Comparison of the Active Species in the RF and Microwave Flowing Discharges of N₂ and Ar–20 %N₂

Abstract

We report a detailed comparison between RF and microwave (HF) plasmas of N₂ and Ar–20 %N₂ as well as in the corresponding afterglows by comparing densities of active species at nearly the same discharge conditions of tube diameter (5–6 mm), gas pressure (6–8 Torr), flow rate (0.6–1.0 slm) and applied power (50–150 W). The analysis reveals an interesting difference between the two cases; the length of the RF plasma (~25 cm) is measured to be much longer than that of HF (6 cm). This ensures a much longer residence time (10⁻² s) of the active species in the N₂ RF plasma [compared to that (10⁻³ s) of HF], providing a condition for an efficient vibrational excitation of N₂(X, v) by (V–V) climbing-up processes, making the RF plasma more vibrationally excited than the HF one. As a result of high V–V plasma excitation in RF, the densities of the vibrationally excited N₂(X, v > 13) molecules are higher in the RF afterglow than in the HF afterglow. Destruction of N₂(X, v) due to the tube wall is estimated to be very similar between the two system as can be inferred from the γ_v destruction probability of N₂(X, v > 3–13) on the tube wall (2–3 × 10⁻³ for both cases) obtained from a comparison between the density of N₂(X, v > 3–9) in the plasmas to that of the N₂(X, v > 13) in the long afterglows. Interestingly enough, densities of N-atoms and N₂(A) metastable molecules in the afterglow regions, however, are measured to be very similar with each other. The measured lower density of N₂ ⁺ ions than expected in the HF afterglow is rationalized from a high oxygen impurity in our HF setup since N₂ ⁺ ions are very sensitive to oxygen impurity .

Introduction

N₂ plasmas and corresponding afterglows have been intensively studied [1–5] with an interest in utilizing excited nitrogen species in various applications such as plasma sterilization [6–8], plasma cleaning [9–11] and surface nitridation [12–14]. Under a controlled flowing condition, an inherent nature of a longer lifetime of a certain excited N₂ species makes it possible to obtain an ‘afterglow’ region with a varying density of N-atoms, N₂(X, v > 13) and N₂(A) metastable molecules and N₂ ⁺ ions [1]. This condition may provide a chance of developing a ‘damage-free’ plasma process in diverse application fields [7, 14].

In this respect, the exact determination of active species density in the plasma as well as in the afterglow would be a first step toward a successful use of them in application. RF and microwave (HF) plasmas in N₂ and Ar–N₂ have been previously studied and the detailed densities of active species in the afterglow under a flowing condition have been carefully measured at two different locations of Ajou University and University of Toulouse [1, 2]. The densities of N-atoms, N₂(X, v > 13) and N₂(A) metastable molecules and N₂ ⁺ ions were determined using the line ratio method [1, 15] and the calibration of the N-atom density by NO titration [3, 4, 16]. These recent studies revealed important characteristics of the two plasma systems, especially in terms of plasma length, plasma temperatures and the changing densities of active species in the plasmas and the afterglows, which were explained as a result of complex kinetic processes of the active species in the N₂ plasmas [1, 2, 4, 5, 16–21]. Recently, we have also reported detailed variation of active species in the RF plasmas and their afterglows of N₂ and Ar–20 %N₂ [5]. Despite such vast reports on the detailed characteristics of the N₂ and Ar–N₂ plasmas, a comprehensive comparison of plasma systems with different sources of plasma power (such as RF and HF) is still missing in the literature, while it can be an invaluable information for choosing the right source of plasma power in specific applications such as medical instruments sterilization [7] and iron nitriding [14] in N₂ afterglows. Luckily enough, we have accumulated enough experimental data set for a quantitative comparison of the two plasma systems of RF and HF for the case of N₂ plasma obtained under very similar flowing conditions. Based on this motivation, here we present our recent analysis on the differences between the two plasmas (RF and HF) and their afterglows in terms of plasma rotational and vibrational temperatures and densities of the active nitrogen species in the respective afterglows of mixed pink afterglow (PA) and late afterglow (LA). The afterglows are compared at the residence times of 7 × 10⁻² s for the RF and 10⁻³ to 6 × 10⁻² s for the HF. We also report the destruction probability of vibrationally excited N₂(X, v) molecules on the RF and HF afterglow tube walls.

