oes in ar and n- determination of electron t and density by line-ratio method

Optical emission spectroscopy in low-temperature plasmas containing argon and nitrogen:

determination of the electron temperature and density by the line-ratio method

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IOP PUBLISHING JOURNAL OF PHYSICS D: APPLIED PHYSICS

J. Phys. D: Appl. Phys. 43 (2010) 403001 (24pp) doi:10.1088/0022-3727/43/40/403001

TOPICAL REVIEW

Optical emission spectroscopy inlow-temperature plasmas containingargon and nitrogen: determination of theelectron temperature and density by theline-ratio methodXi-Ming Zhu and Yi-Kang Pu

Department of Engineering Physics, Tsinghua University, Beijing 100084, People’s Republic of China

E-mail: [email protected]

Received 28 June 2010, in final form 3 August 2010Published 21 September 2010Online at stacks.iop.org/JPhysD/43/403001

AbstractThis article reviews a variety of methods to obtain the electron temperature and density by theemission line ratios for low-temperature plasmas containing argon or nitrogen gas. Based onthe collisional–radiative model of excited particles, the underlying principle of each of thesemethods is described, along with the criterion on how to select an appropriate line-ratiomethod according to the discharge conditions. Limitations on the application of each line-ratiotechnique are also discussed.

(Some figures in this article are in colour only in the electronic version)

List of abbreviations

APPJ atmospheric-pressure plasma jetASDF atomic state distribution functionCCD charge-coupled deviceCCP capacitively coupled plasmaCRM collisional–radiative modelDBD dielectric barrier dischargeDCGD direct current glow dischargeECR electron cyclotron resonance (plasma)EEDF electron energy distribution functionEEPF electron energy probability functiongs ground stateICCD intensified charge-coupled deviceICP inductively coupled plasmaIR infrared radiationMD microwave dischargeNLD neutral loop dischargeOES optical emission spectroscopy

PMT photomultiplier tubeSR synchrotron radiationSRR split-ring resonator (plasma)SWD surface wave sustained dischargeTRG-OES trace rare gases optical emission

spectroscopyTRL tungsten ribbon lampUV ultraviolet (radiation)VDF vibrational distribution functionVUV vacuum ultraviolet (radiation)

List of symbols

A Einstein A coefficientB Einstein B coefficientd plasma dimensionD diffusion coefficiente electronEa activation energy

0022-3727/10/403001+24$30.00 1 © 2010 IOP Publishing Ltd Printed in the UK & the USA

http://dx.doi.org/10.1088/0022-3727/43/40/403001

mailto: [email protected]

http://stacks.iop.org/JPhysD/43/403001

J. Phys. D: Appl. Phys. 43 (2010) 403001 Topical Review

Ee electron kinetic energyEth excitation threshold energy�E energy difference between two excited levelsE/N reduced electric fieldge electron energy distribution function (EEDF)gp electron energy probability function (EEPF)hν photonI emission intensityJ total angle momentum quantum numberK volume-averaged diffusion-controlled reaction

coefficientme electron massn species densityne electron densityneC characteristic electron densityng gas densityp pressureQ rate coefficient of collisional process in the gas phaseQexc rate coefficient of electron-impact excitationQtrans rate coefficient of electron-impact

population transferTe electron temperatureT

highe electron temperature corresponding to the

high-energy electronsT low

e electron temperature corresponding to thelow-energy electrons

Tg gas temperature� escape factorσexc excitation cross section

1. Introduction

Optical emission spectroscopy (OES) is one of the mostwidely used diagnostic methods for low-temperature plasmas(Behringer 1991, Malyshev and Donnelly 1997, Boffardet al 2004, Fantz 2006). It requires only a simpleand inexpensive experimental setup: a diagnostic viewportand a relative intensity-calibrated spectroscopic system,covering a wavelength range of UV–visible–near-IR region(∼200–1100 nm). From the emission spectra of atomicor molecular species, being excited by the electron-impactprocesses in plasmas, one may extract the electron temperature,Te (assuming a Maxwellian electron energy distributionfunction, EEDF), and the electron density, ne (Behringer andFantz 1994, Bibinov et al 1998, 2005, 2008, Kano et al2000, 2001, Pu et al 2000, 2006, Donnelly and Schabel 2002,Donnelly 2004, Zhu and Pu 2005, 2008, Zhu et al 2006,Iordanova and Koleva 2007).

In order to use the OES method to determine the Te

and ne, one usually applies the so-called line-ratio technique.First, for a given pair of excited levels, which emit light, onebuilds up a population model by considering their dominantproduction and depopulation processes. Then, from thismodel, which consists of a set of rate balance equations of thesetwo excited levels and other relevant species, one can solve forthe density ratio of these two levels. This ratio is a function ofplasma parameters (Te, ne, etc) as well as operating parameters(pressure, plasma dimension, etc). By fitting the calculated

density ratio with the measured emission intensity ratio, onecan obtain the plasma parameters with the known operatingparameters. These line-ratio techniques are used for a varietyof low-temperature plasmas at low to atmospheric pressures(Kano et al 2000, Crintea et al 2009, Zhu et al 2009b).

At very low pressures (<1 Pa) and low ionizationratios (<10−5), the excited species are mainly produced bythe electron-impact excitation from the ground state (seeequation (1) in section 2.1.1) and are depopulated by thespontaneous radiation (equation (2)). Therefore one can writea set of rate equations for excited species containing only thesetwo processes. This is called the corona model. With such amodel, by selecting two excited levels with different excitationthreshold energies (Eth), the obtained line ratio is a functionof Te, independent of ne and other plasma parameters. Thisrelationship allows one to obtain Te at pressures ∼0.01–1 Pain electron cyclotron resonance (ECR) plasmas (Pu et al2000, Crolly and Oechsner 2001). By selecting the particularlevels insensitive to the excitation from the metastables, thissimple method may still be extended to higher pressures,say, ∼1–10 Pa, for microwave discharges (Behringer 1991),dc glow discharges (Behringer and Fantz 1994), inductivedischarges (Ma and Pu 2003, Pu et al 2006, Britun et al 2007,Kang et al 2008) and helicon discharges (Foissac et al 2009).A comprehensive review of the line-ratio technique with thecorona model, as well as the excitation cross sections involved,is given by Boffard et al (2004).

Based on this simple method, a diagnostic techniquenamed trace rare gases optical emission spectroscopy (TRG-OES) is developed (Malyshev and Donnelly 1997, Donnelly2004). In particular, traces of Ne, Ar, Kr and Xe with knownconcentrations are added to the reactive gases. The electrontemperature is obtained from the emission line ratios of thePaschen 2p levels of these rare gas atoms. The TRG-OESmethod has been widely used in a variety of low-pressuredischarges, including the chlorine plasmas (Malyshev andDonnelly 1999, Donnelly and Schabel 2002), fluorocarbonplasmas (Schabel et al 2002, Chen et al 2009a, Zhu et al 2009a)and oxygen plasmas (Fuller et al 2000, Stafford et al 2009).

Zhu and Pu (2007a, 2007b) and Zhu et al (2007) developa ne measurement technique of using the line ratios of certainargon 3p, 4p and 5p levels for low-pressure plasmas. Since thelifetimes of these levels are significantly longer than those of2p levels, the electron-impact population transfer processes,being dependent on ne (see equation (8) in section 2.1.2),can be as important as the radiation processes even at lowpressures (1–10 Pa). As a result, the line ratios of these levelsare functions of ne (Boffard et al 2004), nearly independent ofTe (for reasons explained in section 2.1.2). The obtained resultsof ne from this method are in good agreement with those fromthe Langmuir probe in inductive Ar/O2 plasmas (Zhu and Pu2008), as well as those from the method of deriving ne fromthe ion energy distribution function in a capacitively coupledplasma (CCP) (Chen et al 2009b).

At higher pressures (>10 Pa) or with a relatively highionization ratio (>10−5), the line ratios of all the argon-excitedstates are functions of both Te and ne due to the excitationprocesses out of the metastable or excited states, as indicated

2


in the collisional–radiative models (CRM) for argon plasmas(Vlcek 1989, Bogaerts et al 1998, Bultel et al 2002). Usingsuch a model for 1s and 2p levels, Iordanova and Koleva (2007)propose a line-ratio method to simultaneously determine Te

and ne in low-pressure inductively coupled plasmas (ICP). Itis also used to obtain Te and ne in a neutral loop discharge(NLD), with the results in good agreement with those fromthe laser Thomson scattering method (Crintea et al 2009).Using a similar line-ratio method, Palmero et al (2007) obtainTe and ne in a magnetron sputtering plasma. Based on theCRM by Vlcek (1989), Kano et al (2000, 2001) determinethe values of Te and ne with the line ratios of several argon2p, 3s and 5d levels (in Paschen’s notation) in a dc glowdischarge (DCGD) at medium pressures (∼102–104 Pa) and ina low-pressure plasma jet (∼10 Pa). Vries et al (2006) presentanother method: fitting the calculated atomic state distributionfunction (ASDF) with the measured one. They use this methodto obtain the values of Te and ne in a surface wave sustaineddischarge (SWD) at medium pressure (∼103 Pa). For the SWDat atmospheric pressure, Yanguas-Gil et al (2006) developa theoretical approach to determine Te from the excitationtemperature of argon excited levels. A similar method, with theline ratios of argon 2p and 3p levels, is proposed by Akatsuka(2009) and is applied in the investigation of a microwave-excited microplasma (Zhu et al 2008). More recently, Zhuand Pu (2010) find that the atom–atom collision processesmay lead to a non-Boltzmann ASDF of the 2p multiplet atatmospheric pressure. By adding this effect into the CRM, a ne

measurement technique is proposed for non-equilibrium argondischarges. It is used in the investigation of pulsed rf dischargesand microwave microplasmas at atmospheric pressure, withthe results in agreement with those from the Stark broadeningmethod (Zhu et al 2009b, Tian et al 2010).

Thanks to the development of nitrogen CRMs, whichare also called nitrogen kinetic models (Loureiro and Ferreira1986, Guerra et al 2004, Shakhatov and Lebedev 2008), theline-ratio methods to determine Te and ne can be applied forthe nitrogen plasmas under the conditions when the coronamodel is invalid. Such a method is proposed by Zhu and Pu(2005, 2008) and Zhu et al (2006) for low-pressure nitrogenplasmas (1–10 Pa). They use a CRM containing the collisionalprocesses between the metastable molecules N2(A

3�+u ) and

the vibrationally excited ground-state molecules. Based onthis model, Te is obtained by the line ratio of electronicstates N2(C

3�u) and N2(B3�g) and ne is obtained by that of

vibrationally excited levels N2(C3�u, v = 0) and N2(C

3�u,v = 1). With a similar nitrogen CRM, Bibinov et al (1998)establish a line-ratio method to obtain the electron temperaturein a nitrogen DCGD. It is also used in the investigation of ECRand ICP discharges (Bibinov et al 2005, 2008). As for thenitrogen plasmas at medium to high pressures (102–105 Pa),more collisional processes, such as the collisional quenchingof excited molecules and the collisional processes involvingnitrogen atoms and molecular ions, need to be included inthe CRMs (Kim et al 2006, Lebedev and Shakhatov 2006).From such models, one can calculate the population ratiosof N2(C

3�u), N2(B3�g) and N+

2(B2�+

u ) and the vibrationaldistribution functions (VDFs) of these states. By fitting these

ratios with the measured ones, one can obtain the values of Te

and ne and the reduced electric field, E/N , in the stationaryor pulsed dc discharges, microwave discharges and dielectricbarrier discharges in nitrogen (Kim et al 2006, Lebedev andShakhatov 2006, Cicala et al 2009, Isola et al 2010). The lineratio of N2(C

3�u) and N+2(B

2�+u ) is also used to measure

the values of Te or E/N in dielectric barrier discharges in airat atmospheric pressure (Kozlov et al 2001, Paris et al 2005,Wu et al 2008).

