The influence of a DC electric field on the radio-frequency microdischarge
The dependence of ionization frequency in a stationary radio-frequency microdischarge on plasma density and DC voltage applied to the discharge plasma is found. Calculation is fulfilled for a plane geometry in assumption of uniformity of radio-frequency electric field. Розрахована залежність частоти...
Saved in:
| Published in: | Вопросы атомной науки и техники |
|---|---|
| Date: | 2005 |
| Main Author: | |
| Format: | Article |
| Language: | English |
| Published: |
Національний науковий центр «Харківський фізико-технічний інститут» НАН України
2005
|
| Subjects: | |
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/79798 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | The influence of a DC electric field on the radio-frequency microdischarge / N.A. Bogatov // Вопросы атомной науки и техники. — 2005. — № 2. — С. 191-193. — Бібліогр.: 5 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1859950056354873344 |
|---|---|
| author | Bogatov, N.A. |
| author_facet | Bogatov, N.A. |
| citation_txt | The influence of a DC electric field on the radio-frequency microdischarge / N.A. Bogatov // Вопросы атомной науки и техники. — 2005. — № 2. — С. 191-193. — Бібліогр.: 5 назв. — англ. |
| collection | DSpace DC |
| container_title | Вопросы атомной науки и техники |
| description | The dependence of ionization frequency in a stationary radio-frequency microdischarge on plasma density and DC voltage applied to the discharge plasma is found. Calculation is fulfilled for a plane geometry in assumption of uniformity of radio-frequency electric field.
Розрахована залежність частоти іонізації в стаціонарному високочастотному мікророзряді від концентрації плазми і постійної напруги, прикладеної до плазми розряду. Розрахунок виконаний для плоскої геометрії в припущенні однорідності високочастотного поля.
Рассчитана зависимость частоты ионизации в стационарном высокочастотном микроразряде от концентрации плазмы и постоянного напряжения, приложенного к плазме разряда. Расчет выполнен для плоской геометрии в предположении однородности высокочастотного поля.
|
| first_indexed | 2025-12-07T16:16:18Z |
| format | Article |
| fulltext |
THE INFLUENCE OF A DC ELECTRIC FIELD ON THE RADIO-
FREQUENCY MICRODISCHARGE
N.A. Bogatov
Institute of applied physics, Nizhni Novgorod, Russia, bogatov@appl.sci-nnov.ru
The dependence of ionization frequency in a stationary radio-frequency microdischarge on plasma density and DC
voltage applied to the discharge plasma is found. Calculation is fulfilled for a plane geometry in assumption of
uniformity of radio-frequency electric field.
PACS: 52.80.Pi
Discharges with linear dimensions in mm-range
(microdischarges) are actively investigated in the last time
in the connection with the numerous possible applications
[1]. The promising variant of a microdischarge is a radio-
frequency (RF) microdischarge [2,3]. In particularly, it
was suggested to use RF microdischarges in plasma
panels [4]. Ibidem it was the proposal to use one of the
interesting features of a microdischarge consisting in the
possibility to control it by a DC voltage applied to the
plasma along the small dimension. In the contrast to the
usual RF discharges with dimensions much more than the
electron Debye radius where an external DC electric field
is compensated by the plasma polarization, a microplasma
with the dimension about (equal or less than) the Debye
radius allow a DC field to penetrate inside the plasma and
influence the ionization balance at rather low (about
electron temperature) voltage on the plasma boundaries.
This influence consists in increasing of the electron loss
frequency dew to adding of an electron drift pooling in
the DC field to the electrons loss.
In this paper the dependence of electron ionization
frequency needed for maintaining of RF discharge on
plasma density and DC voltage applied to the plasma is
calculated.
We state the basic definitions and assumptions: (1) the
plasma contains electrons and positive ions in
concentration ne and ni respectively; (2) these charges are
produced by electron-molecule collisions at the rate νine
per unit volume, where νi is the frequency of ionization
by an electron; (3) the gas pressure is sufficiently high
for the particles mean free paths to be small compared to
all relevant dimensions. The mean motion of the charged
particles will then be determined by diffusion and
mobility with coefficients De, µe, Di, µi. If plasma contains
several different sorts of ions, we will suppose them to
have the same diffusion and mobility coefficients; (4)
charged particles losses dew to recombination are much
less than diffusion and drift ones. There is no volume
attachment; (5) charged particles reaching the walls stick
to them and recombine there. There is no particles
repelled or emitted by the walls; (6) the value of DC
electric field E is small compared to RF electric field
amplitude ERF. Than diffusion and mobility coefficients
depends only on the latter; (7) RF electric field is not
depend on charged particles densities; (8) discharge occur
between parallel flat electrodes with dimensions much
more than gas gap. Both RF and DC voltages are applied
to these electrodes. In this case RF electric field will be
homogeneous in the discharge volume and νi, De, µe, Di, µ
i will be constant.