Experimental Setups

The two experimental setups of RF and HF plasmas in Ajou and Toulouse, respectively, are reproduced in Fig. 1 for comparison.

Fig. 1

Schematic diagrams and their pictures of the RF (a, b) and the HF (c, d) set-ups in Ajou and Toulouse, respectively, are shown. In the RF (HF) set-up, the inner diameters of the quartz tubes are 6 (5) mm in the discharge region and 21 (18) mm in the afterglow region

The discharge quartz tubes have nearly the same inner diameters (ID) of 6 mm for the RF plasma reactor and 5 mm for the HF plasma reactor and have a length of 30 cm in both cases. In the post-discharge region, the RF discharge tube is connected to a straight quartz tube of 21 mm ID while the HF discharge tube is connected to a bent quartz tube of 18 mm ID itself connected to a 5 L-Pyrex chamber (Fig. 1). For both systems, experiments were conducted at very similar operation conditions of pressure (8 Torr), flow rate (0.5–1.0 slm) and applied power (50–150 W). The emission spectra across the RF reactor are obtained by means of a spectrometer (Monera 500, resolution 0.2–0.8 nm) with a PMT (Hamamatsu R928) using an optical fiber [1]. Across the HF reactor, an optical fiber is connected to an Acton Spectra Pro 2500i spectrometer (grating 600 g/mm) equipped with a Pixis 256E CCD detector (front illuminated 1024 × 256. The above similarities in the geometry of the two plasma systems allow us to compare the two RF and HF plasmas and afterglows to further understand the inherent differences in the type of plasma between the two plasmas. Plasmas are investigated by emission spectroscopy by measuring emission between the two rings of the RF discharge for the case of RF plasma and near the gap of the surfatron cavity (with a spatial resolution estimated to be 5 mm) for the case of HF plasma, respectively. N₂ second positive (2nd pos), N₂ ⁺ first negative (1st neg) and N₂ first positive (1st pos) intensities are recorded at these two positions.

The N₂ and Ar–N₂ RF and HF Plasmas

In the same ranges of gas pressure (6–8 Torr), flow rate (0.6–1.0 slm) and power (50–100 W), it is observed that the plasma region, defined as the most luminous glow downstream of the RF coils and HF gap, respectively, is longer in RF than in HF. For pure N₂, the HF plasma length (L_p) at 8 Torr increases from 1 to 6 cm when the power is increased from 50 to 100 W, while in the RF plasma, L_p varies from 18 to 25 cm for the same power variation. Such an increase of L_p of 2.45 GHz microwave plasmas in HF cavity at 100–140 W has been effectively observed in N₂ plasma at 30 Torr with L_p increasing from 2.5 to 8 cm [13]. The difference is even more pronounced in Ar–x %N₂ gas mixtures in which L_p increases with increasing Ar ratio. L_p is longer than the tube length (30 cm) for the RF plasma in Ar–x %N₂ when x is lower than 20 %. With the HF plasma, it is even possible to decrease x down to 2 % since the HF plasma length is still confined in the tube of 30 cm length. Thus, the comparison between RF and HF is presently limited to results in pure N₂ and in the Ar–20 %N₂ gas mixture.

For low pressure plasmas, it is known that the (minimum) cut-off electron density required to maintain a surface wave discharge depends on the square of the frequency (f²) of the electro-magnetic wave transferring the energy to the gas [22]. It is mentioned that the f² variation of electron density at the plasma end is given in [22] for Ar surface wave plasma at pressure less than 1 Torr. It is extended here to the present RF (13.6 MHz) and HF (2450 MHz) plasma columns to explain our observation that the length of the RF plasma is longer than the HF one at a same gas pressure and transmitted power.