In the following sections, we intend to provide a detaileddiscussion on the line-ratio techniques for low-temperatureplasmas containing argon and nitrogen. This includes theirfundamental principles, applications and limitations. Section 2illustrates three kinds of line-ratio techniques, which are usedunder different discharge conditions. The first method risesfrom the method with the corona model, applicable for plasmascontaining argon and nitrogen at low pressures and with alow ionization ratio. At medium to high pressures or witha relatively high ionization ratio, the second method uses anargon CRM for argon containing plasmas, which includesthe excitation processes from metastable or excited states, aswell as the atom–atom collision processes. The third methoduses a nitrogen CRM for nitrogen-containing plasmas, andit can be used when the corona model is invalid for excitednitrogen molecules. Section 3 further discusses the influenceof discharge conditions on the selection of a line-ratio method,as well as their influence on the collisional processes in the ratebalance. In particular, for gas-mixture discharges, the effect ofother species on the kinetics of argon or nitrogen is discussed.Section 4 discusses some of the practical limitations of theline-ratio methods, due to optical absorption and reflection aswell as the sensitivity and resolution of the spectrometers.

2. Line-ratio methods

In this section, we will describe three kinds of line-ratiomethods used to determine the values of Te and ne forplasmas containing argon or nitrogen. Each of these line-ratio methods needs a population model. This model containsa set of rate balance equations for excited species andother relevant species, in which the sum of the rates of theproduction processes equals that of the depopulation processes,under steady-state conditions. In general, the productionprocesses of excited species include the electron-impactexcitations from the ground state and from the metastablestates, the radiation decay from the higher excited states, etc.The depopulation processes include the spontaneous radiation,the collisional quenching with electrons and with heavyspecies, etc. Although the general rate balance containing allthe possible processes is a very complicated one, under certaindischarge conditions and for certain excited states, only veryfew dominant processes need to be included in a particularmodel. This is the major difference between these modelsdiscussed in this work, i.e. different choices of levels (emissionlines) and the associated processes. For discharges containingargon and nitrogen, the levels of interest for all these modelsare shown in figure 1. In the following, we first describe thepopulation model for some given excited levels under a given

3


Figure 1. A collection of the partial energy diagrams of the relevantspecies used in the line-ratio methods.

discharge condition and how to obtain the line ratios using themodel, and then describe how to determine Te and ne from themeasured spectral data.

2.1. Corona model method

The corona model comes from the modelling of excitedspecies in the solar corona, where the electron density isvery low (∼106 cm−3) and the electron temperature is high(∼100 eV) (Fantz 2006). In this case, only two processesare important: the electron-impact excitation process fromthe ground-state species and the spontaneous radiations fromthe excited species. This model is valid for excited atoms,molecules and ions in low-temperature plasmas with very lowpressures (<1 Pa) and low ionization ratios (<10−5). This isbecause, under these conditions, other collisional processesare not important and the density of metastables is too low tomake a significant contribution to the excitation of the excitedspecies (Pu et al 2000, Crolly and Oechsner 2001, Boffard et al2004, Donnelly 2004).

2.1.1. Te determination. We take the low-pressure Ar/Xedischarges as an example. Usually, strong emission linesfrom the Paschen 2p levels of argon and xenon atoms can beobserved, such as the ones with wavelengths of 750.4 nm (Ar,2p1 → 1s2) and 828.0 nm (Xe, 2p5 → 1s4) (see figure 1). Notethat the 2p levels with zero total angle momentum quantumnumber (J = 0) of rare gases (in Paschen’s notation, 2p1

and 2p3 for Ne, 2p1 and 2p5 for Ar, Kr and Xe) are the mostsuitable for the line-ratio methods with a corona model, sincethese levels have relatively large excitation cross sections fromthe ground state and very small excitation cross sections fromthe metastables (Boffard et al 2004). In a corona model forthese levels, we have the electron-impact excitation from the

ground-state atom,

Ar(gs) + e → Ar(2p1) + e,

Xe(gs) + e → Xe(2p5) + e,(1)

and the spontaneous radiation,

Ar(2p1) → Ar(1s) + hν,

Xe(2p5) → Xe(1s) + hν.(2)

The symbol gs denotes the ground state, 1s denotes the Paschen1s levels, e is for an electron and hν is for a photon.

The rate balance equations of Ar(2p1) and Xe(2p5) are

ne · nAr · QAr(2p1)exc = AAr(2p1) · nAr(2p1),

ne · nXe · QXe(2p5)exc = AXe(2p5) · nXe(2p5),

(3)

where ne is the electron density, nAr and nXe are the densitiesof ground-state argon and xenon atoms and A is the EinsteinA coefficient. Qexc is the excitation rate coefficient from theground state,

Qexc =∫ ∞

Eth

σexc ·√

2Ee

me· ge(Ee) dEe,

=∫ ∞

Eth

σexc ·√

2

me· Ee · gp(Ee) dEe,

(4)

where Ee is the electron kinetic energy, Eth is the excitationthreshold energy, σexc is the excitation cross section, me isthe electron mass, ge is the EEDF, gp is the electron energyprobability function (EEPF) and is related to the EEDF ge

by ge(Ee) = E1/2e gp(Ee). When gp is plotted in a log scale

versus Ee, a linear function indicates a Maxwellian distribution(Donnelly 2004, Pu et al 2006). Note that the electron-impactexcitations from the ground state can also produce excitedatoms in higher levels, such as Ar(2s), Ar(3s), Ar(4d) andAr(5d). The radiation decay of these atoms also contributes tothe production of atoms in 2p levels. This so-called cascadeprocess should be included on the left-hand side of equation (3).As a result, one should use the apparent excitation cross sectionin calculating Qexc from equation (4), which is the sum of theexcitation cross section from the ground state and the cascadecross sections from the higher excited levels (see Boffard et al(2007); we will further discuss the apparent excitation crosssection in section 4.1).

The emission intensity, I , from an excited state x is givenby (in this work it refers to the number of photons emitted perunit volume per unit time from this state)

Ix = Ax · nx, (5)

if the self-absorption process (or the radiation trapping, seeGriem (1997)) can be ignored. In fact, this assumption is validunder the discharge conditions considered in this subsection.Here nx refers to the population density of species in this stateand Ax is its Einstein A coefficient.

4


Figure 2. Ratios of the excitation rate coefficients from the groundstate as functions of electron temperature: Ar(2p1)/Xe(2p5),Ar(3p1)/Ar(2p1), N2(C

3�u)/N2(B3�g) and N+

2 (B2�+

u ,v = 0)/N2(C

3�u, v = 0). A Maxwellian EEDF is assumed. Thecross sections are from Itikawa et al (1986), Majeed and Strickland(1997), Chilton et al (1998), Fons and Lin (1998) andWeber et al (2003).

From equations (3) and (5), the emission line ratio is

IAr(2p1)

IXe(2p5)

= AAr(2p1) · nAr(2p1)

AXe(2p5) · nXe(2p5)

= ne · nAr · QAr(2p1)exc

ne · nXe · QXe(2p5)exc

= C · QAr(2p1)exc

QXe(2p5)exc

,

C ≡ nAr

nXe. (6)

The constant C is the density ratio of the ground-state atomsand can be obtained from the partial pressures of argon andxenon assuming they have equal gas temperatures. For aMaxwellian EEDF, using the experimental cross sections andequation (4), the excitation rate coefficient ratio is a function ofTe (see figure 2). Therefore, once two levels are selected, onemay obtain Te from the measured line ratio using equation (6),taking into account the response function of the spectrometer.

Some of the excitation rate coefficients, such as thosefrom the ground state to the Paschen np (n = 2–5) levels ofargon and xenon and those to the nitrogen states N2(B

3�g),N2(C

3�u) and N+2(B

2�+u ), can be approximated by an

Arrhenius form (Zhu et al 2009a) within the range of electrontemperatures of interest and we have

QAr(2p1)exc

QXe(2p5)exc

∼Q

Ar(2p1)

0 · exp

(−E

Ar(2p1)a

Te

)

QXe(2p5)

0 · exp

(−E

Xe(2p5)a

Te

)

∼ exp

(−E

Ar(2p1)a − E

Xe(2p5)a

Te

)∼ exp

(−�E

Te

), (7)

where Q0 is a constant (pre-exponential factor), Ea is theactivation energy, roughly equal to the threshold energy of

Figure 3. The values of electron temperature in a Ne/Ar/Xe ICPdetermined by the line ratio of 750.4 nm (Ar, 2p1 → 1s2) and828.0 nm (Xe, 2p5 → 1s4) with the corona model and thosedetermined by the Langmuir probe. The dimensionless parameter xc

is a function of the partial pressures of argon, xenon and neon. Thedriving frequency is 13.56 MHz. The discharge power is 100 W(Zhu et al 2009a).

an excited level, and �E is the energy difference between thetwo excited levels.

Equation (7) indicates that, in order to get a functionalform that is sensitive to Te, it is desirable to select twoexcited states with �E comparable to Te. If �E is muchsmaller than Te, the rate coefficient ratio is nearly independentof Te (Ar(3p1)/Ar(2p1), figure 2). Although a large �E

can lead to the line ratio, a very sensitive function of Te

(N+2(B

2�+u ,v = 0)/N2(C

3�u, v = 0), figure 2), one of theemission lines may be too weak to have a good signal-to-noise ratio, when Te in the discharge is low. For example,at Te ∼ 1.5 eV, the emission lines from N+

2(B2�+

u ) are veryweak, owing to the very low number of electrons with energieshigher than the threshold energy, ∼19 eV, for the excitedionization process from N2(X

1�+g ) to N+

2(B2�+

u ) (Zhu andPu 2008). Note that equation (7) is for illustrative purposeonly and the most accurate way to obtain the ratio of the ratecoefficients is using the experimental cross section data directlyand equation (4). For some other levels, their cross sectionsmay behave differently with the electron energy from the levelsdiscussed here and equation (7) may not be appropriate torepresent the dependence of rate coefficients on the electrontemperature over the range of interest. In this case, whenemploying equation (6) to obtain the electron temperature, itis still helpful to select two levels with very different thresholdenergies.

Figure 3 shows the results of determining Te by the lineratio of Ar(2p1) and Xe(2p5) in a Ne/Ar/Xe ICP (Zhu et al2009a). This line-ratio method can be used to obtain Tes in therange of 1–4 eV, being comparable to the energy differencebetween Ar(2p1) and Xe(2p5) (see figure 1). At a constantpower of 100 W, Te is changed by varying the partial pressuresof gases: pNe ∼ 1–10 Pa, pAr � pNe/5, pXe � pNe/20 inthe Ne/Ar/Xe mixture and pAr ∼ 1–8 Pa, pXe � pAr/4 inthe Ar/Xe mixture. A dimensionless parameter xc is used in

5


Table 1. Some works using the line-ratio method to determine Te with the corona model. The method to obtain Thigh

e in the TRG-OEStechnique is included.

