dence plusieurs points qui restent à étudier. Premièrement, la fonction de distribution en énergie des électrons, supposée Maxwellienne ici, s'écarte trop de cette hypothèse pour donner des résultats satisfaisants. Il est alors nécessaire de coupler un solveur de Boltzmann au modèle 0D pour pouvoir calculer la FDEE. Deuxièmement, la variation de la taille de l'expansion cathodique impacte fortement les densités des espèces dans la décharge. Cependant, sa physique est aujourd'hui mal comprise et reste à déterminer pour pouvoir prédire sa surface théoriquement. Enfin, ces travaux ont mis en évidence que la chimie des niveaux vibrationnels de $N_2$ a une importance non négligeable dans les mélanges $Ar/N_2$. Ils devront donc être ajoutés dans la chimie du modèle global à l'avenir.

Cette étude a ainsi défini les paramètres de décharges idéaux pour optimiser la production d'azote atomique dans la MHCD. Cependant, pour pouvoir réaliser un dépôt de nitrure de bore sur une grande surface, il est nécessaire d'augmenter le volume de la décharge.

Nous avons donc ensuite étudié l'expansion du volume plasma pour vérifier que les méthodes proposées permettent effectivement de produire une densité d'azote atomique homogène sur une grande surface. La troisième partie de la thèse a donc été consacrée aux stratégies d'expansion du volume plasma.

Dans un premier temps, nous avons réalisé une étude paramétrique d'un jet MHCD libre. En effet, nous avons vu que pour obtenir une haute densité d'azote atomique de dépôt, nous devons introduire un différentiel de pression entre les deux côtés de la MHCD. Cette étude nous a permis d'établir que la chimie au sein de la MHCD n'est pas modifiée par l'ajout du différentiel de pression, et ainsi que les recommandations faites précédemment pour l'optimisation de la production d'azote atomique restent valables en terme de mélange gazeux et courant de décharge. Cependant, nous avons observé un grand impact des caractéristiques de l'écoulement du gaz dans le trou sur les densités d'azote atomique observées dans le jet. Ainsi, il semble peu intéressant de chercher à maximiser la pression côté cathodique, puisque celle-ci n'a qu'une faible influence sur la densité d'azote atomique que l'on retrouve ensuite dans la chambre basse pression. En revanche, il semble plus important de privilégier une pression plus importante dans la chambre de dépôt pour y obtenir des densités d'azote atomique plus élevées, et un compromis devra être trouvé avec le fait de maintenir une bonne mobilité des atomes à la surface du substrat. La détermination des pressions optimales devra donc se reposer sur la qualité des films déposés.

Ensuite, nous avons placé la MHCD face à une surface simulant un substrat de dépôt. Nous avons alors étudié la répartition spatiale des atomes d'azote dans la chambre basse pression, où aura lieu le dépôt. Nous avons confirmé que la configuration MHCD classique ne convient pas pour le dépôt sur des grandes surfaces, avec des atomes d'azote qui restent trop confinés dans le trou. L'ajout d'un jet permet de transporter les atomes du trou vers la surface du substrat, mais avec une répartition très inhomogène due à des effets aérodynamiques. Enfin, la polarisation du substrat permet d'homogénéiser la densité d'azote atomique sur une large surface de substrat et sera donc la configuration à privilégier pour le dépôt. Il est très intéressant de travailler à la fois avec le différentiel de pression et la polarisation, afin d'aider au claquage de la MCSD et travailler avec une tension de polarisation plus faible.

La configuration étudiée ici diffère cependant de la configuration utilisée dans le réacteur de dépôt. L'influence de ces modifications sera donc à étudier à l'avenir, ce qui conduit aux
perspectives suivantes :

* Premièrement, dans le réacteur de dépôt, le substrat est chauffé à une température ty-pique de 800°C et polarisé à une tension de 200 V. Ce chauffage et les forts gradients de température qu'il implique dans la chambre basse pression, auront des conséquences sur la morphologie de l'écoulement gazeux et donc sur les profils de la densité d'azote atomique. **Une modélisation fluide en 2D des écoulements de gaz dans la chambre de dépôt** semble alors une étape nécessaire à la bonne compréhension de la façon dont les précurseurs et les atomes issus de leur dissociation atteignent le substrat.