The plasma length (L_p) is of crucial importance for the N₂(X, v) excitation by the electron–vibration (e–V), vibration–vibration (V–V) and vibration–translation (V–T) processes as previously reported and applied to results of a N₂ DC flowing discharge [23]. At the end of the RF plasma (L_p = 30 cm, 100 W), the residence time (t_R) is 10⁻² s, one order of magnitude higher than at the end of the HF plasma where t_R = 8 × 10⁻⁴ s (L_p = 6 cm, 100 W). As a consequence, the (V–V) processes are more developed in the RF plasma than in HF one.

The Plasma Gas Temperature

The intensity ratio (P1/P2) of the first two rotational sub-bands (labelled as P1 and P2) of the 1st pos N₂ band at 775 nm is related to the rotational temperature (T_R) of the plasma which is usually between 300 and 1000 K [19]. It is an important characteristic parameter of the N₂ plasma since it is directly related to the gas temperature (T_g), due to the efficient rotational-translational energy transfer. It is found that with an applied power between 50 and 100 W, the RF plasma at 6–8 Torr and 0.5–0.6 slm is a little warmer (T_g = 500–800 K) than the HF plasma at 8 Torr, 1 slm where T_g = 500–600 K. The uncertainty of gas temperature measurements is estimated to be 20 % [19].

The Plasma Vibrational Temperature

The vibrational temperatures can be analyzed from the intensity ratios of the N₂ 2nd pos. sequence Δv = −2 as detailed in [19]. The vibrational T_V(C) and characteristic θ₁(X) temperatures, corresponding to the excited N₂(C ³П_u) and N₂(X ¹Σ ⁺_g ) ground states, respectively, are connected to each other as can be seen from the following two steps:

First, the f(v) vibrational distribution of N₂(X, v) is expressed as follows [24]:

$${\text{f}}\left( v \right) = {\text{f}}\left( 0 \right) \cdot \exp^{{ - v\left( {\frac{{{\text{E}}_{10} }}{{\uptheta_{{1\left( {\text{x}} \right)}} }} - \frac{{\left( {v - 1} \right){\text{E}}_{10} \updelta }}{{{\text{T}}_{\text{g}} }}} \right)}}$$

(1)

with ${\text{f}}\left( 0 \right) = 1 - \exp^{{ - \frac{{{\text{E}}_{10} }}{{\uptheta_{1} \left( {\text{x}} \right)}}}}$ for v < v _T, where v _T is the vibrational number of the Treanor minimum given by $v_{\text{T}} = \frac{{{\text{T}}_{\text{g}} }}{{2\updelta \uptheta_{1} \left( {\text{x}} \right)}} + 0.5$, E₁₀ is the energy difference between the first two vibrational levels E(X, 1)–E(X, 0) (in K) and δ is the anharmonicity constant.

For N₂(X), E₁₀ = 3396 K and δ = 6.22 × 10⁻³.The population of N₂(X, v) is then written as [X, v] = f(v) N₀, where N₀ is the N₂ density.

Second, by considering that the N₂(C, v′) states are mainly produced by electron collisions on the N₂(X, v) ground states, following the Franck–Condon principle (vertical direct excitation by electron collisions), the stationary [C, v′] population is written as follows:

$$\left[ {{\text{C}},v^{\prime } } \right] = \varSigma_{v} \left[ {{\text{X}},v} \right]{\text{ n}}_{\text{e}} {\text{k}}_{\text{e}} \left( {\text{C}} \right){\text{ q}}\left( {{\text{X}},v - {\text{C}},v^{\prime } } \right)/\nu \left( {{\text{C}},v^{\prime } } \right)$$

(2)

where q(X, v–C, v′) is the Franck–Condon factor [24], n_e is the electron density, k_e(C) is the electron excitation rate which depends on the electron excitation cross-sections and on the electron energy distribution and ν(C, v′) = ν_R(C, v′) + N₀ k_Q(C, v′), (ν_R(C, v′) and k_Q(C, v′) are the radiative loss frequency [25] and the collisional quenching rate by the N₂ molecules [26]), respectively. The thresholds between the N₂(C, v′ = 0–3) and the N₂(X, v = 0–8) varying from 9 to 11.5 eV and the value of k_e(C) is approximated to be constant [27]. For the pressure range used in the present work, N₀ k_Q(C, v′) can be neglected in front of ν_R(C, v′).