Excited states selected Plasmas Feed gases Trace gases

Behringer (1991) He(3d1D)/Ar(2p) ECR N2 or CH4 Ar and Heor N+

2 (B2�+

u )/N2(C3�u)

Behringer and Fantz (1994) He(3d1D)/Ar(2p)/N2(C3�u) DCGD He Ar and N2

Pu et al (2000) N+2 (B

2�+u )/N2(B

3�g) ECR N2

Crolly and Oechsner (2001) Ar+(4p2S, 4p2P)/Ar(3p) ECR Ar or N2

or N+2 (B

2�+u )/N2(C

3�u)Donnelly (2004) Ar(2p1, 2p5)/Kr(2p1, 2p5)/Xe(2p1, 2p3, 2p5) ICP Cl2, O2 Ar, Kr and Xe

or Ar/C2F6/C4F8

Boffard et al (2004) Ar(3p1)/Ne(2p1) ICP Ar/NeBritun et al (2007) N+

2 (B2�+

u )/N2(C3�u) ICP N2 or Ar/N2

Chen et al (2009a) Ar(2p1, 2p5)/Kr(2p1, 2p5, 2p7)/Xe(2p3, 2p5) CCP CF4/O2 Ar, Kr and XeStafford et al (2009) Ar(2p1, 2p5)/Kr(2p1, 2p5) SWD O2 Ar, Kr and Xe

/Xe(2p1, 2p3,2p5)Zhu et al (2009a) Ar(2p1, 2p5)/Xe(2p5) ICP, CCP Ar/Xe/CF4

Foissac et al (2009) Ar(3s)/Ar(2p) Helicon Ar

figure 3, which is a function of the partial pressures of argon,xenon and neon. The results are in good agreement with thosefrom the Langmuir probe (Zhu et al 2009a).

The above method can also be used for dischargescontaining excited N2, N+

2 , Ar+, He, Ne and Kr species, aslisted in table 1.

2.1.2. ne determination with extended corona model. As forhigher excited levels, such as Ar(3p1) and Ar(5p5), they havevery small excitation cross sections from the metastables, sinceJ = 0 (as mentioned in section 2.1.1). As a result, their majorproduction source is still the ground-state excitation. However,in the destruction channel, the electron-impact populationtransfer processes,

Ar(3p1) + e ↔ Ar(2s, 3s, 3d, 4d) + e,

Ar(5p5) + e ↔ Ar(4s, 5s, 5d, 6d) + e,(8)

should be added in the corona model, due to the relativelysmall Einstein coefficients of these levels. Therefore, the ratebalance equation becomes

ne · nAr · QAr(3p1)exc =AAr(3p1)

· nAr(3p1)+ ne · nAr(3p1)

· QAr(3p1)

trans ,

ne · nAr · QAr(5p5)exc =AAr(5p5)

· nAr(5p5) + ne · nAr(5p5) · QAr(5p5)

trans ,

(9)

where Qtrans is an effective rate coefficient of the electron-impact population transfer process. Note that, on the left-handside of the equation, only high-energy electrons contributeto the excitation; however, due to the very small excitationthreshold energy of the population transfer process, low-energyelectrons make the maximum contribution to Qtrans, and thusQtrans is only weakly dependent on Te. Therefore, a parameter,neC, named the characteristic electron density, can be definedas (Zhu and Pu 2007a, 2007b)

neC ≡ A

Qtrans. (10)

In many low-pressure ICP and CCP discharges with argonpartial pressures ∼1–10 Pa, the neC of certain excited levels

can be considered as constants. In fact, the values of neC

can be obtained experimentally using a Langmuir probe and aspectrometer: ∼3×1011 cm−3 for argon 3p levels, ∼1011 cm−3

for argon 4p levels and ∼2×1010 cm−3 for argon 5p levels (Zhuand Pu 2008, Zhu et al 2009a). Therefore, the rate equationsof Ar(3p1) and Ar(5p5) can be rewritten as

ne · nAr · QAr(3p1)exc = AAr(3p1)

· nAr(3p1)·(

1 +ne

neC,3p1

),

ne · nAr · QAr(5p5)exc = AAr(5p5)

· nAr(5p5)·(

1 +ne

neC,5p5

).

(11)

The line-ratio equation for Ar(3p1) and Ar(5p5) is

IAr(3p1)

IAr(5p5)

= AAr(3p1) · nAr(3p1)

AAr(5p5) · nAr(5p5)

= ne · nAr · QAr(3p1)exc · (1 + ne/neC,5p5

)

ne · nAr · QAr(5p5)exc · (1 + ne/neC,3p1

), (12)

that is,IAr(3p1)

IAr(5p5)

= C · (1 + ne/neC,5p5)

(1 + ne/neC,3p1),

C ≡ QAr(3p1)exc

QAr(5p5)exc

.

(13)

When Te � 1 eV, the excitation rate coefficient ratio, C,of Ar(3p1) and Ar(5p5) is nearly independent of Te, fromthe calculations based on the cross section measurements(Weber et al 2003, Boffard et al 2004). This is because theircross sections have very close values of the threshold energy.Therefore, the line-ratio equation (13) is basically independentof Te and can be used to determine ne.

In order to use equation (13) to determine ne effectively,at least one of the neC values should be comparable to the ne

value in plasmas. If ne � neC,5p5 < neC,3p1 , the line ratiois nearly independent of ne (the left region in figure 4). Thisis because the spontaneous radiation is a much faster processthan the electron-impact population transfer. Otherwise, if

6


Figure 4. The line ratio of Ar(3p1) and Ar(5p5) versus electrondensity, calculated using equation (13). The excitation coefficientratio is calculated from the cross sections given by Boffard et al(2007). The neC values are from Zhu et al (2009a).

Figure 5. The electron densities in an Ar/O2 ICP determined by theline ratio of 425.9 nm (Ar, 3p1 →1s2) and 357.2 nm (Ar, 5p5 →1s2)with the extended corona model (with the electron-impactpopulation transfer process added) and the results by the Langmuirprobe (Zhu and Pu 2008).

neC,5p5 < neC,3p1 � ne, the line ratio is insensitive to ne as well(the right region in figure 4), since only the electron-impactpopulation transfer is important for both species. Therefore,to make the line ratio a sensitive function of ne, both processesshould play comparable roles in the depopulation of Ar(3p1)or Ar(5p5).

Figure 5 shows the results of determining ne by the lineratio of Ar(3p1) and Ar(5p5) in an Ar/O2 ICP (Zhu and Pu2008). In this plasma, ne is increased by the power at constantpressures of argon and oxygen. This line-ratio technique isvalid when ne is in the range 109–1012 cm−3 (in the middleregion in figure 4). The results are also in good agreementwith those from the Langmuir probe.

The other line ratios of argon 3p, 4p or 5p levels (withJ = 0) can be used instead of the line ratio 3p1/5p5 in the

ne measurement. However, their excitation rate coefficientratio may have a stronger dependence on Te (Zhu et al2009a), and thus the Te in plasmas should be measured beforedetermining ne.

Te and ne can be simultaneously obtained using theabove line ratios. Such an example is given in figure 6for an Ar/Xe/CF4 CCP (Zhu et al 2009a). The Te andne variation versus driving frequency in the electronegativedischarges containing CF4 is different from that in theelectropositive discharges, because the energy balancebetween the electron heating and the energy loss mechanismsis affected significantly by the inelastic collisions with CF4

(Zhu et al 2007).As for the electron-impact excitation processes from the

ground state, only the electrons with energies higher than theexcitation threshold energy (Eth) contribute to the calculationof the excitation rate coefficient, as seen in equation (4).Therefore, when a line-ratio method with the corona model,such as that of using Ar(2p1)/Xe(2p5), is applied to determine‘Te’ in a plasma with a non-Maxwellian EEDF, one obtains an‘electron temperature’ corresponding solely to the high-energytail of an EEDF, T

highe (Donnelly 2004, Pu et al 2006). This

Thigh

e represents the ‘local slope’ of the higher energy tail ofan EEPF when it is plotted in a log scale versus the electronenergy (as discussed after equation (4)).

The low-energy electrons play a dominant role in theelectron-impact population transfer process between excitedspecies (equation (8)). The rate coefficient of this process,Qtrans, may be dependent on the ‘electron temperature’corresponding to the low-energy electrons, T low

e . However,this effect is very weak. As a result, the parameter neC,calculated from Qtrans (equation (10)), is nearly independent ofT low

e , which is experimentally confirmed in low-pressure ICPand CCP discharges (∼1–10 Pa) (Zhu and Pu 2007a, 2007b,Zhu et al 2007). For this reason, T low

e cannot be effectivelyobtained from the corona model in a non-Maxwellian EEDFcase, which is a fundamental limitation of the line-ratio methoddescribed in this subsection.

2.2. Argon CRM method

In low-temperature argon plasmas at pressures >10 Pa or withionization ratio ∼10−4–10−3, the corona model is invalid formost of the excited species, since the excitation process outof metastable atoms is an important production mechanismfor them (Bogaerts et al 1998, Iordanova and Koleva 2007).In addition, several other processes, including the collisionsbetween two argon atoms and the recombination of electronsand ions, can be of importance at medium to high pressures(103–105 Pa) (Rolin et al 2007, Dyatko et al 2008). In thesecases, one should apply an argon CRM (Vlcek 1989, Benoyet al 1991) instead of the corona model to calculate the lineratios.

In argon CRMs, the rate balance equations for the steady-state densities of species, including the excited atoms, theground-state atoms, the atomic ions, the molecular ions as well

7


Figure 6. Te and ne versus the driving frequency at a constant power 50 W in a capacitive discharge, obtained from the line-ratio techniquesusing Ar(2p1)/Xe(2p5) and Ar(3p1)/Ar(5p5), respectively (Zhu et al 2009a).

as the molecular excimers, are

ne

∑y �=x

nyQy→x

e–Ar + nAr

∑y �=x

nyQy→x

Ar–Ar +∑y �=x

�y→xAy→xny

+∑y �=x

∑z �=x

nynzQy,z→x

Ar−Ar + n2enAr+Q

e,e,Ar+→x3-body

+ nenArnAr+Qe,Ar,Ar+→x3-body

= nenx

∑y �=x

Qx→y

e–Ar + nArnx

∑y �=x

Qx→y

Ar–Ar

+∑y �=x

�x→yAx→ynx + 2n2xQ

x,xAr–Ar

+ nx

∑y �=x

nyQx,y

Ar–Ar + n2ArnxQ

Ar,Ar,x3-body + Kx

wallnx. (14)

x refers to a species in a certain state while y and z referto other states or other species. nx , ny and nz refer to theirdensities, respectively, Q is the reaction rate coefficient ofcollisional process in the gas phase, K is the volume-averageddiffusion-controlled reaction coefficient (see Donnelly 2004),A is the Einstein A coefficient and � is the escape factordue to the self-absorption process. The superscripts denotethe species involved in each process. The subscripts give thereaction types: e–Ar, the collision processes between electronsand argon species, Ar–Ar, the collision reactions between twoargon species, 3-body, the three-body collisions, wall, thequenching processes at the chamber wall. From equation (14),one can calculate the population density ratios of the excitedspecies.