* Deuxièmement, dans le réacteur de dépôt, la MHCD est alimentée par une alimentation pulsée. Choisie dans la perspective de l'utilisation de matrices de MHCDs, elle impactera la dynamique de la production d'azote atomique dans la MHCD. **Des études fondamen-tales supplémentaires sont donc à réaliser en régime impulsionnel forcé, grâce à des diagnostics optiques résolus temporellement.** Ainsi, il est possible d'adapter le dispositif TALIF, mais également TDLAS et de spectroscopie d'émission pour obtenir des mesures de densité d'azote atomique, densité des métastables d'argon, densité électronique et température du gaz résolues en temps.

* Enfin, dans ces travaux de thèse, nous nous sommes concentrés sur la production d'azote atomique, en caractérisant sa production et son transport. Cet angle a été adopté à cause de la difficulté avérée de dissociation de l'azote moléculaire. Néanmoins, les atomes de bore sont également nécessaires au dépôt de nitrure de bore et si leur obtention par dissociation thermique du $BBr_3$ semble acquise, il n'en est pas de même de leur transport jusqu'au substrat après l'injection du $BBr_3$ dans la chambre de dépôt. Il est également possible que ce gaz supplémentaire ait des conséquences sur la décharge MCSD. **Des mesures expérimentales de fluorescence induite par absorption laser (LIF) pourront être réalisées dans le volume de la MCSD, pour déterminer la densité d'atomes de bore résolue spatialement.**

Pour finir, dans une dernière partie, nous nous sommes penchés sur la synthèse et la caracté-risation de films de nitrure de bore, en réalisant une étude exploratoire des paramètres de dépôt.

L'étude des premiers dépôts, qui ont prouvé la faisabilité du dépôt de nitrure de bore assisté par micro décharge à cathode creuse, a permis des premières modifications du réacteur initial.

Pour éliminer les impuretés d'oxygène, un pompage poussé par une pompe turbomoléculaire est nécessaire après la mise à l'air du réacteur pour l'introduction du substrat. **Des impuretés de carbone peuvent également être présentes dans les films, en provenance des matériaux utilisés dans la fabrication de la MHCD.** La MHCD subissant un bombardement ionique important, il est important de choisir avec précaution les matériaux la composant. Cela est vrai de la colle utilisée pour l'assembler, qui doit être résistante aux hautes températures même si la tem-pérature du gaz dans le plasma reste faible. Cela est également vrai des matériaux composant les électrodes et le diélectrique. Nous avons vu que **si le molybdène est connu pour sa résistance au bombardement ionique, un plasma d'azote semble capable de le pulvériser, ce qui réduit fortement la durée de vie des MHCDs.** Un attention particulière devra également être portée à l'alumine qui peut être affectée par un contact avec un plasma d'azote, notamment avec des qualités d'alumine variant fortement selon des fournisseurs. Un partage d'expérience avec leurs équipes pourrait être fortement utile à l'amélioration de nos sources MHCD.

Nous avons ensuite mené une étude exploratoire pour déterminer l'influence de différents pa-
ramètres du dépôt sur les films de nitrure de bore déposés. Nous avons observé que malgré une production d'azote atomique moindre, une MHCD de plus grand diamètre n'impacte pas néga- tivement la stœchiométrie des films déposés. En revanche, lorsque le substrat est rapproché de la MHCD, la proportion d'azote dans les films déposés augmente. Nous avons aussi découvert le rôle crucial de l'hydrogène sur la cristallinité du dépôt. Sans hydrogène présent dans la chambre de dépôt, le nitrure de bore déposé a une structure polycristalline, avec une taille de grain très faible et pas de relation d'épitaxie avec le substrat. Lorsque de l'hydrogène est introduit dans la chambre de dépôt, le film prend la forme de cristaux triangulaires ou hexagonaux, dont la taille latérale s'auto-limite à environ 4 µm et se met alors à pousser verticalement.

L'ensemble de ces résultats ont montré la versatilité du procédé, avec la possibilité de créer des dépôts aux propriétés très différentes : du nitrure de bore hexagonal stœchiométrique au nitrure de bore amorphe riche en azote. Nous avons ensuite procédé à la caractérisation poussée de films de nitrure de bore amorphe, de composition B₀.₆₉N. Peu étudié, nos travaux ont mis en évidence ses propriétés intéressantes, en tant qu'isolant électrique flexible à la grande résis- tance mécanique.