As previously described [19], the experimental relative distribution [C, v′ < 4] is obtained by measuring the band head intensities of the N₂ 2nd pos. sequence Δv = –2. If a Boltzmann distribution of [C, v′] is verified, the vibrational temperature T_V(C) can be obtained.

The vibrational distribution of the N₂ ground state [X, v] and the corresponding vibrational temperature θ₁(X) are obtained from the experimental values of T_g and of the [C, v′ < 4] distributions by combining Eqs. (1) and (2).

Figure 2 shows the calculated[C, v′ < 4] distributions normalized to [C, v′ = 0] for the θ₁(X) values of 5, 8 and 20 × 10³ K which are compared with the experimental determined values ([C, v′ < 4]/[C, v′ = 0]) for the RF and HF plasmas. From the comparison, θ₁(X) = 8 × 10³ K and θ₁(X) = 5 × 10³ K are chosen for the RF and HF plasmas, respectively. Note that the [C, v′ < 4] calculated distributions have been found to be weakly influenced by the T_g variations between 500 and 800 K. It is observed a high value of the N₂(C, v = 1) density of the RF plasma which has been previously interpreted as a result of collisions between electrons and the N₂(A) metastable molecules [27, 28].

Fig. 2

Vibrational distributions of N₂(C, v′ < 4) versus v′ for set1 [θ₁(X) = 2 × 10⁴ K], set2 [θ₁(X) = 8 × 10³ K] and set3 [θ₁(X) = 5 × 10³ K]. The experimental points are triangles for RF and stars for HF

Table 1 reproduces the values of T_g (see “The plasma gas temperature” section), θ₁(X), v _T and N₂(X, v = v _T) for the N₂ and Ar–20 %N₂ plasmas at 6 Torr, 100 W for RF where [N₂]_RF = 7 × 10¹⁶ cm⁻³ and at 8 Torr, 100 W for HF where [N₂]_HF = 1.5 × 10¹⁷ cm⁻³. We find a higher θ₁(X) temperature in RF than in HF. This result agrees well with our suggestion of a more vibrationally excited RF plasma than the HF one.

Table 1 Values of T_g, T_v(C), θ₁(X), v _T and N₂(X, v = v _T) for the RF plasma at 6 Torr, 100 W and for the HF plasma at 8 Torr, 100 W

The N₂ and Ar–20 %N₂ RF and HF Afterglows

Afterglows Characteristics

Characteristics of the afterglows can be studied by measuring the emission bands of N₂ 1st pos. (chosen band at 580 nm), N₂ 2nd pos. (chosen band at 316 nm) and N₂ ⁺ 1st neg. (chosen band at 391.4 nm).

The analysis of the N₂ 1st pos. vibrational distribution reveals that the N₂ afterglows are a mixture of pink (PA) and late (LA) afterglows. In a pure LA, the 1st pos. emission is only due to the 3 body recombination of nitrogen atoms. To evaluate the contribution of the LA emission (a_N+N = 1 for pure LA and a_N+N = 0 for pure PA), the a_N+N value is obtained from a comparison between experimental and theoretical vibrational intensities distributions of the ∆v = −4 sequence (see [1–4, 16]).

For the experimental conditions of 8 Torr, 0.5 slm and 100 W in the RF set-up with the tube ID of 21 mm at z = 34 cm (see Fig. 1), a pure N₂ PA is observed. It is followed by an increasing contribution of the LA with increasing z. At z = 51 cm (17 cm downstream from the starting point of the 21 mm quartz tube), the a_N+N value of 0.5 is obtained at the same experimental conditions.

For the HF afterglow, a_N+N of 0.3 is obtained at 3 cm downstream from the starting point of the 18 mm quartz tube (z = 18 cm, Fig. 2) at 8 Torr, 1 slm and 150 W. It increases up to 0.8 at z = 55 cm. In this case, a pure LA is obtained just before the 5 L-reactor (see Fig. 1).