Table 2 lists several of these kinds of line-ratio methodsused in the literature. It can be seen that all of theseworks consider the following processes: the electron-impactexcitation processes from the ground state and metastablelevels, the spontaneous radiation and radiation trapping, aswell as the quenching processes of metastables at the chamberwall. At medium and high pressures, one should pay attention

to the fact that the electron-impact excitation processes out ofthe excited levels, the atom–atom collisions and the three-bodycollisions play important roles. References for the collisioncross sections are listed in table 3.

In the following, we show in detail an example of usingthe line-ratio method with the argon CRM to determine Te andne with the emission lines from the argon 2p levels, whichare usually the strongest emission lines from low-temperatureargon plasmas, as shown in figures 7(a), (c) and (e) for threetypes of argon plasmas (Zhu and Pu 2007a, 2009, Zhu et al2007, 2008). The operating parameters of these experimentsare given in table 4.

Since the pressure or the ionization ratio is higher thanthe cases discussed in section 2.1, the population densities ofAr(1s2) and Xe(1s4) are no longer low. The self-absorptionprocesses can be significant. In this case, the emission intensityis related to the population density of the excited species by(Griem 1997)

Ix→y = �x→y(ny; d, Bx→y, �νx→y) · Ax→y · nx. (15)

Here x and y refer to the upper and lower levels of an opticaltransition, respectively. The escape factor, �, is a function ofthe population density of the lower level (ny), as well as theplasma dimension (d), the Einstein B coefficient for absorption(B) and the spectral line width (�ν), which is caused mainly bythe Doppler broadening, as well as the collisional broadeningwhen the gas pressure is high (>104 Pa) (Wang et al 2005).With d, B and �ν known, the new line ratio is

IAr(2pi→1sk)

IAr(2pj →1sl )

= �2pi→1sk(n1sk

) · A2pi→1sk· n2pi

�2pj →1sl(n1sl

) · A2pj →1sl· n2pj

,

1 � i, j � 10, 2 � k, l � 5. (16)

Here i, j and k, l refer to different 2p and 1s levels, respectively.As seen in equation (16), in order to relate the emission lineratios to the population ratios of 2p levels, one needs to obtain

8


Table 2. The excited levels and processes in some argon CRMs and the selected line ratios used to obtain Te and ne. Note that the work byDonnelly is included for the method to obtain T low

e in the TRG-OES technique. hl refers to the high-lying levels such as the 2s, 3d and 3p;e–Ar means the collision processes between electrons and argon species; Ar–Ar refers to those between argon species;. rad, wall and 3-bodyare for the radiation processes, the quenching processes at chamber wall and the three-body collision processes, respectively. Theseprocesses are described in more detail in table 3.

Modelling Experiments and results

Levels Processes Plasmas Line ratios Parameters

Donnelly (2004) 1s, 2p e–Ar, rad, wall ICP, CCP 2p T lowe

(∼0.1–10 Pa)Iordanova and Koleva (2007) 1s, 2p e–Ar, rad, wall ICP 2p Te, ne

Ar–Ar (∼1–100 Pa)Kano et al (2000) 1s, 2p, hl e–Ar, rad, wall DCGD 2p, 3s, 5d Te, ne

Ar–Ar, 3-body (∼102–104 Pa)Vries et al (2006) 1s, 2p, hl e–Ar, rad, wall SWD 2p, 3s, 4s, Te, ne

Ar–Ar, 3-body (∼103 Pa) 5d, 6d, 7dAkatsuka (2009) 1s, 2p, hl e–Ar, rad, wall APPJa 2p, 3p Te

Ar–Ar, 3-body (∼105 Pa)Zhu et al (2009b) 1s, 2p, hl e–Ar, rad, wall SRR, DBDb 2p ne

Ar–Ar, 3-body (∼105 Pa)

a APPJ refers to atmospheric-pressure plasma jet.b SRR is for split-ring resonator, which is a microwave-excited microplasma. DBD is for dielectric barrierdischarge.

Table 3. Major processes considered in the argon CRMs. The subscripts i and j refer to different levels in the 1s or 2p multiplet. Theparameters involved in calculating the rates of processes are T

highe , the electron temperature corresponding to the high-energy electrons,

T lowe , that corresponding to the low-energy electrons, ne, the electron density, Tg, the gas temperature, ng, the gas density and d, the plasma

dimension.

Processes Parameters References

e–Ar e + Ar ↔ e + Ar(1s, 2p, hl) Thigh

e , ne, ng Chilton et al (1998), Chilton and Lin (1999),Stewart et al (2002),Weber et al (2003),Khakoo et al (2004)

e + Ar(1s) ↔ e + Ar(2p, 3p) T lowe , ne Boffard et al (1999),

Jung et al (2007)e + Ar(1si ) ↔ e + Ar(1sj ) T low

e , ne Bartschat and Zeman (1999),e + Ar(2pi ) ↔ e + Ar(2pj , 2s, 3d) Pokrzywka (2002)e + Ar(1s, 2p, hl) → e + e + Ar+ T low

e , ne Deutsch et al (2004)e + Ar∗

2 → e + Ar + Ar(1s) T lowe , ne Neeser et al (1997)

e + Ar+2 → Ar + Ar(hl) T low

e , ne, Tg Bultel et al (2002)rad Ar(1s4, 1s2) → Ar + hν NIST (2010)

Ar(2p, 3p) → Ar(1s) + hνAr(2s, 3d) → Ar(2p) + hν

Ar–Ar Ar + Ar(2pi ) → Ar + Ar(1s, 2pj ) ng, Tg Chang and Sester (1978),Ar + Ar(3p) → Ar + Ar(2s, 2p, 3d) Inoue et al (1982),

Sadeghi et al (2001)Ar(1s) + Ar(1s) → e + Ar+

2 Tg Bultel et al (2002)3-body e + e + Ar+ → e + Ar(hl) ne, T

lowe , ng, Tg Dyatko et al (2008)

e + Ar + Ar+ → Ar + Ar(hl)Ar(1s) + Ar + Ar → Ar∗

2 + Ar ng, Tg Rolin et al (2007)Ar+ + Ar + Ar → Ar+

2 + Ar

wall Ar(1s5, 1s3)wall−→ Ar ng, Tg, d Bogaerts et al (1998)

the densities of 1s levels, using the line ratios with the sameupper state, such as

IAr(2pi→1sk)

IAr(2pi→1sl )

= �2pi→1sk(n1sk

) · A2pi→1sk

�2pi→1sl(n1sl

) · A2pi→1sl

. (17)

Note that we have tens of equations like (17) for the 2p–1stransitions and thus the densities of four 1s levels can beeasily obtained. This method is called the branching fraction

method, which is described in detail by Boffard et al (2009)and Schulze et al (2008).

Using equations (16) and (17), we obtain the populationdistributions of 2p levels from the spectral data of three typesof plasmas, as shown in figures 7(b), (d) and (f ).

The next step is to calculate the population ratio asa function of Te and ne from the rate balance equations,which contain the dominant production and depopulation

9


Figure 7. Experimental emission spectra of argon plasmas: (a) ICP at 1 Pa, (c) CCP at 120 Pa and (e) SRR at 105 Pa. SRR means split-ringresonator, which is a microwave-excited microplasma. The corresponding population distributions of argon 2p levels are shown in (b), (d)and (f ). n2p and g2p are the population density and the degeneracy degree of 2p levels, respectively. The values of n2p/g2p are normalizedto 100.

Table 4. Operating parameters and plasma parameters for severaltypes of argon plasmas.

ICP CCP SRR

Driving frequency 13.56 MHz 27.12 MHz ∼0.9 GHzDischarge pressure 1–15 Pa 4–120 Pa 103–105 PaAbsorbed power 75 W 50 W ∼1 WPlasmas’ dimension 15 cm 4 cm ∼0.1–1 mmGas temperature ∼400 K ∼400 K ∼500 K

processes. At low pressures (∼1–10 Pa), atoms in the 2plevels are produced mainly by the electron-impact excitationsfrom the ground state as well as from the metastables(1s3 and 1s5). The dominant depopulation process is thespontaneous radiation. At medium pressures (∼102–103 Pa),the densities of the resonance levels (1s2 and 1s4) becomeof the same order as those of the metastables, due to thestrong radiation trapping by the ground state. As a result,the excitations from these resonance levels to the 2p levelsalso play important roles. At high pressures (∼104–105 Pa),the atom–atom collisional processes and the three-bodycollisions are important, owing to the high gas densities(Zhu and Pu 2010).

Figures 8, 9 and 10 show the contour graphs of thepopulation ratios versus Te and ne at 1 Pa, 120 Pa and 105 Pa,respectively. In each contour graph, we show two populationratios—one is more sensitive to the variation of Te and theother is more sensitive to ne. Different population ratios areselected at different pressures, owing to the different kinetic

mechanisms under these discharge conditions. In the followingpart of this section, we discuss the effects of Te and ne on theexcited level population ratios in detail, assuming a constantgas temperature and the plasma dimension (listed in table 4).The effects of variation in these parameters, even though maynot be as significant as Te and ne, are still very important undercertain conditions (section 3.2).

In figure 8, where the pressure is 1 Pa, we find that Te

is very sensitive to the population ratio 2p9/2p10. Both theselevels have large excitation cross sections from the metastablelevel 1s5 (Boffard et al 1999), and thus, under the dischargeconditions shown in this figure, the dominant productionsources of 2p9 and 2p10 are the excitations from 1s5. The ratioof the rate of these excitation processes is nearly a constant,due to their similar excitation threshold energies from 1s5.The significant increase in the ratio 2p9/2p10 with Te is causedby the depopulation mechanisms—the spontaneous radiationsand the self-absorption processes. Not that the selection ruleof the optically allowed transition from a 2p level to a 1s levelis �J = 0, ±1 except J = 0 → J = 0. Thus 2p9 (J = 3)can only decay to 1s5 (J = 2) but 2p10 (J = 1) can decayto 1s5 (J = 2), 1s4 (J = 1), 1s3 (J = 0) and 1s2 (J = 1).When Te increases, the density of 1s5 increases due to theground-state excitation due to the high-energy electrons. As aresult, the self-absorption by 1s5 is largely enhanced and theeffective decay rate from 2p9 to 1s5 is largely reduced. Onthe other hand, the decay of 2p10 by spontaneous radiation isnot much affected by this process, since it can also decay tothe resonance levels (1s2 and 1s4), whose densities are much

10


Figure 8. Contour graph of population ratios of argon 2p levels at1 Pa: 2p3/2p1 and 2p9/2p10, calculated from a CRM (Zhu and Pu2010). The gas temperature Tg is assumed to be 400 K, and theplasma dimension d is assumed to be 15 cm.

Figure 9. Contour graph of population ratios of argon 2p levels at120 Pa: 2p1/2p5 and 2p3/2p10. Tg = 400 K and d = 4 cm areassumed.

lower than the metastables at this pressure. Therefore it is thechange in loss rate which makes the population ratio 2p9/2p10

increase with Te.Figure 8 also shows that the population ratio 2p3/2p1

has a strong ne dependence. As mentioned before, the level2p1 (J = 0) has a relatively large excitation cross sectionfrom the ground state and its excitation cross section from theresonance level 1s2 is quite small. However, the opposite istrue for 2p3, whose ground-state excitation cross section issmall and its excitation cross section from 1s2 is quite large(Zhu and Pu 2010). Under the discharge conditions shownin figure 8, the density of 1s2 significantly increases with ne,due to the electron-impact population transfer processes fromthe metastables. As a result, the population ratio 2p3/2p1 alsoincreases with ne.

