Langmuir probe in ion-beam plasma: theory VS experiment
The paper is devoted to experimental verification of theoretical model of Langmuir probe operation in ion-beam plasma. The mathematical model of single cylindrical Langmuir probe describes dependence of ion current gathered by the probe on the basic parameters of ion-beam plasma. The model covers...
Збережено в:
| Дата: | 2012 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Науковий фізико-технологічний центр МОН та НАН України
2012
|
| Назва видання: | Физическая инженерия поверхности |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/98971 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Langmuir probe in ion-beam plasma: theory VS experiment / S.V. Dudin // Физическая инженерия поверхности. — 2012. — Т. 10, № 3. — С. 273–280. — Бібліогр.: 15 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-98971 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-989712016-04-20T03:02:40Z Langmuir probe in ion-beam plasma: theory VS experiment Dudin, S.V. The paper is devoted to experimental verification of theoretical model of Langmuir probe operation in ion-beam plasma. The mathematical model of single cylindrical Langmuir probe describes dependence of ion current gathered by the probe on the basic parameters of ion-beam plasma. The model covers wide parameters range of the ion-beam plasma, particularly the whole range typical for technological ion-beam systems. The comparison of the results of numerical calculations with the experimental measurement results confirms high reliability of the model in wide range of parameters excluding the case of very low ion beam energy. Статья посвящена экспериментальной проверке теоретической модели, описывающей работу зонда Ленгмюра ионно-пучковой плазме. Математическая модель одиночного цилиндрического зонда Ленгмюра описывает зависимость ионного тока на зонд от основных параметров ионнопучковой плазмы. Модель охватывает широкий спектр параметров ионно-пучковой плазмы, в частности, параметры, типичные для технологических ионно-лучевых систем. Сравнение результатов численных расчетов с экспериментальными результатами подтверждает высокую достоверность этой модели в широком диапазоне параметров за исключением случая очень низкой энергии пучка ионов. Статтю присвячено експериментальній перевірці теоретичної моделі роботи зонда Ленгмюра в іонно-пучковій плазмі. Математичнамодель одиночного циліндричного зондаЛенгмюра описує залежність іонного струму на зонд від основних параметрів іонно-пучкової плазми. Модель охоплює широкий спектр параметрів іонно-пучкової плазми, зокрема, параметри, що є типовими для технологічних іонно-променевих систем. Порівняння результатів чисельних розрахунків з експериментальними результатами підтверджує високу достовірність цієї моделі в широкому діапазоні параметрів за винятком випадку дуже низької енергії пучка іонів. 2012 Article Langmuir probe in ion-beam plasma: theory VS experiment / S.V. Dudin // Физическая инженерия поверхности. — 2012. — Т. 10, № 3. — С. 273–280. — Бібліогр.: 15 назв. — англ. 1999-8074 http://dspace.nbuv.gov.ua/handle/123456789/98971 533.9.082.76 en Физическая инженерия поверхности Науковий фізико-технологічний центр МОН та НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
The paper is devoted to experimental verification of theoretical model of Langmuir probe operation in
ion-beam plasma. The mathematical model of single cylindrical Langmuir probe describes dependence
of ion current gathered by the probe on the basic parameters of ion-beam plasma. The model
covers wide parameters range of the ion-beam plasma, particularly the whole range typical for technological
ion-beam systems. The comparison of the results of numerical calculations with the experimental
measurement results confirms high reliability of the model in wide range of parameters excluding
the case of very low ion beam energy. |
| format |
Article |
| author |
Dudin, S.V. |
| spellingShingle |
Dudin, S.V. Langmuir probe in ion-beam plasma: theory VS experiment Физическая инженерия поверхности |
| author_facet |
Dudin, S.V. |
| author_sort |
Dudin, S.V. |
| title |
Langmuir probe in ion-beam plasma: theory VS experiment |
| title_short |
