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JOURNAL OF PHYSICS D: APPLIED PHYSICS
J. Phys. D: Appl. Phys. 42 (2009) 142003 (5pp)
doi:10.1088/0022-3727/42/14/142003
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Measurement of the electron density in atmospheric-pressure low-temperature argon discharges by line-ratio method of optical emission spectroscopy X M Zhu1 , Y K Pu1 , N Balcon2,3 and R Boswell2 1
Department of Engineering Physics, Tsinghua University, Beijing 100084, People’s Republic of China Research School of Physical Sciences and Engineering, Australian National University, Canberra 0200, Australia 3 CPAT, Universit´e Paul Sabatier, Toulouse 31000, France 2
E-mail:
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Received 20 May 2009, in final form 9 June 2009 Published 26 June 2009 Online at stacks.iop.org/JPhysD/42/142003 Abstract A new collisional–radiative model for atmospheric-pressure low-temperature argon discharges is proposed, which illustrates the significant effect of electron density on the excited atom population distribution. This makes it possible to determine the electron density from the intensity ratio of emission lines of excited atoms. Results of this new method in several types of atmospheric-pressure discharges are found to be in agreement with those of the Stark broadening method and the electric model over a wide electron density range 1011 –1016 cm−3 . (Some figures in this article are in colour only in the electronic version)
broadening of emission line profiles, such as that of hydrogen Balmer lines [8]. At electron densities lower than ∼1013 cm−3 and at atmospheric pressure, this method is inappropriate since the van der Waals broadening or Doppler broadening becomes the dominant broadening process. Another method is to analyse the continuum radiation if it is observed, such as in some recombining plasmas [9]. The last one is the lineratio method, in which the intensity ratio of emission lines is related to the electron density by a collisional–radiative model (CRM) [10]. This method has been successfully used in low- and medium-pressure discharges [10–12]. In this work, with a CRM of atmospheric-pressure discharges, a line-ratio method to determine the electron density from the mostly observed optical emission of argon 2p–1s transitions (in Paschen’s notation) is introduced. To obtain the relationship between the electron density and the line-ratios of optical emissions, the effect of electron density on the excited atom kinetics should be analysed. In
The electron density is one of the most fundamental parameters in gas discharges and plays a very important role in understanding the discharge physics and optimization of the operation of plasmas [1, 2]. Typical methods to measure the electron density include the use of a Langmuir probe [3], microwave interferometery [4], laser Thomson scattering (LTS) [5] and optical emission spectroscopy (OES) [6]. However, in atmospheric-pressure low-temperature discharges, both the probe and the microwave-based methods are difficult to use due to the small plasma dimensions and strong collisional processes. LTS has been proved to be effective but challenging because of the low signal and excessive stray light, as well as the complicated experimental setup [7]. However, the OES-based technique has the advantages of being non-intrusive, inexpensive and convenient. There are three major OES techniques to determine the electron density in low-temperature plasmas. One OES method involves the investigation of the Stark 0022-3727/09/142003+05$30.00
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J. Phys. D: Appl. Phys. 42 (2009) 142003
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In regime (c) (high electron density ∼1015 –1016 cm−3 ), the electron-impact transfer dominates the atom-collision transfer. Similar kinetic pictures of the 2p multiplet have also been obtained in previous argon CRMs [13–15]. The variation of dominant processes of the 2p multiplet, being caused by the variation of electron density, can significantly affect the atomic population distribution, as shown in figure 2. In figure 2(a) of the kinetic regime (a), the population of 2p2 , 2p6 and 2p10 levels is larger than nearby levels, because these three levels have smaller rate coefficients of atom-collision transfer and thus have a smaller depopulation rate [16–18]. In regime (b), excitation from 1s levels becomes the dominant production process. Since the excitation rate coefficients from 1s levels to 2p1 and 2p5 levels are much smaller than those to the other 2p levels [19], one can observe very small populations of 2p1 and 2p5 levels in figure 2(b). In regime (c), strong electron-impact transfer processes between excited levels makes a Boltzmann-like distribution, with the population of each level nearly in proportion to its degeneracy degree, as shown in figure 2(c). Note that the detailed population distribution of 2p levels such as those in figure 2 cannot be obtained from the previous CRMs due to the use of some improper simplifications. Firstly, an effective level was used instead of the individual levels with close excitation energies. For example, 2p6 , 2p7 , 2p8 and 2p9 were combined into one effective level. Thus the difference in populations among these levels, as seen in figure 2, was not shown in the previous CRMs. Besides, an empirical formula was adopted for collisional transfer processes in previous works, in which the large difference in rate coefficients for different 2p levels was neglected. Therefore, the important characteristic of large 2p2 , 2p6 and 2p10 population in regimes (a) and (b) will not be found in those models. In order to obtain the relationship between the electron density and the population distribution (thus line-ratios), we use individual 2p levels and experimental state-to-state