In figure 9, where the pressure is 120 Pa, the populationratio 2p1/2p5 shows its variation with Te. With J = 0, these

Figure 10. Contour graph of population ratios of argon 2p levels at105 Pa: 2p1/2p5 and 2p9/2p6. Tg = 500 K and d = 100 µm areassumed.

two levels have relatively large ground-state excitation crosssections, as discussed above. Thus, even at low Tes (∼1–2 eV),as found in many medium-pressure plasmas (∼102–103 Pa)(Kano et al 2000, Vries et al 2006, Iordanova and Koleva 2007),the ground-state excitation due to the high-energy electronsis still important for these two levels. The excitations fromthe 1s levels are also important. Since 2p1 has a larger ratecoefficient than 2p5 for the ground-state excitation but 2p5 haslarger excitation rate coefficients from the 1s levels, the ratio2p1/2p5 increases with Te, as seen in figure 9.

However, for the other 2p levels with J �= 0, only theexcitations from the 1s levels are important. Their populationratios (such as 2p3/2p10) are nearly independent of Te, due tothe close excitation threshold energies from the 1s levels. But itcan have a strong dependence on ne, as shown in figure 9. Thene dependence comes from two different production sourcesof 2p3 and 2p10, even though both are excited mainly from the1s levels: 2p3 from the resonance level 1s2 and 2p10 from themetastable level 1s5. Due to the electron-impact populationtransfer from 1s5 to 1s2, the density ratio 1s2/1s5 increaseswith ne. As a result, the population ratio 2p3/2p10 increaseswith ne.

In figure 10, at atmospheric pressure, the populationratio 2p1/2p5 also varies with Te for the same reasons as infigure 9. On the other hand, the population ratio 2p9/2p6

is selected to show its variation with ne. This is becausetheir depopulation processes have different dependence onne. At atmospheric pressure (gas temperature ∼500 K, plasmadimension ∼100 µm), the 2p6 level is depopulated mainly bythe collisional quenching with the electrons, while 2p9 hasan additional important destruction channel—the collisionalquenching with the ground-state atoms. Therefore, for the2p9 level, its rate of decrease with ne is slower than that for2p6 level. This causes the population ratio 2p9/2p6 to increasewith ne.

At atmospheric pressure, the gas temperature, Tg, canaffect the rate of the atom–atom collisional quenching process,

11


Figure 11. Te and ne versus neutral gas pressure, determined by fitting the calculated population ratios of argon 2p levels with thoseobtained from the experimental line ratios: (a) ne for an argon ICP at pressures 1–15 Pa, (b) ne for an argon CCP at pressures 4–120 Pa,(c) ne for an argon SRR at pressures 103–105 Pa, (d) Te for ICP, (e) Te for CCP and (f ) Te for SRR. The ‘probe’, ‘IEDF’ and ‘broadening’refer to the Langmuir probe method (Zhu and Pu 2008), the method of deriving ne from the measured ion energy distribution function (Chenet al 2009b) and the Stark broadening method (Zhu et al 2008).

due to its effect on the gas density, ng (∼T −1g ), and that

on the collisional quenching rate coefficient (∼T1/2

g , Rolinet al (2007) and Zhu and Pu (2010)). When Tg increases,the reduction in the rate of atom–atom collision process(∼n2

g × T1/2

g ∼ T−3/2

g ) is faster than that of the electron–atomprocess (∼ng ∼ T −1

g ). As a consequence, the population ratio2p9/2p6 increases with Tg. For example, the ratio of 2p9/2p6 ata gas temperature of 1000 K is larger than that at 500 K (usedin figure 10) by ∼5%. This will cause the variation in the valueof ne, obtained from the line-ratio method, as much as 40%.In this case, while using the line-ratio method, one needs toestimate the gas temperature by the OES method (Wang et al2005, Zhu et al 2008).

As seen in figures 8, 9 and 10, the values of Te and ne

can be simultaneously obtained from the intersection of twocontour lines. However, the most accurate values of Te and ne

can be obtained by fitting the experimental with the calculatedpopulation distributions for all the 2p levels at the same time.Figure 11 shows the results of this method for several argonplasmas. They agree well with the data from a Langmuir probe,nes derived from the ion energy distribution function (Chenet al 2009b) or by the Stark broadening method. The line-ratio method has the prominent advantage of being a universalmethod for many different types of plasmas when a suitableCRM is used.

A Maxwellian EEDF is often assumed in the CRMsto calculate line ratios. For the low-pressure plasmas, thisassumption is often proved to be valid from the Langmuirprobe data (Zhu and Pu 2007a, 2007b) or the laser Thomson

scattering data (Crintea et al 2009). Otherwise, the TRG-OES method to determine T

highe and T low

e separately isrecommended, which uses different line ratios either sensitiveto the high-energy EEDF tail or the low-energy EEDFbulk (Donnelly (2004), Chen et al (2009a) and Staffordet al (2009), see tables 1 and 2). At medium to highpressures (∼102–105 Pa), however, all the line ratios of 2plevels may be affected mainly by the EEDF bulk. Thisis because the excitation processes from 1s levels dominatethe excitation processes from the ground state. In thiscase, one has to assume a Maxwellian EEDF for the low-energy electrons, while using the CRMs to calculate theline ratios of these 2p levels. It may be a reasonableassumption for many low-temperature plasmas, since thenon-Maxwellian EEDF is usually caused by the inelasticcollisions of the high-energy electrons with the ground-statespecies or by the non-local heating of these energetic electrons(Godyak 2006).

2.3. Nitrogen CRM method

For nitrogen plasmas at pressure ∼10–105 Pa, the coronamodel is invalid, due to the collision processes betweenmetastable molecules, excited molecules and vibrationallyexcited ground-state molecules, as well as the electron collisionprocesses with these molecules (Piper 1988a, 1988b, 1989,Adamovich et al 1998, Mihajlov et al 1999, Ahn et al 2004,Dilecce et al 2006, 2007, 2010). In this case, in order to applythe line-ratio methods to determine Te or ne, one should use

12


Table 5. The excited states and processes considered in several nitrogen CRMs used for the line-ratio techniques. e–N2 or e–N+2 represents

the collision processes between electrons and nitrogen molecules or molecular ions; N2–N2 and N2–O2 are for the molecule–moleculecollisions; rad and wall are for the radiation processes and the collision processes at the chamber wall, respectively. These processes aredescribed in more detail in table 6.

Modelling Experiments and results

States Processes Plasmas Parameters

Bibinov et al (1998) N2(X), N2(C), e–N2, rad, wall, N2(X)–N2(X) DCGD Te

N+2 (B) (N2, ∼10–30 Pa)

Kozlov et al (2001) N2(X), N2(C), e–N2, rad, N2(C)–N2/O2, DBD E/N

N+2 (B) N+

2 (B)–N2/O2 (air, ∼105 Pa)Lebedev and Shakhatov (2006) N2(X), N2(A), e–N2, rad, wall, N2(X)–N2(X), DCGD, MDb E/N , ne

N2(B), N2(C)a N2(A)–N2(A), N2(A/B/C)–N2(X) (N2, ∼102–103 Pa)Zhu and Pu (2008) N2(X), N2(A), e–N2, rad, wall, N2(X)–N2(X), ICP Te, ne

N2(B), N2(C) N2(A)–N2(A), N2(A/B)–N2(X) (N2, ∼0.1–10 Pa)Isola et al (2010) N2(X), N2(C), e–N2, e–N+

2 , rad pulsed DCGD Te, ne

N+2 (B) (N2, ∼300 Pa)

a The model also includes some other species, such as N2(a′1�−

u ), N2(a1�g), N(4S), N(2D), N(2P), as well as the relevant

kinetic processes.b MD refers to microwave discharge.

Figure 12. Experimental emission spectra of a nitrogen CCP (pressure 10 Pa, driving frequency 13.56 MHz, power 80 W, Chen et al(2009b)): (a) part of the second positive system, SPS (N2, C 3�u → B 3�g); (c) part of the first positive system, FPS(N2, B 3�g → A 3�+

u ). Partial energy diagrams of states N2(A3�+

u ), N2(B3�g) and N2(C

3�u) are given in (b) and (d).

more detailed CRMs (Bibinov et al 1998), which are also callednitrogen kinetic models (Guerra and Loureiro 1997, Guerraet al 2001, 2004, Sa et al 2004).

Table 5 lists several works of using nitrogen CRMs todetermine Te and ne in nitrogen-containing plasmas (line-ratiomethods for gas-mixture discharges are further discussed insection 3.3). Although the works in table 5 are different indetails, we may use that by Zhu and Pu (2008) as an exampleto outline their general principle.

Usually, the strongest emission bands in low-temperaturenitrogen plasmas with a relatively low ionization ratio∼10−6–10−4 are the second positive system (N2, C 3�u →B 3�g) and the first positive system (N2, B 3�g → A 3�+

u ), asshown in figure 12. For low-pressure ICP and CCP discharges(<∼103 Pa), the important production processes for theexcited molecules N2(C

3�u) and N2(B3�g) are the electron-

impact excitation from the vibrationally excited ground-state molecules N2(X

1�+g ,v) and the reactions between

13


N2(X1�+

g ,v) and N2(A3�+

u ) (see table 6). As a result, tocalculate the line ratios of those two emission band systems,we should solve the rate balance equations of N2(X

1�+g ,v),

N2(A3�+


3�u):

ne

∑v′ �=v

nX,v′Qv′→ve−N2

+ nX,v−1

∑w

nX,v′+1Qv−1,v′+1→v,v′N2(X)−N2(X)

+ nX,v+1

∑v′

nX,v′Qv+1,v′→v,v′+1N2(X)−N2(X) + Kv+1→v

wall nX,v+1

= nenX,v

∑v′ �=v

Qv→v′e−N2

+ nX,v

∑v′

nX,v′+1Qv,v′+1→v+1,v′N2(X)−N2(X)

+ nX,v

∑v′

nX,v′Qv,v′→v−1,v′+1N2(X)−N2(X) + Kv→v−1

wall nX,v, (18)

ne

∑v

nX,vQX,v→Ae−N2

+ nB

(∑v

nX,v

)QB→A

N2(B)−N2(X)

+ ABnB = nenAQA→Xe−N2

+ nA

∑

5�v�14

nX,v

QA→B

N2(A)−N2(X)

+ 2n2A

(Q

A,A→BN2(A)−N2(A) + Q

A,A→CN2(A)−N2(A)

)+ KA

wallnA, (19)

ne

∑v

nX,vQX,v→Be−N2

+ nA

∑

5�v�14

nX,v

QA→B

N2(A)−N2(X)

+ n2AQ

A,A→BN2(A)−N2(A) +

∑v′′

AC,v′′nC,v′′

+

(∑v

nX,v

) ∑v′′

nC,v′′QC,v′′→BN2(C)−N2(X) = nenBQB→X

e−N2

+ nB

(∑v

nX,v

)QB→A

N2(B)−N2(X) + ABnB, (20)

ne

∑v

nX,vQX,v→C,v′′e−N2

+ n2AQ

A,A→C,v′′N2(A)−N2(A)