Langmuir probe in ion-beam plasma: theory VS experiment |
| title_full |
Langmuir probe in ion-beam plasma: theory VS experiment |
| title_fullStr |
Langmuir probe in ion-beam plasma: theory VS experiment |
| title_full_unstemmed |
Langmuir probe in ion-beam plasma: theory VS experiment |
| title_sort |
langmuir probe in ion-beam plasma: theory vs experiment |
| publisher |
Науковий фізико-технологічний центр МОН та НАН України |
| publishDate |
2012 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/98971 |
| citation_txt |
Langmuir probe in ion-beam plasma: theory VS experiment / S.V. Dudin // Физическая инженерия поверхности. — 2012. — Т. 10, № 3. — С. 273–280. — Бібліогр.: 15 назв. — англ. |
| series |
Физическая инженерия поверхности |
| work_keys_str_mv |
AT dudinsv langmuirprobeinionbeamplasmatheoryvsexperiment |
| first_indexed |
2025-07-07T07:17:12Z |
| last_indexed |
2025-07-07T07:17:12Z |
| _version_ |
1836971598857371648 |
| fulltext |
273
INTRODUCTION
It is known, that in transport space of intense ion
beam the ion-beam plasma (IBP) appears as a re-
sult of the beam space charge neutralization by elec-
trons [1, 2]. The interest to research of IBP is stim-
ulated by wide extension of different ion-beam tech-
nologies [3 – 6], where the charged, excited, chem-
ically active particles and electromagnetic radiation
hit the processed surface immediately from the ion-
beam plasma.
One of the most attractive methods for measur-
ing of the ion-beam plasma parameters is the Lang-
muir probe method, which permit to measure local-
ly practically all essential plasma parameters in wide
range of their change. However, the probe mea-
surements in IBP have specific peculiarities connect-
ed with complex composition of the plasma, partic-
ularly with the presence in the plasma of two ion
groups with dramatically different energies: the beam
ions (usually hundreds-thousands eV) and cold
plas-ma ions with temperature much less than 1 eV.
Naturally, the response of these two ion groups to
the electric field around the probe is different. Slow
ion behavior is similar to common plasma, the ions
tend to form positive space charge around negati-
vely biased probe while the fast ions don’t “feel”
the probe voltage and provide constant background
of positive space charge with no dependence on
the probe voltage.
A mathematical model describing dependence of
ion current gathered by single cylindrical Langmuir
probe on the basic parameters of ion-beam plasma
has been presented in [7]. However, there was no
comparison of the simulation results with experiment.
The aim of the present work is experimental verifi-
cation of the theoretical model.
UDC 533.9.082.76
LANGMUIR PROBE IN ION-BEAM PLASMA: THEORY VS EXPERIMENT
S.V. Dudin
V.N. Karazin Kharkiv National University
Ukraine
Received 14.09.2012
The paper is devoted to experimental verification of theoretical model of Langmuir probe operation in
ion-beam plasma. The mathematical model of single cylindrical Langmuir probe describes depen-
dence of ion current gathered by the probe on the basic parameters of ion-beam plasma. The model
covers wide parameters range of the ion-beam plasma, particularly the whole range typical for tech-
nological ion-beam systems. The comparison of the results of numerical calculations with the exper-
imental measurement results confirms high reliability of the model in wide range of parameters ex-
cluding the case of very low ion beam energy.
Keywords: Langmuir probe, ion-beam plasma, plasma simulation.
Статья посвящена экспериментальной проверке теоретической модели, описывающей работу
зонда Ленгмюра ионно-пучковой плазме. Математическая модель одиночного цилиндрического
зонда Ленгмюра описывает зависимость ионного тока на зонд от основных параметров ионно-
пучковой плазмы. Модель охватывает широкий спектр параметров ионно-пучковой плазмы, в
частности, параметры, типичные для технологических ионно-лучевых систем. Сравнение
результатов численных расчетов с экспериментальными результатами подтверждает высокую
достоверность этой модели в широком диапазоне параметров за исключением случая очень
низкой энергии пучка ионов.
Ключевые слова: зонд Ленгмюра, ионно-пучковая плазма, моделирование плазмы.