La qualité des films obtenus (homogénéité, stabilité, etc...) ainsi que la compréhension fine des mécanismes qui la contrôlent restent à améliorer. En s'appuyant sur les résultats de la caractéri- sation de la MHCD, une étude paramétrique détaillée doit alors être réalisée pour déterminer si les conditions permettant d'optimiser la production d'azote atomique dans la MHCD et la MCSD ont bien un effet bénéfique sur les films. Pour mieux comprendre le rôle de l'hydrogène, des travaux de simulations de dynamique moléculaire peuvent être poursuivis pour déterminer précisément les mécanismes de nucléation et dépôt du nitrure de bore. Enfin, les résultats de l'étude applicative ont mis en évidence des aspects du comportement du plasma dont l'étude est à poursuivre : l'étude de l'écoulement des gaz en présence du plasma, la dissociation du BBr₃ dans la MCSD et la dégradation de la MHCD.

Ce travail de thèse a permis de démontrer que les MHCD peuvent être utilisées pour dissocier l'azote moléculaire et produire de l'azote atomique, et leur volume plasma peut également être étendu afin de produire des dépôts de nitrure de bore sur de grandes surfaces. Il souligne la complémentarité des approches expérimentales et de modélisation, mais également des approches fondamentales et applicatives.
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# Cross-comparison of diagnostic and 0D modeling of a micro-hollow cathode discharge in the stationary regime in an Ar/N₂ gas mixture

Alice Remigy<fnref n="1" /> ID, Salima Kasri<fnref n="1" />, Thibault Darny<fnref n="2" />, Hiba Kabbara<fnref n="1" />, Ludovic William<fnref n="1" />, Gérard Bauville<fnref n="2" />, Kristaq Gazeli<fnref n="2" /> ID, Stéphane Pasquiers<fnref n="2" />, João Santos Sousa<fnref n="2" /> ID, Nelson De Oliveira<fnref n="3" /> ID, Nader Sadeghi<fnref n="4" />, Guillaume Lombardi<fnref n="1" /> and Claudia Lazzaroni<fnref n="1" />,*, ID

E-mail: claudia.lazzaroni@lspm.cnrs.fr

Received 28 July 2021, revised 9 November 2021

Accepted for publication 23 November 2021

Published 6 December 2021

<figure><img src="image_108.png" /></figure>

CrossMark

## Abstract

A micro-hollow cathode discharge (MHCD) operated in Ar/N₂ gas mixture, working in the normal regime, was studied both experimentally and with a 0D (volume-averaged) model in this work. This source provides high electron densities (up to 10¹⁵ cm⁻<fnref n="3" />) at low injected power (1 W). To understand the mechanisms leading to the production of N atoms, the densities of electrons, N atoms and argon metastable atoms (Ar*) were monitored over a wide range of experimental conditions. Electrons, N atoms and Ar* densities were probed by means of optical emission spectroscopy, vacuum ultra violet Fourier transform spectroscopy and tunable diode laser absorption spectroscopy, respectively. Measurements showed that using a smaller hole diameter enables to work with less injected power, while increasing the power density inside the hole and, subsequently, increasing the densities of excited species. Varying the percentage of N₂ in the gas mixture highlighted that, up to 80%, the density of N atoms increases although the dissociation rate drops. Looking at the processes involved in the production of N atoms with the help of the 0D model, we found that at very low N₂ fraction, N atoms are mostly produced through dissociative electron-ion recombination. However, adding more N₂ decreases drastically the electron density. The density of N atoms does not drop thanks to the contribution of Ar* atoms, which are the main species dissociating N₂ between 5% and 55% of N₂ in the gas mixture. A reasonable agreement is found between the experiments and the model results. This study shows that, with this MHCD, it is possible to significantly modify the production of N atoms when modifying the physical parameters, making it particularly relevant for applications requiring a N atoms source, such as nitride deposition.