+

(∑v

nX,v

) ∑v′′′>v′′

nC,v′′′QC,v′′′→C,v′′N2(C)−N2(X)=nenC,v′′Q

C,v′′→Xe−N2

+

(∑v

nX,v

)nC,v′′

∑v′′′<v′′

QC,v′′→C,v′′′N2(C)−N2(X)

+

(∑v

nX,v

)nC,v′′Q

C,v′′→BN2(C)−N2(X) + AC,v′′nC,v′′ . (21)

Here v and v′ refer to the vibrational levels in the ground state,v′′ and v′′′ refer to the vibrational levels of state N2(C

3�u).nX, nA, nB and nC are the densities of states N2(X

1�+g ),

N2(A3�+


3�u), respectively. Just asdefined in section 2.2, Q is the rate coefficient for gas-phasecollisions, K is the diffusion-controlled reaction coefficientand A is the Einstein A coefficient. The superscripts andsubscripts denote the species involved in each process, as listed

in table 6. The self-absorption processes are not consideredfor the optical transitions from N2(B

3�g) to the metastablestate N2(A

3�+u ), due to the small Einstein B coefficients for

absorption (equation (15)). For the nitrogen ICP dischargesinvestigated here (Zhu and Pu 2005), the vibration–translationrelaxation processes by nitrogen molecules are not as importantas the vibration–vibration transfer processes and can beignored (Zhu et al 2006). The nitrogen atoms and their relevantprocesses, including the energy transfer with N2(A

3�+u ) and

the vibration–translation relaxation with N2(X1�+

g ,v > 0),are not included in the model, due to the low dissociation ratioof nitrogen molecules in this ICP discharge (<0.1%). In thecase of a relatively high dissociation ratio, ∼1–10%, theseprocesses and the kinetic modelling of nitrogen atoms shouldbe included, such as that for a nitrogen ECR plasma (Bibinovet al 2005).

By solving the rate balance equations (18)–(21), thepopulation ratios N2(C

3�u)/N2(B3�g) and N2(C

3�u,v =1)/N2(C

3�u, v = 0) can be calculated, as plotted in figure 13(at 1 Pa) and figure 14 (at 10 Pa). In the calculation, one alsoneeds the plasma dimension and the gas temperature, due tothe presence of diffusion-controlled deactivation at the walland collisions between heavy species (Zhu and Pu 2008).

According to the nitrogen CRM above, the electron-impact excitation processes from the ground state are importantfor both N2(C

3�u) and N2(B3�g). In addition, these two

states have an energy difference, �E, ∼3.7 eV (figure 12).Therefore, the population ratio of N2(C

3�u)/N2(B3�g) is

sensitive to the variation of Te in the range 1–4 eV, asseen in figures 13 and 14. The �E between vibrationallevels N2(C

3�u,v = 1) and N2(C3�u, v = 0) is much

smaller than the Te values. Thus their population ratio isinsensitive to the variation of Te. The low-lying vibrationallevels, N2(X

1�+g ,v = 1–8), are produced mainly by the

electron-impact vibrational excitation from N2(X1�+

g ,v = 0)and depopulated by both electron collisions and vibration–vibration transfer processes (note that the vibration–vibrationtransfer is dominant in both the production and depopulationof intermediate vibrational levels with v ∼ 10–40, Guerraet al (2004)). Owing to the electron-impact excitation, theconcentration of molecules N2(X

1�+g , v = 1–8) significantly

increases with ne, which, according to the Franck–Condonprinciple, can lead to the increase in ratio N2(C

3�u,v =1)/N2(C

3�u, v = 0) versus ne, as shown in figures 13 and14. Unlike the vibrational levels of the ground state, theselevels do emit light.

For the first positive system (N2, B 3�g → A 3�+u ), the

self-absorption processes can be ignored due to the smallEinstein B coefficients. For the second positive system (N2,C 3�u → B 3�g), they are ignored since the lower stateN2(B

3�g) is an excited state and has a very low density.Therefore, the measured emission line ratios are related to theexcited state population ratios by

IN2(C)

IN2(B)

= AC · nC

AB · nB

, (22)

IN2(C,v=1)

IN2(C,v=0)

= AC,v=1 · nC,v=1

AC,v=0 · nC,v=0. (23)

14


Table 6. Major processes in the nitrogen CRMs used for the emission line-ratio methods. Here v and v′ refer to different vibrational levelsin an electronic state. The parameters involved in calculating the rates of processes are T

highe and T low

e , the electron temperaturescorresponding to the high-energy and low-energy electrons, respectively, ne, the electron density, Tg and ng, the gas temperature and densityand d, the plasma dimension.

Processes Parameters References

e–N2 e + N2(X) ↔ e + N2(A/B/C/a′/a) Thigh

e , ne, ng Itikawa et al (1986), Itikawa (2006),e + N2(X) → e + e + N+

2 (X/B) Majeed and Strickland (1997)a

e + N2(X, v) ↔ e + N2(X, v′) T lowe , ne Mihajlov et al (1999)

e–N+2 e + N+

2 (X) ↔ e + N+2 (B) T low

e , ne Tabata et al (2006)N2(X)–N2(X) N2(X, v) + N2(X, v′) ↔ Tg Adamovich et al (1998),

N2(X, v + 1) + N2(X, v′ − 1) Ahn et al (2004)N2(A)–N2(A) N2(A) + N2(A) → N2(B) + N2(X) Tg Piper (1988a, 1988b)

N2(A) + N2(A) → N2(C) + N2(X)N2(A)–N2(X) N2(A) + N2(X, 5 � v � 14) → Tg Piper (1989)

N2(B) + N2(X)N2(B)–N2(X) N2(B) + N2(X) → N2(A) + N2(X) ng, Tg Guerra et al (2004)N2(C)–N2/O2 N2(C, v) + M → N2(C, v′)/N2(B) + M ng, Tg Dilecce et al (2006, 2007),

v′ < v, M = N2/O2 Lebedev and Shakhatov (2006)N+

2 (B)–N2/O2 N+2 (B) + M → N+

2 (X) + M ng, Tg Dilecce et al (2010)M = N2/O2

rad N2(B) → N2(A) + hν Gilmore et al (1992)N2(C) → N2(B) + hνN+

2 (B) → N+2 (X) + hν

wall N2(X, v)wall−→ N2(X, v − 1) ng, Tg, d Black et al (1974)

N2(A)wall−→ N2(X) ng, Tg, d Augustyniak and Borysow (1994)

a The state-to-state excitation cross sections can be calculated according to the Franck–Condon principle, with theFranck–Condon factors from Lofthus and Krupenie (1977).

Figure 13. Contour graph of population ratios of nitrogenmolecules at 1 Pa: N2(C

3�u)/N2(B3�g) (×100) and N2(C

3�u,v = 1)/N2(C

3�u, v = 0), calculated using a nitrogen CRM (Zhuand Pu 2008). Tg = 400 K and d = 15 cm are assumed.

IN2(C,v=0) and IN2(C,v=1) are the emission intensities fromvibrational levels 0 and 1 of state N2(C

3�u), similar to IAr(2p1)

and IXe(2p5) used in equation (6). IN2(B) and IN2(C) are thesum of emission intensities from all the vibrational levels ofstates N2(B

3�g) and N2(C3�u), respectively. A and n are

the Einstein A coefficients and the species densities, as usedin equations (19)–(21).

Using the line-ratio equations (22) and (23) and thecalculated contour graphs as in figures 13 and 14, the values ofTe and ne in nitrogen plasmas are obtained. Figure 15 shows

Figure 14. Contour graph of population ratios of nitrogenmolecules at 10 Pa: N2(C

3�u)/N2(B3�g) (×100) and N2(C

3�u,v = 1)/N2(C

3�u, v = 0) · Tg = 400 K and d = 15 cm are assumed.

the results of this method in a nitrogen ICP discharge (Zhu andPu 2005, 2008, Zhu et al 2006). In figure 15(a), Te is tunedby varying the pressure at a constant power. ne increases withpower at a constant pressure in figure 15(b). In both cases,the results of line-ratio method with nitrogen CRM agree wellwith those obtained by the Langmuir probe.

As for nitrogen plasmas with non-Maxwellian EEDFs,Bibinov et al (1998, 2005, 2008) develop a method todetermine both T

highe (for electrons with energies >11 eV) and

T lowe (for electrons in the energy range 1.5–4.5 eV). T

highe is

obtained using the line ratio of two excited states N2(C3�u)

15


Figure 15. Te and ne obtained by fitting the measured with the calculated population ratios N2(C3�u)/N2(B

3�g) and N2(C3�u,

v = 1)/N2(C3�u, v = 0): (a) Te for a nitrogen ICP versus pressure at constant power 600 W, (b) ne versus power at constant pressure 2 Pa.

The ‘probe’ refers to the Langmuir probe method (Zhu and Pu 2005, 2008, Zhu et al 2006).

and N+2(B

2�+u ). These excited species are produced mainly

by the excitation processes due to high-energy electrons. T lowe

is determined by the line ratio N2(C3�u,v = 4)/N2(C

3�u,v = 0). At low pressures (0.1–100 Pa), this line ratiodepends on the population ratio of N2(X

1�+g ,v = 4-7)

and N2(X1�+

g ,v = 0–1), according to the Franck–Condonprinciple (Levaton et al 2004). This population ratio issignificantly affected by the vibrational excitation processesdue to low-energy electrons. In addition, �E betweenN2(X

1�+g ,v = 4–7) and N2(X

1�+g ,v = 0–1) is as large as

∼1.5 eV. Therefore, this ratio can be sensitive to the variationof T low

e .

3. Conditions of using line-ratio methods

The conditions of using each line-ratio method have beenbriefly discussed in section 2—the corona model can beused for plasmas with low pressure and low ionization ratio;otherwise, the argon or nitrogen CRMs should be applied. Inthis section, we further discuss this point.

3.1. Pressure and ionization ratio

To distinguish the conditions for different line-ratio methods,we propose some ‘application regions’, whose scopes arefunctions of pressure and ionization ratio (see figures 16and 17). These regions have different major collisional–radiative processes and thus different line-ratio methods shouldbe chosen for each of them. The scopes of application regionsare determined using the argon and nitrogen CRMs in section 2,together with the experimental results in the reference worksin tables 1, 2 and 5, and figures 16 and 17.