Condition (7) is satisfied if discharge dimensions are
much less than the vacuum wavelength of the RF field
and RF conductivity current density is much less than RF
displacement current: σE HF << ε0 ωE HF (σ - plasma
conductivity, ω - circular frequency of the RF field, ε0 -
vacuum permeability). It takes place at sufficiently high
frequency:
ω >>
eμe
ε0
ne , (9)
where e - charge of electron. For example, in a xenon at
the degree of ionization equaled 10-8 which is typical for
microdischarges in radio-frequency plasma display panel
cells [5] condition (1) start to be fulfilled in the meter
wavelength range. For the discharge in xenon the
condition (3) impose the following restriction on the
pressure P and discharge gas gap L: LP>>50 µm×Torr.
At the above assumptions stationary charged particles
balance equations and Poison equation take the following
form:
dΓ e
dx
=
dΓ i
dx
=ν i ne , (10)
Γ e=−De
dne
dx
−μe Ene , (11)
Γ i=−D i
dni
dx
μi Eni , (12)
dE
dx
= e
ε0
ni−ne , (13)
here Γ e and Γ i - electron and ion flows. We point out
that RF electric field does not influence on the mean
motion of charged particles, it only determines the value
of kinetic coefficients. In accordance to conditions (4,3)
charged particles densities and flows should satisfy the
following boundary conditions:
ne ,i x1 =ne ,i x2 =0 , Γ e ,i x1 ≤0 ,
Γ e ,i x2 ≥0 , (14)
where x1,2 - electrodes coordinates (x2-x1=L). Choose the
origin of coordinate in the center of the gas gap and use
dimensionless variables with normalization factors:
Problems of Atomic Science and Technology. Series: Plasma Physics (11). 2005. № 2. P. 191-193 191
length- xn=L/2 , density - nn=
4ε0 De
eμe L2 , electric
field- En=
2De
μe L
, particles flow - Γ n=
ε0
e
De
2
μe
2
L
3
, voltage - U n=
De
μe
=T e (Te - electron temperature).
In terms of the dimensionless variables equations (10-14)
becomes:
Γ e
' =Γ i
'=αne , (15)
Γ e=−ne
' −Ene , (16)
Γ i=−βni
'γ Eni , (17)
E '=ni−ne , (18)
ne ,i 1 =ne , i−1 =0 , Γ e ,i −1 ≤0 ,
Γ e ,i 1 ≥0 , (19)
where α=
ν i L2
4De
, β=
Di
De
, γ=
μi
μe
. In non-
equilibrium plasma which a plasma of RF discharge
belongs to, the following relations between parameters
are fulfilled:
β << γ << 1 .
DC voltage on the electrodes is:
U=∫
−1
1
Edx .
There are well known the solutions of this problem at
high and low plasma density limits. At high plasma
density or large discharge size when r d << 1 (
r d= 1
ne
- dimensionless electron Debye radius),
nontrivial solution satisfying boundary conditions exists
at:
α=α1= π
2
2
γ .
192
In this case the value of the ionization frequency needed
for maintaining of the discharge does not depend on the
DC voltage applied to the electrodes because external DC
field is compensated in plasma by the volume charges of
the thin electrode sheets and does not influence on the
ambipolar diffusion of charged particles to the electrodes.
In the another limit - low plasma density or small
discharge size - when r d >> 1
γ
, the condition for
nontrivial solution existing is:
α=α2= π
2
2
U
4
2
.
In this case the plasma volume charge is too small to
influence the electron motion (and to change the external
field). Electron losses are determined by free electron
diffusion and drift in the external electric field.
In the intermediate region 1
γ≤rd≤1 parameter α
takes values in the interval (α1,α2). This region occupies
some orders of value of the electron density.
The dependencies of α on the maximum electron
density nem in a discharge in xenon (γ = 2.67⋅10-3) at
different U obtained by numerical calculations are shown
on the figure. There is also the typical loading curve of
RF source: the dependence of ionization frequency
realized by RF source on plasma density (curve 1).
Stationary states of discharge takes place in the
intersection points of curve 1 with appropriate curve α
(nem). As equations (15-19) always have trivial solution,
without plasma, one can see from the figure that system
can have one, two or three stationary states depending on
parameters γ, U and parameters of RF source: output
amplitude and output impedance. Stationary state is stable
if at nem increasing, curve α(nem) goes above loading curve
1, in another case stationary state is unstable. When
system have three stationary state, two of them are stable
- without plasma (discharge switch off) and with plasma
(discharge switch on). That means that such a discharge
cell has a "memory" feature which is of great importance
in some applications. Driving the DC voltage on the
electrodes it is possible to control discharge: both to tune
discharge parameters in some extent and to switch the
state of the discharge making it "turn on" or "turn off".
REFERENCES
1.C.G. Wilson, Y.B. Gianchandani, R.R. Arslanbekov, V.
Kolobov, A.E. Wendt. Profiling and modeling of dc
nitrogen plasmas // J. Appl. Phys. 2003, v.94, N5,
p.2845-2851.
2.M. Kurihara, T. Makabe. Two-dimensional modeling of
a microcell plasma in a mixture of Ne/Xe driven by a
capacitively coupled high-frequency source // J. Appl.