The measured larger z values for the RF afterglows (the mixed PA and LA of 0 < a_N+N < 1) than for the HF indicate longer afterglow times. For the RF afterglow, it is calculated to be 7 × 10⁻² s at z = 51 cm (Fig. 1) by assuming a laminar flow in the 21 mm quartz tube.

As for the HF afterglow, it is estimated to be 1.5 × 10⁻³ s at z = 18 cm (Fig. 2) for a post-discharge jet with low radial expansion having the same gas velocity than in the discharge tube of 5 mm ID, as calculated in [29]. At z > 20 cm, a laminar flow is assumed in the tube of dia. 18 mm, giving a residence time of 6 × 10⁻² s at z = 55 cm.

Densities of N, N₂(A), N₂(X, v > 13) and N₂ ⁺

In the LA (a_N+N = 1), the N-atoms recombine as follows [1–4, 16]:

$$\begin{aligned} {\text{N}} + {\text{N}} + {\text{N}}_{2} \to {\text{N}}_{2} \left( {{\text{B}},11} \right) + {\text{N}}_{2} \hfill \\ {\text{N}}_{2} \left( {{\text{B}},11} \right) \to {\text{N}}_{2} \left( {A,7} \right) + {\text{hv}}\left( { 5 8 0\,{\text{nm}}} \right) \hfill \\ \end{aligned}$$

(a)

When a_N+N < 1 (that is, a mixture of LA and PA), the a_N+N fraction of the measured ${\text{I}}_{580}^{\text{m}}$ intensity can be related to the square of the N-atom density as follows:

$${\text{a}}_{{{\text{N}} + {\text{N}}}} \text{I}_{580}^{\text{m}} = {\text{ k}}_{3} \left[ {\text{N}} \right]^{2}$$

(3)

The calibration coefficient k₃ is obtained by the use of NO titration, which also gives an independent access to the N-atom density.

In the RF N₂ plasma, it is found that the N-atom density slowly increases from 1 to 2 × 10¹⁵ cm⁻³ as the RF power increases from 50 to 130 W under the condition of 8 Torr, 0.5 slm and z = 51 cm (residence time of 7 × 10⁻² s) where a_N+N = 0.5. In Ar–20 %N₂, the N-atom density is about 2 × 10¹⁵ cm⁻³ at 10 – 50 W.

For the HF case (see Table 2), the N-atom density slowly increases from 1.0 to 1.2 × 10¹⁵ cm⁻³ for the residence times between 1.5 × 10⁻³ and 6 × 10⁻² s. Thus, it can be concluded that the N-atom density is about the same in the afterglow regions after the RF and HF plasmas considering the uncertainty on N-atom density to be 30 % [4].

Table 2 Active specie densities and γ_v values after the N₂ HF and RF plasmas at 8 Torr, 1–0.5 slm and 100 W at various afterglow times

Densities of the other active species (N₂(A), N₂(X, v > 13) and N₂ ⁺) are then obtained by the line-ratio method as developed in [1].

For the N₂(A) density determination, the main N₂(C) excitation is considered from the following pooling reaction:

$$\begin{aligned} & {\text{N}}_{2} \left( {\text{A}} \right) + {\text{N}}_{2} \left( {\text{A}} \right) \to {\text{N}}_{2} \left( {{\text{C}},{\text{v}} = 1} \right) + {\text{N}}_{2} \\ & {\text{N}}_{2} \left( {{\text{C}},{\text{v}} = 1} \right) \to {\text{N}}_{2} \left( {{\text{B}},{\text{v}} = 0} \right) + {\text{N}}_{2} 2{\text{nd}}\;{\text{pos }}\left( {316\,{\text{nm}}} \right) \\ \end{aligned}$$

(b)

Then, the following line–ratio is considered:

$${\text{a}}_{{{\text{N}} + {\text{N}}}} I_{580}^{\text{m}} /{\text{I}}_{316}^{\text{m}} = k_{4} \left( {\left[ {\text{N}} \right]/\left[ {{\text{N}}_{2} {\text{A}}} \right]} \right)^{2}$$

(4)

The k₄ coefficient is calculated from the rate coefficients of reactions (a) and (b) as reported in [1–4, 16] for the two RF and HF studied afterglows.

