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Measurement of the electron density in a subatmospheric dielectric barrierdischarge by spectral line shape

Lifang Dong,a Yuyan Qi, Weiyuan Liu, and Weili FanCollege of Physics Science and Technology, Hebei University, Baoding 071002, China

Received 22 December 2008; accepted 8 June 2009; published online 7 July 2009

The electron density in a subatmospheric dielectric barrier discharge by using argon spectral line

shape is measured for the first time. With the gas pressure increasing in the range of 1104 Pa–6104 Pa, the line profiles of argon 696.54 nm are measured. An asymmetrical

deconvolution procedure is applied to separate the Gaussian and Lorentzian profile from the

measured spectral line. The gas temperature is estimated by using rotational temperature of N2+. By

subtracting the van der Waals broadening and partial Lorentzian instrumental broadening from the

Lorentzian broadening, the Stark broadening is obtained and used to estimate the electron density.

It is found that the electron density in dielectric barrier discharge increases with the increase in gas

pressure. ©   2009 American Institute of Physics.  DOI: 10.1063/1.3159891

I. INTRODUCTION

Dielectric barrier discharges  DBDs, also referred to as

silent discharges, are characterized by the presence of at least

one insulating dielectric layer in contact with the discharge

between two planar or cylindrical electrodes connected to an

ac power supply. In recent years, it has been a subject of 

great interest due to their potential industrial applications

including large-area flat plasma display panels, surface modi-

fication of polymers, reduction of pollutants, and generation

of UV and vacuum UV  VUV  radiation.1–4

In order to op-

timize this kind of plasmas for the industry applications, it is

necessary to know the plasma parameters, such as electron

density and electron temperature, which mainly determine

the characteristics of the discharge.

Plasma-broadened and shifted spectral lines have been

used as an important noninterfering plasma diagnostic tech-

nique. In previous work, we measured the electron density in

individual microdischarge channel by stark broadening.5,6

Balcon  et al.7

measured the average electron density for the

filamentary mode in dielectric barrier discharge by  H   stark 

broadening. However, to the best of our knowledge, there is

no report on the study of the variations of electron density

with the gas pressure in subatmospheric dielectric barrier dis-

charge up to now.

In this paper, we measure the electron density in a sub-

atmospheric dielectric barrier discharge by using Stark 

broadening. The results show that the electron density varies

from 8.41014 cm−3 to 1.51015 cm−3 with the gas pres-

sure increasing from 1104

Pa to 5104

Pa.

II. THEORY

In experiments, the spectral lines emitted from plasma

are subject to various broadening mechanisms including

natural broadening, Doppler broadening, instrumental broad-

ening, and pressure broadening, which include resonance,

van der Waals, and Stark broadening. The natural broadening

and resonance  broadening are generally negligible in high

density plasma.8

Doppler broadening originates from the sta-

tistical velocity distribution of the emitting atoms. The re-

lated intensity profile follows a Gaussian distribution if theemitting atom has a Maxwell velocity distribution. The van

der Waals broadening is caused by the dipolar interaction

between excited atom and the induced dipole from the neu-

tral perturber, whose profile follows a Lorentzian function.

The Stark broadening is determined by electron impact

broadening and plasma ion impact broadening. The electron

impact broadening gives a symmetrical Lorentzian profile,

and the smaller contribution of ion broadening is asymmetri-

cal in nature. Thus the Stark profile is the combination of 

these two broadenings and exhibits an asymmetrical Lorent-

zian profile. The apparatus induces another broadening on

the line profile, which depends upon the width of the slit on

the monochromator and the dispersion of its diffraction sys-tem. In many cases, the apparatus function can be approxi-

mated by a Voigt function composed by Gaussian profile and

Lorentzian profile.

A. Stark broadening

The Stark broadening and shift of a certain spectral line

spontaneously emitted from atoms in the plasma allows the

determination of electron density in a rapid and inexpensive

way.The Stark effect is determined by electrons impact and

plasma ions impact. Its profile is described as an asymmetri-

cal Lorentzian spectral line profile   j,

 j =1

 

0

W  R d  

1 +  − 0 − d e/ e −  4/3 22,   1

where   W  R    represents the microfield strength distribution

function, depending upon the dimensionless parameter R  that

accounts for the Debye shielding and ion-ion correlations.aElectronic mail: donglf@mail.hbu.edu.cn.