Keywords: optical emission spectroscopy, absorption spectroscopy, global model, Ar/N₂ discharge, microplasma

(Some figures may appear in colour only in the online journal)

<footnote n="1">¹ Université Sorbonne Paris Nord, Laboratoire des Sciences des Procédés et des Matériaux, LSPM, CNRS, UPR 3407, F-93430 Villetaneuse, France</footnote>

<footnote n="2">² Université Paris-Saclay, CNRS, Laboratoire de Physique des Gaz et des Plasmas, 91405 Orsay, France</footnote>

<footnote n="3">³ Synchrotron Soleil, Orme des Merisiers, St. Aubin, BP 48, CEDEX, 91192 Gif sur Yvette, France</footnote>

<footnote n="4">⁴ LTM (URA5129) and LIPhy (URA5588), Université Grenoble-Alpes and CNRS, Grenoble, France</footnote>

<footnote>* Author to whom any correspondence should be addressed.</footnote>
# 1. Introduction

Microplasmas, defined by a micrometric scale of at least one of their dimensions, have drawn attention in recent years with applications in various fields, such as thin film deposition and nanomaterial synthesis [1–3], surface treatment [4, 5], sterilization [6, 7], lighting [8–10] and micro-propulsion [11]. Thanks to their small size, microplasmas can be generated at high pressure (up to atmospheric) with low injected power (1 W). Furthermore, they yield high power densities up to 100 kW cm⁻³ and even higher in some cases [12]. Those are significant advantages compared to conventional non-thermal plasma sources.

Micro hollow cathode discharge (MHCD) is a particular geometry of a microplasma source. It consists of an electrode-dielectric-electrode assembly that is drilled, at least partially, with a hole between a few tens and hundreds of micrometers in diameter. It was first introduced in the 1990s by Schoenbach *et al* [13, 14]. At very low discharge current (<0.1 mA), the DC MHCD works in the abnormal regime where the plasma is confined inside the hole. Despite the use of DC power supply, a self-pulsing regime appears at intermediate current values (typically between 0.1 and 0.5 mA) and the plasma oscillates between the interior and the exterior of the hole. The normal regime, attained at higher currents, is characterized by an expansion of the plasma on the cathodic surface. MHCDs provide high electronic densities (up to 10¹⁵ cm⁻³ [15]), which is expected to yield high precursor dissociation. This would be especially suited for the production of N atoms, which are needed for many applications, among which the synthesis of novel nanomaterials [16] and large band gap nitrides such as hexagonal boron nitride (h-BN) for high power electronics [17]. To shift from the harmful nitrogen-containing precursors currently used in the industry (ammonia $NH_3$, borazine $B_3H_6N_3$) to molecular nitrogen ($N_2$), one has to overcome its high bonding energy (9.5 eV), which prevents dissociation rates higher than a few percent at low processing temperatures (<800 °C) [18]. Efforts to improve the production of nitrogen atoms (N) showed that the controlled addition of argon (Ar) in the operating gas mixture enhances the dissociation of $N_2$ [19, 20]. For the deposition of h-BN, our team opted for boron tribromide (BBr₃) as the boron precursor [1]. It is added downstream of the MHCD and dissociated thermally.

In this paper, we have experimentally studied the production of N atoms in a MHCD working in the normal regime, in an Ar/N₂ gas mixture. To obtain complete understanding of the chemistry at stake, a volume averaged (0D) model of the discharge was developed. The density of N atoms was monitored by means of two different absorption spectroscopy methods. The challenging vacuum ultra violet (VUV) spectral range of N atoms dipole transitions (≈120 nm) led us to use the state-of-the-art Fourier transform spectrometer (FTS) of the SOLEIL synchrotron. In addition, the density of argon atom metastables (Ar(1s₅), hereafter denoted as Ar*) was monitored, by means of tunable diode laser absorption spectroscopy, since those species may lead to the dissociation of $N_2$ through the reaction $Ar^m + N_2 \rightarrow N + N + Ar$ [21]. The electronic density was probed as well, using optical emission

spectroscopy (OES), to understand how the electrons (e) participate in the dissociation process.

Section 2 describes the three experimental setups as well as the 0D model employed to characterize the discharge. Section 3 discusses the influence of different experimental parameters (hole diameter, gas pressure and mixture) on the production of N atoms.