In figure 16, there are four application regions for low-temperature argon plasmas in the pressure range ∼0.1–105 Pa

Figure 16. A diagram for the line-ratio methods used inlow-temperature argon plasmas with different regions: C for thecorona model region, L for the low-pressure region, H for thehigh-pressure region and B for the Boltzmann-plot method region.A gas temperature of 400 K and a dependence of plasma dimensionon the pressure, d = 10 × p−3/5 (d in cm, p in Pa), are assumed(Zhu and Pu 2009).

and in the ionization ratio range ∼10−6–10−3. In the C-region,the corona model is valid and the line-ratio method describedin section 2.1.1 can be applied to measure the electrontemperature (Crolly and Oechsner 2001). In the L-region(low-pressure region), due to the excitation processes frommetastable levels, one needs to use an argon CRM to determineboth Te and ne (Iordanova and Koleva 2007, Crintea et al 2009).In the H-region (high-pressure region), the excitations out ofexcited levels, the atom–atom collisions and the three-bodycollisions should be added in the CRM (Kano et al 2000, Vrieset al 2006). This difference in major processes between theL-region and H-region will affect the selection of line ratios,

16


Figure 17. A diagram for the line-ratio methods used inlow-temperature nitrogen plasmas with different regions: C for thecorona model region, L for the low-pressure region and H for thehigh-pressure region. A gas temperature of 400 K and a dependenceof plasma dimension on the pressure, d = 10 × p−3/5 (d in cm, pin Pa), are assumed (Zhu and Pu 2009).

as shown in figures 8–10. At high to atmospheric pressure andwith relatively high ionization ratio (B-region), the electron–atom collision processes are dominant in both production anddepopulation of the excited atoms, which, as a result, mayhave a Boltzmann (or Boltzmann-like) population distribution.The Boltzmann-plot method—deriving Te from the excitationtemperature of excited atoms—can be used in this region(Garcıa et al 2000). However, a non-Boltzmann ASDFis caused due to the atom–atom collisions in atmospheric-pressure plasmas with a low ionization ratio (Zhu and Pu 2009).The Boltzmann-plot method is invalid in this case and a CRMis needed in the determination of Te and ne, accounting for thenon-Boltzmann ASDF (Zhu et al 2009b).

Note that the selection of line-ratio methods is not onlyaffected by the operating conditions but also depends on thecharacteristics of excited levels. Even in the low-pressureregion in figure 16, the corona model can be valid if specialexcited levels are chosen, such as Ar(3p1) and Ar(5p5), asdescribed in section 2.1.2. This is because the electron-impact excitation processes from metastable levels to 3p1 and5p5 are very weak (Boffard et al 2004). Therefore, theirdominant production process is the excitation from the groundstate. As for the depopulation mechanism, the electron-impactpopulation transfer process should be added in the coronamodel. With this extended corona model, ne can be determinedby the line ratio Ar(3p1)/Ar(5p5) (Zhu and Pu 2007a).

The region diagram for nitrogen plasmas is shown infigure 17. The corona model can be used in the C-region(Pu et al 2000, Britun et al 2007). There are two kindsof nitrogen CRMs, proposed for the L-region and H-region,respectively (Guerra et al 2004, Zhu and Pu 2005). In additionto the species and processes in the corona model, the formerCRM also includes the metastable species N2(A

3�+u ) and

N2(X1�+

g ,v > 0) and the collisional processes between thesemolecules (Bibinov et al 1998, Zhu and Pu 2008). In addition,the latter CRM includes N2(a

′ 1�−u ), N2(a

1�g), N(4S), N(2D)and N(2P), owing to their collisional processes with N2(A

3�+u )

and N2(X1�+

g ,v > 0), which can be important at mediumpressures (∼103 Pa) (Lebedev and Shakhatov 2006).

With the pressure and ionization ratio roughly known, onecan choose a suitable line-ratio method according to the regiondiagrams (figures 16 and 17).

3.2. EEDF, plasma dimension and gas temperature

Even though the pressure and ionization ratio are the mostimportant parameters in determining the dominant processesfor a given pair of levels (thus affecting the results of the lineratios obtained from the models), under certain conditions,the variation in the EEDF, the plasma dimension and the gastemperature may also change the identification of dominantprocesses in a very significant way (Zhu and Pu 2010). Thisis particularly true around the borderline between two regionsin figures 16 and 17, which are plotted with a constant gastemperature of 400 K, with the assumption of a MaxwellianEEDF and an assumed dependence of plasma dimension onthe pressure, d = 10 × p−3/5 (d in cm, p in Pa, Zhu andPu (2009)).

In a plasma with a non-Maxwellian EEDF, the ground-state excitation is sensitive to the variation of EEDF tail (T high

e )while the metastable-level excitation is sensitive to the EEDFbulk (T low

e ). Therefore, in figures 16 and 17, if Thigh

e > T lowe ,

the C-region is expanded somewhat to the right, while in theopposite case, the L-region is expanded to the left where thepressures and ionization ratios are lower.

Both the plasma dimension, d, and the gas temperature, Tg,can affect the diffusion-controlled quenching and the radiationtrapping. At a constant pressure, the diffusion-controlledquenching is increased by decreasing d or by increasing Tg,and as a result, the metastable density becomes lower and theC-region is expanded to the right (Zhu and Pu 2010). Theradiation trapping process, being important to the relationshipof the line ratios with Te at low pressures (see the abovediscussion about figure 8), is enhanced by increasing d or bydecreasing Tg, since Tg can affect the broadening width ofemission lines.

At atmospheric pressure, the atom–atom collisionbecomes a very important process (see the above discussionon figure 10), whose rate increases with Tg (Zhu and Pu 2010).Therefore, in figure 16, the high-pressure nonequilibriumregion—the H-region—is expanded to higher ionization ratioregions with an increase in Tg.

3.3. Gas-mixture discharges

Although the region diagrams—figures 16 and 17—are plottedfor pure argon and pure nitrogen discharges, respectively,they may also be used to select line-ratio methods for gas-mixture discharges containing argon or nitrogen, after theenergy transfer processes for excited species, such as

Ar(1s, 2p, 3p, 5p) + O2 → Ar(1S) + O + O, (24)Ar(1s, 2p, 3p, 5p) + CF4/CH4/C2H2/SF6

→ Ar(1S) + product, (25)N2(A) + O2 → N2(X) + O + O, (26)

17


are considered (Velazco et al 1978, Guerra et al 2001, Sadeghiet al 2001). These are the depopulation processes for therelevant excited species or metastable species, which playimportant roles in the rate balance equations. For excitedspecies with large Einstein coefficients, such as Ar(2p), thesekinds of processes should be included in the CRM at highpressures (>103–104 Pa). For those with small Einsteincoefficients, such as Ar(5p), it should be added in the modelstarting at an even lower pressure (∼100 Pa). For themetastable species, these processes can be important at lowpressures (∼1 Pa), since their magnitude will be comparableto that of diffusion-controlled deactivation at the chamberwall. When the densities of the metastable species are largelyreduced by processes (24)–(26), the excitation processes fromthe metastables may be much weaker than those from theground state, and, as a result, one may use the corona modelinstead of a CRM.

On the other hand, some reactions can produce excitedspecies used in a line-ratio method. Such an example is thePenning ionization (Petrov et al 2000),

He(21S, 23S) + N2(X) → He(11S) + N+2(B) + e. (27)

When this kind of process is present, one should make a carefulexamination—whether it becomes the major productionprocess for excited species instead of the electron-impactexcitation process. For example, in helium plasmas withnitrogen impurity, the emission intensity of N+

2(B2�+

u ) hassensitive functions on the densities of the metastable atoms,He(21S) and He(23S) (DeJoseph et al 2007). In this case,the Penning ionization process, as well as the other relevantprocesses of He(21S) and He(23S), should be included in thepopulation model of nitrogen species to calculate the emissionline ratios.

4. Limitations

In this section, we discuss the limitations in the application ofline-ratio methods. One of them is about the measurementrange of Te and ne (see figures 2 and 4). As mentionedbefore, one should select excited species with suitable energydifference (�E, equation (7)) and characteristic electrondensity (neC, equation (10)) according to the Te and ne valuesin the plasmas to be investigated (therefore, one needs a roughestimation of these ‘to be measured’ parameters at first). Forsimilar reasons, a careful selection of the correct CRMs isneeded, according to the discharge conditions, in order toobtain the optimal sensitivity of the line ratio to Te and ne

(see figures 8–10 and tables 2 and 5). In addition, there aresome practical considerations for the application of line-ratiomethods, as discussed in the following.

4.1. Optical absorption and reflection

Usually, there are two kinds of optical absorption processes(also called self-absorption process or radiation trapping) inlow-temperature plasmas.

One is the absorption process by species in the metastableor excited states. For example, the photons emitted in the

Figure 18. A schematic energy diagram for some argon atomiclevels, with the resonance radiation and the cascade process shown.

optical transition of Ar(2p2) → Ar(1s5) are re-absorbed by theAr(1s5) atoms in plasmas (figure 18). Due to this absorptionprocess, as mentioned earlier, the densities of lower levels canbe determined using the branching fraction method (Boffardet al 2009), which are used to calculate the population ratios ofthe upper levels from the measured emission line ratios usingequation (16).

The other absorption process is the resonance radiationtrapping by the ground state. For example, the VUV photonsemitted in the resonance transition of Ar(3s2) → Ar(1S)are re-absorbed by the ground-state atoms Ar(1S) (figure 18).Obviously, the effective decay rate by resonance radiation, forexample, Ar(3s2) → Ar(1S), can be significantly reducedby increasing the pressure (thus Ar(1S) density). As aresult, the cascade processes out of resonance levels, forexample, Ar(3s2) → Ar(2p2), are enhanced. As mentionedin section 2.1.1, the apparent excitation cross sections, beingused in the corona model (equation (4)), are the sum ofdirect excitation cross sections and cascade cross sections.Therefore, the apparent cross sections vary with the gaspressure due to the pressure-dependent cascade cross sections.The escape factor of resonance radiation trapping is a functionof ng×T

−1/2g ×leff at low pressures <100 Pa (leff is an effective

path length, of the order of the plasma dimension). Thus,with ng, Tg and leff known, the apparent cross sections ina plasma can be calculated, based upon the excitation crosssections measured at a variety of gas pressures (Boffard et al2004, 2007). The calculation procedure is described in detailby Schabel et al (2002). For plasmas at higher pressures(>100 Pa), the CRMs are used instead of the corona model.The CRMs use the direct excitation cross sections of electron-impact processes, which do not suffer from the radiationtrapping effect.

Emission lines from plasmas can be reflected on thedischarge chamber walls, which, sometimes, contribute to

18


Table 7. Spectroscopic systems used to record the emission lines in references. CCD refers to charge-coupled device, ICCD refers tointensified CCD and PMT refers to photomultiplier tube. TRL means tungsten ribbon lamp, SR means synchrotron radiation and D2 lamp isdeuterium lamp.

Lines Spectrometer Wavelength (nm) Resolution (Å) Detector Calibration References

Ar, TRIAX550, 330–500 ∼0.5 PMT TRL Zhu and Pu (2007a)5p → 1s Jobin YvonAr, SPEX 1870c 335–925 ∼1 ICCD TRL Boffard et al (2004)3p → 1sAr, HR4000, 735–915 ∼2 CCD TRL Chen et al (2009a)2p → 1s Ocean OpticsXe, Avaspec2048, 600–1100 ∼4 CCD TRL Zhu et al (2009a)2p → 1s Avantes Inc.N+

2 , AS50, 110–400 ∼3 PMT D2 lamp, Bibinov et al (2008)B 2�+

u → X 2�+g Jobin Yvon TRL

N2, SQ2000, 200–530 ∼6 CCD SR, Zhu et al (2006)C 3�u → B 3�g Ocean Optics TRLN2, Avaspec2048, 200–1100 ∼8 CCD TRL Cicala et al (2009)B 3�g → A 3�+

u Avantes Inc.

the emission intensities recorded by a spectroscopic system.The reflectivity of some stainless steel chamber walls maybe wavelength dependent. The observed emission line ratiosare thus affected. This reflection effect can be enhanced dueto the films deposited by CH4/N2 plasmas (Pu et al 2005a),owing to the interference between the light reflected from thefilm surface and that which re-emerged from the surface afterbeing reflected by the stainless steel chamber wall. Pu et al(2005b) find that this effect can cause errors ∼20% in the Te

measurement by the line ratio of lines 391.4 nm and 762.6 nm(see figure 12). They use a practical method to eliminate theoptical reflection effect. It is to arrange a black-surface platewith a very small reflection coefficient facing the diagnosticviewport.