JOURNAL OF APPLIED PHYSICS  106, 013301 2009

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The full width at half maximum   FWHM   of Stark 

broadening   t  and Stark shift  d t  are complex functions of the

electron density   N e   and electron temperature   T e, expressed

as9–11

 t  = 2 1 + 1.75 10−4 N e1/4  1 − 0.068 N e

1/6T e

−1/2

10−16 e N e.   2

Due to the asymmetry of plasma-broadened atom line,

the shift at the half width of the spectral line is slightly dif-

ferent from the one measured at the peak of line profile and

can be calculated from9–11

d t  = d e 3.2 10−4 N e1/4  e 1 − 0.068 N e

1/6T e

−1/2

10−16 N e .   3

In Eqs.   1–3,    e   and   d e   are electron impact Stark 

broadening and shift, respectively,      is the ion-broadening

parameter, and N e  and  T e  are the electron density  cm−3  and

temperature K.

B. van der Waals broadening

Van der Waals broadening results from the dipole inter-

action of an excited atom with the induced dipole of a neutral

ground state atom of number density  N . This is a short-range

C 6 / r 6 interaction. Griem’s9

estimation for the FWHM  v

 can

be written12

as

 vcm = 8.18 10−12

2a  R22/5T g/ 

3/10 N ,   4

where

 R2 = RU 2 − R L

2 .   5

 R2

is the difference of the squares of coordinate vectors   ina0  units of the upper and lower level,  T g   is the gas tempera-

ture, and      is the atom-perturber reduced mass in a.m.u.

 =19.97 for excited Ar perturbed by Ar atoms, and  N  can

be obtained from the equation of the ideal gas. Values of   a ,

the mean atomic polarizability of the neutral   perturber, are

tabulated for different elements by Allen:13

for argon   a 

=16.5410−25 cm3. If the required value of   a   is not tabu-

lated, it  can be estimated either from the expression given by

Allen13

or by Griem:9

a  = 9/2a033 E  H /4 E EXC2 ,   6

where   E  H    is the ionization potential of hydrogen

109 737.32 cm−1 and  E EXC is the energy cm−1  of the first

excited level of the perturber. In the Coulomb approxima-

tion, the values of   RU   and   R L   in Eq.   5  may be calculated

from

 R j2 =

1

2n j25n j

2 + 1 − 3l jl j+1 ,   7

where the square of effective quantum number  n j is

n j2 = E  H / E IP − E  j,   8

and  E IP   is the ionization potential of the studied element and

 E  j is the energy of the upper or lower levels of the transition.

III. EXPERIMENTAL SETUP

The experimental device is shown in Fig.  1. Two cylin-

drical containers, with diameters of 65 mm, sealed with 1.5

mm thick glass plates are filled with water. A metallic ring

immerses in the water of each container and is connected to

a power supply. Thus, the water acts as a liquid electrode. A

glass frame with the thickness of 1.5 mm is placed between

the dielectric layers, serving as the lateral boundary. Thus,

the discharge gap is 1.5 mm. A sinusoidal ac voltage with a

frequency of 50 kHz is applied to the electrodes. All of the

apparatus are enclosed in a big chamber filled with argon.

The voltage applied to the electrode is measured with a Tek-

tronix high voltage probe  ratio 1:1000  connected to an os-

cilloscope  Tektronix TDS 3054, 500 MHZ. The discharge

gas is argon with a purity of about 99.92%. Optical emission

spectra from the plasma are collected with a converging lens

and an optical fiber and detected by a monochromator  AC-

TON SP-2758, 2400 groove/mm grating, resolution 0.01 nmwith a charge coupled device   1340400 pixels. The

opening of the slit input of the monochromator is set to50    m. The calibration of the instrumental function is made

with a He–Ne laser 632.8 nm line and is found to be a

Lorentzian component   L =0.002 38 nm  and a Gaussian

component G =0.016 68 nm.

IV. RESULTS AND DISCUSSION

As is well known, breakdown is the most critical aspect

of the discharge, since essentially all the energy, which is put

into the plasma electrons, is delivered in this phase. It is also

the critical phase for determining what chemical reactions

occur. It is necessary to investigate the plasma parameters at

the phase of breakdown. So, the electron density in dis-charges at critical breakdown voltage  named as critical dis-

charge in the context below   is investigated.

The critical discharges undergo two modes, a diffuse

mode and a filamentary mode. When the gas pressure is

varying in the range of 1104 Pa–5104 Pa, the gas be-

tween electrodes ignites in a diffuse mode, in which a plasma

completely fills the cross section of the discharge space.

However, the gas ignites in a form of filamentary mode, the

discharge no longer permeate on the whole electrodes, when

the gas pressure is increased to 6104 Pa.

It is found that the spectral lines profiles change with the

gas pressure. Figure 2  gives the profiles of argon 696.54 nm

FIG. 1. Schematic diagram of the experimental setup.

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at different gas pressures. As a reference source of unshifted

argon spectral line, a low pressure argon discharge in a small

tube at gas pressure of about 10 Pa is used. It can be clearly

seen that the broadenings and shifts of the line profile in-

crease with the increasing of gas pressure.

In many cases, the shift of the line profile is mostly

caused by Stark shift, while the van der Waals shift is rela-

tively small and can be negligible. Djurovic   et al.