Статтю присвячено експериментальній перевірці теоретичної моделі роботи зонда Ленгмюра
в іонно-пучковій плазмі. Математична модель одиночного циліндричного зонда Ленгмюра описує
залежність іонного струму на зонд від основних параметрів іонно-пучкової плазми. Модель
охоплює широкий спектр параметрів іонно-пучкової плазми, зокрема, параметри, що є типовими
для технологічних іонно-променевих систем. Порівняння результатів чисельних розрахунків з
експериментальними результатами підтверджує високу достовірність цієї моделі в широкому
діапазоні параметрів за винятком випадку дуже низької енергії пучка іонів.
Ключові слова: зонд Ленгмюра, іонно-пучкова плазма, моделювання плазми.
S.V. Dudin, 2012
ФІП ФИП PSE, 2012, т. 10, № 3 vol. 10, No. 3274
MODEL DESCRIPTION
Let us review first the mathematical model, which
describes the dependence of ion current gathered
by a single cylindrical Langmuir probe on the basic
parameters of ion-beam plasma, such as probe po-
tential, cold and beam ion densities, relation between
ion and electron temperatures.
The model is built for collisionless case, because
transport of ion-beams takes place at low pressures.
A current of cold ions on infinite single cylindrical
Langmuir probe is considered. It is assumed that
the ion temperature Ti is much less than electrons
temperature Te and electron distribution is Max-
wellian. The following dimensionless variables and
parameters are used in our model:
e
e
kT
ϕψ = ,
De
rx =
λ
,
0
i
i
e
n
n
η = ,
0
b
b
e
n
n
η = ,
0
e
e
e
n
n
η = , p
p
De
r
x =
λ
, p
p
e
e
kT
ϕ
ψ = ,
0
22
i
e
p i
i
Ii
kTr Len
m
=
π , i
e
T
T
τ = .
Here ϕ – potential in point with radius r; ni, nb, ne –
densities of cold ions, beam ions and electrons, re-
spectively; ne0, ni0 – densities of electrons and cold
ions at infinity, rp, ϕp, L – radius, potential and length
of probe; Ii – current of cold ions to the probe; mi –
ion mass; e – electron charge; k – Boltzmann’s con-
stant; 2
04
e
De
e
kT
n e
λ =
π
– Debye length.
The analogous dimensionless parameters are
used in the most of theoretical works dealing with
computation of ion current to Langmuir probe [8 −
10], but we have introduced additional parame-
ter: “portion of ion beam in plasma”:
0
0
0
i
i
e
n
n
η = . The
value of this parameter changes from 0 (case of
“pure” ion-beam plasma without cold ions), to 1
(case of “classic” plasma without beam).
Poisson’s equation in dimensionless variables can
thus be written as follows:
( )
2
0 02
1 1exp( ) 1p
i i
xd d i
dx x dx x
ψ ψ+ = ψ − η − −η −ψ
,
(1)
where the first term of right part is the dimension-
less density of electrons, the second is the density
of slow ions, the third is the density of beam of
ions, which is constant.
For determination of initial conditions let us ta-
ke a region in which the following conditions are
satisfied: kTe >> |eϕ| >> kTi, ne ≈ ni + nb. In this
region the current density of cold ions can be de-
fined as 2
iIj
rL
=
π , and on the other hand, the den-
sity of cold ions is determined by potential ϕ:
( )
0
2
i
i
e
j en
m
−ϕ
= .
From this equation an analytic expression for
radial distribution of potential can be found:
2 2
2( ) pi x
x
x
−
ψ = .
The initial conditions for equation (1) are set on
the cylindrical surface with dimensionless radius x0,
which is in the region defined above. The potential
of this surface we define as ψ0 = −bτ where b > 1
(for example, b = 5). Radius x0 and derivative of
potential at x = x0 can thus be written as follows:
0
1
px ix
b
=
τ ,
0 0
2d b
dx x
ψ τ =
.
We solved Poisson’s equation using the fourth
order Runge-Kutta method.