rate coefficients in the new CRM [16–19]. The excited atom population distribution is generally affected by the electron density ne , the electron temperature Te and the gas temperature Tg . However, for the atmosphericpressure low-temperature argon discharges used in this work, the electron temperature (or effective electron temperature) is found to be in a narrow range 1–2 eV and the gas temperature is in the range 300–600 K [20–23]. Therefore, their effect on the distribution is very small compared with the electron density, whose range of variation can be several orders of magnitude greater. Therefore, the kinetic picture under typical conditions shown in figures 1 and 2 can be used. The next important parameter is the plasma dimension. Even though its value may vary over a wide range (0.1–10 mm), it has a quite limited effect on the population distribution compared with the electron density, since the diffusive processes are strongly limited by the collisions at atmospheric pressure. Atmospheric-pressure plasmas are optically thin for photons of non-resonance lines due to large collisional broadening [24, 25]. Therefore, the line-ratio of these optical emissions is I1 A1 n 1 = . (5) I2 A2 n2
Figure 1. Reaction rates of dominant kinetic processes of argon 2p levels versus the electron density in atmospheric-pressure discharges. The electron temperature, gas temperature and plasma dimension are assumed to be 1 eV, 600 K and 100 µm. Here ‘gs-exc’ and ‘1s-exc’ are for the electron-impact excitation from the ground state and from 1s levels, while ‘e-tran’ and ‘atom-tran’ are for the electron-impact and atom-collision population transfer from a 2p level to other excited levels.
atmospheric-pressure argon discharges, the dominant kinetic processes of argon 2p levels include the electron-impact excitation from the ground state, e + Ar(gs) → e + Ar(2pi ),
(1)
the electron-impact excitation from 1s levels, e + Ar(1s) → e + Ar(2pi ),
(2)
the electron-impact population transfer from a 2p level to other excited levels, ! " e + Ar(2pi ) → e + Ar 2pj , (3) e + Ar(2pi ) → e + Ar(1s, 2s, 3p, 3d, . . .),
and the atom-collision population transfer, ! " Ar(gs) + Ar(2pi ) → Ar(gs) + Ar 2pj , Ar(gs) + Ar(2pi ) → Ar(gs) + Ar(1s).
(4)
Here gs means the ground state of an argon atom; 1s, 2p, 2s, 3p and 3d are excited levels in Paschen’s notation; subscripts i and j refer to the ith and j th 2p levels. Under typical conditions for microdischarges, that is, atmospheric pressure, electron temperature of 1 eV, gas temperature of 600 K and plasma dimension of 100 µm, the variation of the reaction rate of the above processes versus the electron density is obtained from the CRM, as shown in figure 1. There are three kinetic regimes with different dominant processes. In regime (a) (low electron density ∼1011 –1012 cm−3 ), the excitation from the ground state and the atom-collision transfer are important to the rate balance of excited atoms. In regime (b) (medium electron density ∼1013 –1014 cm−3 ), the excitation from the 1s levels becomes more important than that from the ground state, since the density of 1s levels increases with the electron density. 2
J. Phys. D: Appl. Phys. 42 (2009) 142003
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Figure 2. Population distribution of 2p levels at typical electron densities (ne ) for the three regimes in figure 1.
and 2p6 ) has an additional advantage that the emissions from these levels are spread over a very narrow wavelength range (2p1 –1s2 , 750.4 nm; 2p3 –1s4 , 738.4 nm; 2p6 –1s5 , 763.5 nm). This makes the OES measurement, as well as the intensity calibration, relatively easy. By using the population ratios R13 and R36 , the electron densities in three types of atmospheric-pressure discharges are measured, including an rf glow discharge, an rf filament discharge and a microwave microdischarge [22, 23]. The operating parameters and plasma parameters of those discharges are listed in table 1. From figure 4, it is found that the results of the line-ratio method are in good agreement with those of the Stark broadening method [22, 23] and the electric model [22, 26]. The limited difference between results of OES measurement and the electric model can be caused by the nonuniformity of discharges, since the former gives an averaged result from the emission intensity while the latter assumes a uniform plasma. The error bar in figure 4 is caused mainly by the uncertainty of the experimental rate coefficients of atomcollision population transfer [16–18]. This line-ratio method can also be used for the atmospheric-pressure non-equilibrium discharges with relatively high gas temperature, say, Tg $ 1000–2000 K [21]. According to the ideal gas law, the gas density ng will decrease when Tg increases. As a result, in figure 1, both the reaction rate of electron-impact excitation from the ground state (gsexc) and that of atom-collision population transfer (atom-trans) become smaller. The transition between regimes (a) and (b) or that between (b) and (c) occurs at lower electron densities. As a result, the R13 and R36 curves in figure 3 will move leftwards. The effect of Te on the line-ratio of two excited levels can be generally estimated as f $ exp(!E/Te ) where !E is the energy gap between two levels [10]. For argon 2p levels used here, !E $ 0.2 eV % Te and thus f $ 1. In fact, the Te effect on these line-ratios is not important unless Te is as low as 0.1–0.2 eV, such as in some recombining plasmas [9]. In this method, one utilizes the significant variation of the line-ratio, being nearly proportional to the logarithm of the electron density (see figure 3), during the variation of dominant kinetic processes. Due to this nonlinear dependence of lineratio on the electron density, the uncertainty from either the OES measurement or the CRM calculation will be enlarged.