14

foundthat the contributions of van der Waals shift to the shift of 

argon spectral line are in the range 1%–9% in plasma of an

atmospheric pressure wall stabilized argon arc with electron

densities of   0.74–2.91022 m−3 and electron tempera-

tures of  9280–10750 K. So, in our experiment, the increase

in the spectral line shift indicates the increasing in the elec-

tron density with the gas pressure.

In order to get the Stark broadening, the Lorentzian pro-

file must be known. Here we used the method for deconvo-

lution of asymmetric line profiles.5

As is well known, the

measured line profiles are the results of convolution of 

Lorentzian profile and Gaussian profile. The Lorentzian pro-

file comprises two parts: a symmetrical part and an asym-metrical part. The symmetrical Lorentzian profile comprises

van der Waals Lorentzian and partial instrumental Lorentzian

component. The asymmetrical one is Stark broadening

Lorentzian profile. The Gaussian type induces the Doppler

broadening and a majority of instrumental broadening. Thus,

the total spectral line profile   K    is the convolution of 

Gaussian  G   and Lorentzian profile  L, described by

K  = −

G − y L ydy  = −

+

0

1

G   /2

exp

− 2 y − 2

G

2

    W  R d  

1 +  y − 0 − d /w

 −  

4/3

 2

2

dy ,   9

where   G,   w,   d , and     are fitted to the experiment data.

We compiled a deconvolution procedure to separate   Lprofile from the measured spectral lines. The Lorentzian

broadening thus can be obtained. Figure 3 gives a deconvo-

lution result for Ar I 696.54 nm of discharge at the gas pres-

sure of 5104 Pa.

The Stark broadening can be obtained after subtracting

the calculated van der Waals broadening from the gas tem-

perature and measured partial instrumental broadening from

the deconvolved Lorentzian profiles.

For the argon plasma in our experiment with argon as the

perturber, the reduced mass     is equal to 19.97 and the pa-

rameter a  is 16.5410−25 cm3. Accordingly, the Eq.  4  can

be written in terms of the gas temperature as

 v696.54 =

1.52  a

Tg0.7  nm ,   10

where   a   is a ratio of discharge gas pressure to atmospheric

pressure.

The gas temperature in discharge is usually estimated

from analysis of the rotational spectra of molecular species

present in the plasma.15–17

However, it is no longer suitable

for pure argon discharge. For estimating the gas temperature,

the rotational temperature in air/argon mixture discharge are

studied by analyzing the first negative band of N 2

+

and shownin Fig. 4. It is found that the gas temperature varies from 420

to 460 K with the gas pressure changing from 1104 Pa to

5104 Pa

Figure 5  shows the variations of Lorentzian widths, van

der Waals broadenings, Stark broadening, and the electron

density with gas pressure increasing, respectively. It reveals

that the electron density in the discharge domain increase

from 8.41014 cm−3 to 1.51015 cm−3 with gas pressure

increasing from 1104 Pa to 5104 Pa. The relative error

of the electron density is estimated to be about 15% by con-

sidering the error induced by deconvolution method and the

experimental errors. The results prove the electron density in

dielectric barrier discharge is lower than that in dc glow dis-charge measured by Penache  et al.,

18which increases from

91014 cm−3 to 51015 cm−3 when the gas pressure

changes from 5103 Pa to 4104 Pa.

It is worth pointing out that the electron density obtained

here is much higher than that estimated by discharge current

or power balance.7

In order to explain the discrepancy, an-

other experiment was carried out in dielectric barrier dis-

charge in argon at pressure in the range of 1104 – 5

104 Pa. In the experiment, the light emission from total

discharge area and light emission of a small area of 0.25 mm

in diameter were measured by two photomultiplier tubes

RCA7265, respectively, and recorded by an oscilloscope

FIG. 2. The total profiles of Ar I 696.54 nm as a function of gas pressure.

FIG. 3. Typical deconvolution result for Ar I 696.54 nm in argon discharge

at the pressure of 5104 Pa.   C -convolution profile,   G-Gaussian profile,

 L-Lorentzian profile.

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Tektronix TDS 3054, 500 MHZ. The waveforms of voltage

and discharge current were also recorded. From Fig. 6, it can

be clearly seen that the discharge in the small area is not

ignited every half cycle of the applied voltage. In other

words, the discharge actually does not filled the entire area at

any time although the image of discharge exposed over a

long time   many half cycles   is homogeneous. The actual

discharge area here in each half cycle is much less than the

exposure area in image, which is generally used in the elec-

tron density estimation by discharge current or power bal-

ance. The electron density will be much less than the true

value if discharge area is overestimated. On the other hand,

FIG. 4. The measurement of gas temperature in dielectric barrier discharge

by emission spectrum.  a  The spectrum of the first negative band of N 2+ in

dielectric barrier discharge at gas pressure of 2104 Pa. b  The rotational

temperature is estimated by the slope of ln I /  J + J +1   vs  J  J +1 .  cThe gas temperature in dielectric barrier discharge with the gas pressure

increasing from 1104 to 7104 Pa in different argon concentrations in

gas mixture.