SIMULATION RESULTS
As a result of numerical computations we have got a
data array of cold ion current dependence on four
parameters i(ψp, xp, ηi0, τ). The values of dimen-
sionless potential were changed from 0 to 50, the
dimensionless probe radius xp from 0.25 to 100 that
corresponds to the change of plasma density from
108 to 1013 сm−3. Temperatures ratio was 0.01. A
set of the calculation results is presented graphically
in fig.1.
For the limiting case of the large probe (xp = 100
in the fig. 1) we can make a conclusion, that for any
values of parameter ηi0, as in the case of “classic”
plasma, saturation of ion current takes place. The
saturation current density can be presented by for-
mula, which is analogous to the well known Bohm’s
formula for plasma without ion beam:
LANGMUIR PROBE IN ION-BEAM PLASMA: THEORY VS EXPERIMENT
ФІП ФИП PSE, 2012, т. 10, № 3 vol. 10, No. 3276
fig. 1.
EXPERIMENTAL TECHNIQUES
In order to provide the experimental verification of
the described model in wide range of parameters
the experimental investigation was conducted using
two different ion sources.
The first experimental setup (Device 1, see fig.4)
with a multichannel Hall type ion source “Radical-
M” generating ion beam with diameter of about 50
mm, mean ion energy about 500 eV and current 1
− 50 mA. The stainless steel transport chamber with
length of 17 cm has appro-ximately rectangular
cross-section. The argon pressure in the chamber
was 10−4 – 10−3 Torr.
The second experimental setup (Device 2, see
fig. 5) is based on a single-grid ICP ion source with
RF biasing [11]. The plasma is generated by 2-turns
shielded inductive coil placed inside the metallic vac-
uum chamber with 250 mm inner diameter and 80
mm length. RF power (13.56 MHz) in the range 0
− 1000W is applied to the inductor through a match-
ing box. For the control of the plasma potential the
discharge chamber was designed as a potential elec-
trode insulated from the grounded flange holding the
0.12 mm thick stainless steel extraction grid with
Fig. 3. Radial distribution of densities of electrons ηe and ions η i in comparison with potential distribution at several
η i0 values. ηe − thin line, η i − bold line.
Fig. 4. Scheme of experimental Device 1. 1 – ion source, 2
– multigrid energy analyzer, 3 – flat probe with guard ring,
4 – target, 5 – Langmuir probe, 6 – transport chamber. Fig. 5. Scheme of experimental Device 2.
LANGMUIR PROBE IN ION-BEAM PLASMA: THEORY VS EXPERIMENT
277
holes of 0.24 mm diameter. The working area of
the grid is 450 cm2 and optical transparency is
0.4. RF (13.56 MHz) bias voltage required for the
ion acceleration is applied between the grounded
grid and the source chamber. The RF bias is sup-
plied through a capacitor allowing DC positive self-
bias generation on the electrode which is greater
then the grid by area. The DC self-bias potential of
the electrode was the measured value and is used
below as a main parameter governing the ion ener-
gy and emission characteristics of the source. All
potentials in this work are measured versus the
grounded beam transport chamber.
In the described experiments the source was at-
tached to the 400 mm diameter metallic ion beam
transport chamber pumped by a turbo pump with
700 l/s throughput. The residual pressure in the sys-
tem was better then 10−5 Torr. The 300 mm diame-
ter target accepting the ion beam was placed at 100
mm distance from the source grid. The target was
equipped with the 20 mm diameter single-grid re-
tarding-field energy analyzer analogous to the de-
vice used in previous works [11 − 13]. The EA grid
holes diameter is 0.1 mm, thickness is 0.12 mm and
optical transparency is 0.2. Also, a linear array of
plane probes biased at −25 V was mounted on the
target to measure radial ion current density profile.
In order to measure ion current density from the
ICP to the IOS an additional planar probe was
mounted on the extraction grid at the source axis
and also was biased at −25 V.
For measurement of the plasma parameters
in both devices Langmuir probes (0.1 mm diame-
ter, 5 mm length) were inserted in the IBP region.
The probe measurements were conducted using the
PlasmaMeter version 5.3 probe system [14, 15]
designed in the V.N. Karazin Kharkiv National
University. The current measurement unit and volt-
age amplifier of the PlasmaMeter are optically iso-
lated from the digital controller connected to ground.