It is concluded that a nearly constant value of [N₂(A)] = 1–2 × 10¹¹ cm⁻³ is obtained as the RF power increases from 50 to 100 W in N₂ and from 10 to 50 W in Ar–20 %N₂ at the residence time of 7 × 10⁻² s.

The N₂(A) density at the residence time of 1.5 × 10⁻³ s is 1–5 × 10¹¹ and 5 × 10¹² cm⁻³, respectively, after the N₂ and Ar–20 %N₂ HF plasmas under the condition of 8 Torr, 1 slm and 100–150 W. As shown in Table 2, the N₂(A) density is nearly constant for the residence times up to 3.5 × 10⁻² s. By this method, the N₂(A) density is estimated to be in the range 10¹¹–10¹² cm⁻³.

Then, the N₂(X, v > 13) density is deduced by considering that the N₂(B, v = 11) state in the PA is produced by the following main reaction:

$${\text{N}}_{2} \left( {\text{A}} \right) + {\text{N}}_{2} \left( {{\text{X}},v > \, 13} \right) \to {\text{N}}_{2} \left( {{\text{B}},v = 11} \right) + {\text{N}}_{2} \left( {\text{X}} \right)$$

(c)

The ratio of a_N+N ${\text{I}}_{580}^{\text{m}}$ (LA) and (1 − a_N+N) ${\text{I}}_{580}^{\text{m}}$ (PA) is as follows:

$$\left( {{\text{a}}_{{{\text{N}} + {\text{N}}}} / \, 1 - {\text{a}}_{{{\text{N}} + {\text{N}}}} } \right) \, \left[ {\text{A}} \right] \, \left[ {{\text{X}},v > \, 13} \right]{\text{ k}}_{\text{c}} = \, \left[ {\text{N}} \right]^{2} {\text{k}}_{\text{a}} \left[ {{\text{N}}_{2} } \right]$$

(5)

Here, the N₂(X, v > 13) density is determined from a_N+N values, the N-atoms and the N₂(A) densities.

A nearly constant [N₂(X, v > 13)] density of 1–2 × 10¹⁴ cm⁻³ is obtained at 50–100 W for pure RF N₂ and at 10–50 W for the Ar–20 %N₂ gas mixture.

At the residence time of 1.5 × 10⁻³ s after the HF plasma (8 Torr, 1 slm and 100 – 150 W), the [N₂(X, v > 13)] density is 5–6 × 10¹³ cm⁻³ for both N₂ and Ar–20 %N₂.

Such [N₂(X, v > 13)] density can be considered as an estimated value which can vary depending on the k_c rate coefficient.

The measured N-atoms and N₂(X, v > 13) densities above are in the same order of magnitude with the values reported in [14] in which [N₂(X, v > 4)] = 3 × 10¹³ cm⁻³ and [N] = 6 × 10¹⁴ cm⁻³ are obtained in N₂ and Ar–N₂ afterglow of HF plasmas at 7 Torr, 3 slm and 200 W.

It should be noted that the N₂(X, v > 13) densities found in the present RF and HF afterglows are about one order of magnitude lower than the N₂(X, v = 7–9) densities in the corresponding plasmas (see Table 1). This result is used to determine the rate of destruction of these vibrational molecules on the tube wall in the following section.

For the N₂ ⁺ ions, the following dominant reactions in PA are considered [1]:

$${\text{N}}_{2} \left( {{\text{a}}^{\prime } } \right) \, + {\text{ N}}_{2} \left( {{\text{a}}^{\prime } } \right) \, \to {\text{e}} + {\text{ N}}_{2}^{ + } \left( {\text{X}} \right) \, + {\text{ N}}_{2} \left( {\text{X}} \right) \,$$

(d)

$$\begin{aligned} & {\text{N}}_{2}^{ + } \left( {\text{X}} \right) \, + {\text{ N}}_{2} \left( {{\text{X}},v > \, 12} \right) \, \to {\text{ N}}_{2}^{ + } \left( {\text{B}} \right) \, + {\text{ N}}_{2} \left( {\text{X}} \right) \\ & {\text{N}}_{2}^{ + } \left( {{\text{B}},0} \right) \to {\text{N}}_{2}^{ + } \left( {{\text{X}},0} \right) + {\text{ h}}v\left( {391\,{\text{nm}}} \right) \\ \end{aligned}$$

(e)

where reaction (d) is for the Penning ionization in the afterglow and reaction (e) indicates the excitation of N₂ ⁺(X) by vibrational molecules N₂(X > 12).