4.2. Spectroscopic system

Table 7 lists several typical spectroscopic systems used for theline-ratio methods. The line-ratio methods only need a lowor moderate spectral resolution (usually, several angstroms)to distinguish between the emission lines or bands. Therequirement of detector sensitivity is not high unless some veryweak lines are needed to be recorded, such as those out of argon4p and 5p levels (see figure 19), for which a photomultipliertube (PMT) or an intensified charge-coupled device (ICCD)should be used.

The wavelength and intensity calibration of a spectro-scopic system is necessary for the application of line-ratiomethods. Wavelength calibration can be done using atomicemission lines, from a low-pressure mercury lamp or a plasma(Fantz 2006). Tungsten ribbon lamps with temperatures∼2000–3000 K are suitable for intensity calibration in thewavelength range 300–1100 nm (Bibinov et al 1997). Atshorter wavelengths, one can use synchrotron radiation (SR)or secondary standard light sources, such as a deuterium lamp.In some special cases, two emission lines with similar wave-lengths are used. For example, Britun et al (2007) use the391.4 nm and 394.3 nm bands from N+

2(B2�+

u ,v = 0) andN2(C

3�u,v = 2). Crolly and Oechsner (2001) use the 454.5and 451.1 nm lines from Ar+(4p2P3/2) and Ar(3p5). In this

Figure 19. Experimental emission spectra containing the weakemission lines out of argon 4p and 5p levels (CCP,Ar/O2 = 0.5/2 Pa, driving frequency 27.12 MHz, power 200W,Chen et al (2009b)). The spectral resolution of the spectroscopicsystem used is ∼0.5 Å. The detector is a PMT in photon countingmode (cooled to 5 ◦C).

case, the requirement of intensity calibration may be reduced,assuming the response function of the spectroscopic systemvaries smoothly at these wavelengths.

4.3. Temporal and spatial resolution

Temporally and spatially resolved diagnostics of low-temperature plasmas can be accomplished using the line-ratiomethods, if one uses time–space dependent CRMs. In thesemodels, the rate balance equation of an excited state, x, iswritten as

∂nx(�r, t)∂t

+ ∇r · (−Dx · ∇r · nx(�r, t))=

∑i

Ri[ne(�r, t), Te(�r, t), nx(�r, t), ny,y �=x(�r, t),

Tg(�r, t)]. (28)

19


Figure 20. The lifetime of excited species (curves) and the temporalresolution achieved in the references (squares). The gas temperatureis assumed to be 400 K.

Here y refers to the other excited species except x, as well asthe ground-state species, n is the species density, �r and t referto the position and the time, D is the diffusion coefficient,R is the rate of the collisional–radiative processes, which isa function of plasma parameters (ne, Te, nx , ny , Tg). Usingthese kinds of rate balance equations, one can obtain thetime–space dependent plasma parameters from the populationdensity ratios of excited species (from the measured emissionline ratios) (Kozlov et al 2001, Schulze et al 2010). In thefollowing, we use some examples to illustrate the temporaland spatial resolution achieved by these kinds of line-ratiomethods, which not only depend on the instrument used inthe experiment, but also depend on the collisional processes.

Hu and Pu (2009) investigate the emission spectra fromneon atoms in an afterglow plasma. A PMT is used asthe detector of the spectroscopic system, whose temporalresolution is ∼30 ns. Schulze et al (2010) investigate a low-pressure Ar/Ne plasma by the phase resolved OES method.The spectroscopic system containing a fast-gateable ICCDcamera has a temporal resolution of ∼5 ns. Higher temporalresolution, ∼0.1–0.2 ns, is achieved by means of the cross-correlation spectroscopy technique (Kozlov et al 2001), inthe investigation of dielectric barrier discharges in air atatmospheric pressure. Figure 20 shows the temporal resolutionvalues above, together with the lifetimes of excited speciesrelevant in the line-ratio methods. The lifetimes are calculatedby considering the spontaneous radiation processes as well asthe collisional quenching processes. The temporal resolutionof the spectroscopic system used by Schulze et al (2010)(∼5 ns) is shorter than the species lifetimes at low pressures.In this case, note that the actual temporal resolution achievedin the determination of plasma parameters (Te, ne, E/N ) byan OES method cannot be better than the lifetime of excitedspecies observed (>10 ns).

As for the spatially resolved measurement, the OESmethod suffers from a fundamental challenge: the signal iseither a volume-averaged one or a ‘line’-averaged one if oneuses a fine collimator. By moving a light collecting optical fibrestep by step, Chen et al (2007) do a spatially resolved OESinvestigation of low-pressure Ar/N2 plasmas, with a spatial

Figure 21. The energy-loss mean free path of species (curves) andthe spatial resolution achieved in the references (squares). The gastemperature is assumed to be 400 K. The ionization ratio of argonplasma and nitrogen plasma is assumed to be 10−4.

resolution of ∼3 mm. Two-dimensional spatially resolvedOES measurement can be accomplished using spectroscopicsystems containing ICCD cameras, with a spatial resolutionof ∼0.1–1 mm (Kozlov et al 2001, Schulze et al 2010).When a microscope mirror system is used together with thespectroscopic system, the spatial resolution can be as highas ∼10 µm (Tian et al 2010). Figure 21 compares thesespatial resolution values with the energy-loss mean free path ofsome species in low-temperature plasmas, which are calculatedusing the argon and nitrogen CRMs assuming ionization ratio10−4 and Tg 400 K. The energy-loss mean free path of excitedspecies is the fundamental spatial resolution limit of the OESmethods, which can be as large as ∼1–10 µm, as seen infigure 21.

Sometimes, the spatial distribution of the metastablespecies, such as the vibrationally excited ground-state nitrogenmolecules, N2(X

1�+g , v > 0), also affects the spatial

resolution in determining Te and ne. This is because theirvibrational distribution can be very much spatially uniform,due to their extremely long energy-loss mean free paths (seefigure 21). Such an example is the line-ratio method of usingN2(C

3�u,v = 1)/N2(C3�u, v = 0). Molecules in these two

levels come mainly from the ground-state excitations, whichcan be enhanced due to the increase in Te and ne. Thus theemission intensities from these levels vary strongly with Te

and ne. However, these two levels have very similar excitationthreshold energies; as a result, the ratio of their excitationrates is nearly a constant and can be represented by theFranck–Condon factors. On the other hand, according to theFranck–Condon principle, the population ratio N2(C

3�u, v =1)/N2(C

3�u,v = 0) varies only with the VDF of the ground-state molecules, which can be very uniform in space due totheir long energy-loss mean free paths, despite the possibilityof a very non-uniform distribution of Te and ne. Therefore,using the nitrogen CRMs for vibrationally excited ground-statemolecules, one can only obtain the volume-averaged Te andne. For this reason, this line-ratio method is not suitable forspatially resolved optical diagnostics (Zhu et al 2006).

20


5. Conclusions

The line-ratio method which focuses on the excited argonand nitrogen species can be used to determine the electrontemperature and density in a variety of low-temperatureplasmas containing argon and nitrogen. It is a non-intrusiveand in situ diagnostic method and has the prominent advantageof being a universal method for many different types of low-temperature plasmas at low to atmospheric pressures. With asuitable experimental setup, it can also be used for temporallyand spatially resolved optical diagnostics.

The line-ratio method requires a relative intensity-calibrated spectroscopic system and, more crucially, a suitablepopulation model—the corona model or the CRM—for excitedspecies in the plasmas to be investigated. The emphasis ofthese models is the identification of major production anddepopulation processes under different discharge conditionsand for different kinds of excited species. The quality of themodelling results, which determines the accuracy of diagnosticresults by the line-ratio method, depends on the existenceand quality of cross section and rate coefficient data for thecollisional–radiative processes. Owing to the tremendousprogress in this field (Itikawa 2006, Boffard et al 2007,Gargioni and Grosswendt 2008), the line-ratio method willbe further developed in the future.

Acknowledgments

The authors are grateful to Professor V M Donnelly, ProfessorM A Lieberman, Dr V A Godyak, Professor U Czarnetzki,Professor R Boswell, Professor C C Lin, Dr T K Chu andDr J B Boffard for enlightening discussions. They thankDrs A A Mihajlov, I V Adamovich, V Guerra and H Akatsukafor providing rate coefficient data and helpful discussions.They also thank Wen-Cong Chen, Da-Wei Hu, Jiang Li andYu-Dong Pu for their help with the experiment. The work issupported in part by the National Natural Science Foundationof China under Grant Nos 10775087 and 10935006.

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Zhu X M and Pu Y K 2005 Determining the electron temperature ininductively coupled nitrogen plasmas by optical emissionspectroscopy with molecular kinetic effects Phys. Plasmas12 103501

Zhu X M and Pu Y K 2007a A simple collisional–radiative modelfor low-pressure argon discharges J. Phys. D: Appl. Phys.40 2533–8

Zhu X M and Pu Y K 2007b A simple collisional–radiative modelfor low-pressure argon–oxygen mixture discharges J. Phys. D:Appl. Phys. 40 5202–5

Zhu X M and Pu Y K 2008 Using OES to determine electrontemperature and density in low-pressure nitrogen and argonplasmas Plasma Sources Sci. Technol. 17 024002

Zhu X M and Pu Y K 2009 Nonequilibrium excited particlepopulation distribution in low-temperature argon discharges J.Phys. D: Appl. Phys. 42 182002

Zhu X M and Pu Y K 2010 A simple collisional–radiative model forlow-temperature argon discharges with pressure ranging from1 Pa to atmospheric pressure: kinetics of Paschen 1s and 2plevels J. Phys. D: Appl. Phys. 43 015204

Zhu X M, Pu Y D, Guo Z G and Pu Y K 2006 A novel method todetermine electron density by optical emissionspectroscopy in low-pressure nitrogen plasmas Phys. Plasmas13 123501

Zhu X M, Chen W C, Zhang S, Guo Z G, Hu D W and Pu Y K 2007Electron density and ion energy dependence on drivingfrequency in capacitively coupled argon plasmas J. Phys. D:Appl. Phys. 40 7019–23

Zhu X M, Chen W C and Pu Y K 2008 Gas temperature, electrondensity and electron temperature measurement in amicrowave excited microplasma J. Phys. D: Appl. Phys.41 105212

Zhu X M, Chen W C, Li J and Pu Y K 2009a Determining theelectron temperature and the electron density by a simplecollisional–radiative model of argon and xenon in low-pressuredischarges J. Phys. D: Appl. Phys. 42 025203

Zhu X M, Pu Y K, Balcon N and Boswell R 2009b Measurement ofthe electron density in atmospheric-pressure low-temperatureargon discharges by line-ratio method of optical emissionspectroscopy J. Phys. D: Appl. Phys. 42 142003

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oes in ar and n- determination of electron t and density by line-ratio method

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