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

Lifang Dong,a?Yuyan Qi,Weiyuan Liu,and Weili Fan

College of Physics Science and Technology,Hebei University,Baoding071002,China

?Received22December2008;accepted8June2009;published online7July2009?

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

shape is measured for the?rst time.With the gas pressure increasing in the range of1

?104Pa–6?104Pa,the line pro?les of argon696.54nm are measured.An asymmetrical

deconvolution procedure is applied to separate the Gaussian and Lorentzian pro?le 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.?2009American 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?at plasma display panels,surface modi-?cation of polymers,reduction of pollutants,and generation of UV and vacuum UV?VUV?radiation.1–4In 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.7measured the average electron density for the ?lamentary 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 from8.4?1014cm?3to1.5?1015cm?3with the gas pres-sure increasing from1?104Pa to5?104Pa.

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.8Doppler broadening originates from the sta-tistical velocity distribution of the emitting atoms.The re-lated intensity pro?le follows a Gaussian distribution if the emitting 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 pro?le 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 pro?le, and the smaller contribution of ion broadening is asymmetri-cal in nature.Thus the Stark pro?le is the combination of these two broadenings and exhibits an asymmetrical Lorent-zian pro?le.The apparatus induces another broadening on the line pro?le,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 V oigt function composed by Gaussian pro?le and Lorentzian pro?le.

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 pro?le is described as an asymmetri-cal Lorentzian spectral line pro?le j???,

j???=

1

?

?

?W

R

???d?

1+?????0?d e?/?e??4/3?2?2

,?1?

where W R???represents the micro?eld strength distribution function,depending upon the dimensionless parameter R that accounts for the Debye shielding and ion-ion correlations.

a?Electronic mail:donglf@http://www.wendangku.net/doc/34fdde0e4a7302768e993908.html.

JOURNAL OF APPLIED PHYSICS106,013301?2009?

0021-8979/2009/106?1?/013301/5/$25.00?2009American Institute of Physics

106,013301-1

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?4N e1/4???1?0.068N e1/6T 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 pro?le and can be calculated from9–11

d t=?d e?3.2?10?4N e1/4??e??1?0.068N e1/6T e?1/2??

?10?16N 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 C6/r6interaction.Griem’s9estimation for the FWHM?v can be written12as

?v?cm?=8.18?10?12?2?aˉR2?2/5?T g/??3/10N,?4?where

R2=R U2?R L2.?5?R2is the difference of the squares of coordinate vectors?in a0units?of the upper and lower level,T g is the gas tempera-ture,and?is the atom-perturber reduced mass in a.m.u.??=19.97for excited Ar perturbed by Ar atoms?,and N can be obtained from the equation of the ideal gas.Values of aˉ, the mean atomic polarizability of the neutral perturber,are tabulated for different elements by Allen:13for argon aˉ=16.54?10?25cm3.If the required value of aˉis not tabu-lated,it can be estimated either from the expression given by Allen13or by Griem:9

aˉ=?9/2?a03?3E H/4E EXC?2,?6?where E H is the ionization potential of hydrogen ?109737.32cm?1?and E EXC is the energy?cm?1?of the?rst excited level of the perturber.In the Coulomb approxima-tion,the values of R U and R L in Eq.?5?may be calculated from

R j2=1

2

n j?2?5n j?2+1?3l j?l j+1??,?7?

where the square of effective quantum number n j?is n j?2=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 of65mm,sealed with1.5 mm thick glass plates are?lled 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 of1.5mm is placed between the dielectric layers,serving as the lateral boundary.Thus, the discharge gap is1.5mm.A sinusoidal ac voltage with a frequency of50kHz is applied to the electrodes.All of the apparatus are enclosed in a big chamber?lled with argon. The voltage applied to the electrode is measured with a Tek-tronix high voltage probe?ratio1:1000?connected to an os-cilloscope?Tektronix TDS3054,500MHZ?.The discharge gas is argon with a purity of about99.92%.Optical emission spectra from the plasma are collected with a converging lens and an optical?ber and detected by a monochromator?AC-TON SP-2758,2400groove/mm grating,resolution0.01nm?with a charge coupled device?1340?400pixels?.The opening of the slit input of the monochromator is set to 50?m.The calibration of the instrumental function is made with a He–Ne laser632.8nm line and is found to be a Lorentzian component???L=0.00238nm?and a Gaussian component???G=0.01668nm?.