The N₂ ⁺ density is deduced from the N₂(X, v > 12) and N₂(A) densities by considering the line-ratio I₃₉₁/I₃₁₆ from reactions (e) and (b):

$${\text{I}}_{391} /{\text{I}}_{316} = {\text{k}}_{5} \left( {\left[ {{\text{N}}_{2}^{ + } } \right] \, \left[ {{\text{N}}_{2} \left( {{\text{X}},{\text{v}} > 12} \right)} \right]/\left[ {{\text{N}}_{2} \left( {\text{A}} \right)} \right]^{2} } \right),$$

(6)

The k₅ coefficient is calculated from the rate coefficients of reactions (e) and (b) [4, 16].

By taking [N₂(X), v > 12] = [N₂(X), v > 13], it is found that the N₂ ⁺ density increases from 5 × 10⁸ to 2 × 10⁹ cm⁻³ for the case of the RF N₂ plasma, when the RF power is raised from 70 to 100 W. In Ar–20 %N₂ RF gas mixture, the N₂ ⁺ ion density remains at 5 × 10⁸ cm⁻³ at 10–50 W. After the HF afterglows, the N₂ ⁺ density is in the range (0.2–1.4) × 10⁸ cm⁻³ as reported in Table 2.

The observed strong variations of the N₂ ⁺ density originate from the fact that it is very sensitive to air impurity. By applying the intensity line-ratio method in comparison of I₃₂₀ of the NO_β band to a_N+N I₅₈₀, an O-atom density of 9 × 10¹² cm⁻³ (that is, 30 ppm at 8 Torr) and N₂ ⁺ density of 10⁹ cm⁻³ have been previously determined in the RF afterglow [1]. In the HF afterglow, the O-atom density is in the order of 10¹⁴ cm⁻³ (that is, 400 ppm or 4 × 10⁻⁴ [O]/[N₂] ratio) and the N₂ ⁺ density is 10⁸ cm⁻³. These results clearly show that N₂ ⁺ ions produced in the afterglow by the Penning ionization N₂(a′) + N₂(a′) reaction are strongly correlated to the amount of O-atom impurity.

Destruction Probability of N₂(X, v > 3–13) on the Tube Walls

Densities of the N₂(X, v > 3) vibrational levels are found to be of 3 and 4 × 10¹⁵ cm⁻³ in the respective RF and HF plasmas and about 10¹⁴ cm⁻³ for N₂(X, v > 13) in the afterglows. By assuming a “plateau” of N₂(X, v > v _T), which means that a nearly constant vibrational density is reached after the Treanor minimum with v _T = 3 and before a drop of high N₂(X, v) density by (V–T) vibration–translation reactions, typically at v > 35 as described in [30], we evaluate a γ_v destruction probability of the N₂(X, v > 3–13) vibrational levels on the tube walls.

The same procedure as in [31] for N-atoms is taken here for the calculations of the γ_v recombination probability of the N₂(X, v > 3–13) molecules on the tube wall.

It is written as follows:

$$\left[ {{\text{X}},{\text{v}} > \, 3 \, {-} \, 13} \right]_{\text{z}} = \, \left[ {{\text{X}},{\text{v}} > \, 3 \, {-} \, 13} \right]_{{{\text{z}} = 0}} \cdot \, \exp [ \, -\upupsilon_{{{\text{X}},{\text{v}}}} {\text{z}}/{\text{v}}],$$

(7)

where υ_X,v = γ_v<c>/2R, <c> is the thermal gas velocity (<c> = 5 × 10⁴ cm s⁻¹) and R the tube radius.

z = 0 is taken at the RF and HF plasma end, which is at z = 25 cm in RF and at z = 6 cm in HF, respectively.