FIG. 5. Variations of the Lorentzian broadening, the Stark broadening, the

van der Waals broadening of argon 696.54 nm spectral line, and the electron

density with the increase of gas pressure.

FIG. 6.   Color online a   Image of diffuse discharge at 1104 Pa. Dis-

charge area is 3030 mm2. Exposure time is 66.7 ms.   b   From top to

bottom the curves are waveforms of voltage, current, light from total dis-

charge area, and light from a small area of 0.25 mm in diameter,

respectively.

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the spectral line profile should vary with time in each dis-

charge current because the electron density changes with

time. A narrow profile corresponds to small electron density

while a wide profile corresponds to a large electron density.

It is obvious that the recorded spectral line profile is a tem-

poral integral and the widest profile is usually recorded. Thus

the electron density estimated by Stark broadening should be

the peak value of the electron density.

V. CONCLUSION

In this work, the electron density in a subatmospheric

DBD is estimated by using the Stark broadening of atomic

spectral line. With the gas pressure increasing in the range of 

1104 Pa–6104 Pa, the line profiles of argon 696.54 nm

are measured. An asymmetrical deconvolution procedure is

applied to separate the Gaussian and Lorentzian profiles

from the measured spectral line. The gas temperature is es-

timated by using rotational temperature of N2+. By subtract-

ing the van der Waals broadening and partial Lorentzian in-

strumental broadening from the Lorentzian broadening, the

Stark broadening is obtained. It is found that the electron

density in dielectric barrier discharge increases with the in-

crease in gas pressure.

ACKNOWLEDGMENTS

This work is supported by the Natural Science Founda-

tion of China under Grant Nos. 10575027 and 10775037, the

Specialized Research Fund for the Doctoral Program of 

Higher Education of China  Grant No. 20050075001, and

the Natural Science Foundation of Hebei Province, China

Grant Nos. A2006000950 and A 2008000564.

1H. S. Uhm, E. H. Choi, G. Cho, and K. Whang,  J. Plasma Phys.   67, 49

2002.2B. Eliasson and U. Kogelschatz,  IEEE Trans. Plasma Sci.  19, 309 1991.

3Z. Fang, Y. Qiu, and Y. Luo,  J. Phys. D: Appl. Phys.  36, 2980 2003.

4S. K. Dhali and I. Sardja,  J. Appl. Phys.  69, 6319 1991.

5L. F. Dong, J. X. Ran, and Z. G. Mao,  Appl. Phys. Lett.   86, 161501

2005.6L. F. Dong, Y. Y. Qi, Z. C. Zhao, and Y. H. Li,   Plasma Sources Sci.

Technol.  17, 015015 2008.7N. Balcon, A. Aanesland, and R. Boswell,   Plasma Sources Sci. Technol.

16, 217 2007.8S. Pellerin, K. Musiol, B. Pokrzywka, and J. Chapelle,  J. Phys. B  29, 3911

1996.9H. R. Griem,   Plasma Spectroscopy  McGraw-Hill, New York, 1964, p.

492.10

R. Konjevic, Plasma Sources Sci. Technol.  10, 356 2001.11

D. Nikolić, S. Djurović, Z. Mijatović, R. Kobilarov, B. Vujičić, and M.

Ćirišan, J. Quant. Spectrosc. Radiat. Transf.  86, 285 2004.12

D. E. Kelleher,  J. Quant. Spectrosc. Radiat. Transf.  25, 191 1981.13

C. W. Allen,  Astrophysical Quantities The Athlone Press, London, 1964p. 87.

14S. Djurović, D. Nikolić, Z. Mijatović, R. Kobilarov, and N. Konjević,

Plasma Sources Sci. Technol.  11, A95 2002.15

X. Duten, A. Rousseau, A. Gicquel, K. Hassouni, and P. Leprince, J. Phys.

D: Appl. Phys.  35, 1939 2002.16

B. A. Cruden, M. V. V. S. Rao, S. P. Sharma, and M. Meyyappan,  Appl.

Phys. Lett.  81, 990  2002.17

Q. Wang, F. Doll, V. Donnelly, D. J. Economou, N. Sadeghi, and G. F.

Franz, J. Phys. D: Appl. Phys.  40, 4202 2007.18

C. Penache, M. Miclea, A. Bräuning-Demian, O. Hohn, S. Schössler, T.

Jahnke, K. Niemax, and H. Schmidt-Böcking,  Plasma Sources Sci. Tech-

nol.  11, 476 2002.

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