Д.О. Наймарк
Побудовано математичну модель роботи одиночного циліндричного зонда Ленгмюра, яка описує
взаємозв'язок струму позитивних іонів, що збирається зондом, з основними параметрами електронегативної
плазми, такими як: потенціал зонда, густина електронів, позитивних та негативних іонів, співвідношення
температур електронів та іонів. Модель грунтується на теорії радіального руху заряджених частинок. Вона
перекриває широку область параметрів електронегативної плазми, зокрема, весь діапазон, характерний для
технологічних систем. Проведено експериментальні вимірювання, які підтверджують високу достовірність
моделі. Модель може бути використана під час проведення зондових досліджень електронегативної плазми
в лабораторних і технологічних системах, а також для подальшого вдосконалення теорій приповерхневих
шарів в газорозрядній плазмі.
-30 -20 -10 0
-15
-10
-5
0
5
10
15
I,
m
A
U, V
p = 1mTorr
a = 0,94
ae= 15,67
a)
-50 -40 -30 -20 -10 0
-30
-20
-10
0
10
20
30 p = 5mTorr
a = 0,9603
ae= 24.19
I,
m
A
U, V
b)
Fig. 4. a) Probe trace for O2. α = 0,94, αe = 15,67;
b) probe trace for gas mixture of 20% Ar and 80%
SF6. α = 0,9603, αe = 24,19. Solid curve:
experimentally measured. Points: calculation results
0,00 0,25 0,50 0,75 1,00
0,0
0,1
0,2
0,3
0,4
0,5
i
a
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
Fig. 5. Dependencies of the dimensionless probe
current i on the parameter α for different γ in the
large probe limit (xp = 100)
|