PlasmaMeter communicates with the controlling
computer via a USB interface. The PlasmaMeter
can measure probe currents up to 300 mА at probe
voltages from −80 to 80 V. To avoid the probe
melting, over-current protection is provided that
automatically decreases the probe voltage so that
the current drawn through the probe tip never ex-
ceeds 0.5 A. Both the ADC and DAC are 16 bits.
This in combination with the high linearity of the
amplifiers (better than 0.03%), a low internal noise,
and the advanced differentiation procedure used
allows measurement of the EEPF to 3 orders of
magnitude. The sensitivity is usually limited by plas-
ma noise rather than hardware measurement limita-
tions.
EXPERIMENTAL RESULTS AND
DISCUSSION
As it was mentioned in Introduction, the main focus
of the present research is to find out the influence of
parameters of two groups of ions (namely the fast
beam ions and slow plasma ions) on the Langmuir
probe trace. The measured current-voltage char-
acteristics of Langmuir probe are shown in fig. 6 for
the Device 1 and in fig. 7 for the Device 2.
The curves in the fig. 6 was measured at the same
parameters, but at different probe positions includ-
ing the positions at the beam axis, at the beam edge
and outside the beam, that allows to research the
dependence of shape of the probe characteristics
on the slow/fast ions ratio with constant ion beam
energy.
Otherwise, all the probe curves presented in the
fig. 7 are measured at the same probe position (cen-
ter of the beam transport chamber), but with differ-
ent ion beam energies in order to reveal the fast ion
energy impact on the probe trace. It should be not-
ed that in all the cases the fast ion current to the
probe calculated using the known ion beam current
density and the probe cross-section area was sig-
nificantly less then the slow ion current to the probe,
so in the comparison of the theoretic and experi-
Fig. 6. Langmuir probe characteristics measured in the
Device 1. Different curves was measured at different radial
prove distances r from the ion beam axis.
S.V. DUDIN
ФІП ФИП PSE, 2012, т. 10, № 3 vol. 10, No. 3
ФІП ФИП PSE, 2012, т. 10, № 3 vol. 10, No. 3278
mental results below under the ion current to the
probe we understand just the cold ion current.
The ion beam energy and current density was
measured using the retarding field energy analyzer
and the flat probes. Some of the measured ion en-
ergy distribution functions are presented in fig. 8.
Fast and slow ion peaks are clearly visible. The fast
ion peak at high acceleration voltages can be rela-
tively broad, so mean ion beam energy was used in
further analysis.
In order to verify reliability of the mathematical
model described in the first part of the present pa-
per the direct comparison of the calculated and ex-
perimentally measured probe characteristics was
done. Such comparison for the results from the
Devices 1 and 2 is illustrated by fig. 9 and 10, re-
Fig. 7. Langmuir probe characteristics measured in the
Device 2. Different curves was measured with different
acceleration voltages цacc.
Fig. 8. Measured ion energy distribution functions. Fig. 9. Comparison of calculated and experimentally
measured probe characteristics for Devices 1. Radial probe
positions r are the same as in fig.6.
LANGMUIR PROBE IN ION-BEAM PLASMA: THEORY VS EXPERIMENT
279
spectively. The calculated dimensionless ion currents
were transformed to dimensional form, then elec-
tron current calculated using the measured electron
temperature was added allowing to obtain complete
probe current. The fast ion density was calculated
from the measured ion beam energy and current
density, slow ion and electron densities was calcu-
lated from a guess value of the parameter ηi0. Next,
using the successive approximation method the right
value of ηi0 was searched for the best coincidence
of the theoretic and experimental data.
One can see good agreement of the theory and
the experiment for the whole set of parameters ex-
cluding the case of very low energy of the ion beam.
Presumably it can be explained by the fast ion mo-
tion distortion by the electric field around the probe
which isn’t taken into account by the described
model. This looks natural for the lowest ion ener-
gies if we compare the probe voltage (up to 50 V in
the fig. 10) to the 25 eV ion energy for the last graph
in the fig. 10. Thus, we can conclude that the area
of applicability of the developed model is limited
from the side of low ion beam energy.