Figure 3. Population ratios R13 and R36 versus the electron density under the discharge condition in figure 1.
Here I1 andI2 are the intensities of emission lines in 2p–1s transitions, A1 and A2 are the Einstein coefficients and n1 and n2 are the densities of two different 2p levels. One can obtain the electron density by comparing the population ratio n1 /n2 in the distribution given by the CRM (as in figure 2) with the measured line-ratio I1 /I2 . As seen in figure 2, there are three groups of 2p levels with different relationships to the variation of electron density. For our purpose, we can select a representative 2p level from each group, for example, 2p1 , 2p3 and 2p6 levels. The population ratios R13 (n2p1 /n2p3 ) and R36 (n2p3 /n2p6 ) are plotted as functions of electron density in figure 3, under the condition shown in figure 1. It is found that R13 decreases significantly with the electron density in the range 1011 –1013 cm−3 , during the transition from regime (a) to regime (b). This is because 2p1 and 2p3 levels have similar rate coefficients of excitation from the ground state, but very different excitation rate coefficients from the 1s levels. Similarly, R36 increases significantly with the electron density during the transition from regime (b) to regime (c), since 2p6 has a smaller rate coefficient of atom-collision transfer than 2p3 while they have similar rate coefficients for electron-impact transfer. Even though one can use other sets of 2p levels to determine the electron density as well, this set (2p1 , 2p3 3
J. Phys. D: Appl. Phys. 42 (2009) 142003
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Table 1. Operating parameters and plasma parameters for three types of argon discharges.
Source Pressure Power Plasma dimensions Electron density Electron temperature Gas temperature
Rf glow discharge
Rf filament discharge
Microwave microdischarge
13.56 MHz, pulsed width 5 µs, period !1 ms 760 Torr ∼100 W ∼100 × 100 × 5 mm ∼1011 –1012 cm−3 ∼1–2 eV ∼300–600 K
13.56 MHz, pulsed width 5 µs, period "100 µs 760 Torr ∼100 W ∼5 × 0.1 × 0.1 mm ∼1015 cm−3 ∼1–2 eV ∼300–600 K
900 MHz, continuous ∼740 Torr 1–5 W ∼1 × 0.1 × 0.1 mm ∼1013 –1014 cm−3 ∼1–2 eV ∼300–600 K
Acknowledgments The authors are grateful to Dr Felipe Iza for the helpful discussion and to Wen-Cong Chen for the help in the experiment. This work is in part supported by the National Natural Science Foundation of China under Grant No 10775087.
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Figure 4. Comparison of electron density from the line-ratio method, the Stark broadening method and the electric model in three types of atmospheric-pressure argon discharges.
Therefore, the line-ratio method may not provide the electron density measurement as accurately as the LTS. However, due to the nonlinear dependence, the line-ratio method does not suffer from the low signal-to-noise ratio problem as the LTS at low electron densities. This is a unique advantage of all the line-ratio methods for low-, medium-, high- and atmosphericpressure discharges [10–12]. The kinetic processes involved in argon discharges, including the electron-impact processes and collisions between heavy particles, are also important in many other types of gas discharges, such as helium, neon, nitrogen and air, at atmospheric pressure [24, 27]. Similar line-ratio methods, using the variation of dominant mechanisms of excited particles versus the electron density, can be expected in those gases when the proper CRMs are developed in the future. In conclusion, a new line-ratio method to measure the electron density is proposed for atmospheric-pressure argon discharges. The electron density is obtained by comparing the line-ratios of argon 2p–1s transitions predicted from a collisional–radiative model with those from optical emission spectroscopy. The validity of this method is confirmed in three types of typical atmospheric-pressure discharges over a wide electron density range. This method may have potential applications in the recently developed spatially and temporally resolved optical diagnostics for atmosphericpressure discharges [28, 29]. 4
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