Phys. 2001, v.89, N12, p.7756-7763.
3.N. Bogatov, Yu. Brodsky, S. Golubev. Radio-frequency
plasma display cell // J. SID. 2003, v11, N4, p.685-692.
4.Patent of RF N2117335. Method for driving a plasma
display / N. Bogatov, Yu. Brodsky, S. Golubev // 1997.
5.L.C. Pitchford, J.Kang, C.Punset, J.P.Boeuf. Calculated
characteristics of radio-frequency plasma display panel
cells including the influence of xenon metastables //
J.Appl. Phys. 2002, v.92, N12, p.6990-6997.
-5 -4 -3 -2 -1 0 1 2 3 4 5 6 7
log(nem)
-3
-2
-1
0
1
2
lo
g(
α)
U=23
U=14
U=7
U=0
1
Dependence of α on nem at different U. γ = 2.67⋅10-3 ; curve 1 is loading curve or RF generator
ВЛИЯНИЕ ПОСТОЯННОГО ЭЛЕКТРИЧЕСКОГО ПОЛЯ НА ВЫСОКОЧАСТОТНЫЙ
МИКРОРАЗРЯД
Н.А. Богатов
Рассчитана зависимость частоты ионизации в стационарном высокочастотном микроразряде от концентрации
плазмы и постоянного напряжения, приложенного к плазме разряда. Расчет выполнен для плоской геометрии в
предположении однородности высокочастотного поля.
ВПЛИВ ПОСТІЙНОГО ЕЛЕКТРИЧНОГО ПОЛЯ НА ВИСОКОЧАСТОТНИЙ МІКРОРОЗРЯД
М.О. Богатов
Розрахована залежність частоти іонізації в стаціонарному високочастотному мікророзряді від концентрації
плазми і постійної напруги, прикладеної до плазми розряду. Розрахунок виконаний для плоскої геометрії в
припущенні однорідності високочастотного поля.
194
|
| id | nasplib_isofts_kiev_ua-123456789-79798 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1562-6016 |
| language | English |
| last_indexed | 2025-12-07T16:16:18Z |
| publishDate | 2005 |
| publisher | Національний науковий центр «Харківський фізико-технічний інститут» НАН України |
| record_format | dspace |
| spelling | Bogatov, N.A. 2015-04-04T19:47:23Z 2015-04-04T19:47:23Z 2005 The influence of a DC electric field on the radio-frequency microdischarge / N.A. Bogatov // Вопросы атомной науки и техники. — 2005. — № 2. — С. 191-193. — Бібліогр.: 5 назв. — англ. 1562-6016 PACS: 52.80.P https://nasplib.isofts.kiev.ua/handle/123456789/79798 The dependence of ionization frequency in a stationary radio-frequency microdischarge on plasma density and DC voltage applied to the discharge plasma is found. Calculation is fulfilled for a plane geometry in assumption of uniformity of radio-frequency electric field. Розрахована залежність частоти іонізації в стаціонарному високочастотному мікророзряді від концентрації плазми і постійної напруги, прикладеної до плазми розряду. Розрахунок виконаний для плоскої геометрії в припущенні однорідності високочастотного поля. Рассчитана зависимость частоты ионизации в стационарном высокочастотном микроразряде от концентрации плазмы и постоянного напряжения, приложенного к плазме разряда. Расчет выполнен для плоской геометрии в предположении однородности высокочастотного поля. en Національний науковий центр «Харківський фізико-технічний інститут» НАН України Вопросы атомной науки и техники Low temperature plasma and plasma technologies The influence of a DC electric field on the radio-frequency microdischarge Вплив постійного електричного поля на високочастотний мікророзряд Ияние постоянного электрического поля на высокочастотный микроразряд Article published earlier |
| spellingShingle | The influence of a DC electric field on the radio-frequency microdischarge Bogatov, N.A. Low temperature plasma and plasma technologies |
| title | The influence of a DC electric field on the radio-frequency microdischarge |
| title_alt | Вплив постійного електричного поля на високочастотний мікророзряд Ияние постоянного электрического поля на высокочастотный микроразряд |
| title_full | The influence of a DC electric field on the radio-frequency microdischarge |
| title_fullStr | The influence of a DC electric field on the radio-frequency microdischarge |
| title_full_unstemmed | The influence of a DC electric field on the radio-frequency microdischarge |
| title_short | The influence of a DC electric field on the radio-frequency microdischarge |
| title_sort | influence of a dc electric field on the radio-frequency microdischarge |
| topic | Low temperature plasma and plasma technologies |
| topic_facet | Low temperature plasma and plasma technologies |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/79798 |
| work_keys_str_mv | AT bogatovna theinfluenceofadcelectricfieldontheradiofrequencymicrodischarge AT bogatovna vplivpostíinogoelektričnogopolânavisokočastotniimíkrorozrâd AT bogatovna iâniepostoânnogoélektričeskogopolânavysokočastotnyimikrorazrâd AT bogatovna influenceofadcelectricfieldontheradiofrequencymicrodischarge |