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?lamentary mode.When the gas pressure is varying in the range of1?104Pa–5?104Pa,the gas be-tween electrodes ignites in a diffuse mode,in which a plasma completely?lls the cross section of the discharge space. However,the gas ignites in a form of?lamentary mode,the discharge no longer permeate on the whole electrodes,when the gas pressure is increased to6?104Pa.

It is found that the spectral lines pro?les change with the gas pressure.Figure2gives the pro?les of argon696.54

nm FIG.1.Schematic diagram of the experimental setup.

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 10Pa is used.It can be clearly seen that the broadenings and shifts of the line pro?le in-crease with the increasing of gas pressure.

In many cases,the shift of the line pro?le is mostly caused by Stark shift,while the van der Waals shift is rela-tively small and can be negligible.Djurovic et al.14found that 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 ?0.74–2.9??1022m ?3and 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-?le must be known.Here we used the method for deconvo-lution of asymmetric line pro?les.5As is well known,the measured line pro?les are the results of convolution of Lorentzian pro?le and Gaussian pro?le.The Lorentzian pro-?le comprises two parts:a symmetrical part and an asym-metrical part.The symmetrical Lorentzian pro?le comprises van der Waals Lorentzian and partial instrumental Lorentzian component.The asymmetrical one is Stark broadening Lorentzian pro?le.The Gaussian type induces the Doppler broadening and a majority of instrumental broadening.Thus,the total spectral line pro?le K ???is the convolution of Gaussian G ???and Lorentzian pro?le L ????,described by K ???=????

G ???y ?L ??y ?dy =

???+??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 ?tted to the experiment data.We compiled a deconvolution procedure to separate L ????pro?le from the measured spectral lines.The Lorentzian broadening thus can be obtained.Figure 3gives a deconvo-lution result for Ar I 696.54nm of discharge at the gas pres-sure of 5?104Pa.

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 pro?les.For the argon plasma in our experiment with argon as the perturber,the reduced mass ?is equal to 19.97and the pa-rameter a ˉis 16.54?10?25cm 3.Accordingly,the Eq.?4?can be written in terms of the gas temperature as ?v ?696.54?=1.52?a Tg 0.7?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.15–17However,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 ?rst negative band of N 2+and shown in Fig.4.It is found that the gas temperature varies from 420to 460K with the gas pressure changing from 1?104Pa to 5?104Pa Figure 5shows 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 8.4?1014cm ?3to 1.5?1015cm ?3with gas pressure increasing from 1?104Pa to 5?104Pa.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 9?1014cm ?3to 5?1015cm ?3when the gas pressure changes from 5?103Pa to 4?104Pa.It is worth pointing out that the electron density obtained here is much higher than that estimated by discharge current or power balance.7In order to explain the discrepancy,an-other experiment was carried out in dielectric barrier dis-charge in argon at pressure in the range of 1?104–5?104Pa.In the experiment,the light emission from total discharge area and light emission of a small area of 0.25mm in diameter were measured by two photomultiplier tubes ?RCA7265?,respectively,and recorded by an

oscilloscope

FIG.2.The total pro?les of Ar I 696.54nm as a function of gas

pressure.FIG.3.Typical deconvolution result for Ar I 696.54nm in argon discharge at the pressure of 5?104Pa.C -convolution pro?le,G -Gaussian pro?le,L -Lorentzian pro?le.

?Tektronix TDS 3054,500MHZ ?.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 ?lled 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 ?rst negative band of N 2+in dielectric barrier discharge at gas pressure of 2?104Pa.?b ?The rotational temperature is estimated by the slope of ln ?I /?J ?+J ?+1??vs J ??J ?+1?.?c ?The gas temperature in dielectric barrier discharge with the gas pressure increasing from 1?104to 7?104Pa in different argon concentrations in gas

mixture.

FIG.5.Variations of the Lorentzian broadening,the Stark broadening,the van der Waals broadening of argon 696.54nm spectral line,and the electron density with the increase of gas

pressure.FIG.6.?Color online ??a ?Image of diffuse discharge at 1?104Pa.Dis-charge area is 30?30mm 2.Exposure time is 66.7ms.?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 0.25mm in diameter,

respectively.

the spectral line pro?le should vary with time in each dis-charge current because the electron density changes with time.A narrow pro?le corresponds to small electron density while a wide pro?le corresponds to a large electron density. It is obvious that the recorded spectral line pro?le is a tem-poral integral and the widest pro?le 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 1?104Pa–6?104Pa,the line pro?les of argon696.54nm are measured.An asymmetrical deconvolution procedure is applied to separate the Gaussian and Lorentzian pro?les 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.10575027and10775037,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.A2006000950and A2008000564?.

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