Thus, in the present work the experimental ver-
ification of the theoretical model of Langmuir probe
operation in ion-beam plasma has been carried out.
The mathematical model of single cylindrical
Langmuir probe describes dependence of ion cur-
rent gathered by the probe on the basic parameters
of ion-beam plasma. The model covers wide pa-
rameters range of the ion-beam plasma, particularly
the whole range typical for technological ion-beam
systems. The results of numerical calculations are
presented for the probe current versus probe di-
mensions and potential as well as the plasma pa-
rameters. The analytical expression for the ion cur-
rent (modification of the Bohm formula) is derived
for the large probe limit. For the numerical results
the approximation formula is constructed, simplify-
ing practical usage of the results. The comparison
of the results of numerical calculations with the ex-
perimental measurement results confirms high reli-
ability of the model in wide range of parameters
excluding the case of very low ion beam energy.
REFERENCES
1. Gabovich M.D.//UFN.− 1977.− Vol. 121, No. 2.
− P. 259-284.
2. Dudin S.V., Zykov A.V., Farenik V.I. Low Ener-
gy Intense Ion Beams Space Charge Neutraliza-
Fig. 10. Comparison of calculated and experimentally
measured probe characteristics for Devices 2. Probe is
located at the center of the beam transport chamber.
S.V. DUDIN
ФІП ФИП PSE, 2012, т. 10, № 3 vol. 10, No. 3
ФІП ФИП PSE, 2012, т. 10, № 3 vol. 10, No. 3280
tion//Rev. Sci. Instrum. − 1994. − Vol. 65, No. 4,
Part II. − P. 1451-1453.
3. Brown I.G. The Physics and Technology of Ion
Sources: Second, Revised and Extended Edition.
− Wiley-VCH: New York, 2004.
4. Reece Roth J., Industrial Plasma Engineering//
Applications to Nonthermal Plasma Processing
(CRC Press). − 2001. − Vol. 2.
5. Rius G., Llobet J., Esplandiu M.J., Sole L., Borri-
se X., Perez-Murano F.//Microelectronic Engi-
neering. − 2009. − Vol. 86. − P. 892.
6. Kaufman H.R. Technology of ion beam sources
in sput-tering//J. Vac. Sci. Technol. − 1979. −
Vol. 15, No. 2. − P. 272-276.
7. Antonova T.N., S Dudin.V., Farenik V.I.//Prob-
lems of Atomic Science and Technology. − 2003.
− No. 1. − P. 147-149.
8. Bernstein I.B., Rabinowitz I. Theory of Electro-
static Probes in a Low Density Plasma//Phys.
Fluids, 1959. − Vol. 2. − P. 112-115.
9. Laframboise J. Rarefied Gas Dynamics. Vol. 2/
Ed J.H. de Leeuw, N.Y. − Academic Press,
1966. − 22 p.
10. Fernandez Palop J.I., Ballesteros J, Colomer V.
and Hernandez M.A. Theoretical ion current to
cylindrical Langmuir probes for finite ion tem-
perature values//J. Phys. D: Appl. Phys. − 1996.
− Vol. 29. − P. 2832-2840.
11. Dudin S.V., Rafalskyi D.V. and Zykov A.V.//Rev.
Sci. Instrum. − 2010. − Vol. 81. − P. 083302.
12. Dudin S.V. and Rafalskyi D.V.//Europhys. Lett.
− 2009. − Vol. 88. − P. 55002.
13. Rafalskyi D.V. and Dudin S.V.//Appl. Phys. Lett.
− 2010. − Vol. 97. − P. 051501.
14. Dudin S.V.//Devices and techniquie of experi-
ment. − 1994. − No. 4. − P. 78-82.
15. McNeely P., Dudin S., Christ-Koch S., Fantz U.
//Plasma Sources Sci. Technol.− 2009. − Vol. 18.
− P. 014011.
LANGMUIR PROBE IN ION-BEAM PLASMA: THEORY VS EXPERIMENT
|