For such positions, the flow velocity in the RF set-up can be directly calculated from the gas flow rate and from the tube i.d. (21 mm) for a laminar flow.

From Eq. 7, it is found γ_v = 2 × 10⁻³ after the RF plasma at z = 25 cm (residence time of 7 × 10⁻² s). At z > 20 cm after the HF plasma, it is obtained: γ_v = 5 × 10⁻³ at the residence time of 2 × 10⁻² s and γ_v = 3 × 10⁻³ at the residence time of 3.5 × 10⁻² s where a laminar flow is expected.

We note that the same range of γ_v values are obtained after the RF and HF plasmas (γ_v = 2–5 × 10⁻³) at long times (7 and 3.5 × 10⁻³ s) when the parts of LA and PA are in equality.

The present γ_v values are about 2–5 times higher than the previous published value [32] for the first N₂(X, v = 1) state: γ₁ = 10⁻³ on Pyrex and quartz tube walls. They are largely higher than the γ_N values of N-atoms recombination on quartz and Pyrex tube walls: γ_N = 10⁻⁵–10⁻⁴ [31]. Such results could come from vibrational relaxation of the N₂(X, v) molecules on the tube wall by N₂(X, v) + wall → N₂(X, v–n) +wall, with n ≥ 1, faster than for the N-atoms with N + wall → 1/2 N₂ + wall.

The loss frequency of the N₂(X, v > 3–13) on the tube wall is in the range of 50–150 s⁻¹.

It can be compared to the following volume losses: 10 s⁻¹ for the reaction N₂(X, v > 13) + O with a rate of 10⁻¹³ cm³ s⁻¹ [33] with [O] = 10¹⁴ cm⁻³; 1–5 s⁻¹ for the reaction N₂(X, v) + N → N₂(X, w) + N, with a rate k(v = 10–15, w = 0,15) = 1–5 × 10⁻¹⁵ cm³ s⁻¹ [34] and [N] = 10¹⁵ cm⁻³.

As for the (V–V) and (V–T) collisions, it is given in [35] the characteristic frequencies at 5 Torr, 500 K: υ(V–V) = 2 10³s⁻¹ for N₂(1) + N₂(0) → N₂(0) + N₂(1) and υ(V–T) = 4 10⁻³ s⁻¹ for N₂(1) + N₂ → N₂(0) + N₂.

Outside the high V–V frequency, these frequencies are low in comparison to the N₂(X, v > 3–13) loss frequency on the tube wall: 50–150 s⁻¹.

Conclusion

To conclude, the presently analyzed N₂ RF and HF flowing plasmas with nearly the same discharge parameters (tube diameters, gas pressure, flow rates and electrical power) produce long time afterglows with about the same N atoms and N₂(A) densities. The main difference between RF and HF appears in the plasma length, which is longer in RF than in HF. As a consequence, the residence time of the active species is increased in the RF plasma, allowing in comparison to HF plasmas an enhancement of N₂(X, v) excitation by (V–V) collisions. Such an effect is detected as a higher density of vibrationally excited N₂(X, v) molecules in the RF plasma and particularly in the afterglow where a pure pink afterglow is observed in RF, ‘not in HF’.

If about equal densities of N and N₂(A) are found in the long time RF and HF afterglows, it appears a higher N₂(X, v > 13) and N₂ ⁺ densities in the RF afterglow which can be related to high N₂(V–V) excitation until the plasma end. The present results concern first the N-atom density calibrated by NO titration with an accuracy of 30 %. Then the other active species densities: N₂(A), N₂(X, v > 13) and N₂ ⁺ are obtained by a line-ratio method, giving the order of magnitude of density, depending on kinetic rates of the chosen dominant reactions.

A new result obtained with these RF and HF afterglows concerns the γ_v destruction probability of the N₂(X, v ≥ 3–13) vibrational levels on the quartz tube wall, which is more than one order of magnitude higher than for the N-atoms, certainly as the result of a more easy climbing down of N₂(X, v) on the tube wall.