22P018-O
Measurement of Vibrational and Rotational Temperatures of N2+ of Nitrogen
Discharge Plasma by First Negative System
First Negative Systemによる窒素プラズマ中のN2+の振動温度，回転温度計測
Hirokazu Kawano, Atsushi Nezu, Haruaki Matsuura and Hiroshi Akatsuka
川野泰和, 根津 篤，松浦治明，赤塚 洋
Research Laboratory for Nuclear Reactors, Tokyo Institute of Technology
2-12-1-N1-10, Ookayama, Meguroku, Tokyo 152-8550, Japan
東京工業大学 原子炉工学研究所 〒152-8550 東京都目黒区大岡山2-12-1-N1-10
Band Spectrum of the first negative system of the N2+ is measured by optical emission spectroscopy
measurement to examine the vibrational and rotational temperatures of B2Σ state. The experimentallymeasured spectra are compared with the ones calculated theoretically to determine the temperatures of thegenerated plasma. We generated a microwave discharge nitrogen plasma in a cylindrical quartz tube (26mm inside diameter) with its discharge pressure 1.0 Torr. It was found that Tvib
1.8 - 3.4 eV and Trot
0.13 - 0.34 eV at N2+ B 2Σ (Δv = 1), whereas Tvib
0.69-0.87 eV and Trot
0.08-0.18 eV at C3Π (Δv =4) of N2. Tvib and Trot of N2+ were higher than those of N2.

1. Introduction
Nitrogen plasma plays an important role inmaterial or electronic engineering. [1] For example,
in semiconductor industry, nitrogen plasma isapplied as a nitrogen radical source at practicallevel.[2] Therefore, we have studied characteristicsof nitrogen plasmas and examined thedependence of their plasma parameters ondischarge conditions.[3]In previous spectroscopic studies, we treated
only neutral molecules. Therefore, as a next step,
we focus on vibrational (Tvib) and rotationaltemperatures (Trot) of nitrogen molecular ions.
In this study, we analyzed the first negativesystem (1stNS) from N2+ and the second positive
system (2ndPS) from N2 by optical emission
spectroscopy (OES). And we examined Tvib andTrot of N2+ to understand the relationship between
temperatures of ions and those of neutrals.
2. Experimental setup
Figure 1 shows the block diagram of theexperimental setup.[4] Nitrogen plasma wasgenerated using a rectangular waveguide with acavity and a quartz tube (26 mm inside diameter).
The quartz tube was aligned in the direction of theelectric field of the waveguide, and its one end wasinserted into a vacuum chamber. The microwave
frequency was 2.45 GHz and the output power wasset at 500 W. The discharge pressure was set at
about 1.0 Torr. We measured the plasma at four
points. The distances were 0, 60, 100, 140 mm fromthe intersection of the quartz tube and thewaveguide to the direction of the gas flow.

Fig.1. Block diagram of microwave discharge apparatus
and measurement system

3. Theoretical calculation
Generally, the line intensity of radiativetransition of molecules is given as a product of avibration-dependent part and a rotation-dependentpart.
(1)
If we assume the Boltzmann distribution for thevibrational and rotational states of the upper state,
andcan be written as follows:
(()),

(2)
(3)

where v is the frequency of the emitted light, k isthe Boltzmann constant, Evib and Erot are thevibrational and rotational energies of the upper state,
respectively, qv’v” is the Franck-Condon factor, andSJ’J” is the Hönl-London factor. [5], [6]In this study, we analyzed the structures of the1stNS (B 2u+  X 2g+) of N2+ and 2ndPS (C 3u B 3g) of N2 to estimate the vibrational androtational temperatures.
Applying eqs. (1) – (3), we can describe theunique rotation-vibration spectrum as a function ofvibrational and rotational temperatures. Thus, wecan determine these temperatures by fitting thespectra observed experimentally with the calculatedones.
Figure 2 shows an example of comparison
between the experimentally observed spectrum andthe calculated one (z = 100 mm, P = 1.0 Torr).

vibrational and rotational temperatures of N2+ B2Σ
and N2 C3Π states to find relationship between Tvib
and Trot of ion’s and those of neutrals.
It was found that Tvib
1.8 - 3.4 eV and Trot
0.13 - 0.34 eV for B2Σ (Δv = 1) of N2+, whereas Tvib
0.69 - 0.87 eV and Trot
0.08 - 0.18 eV at C3Π
(Δv = 4) for N2. Tvib and Trot of N2+ were higher thanthose of N2.

(a)

(b)

Fig.2. Example of comparison between spectra
calculated theoretically and observed experimentally.

4. Results and Discussion
Figure 3 shows Tvib and Trot of N2+ and N2
obtained from 1stNS and 2ndPS, respectively. Itwas found that Tvib
1.8 - 3.4 eV and Trot
0.132+- 0.34 eV for B Σ (Δv = 1) of N2 , whereas Tvib
0.69 - 0.87 eV and Trot
0.08 - 0.18 eV for C3Π
(Δv = 4) of N2.
For both N2+ and N2, Trot decreased as the plasma
flowed to the downstream direction. Trot is anapproximate value to the gas temperature if
rotational-translational relaxation is sufficient. Thus,it is considered that Trot decrease as the plasma
flows to the downstream region.
It was found that Tvib and Trot of N2+ were higher
than those of N2. It is considered that this is partly
because Tvib and Trot of N2+ are influenced by iontemperature.
5. Conclusions
We measured the band spectra of thenitrogen-molecular ion (N2+ 1stNS) and the neutral
nitrogen molecule (N2 2ndPS), determined theFig.3. Vibrational and rotational temperatures measured
experimentally (a) vibrational temperature of N2 (C3Π)
and N2+ (B2Σ) (b) rotational temperature of N2 (C3Π) andN2+ (B2Σ).
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Phys. 101 (2007) 345701.
[4] T. Sakamoto, K. Naoi, H. Matsuura, andH. Akatsuka: JJAP. 45 (2006) 243.
[5] L. Klynnin and P. Pages: Physica. Scripta. 25 (1982)
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