# 2. Experimental setup and description of the model

## 2.1. Plasma source

The MHCD device, schematized in figure 1(a), uses alumina ($Al_2O_3$) as the dielectric (750 µm thick), which is placed between two molybdenum electrodes (100 µm thick each). The dielectric and electrodes are assembled together using an epoxy glue suited for high-temperature operation. A hole is drilled through the assembly using a marking laser. Three different hole diameters have been used in this study: 0.4, 1 and 2 mm. This MHCD device is placed in the reactor illustrated in figure 1(b), at the junction between two vacuum chambers. A gas mixture of Ar/N₂, with varying proportions of each gas, is injected in the upstream chamber (left hand side) at a constant total flow rate of 100 sccm. A pipe links the two chambers, maintaining them at the same pressure. This pressure, ranging from 30 to 90 mbar, is regulated using a pump and manual valve, pumping in the downstream chamber (right hand side).

The MHCD is then ignited using a negative DC power supply (0–1000 V). The electrode in the upstream chamber is connected to the negative high voltage of the power supply, being thus the cathode, while the anode is connected to the ground and faces the downstream chamber, as represented in figure 1(b). The electrical parameters of the discharge are monitored through two voltage probes. The first probe is located post the ballast resistor $R_b = 480$ kΩ, used to limit the discharge current, and measures the discharge voltage $V_d$ delivered to the plasma. The second probe is used to record the voltage $V_I$ across the 180 Ω resistor $R_m$, in order to measure the discharge current $I_d$. Because the pair ($V_d, I_d$) is determined by the discharge conditions, a current $I_d = 1$ mA is used as a reference, while the voltage $V_d$ is not set by the operator and its value adapts to fit the conditions. At such discharge current, the MHCD operates in the normal regime, with continuous discharge voltage and current.

Three different optical diagnostics were used to evaluate the density of electrons, N atoms and argon metastables in the plasma, respectively, as described in sections 2.2–2.4.

## 2.2. OES: stark broadening of $H_β$ for electron density determination

The electron density was measured using the Stark broadening of the $H_β$ line at $\lambda_{H_β} = 486.135$ nm, which is very sensitive to this type of broadening. To observe the line, 1% of hydrogen gas was added into the gas mixture. It should be noted that, at this low percentage, hydrogen does not affect the discharge behavior, with no modification of its current-voltage characteristic.
<figure><img src="image_109.png" /><figcaption>Figure 1. Scheme of (a) the MHCD configuration and (b) the reactor used in the experiments.</figcaption></figure>

A SOPRA Ebert-Fasti monochromator with a 2 m focal length, with a 1200 grooves per mm grating, was used. It is backed by a PIMAX3-1024i (Roper Scientific) CCD camera with a 12.8 × 12.8 µm² pixel size. A lens with a 30 mm focal length focuses the light emitted by the plasma into the entry slit, 100 µm wide, of the monochromator. The $H_β$ line is recorded at the third diffraction order of the grating, for which the reverse dispersion is 60.7 pm mm⁻¹, yielding to 0.7765 pm per pixel. Two filters placed before the monochromator eliminate the light from other diffraction orders of the grating. A low-pass filter, with a 550 nm cutoff wavelength, filters out the emission in the second diffraction order, and a high-pass filter, with a 400 nm cutoff wavelength, suppresses the intense emission of molecular nitrogen second positive system. To avoid the contribution of the light coming from the emission of the cathodic expansion, the monochromator is facing the anodic side. The $H_β$ line profile results from different physical phenomena:

* the apparatus function ($\Delta\lambda_I$) that depends on the width of the slit, the grating, the CCD and the optical aberration. In our case, the instrumental broadening induces a Gaussian profile and $\Delta\lambda_I$ is measured to be of 7.5 pm, using an argon ionic line.

* the Doppler broadening ($\Delta\lambda_D$), due to the thermal agitation of the particles, also induces a Gaussian profile and is calculated as follows [22]:

$$ \Delta\lambda_D = \lambda_{H_β} \sqrt{8 \ln(2) \frac{k_B T_g}{c^2 M}} = 7.16 \times 10^{-7} \times \lambda_{H_β} \sqrt{\frac{T_g}{M}} \quad (1) $$

where $T_g$ is the gas temperature, c the speed of light, M the mass of the hydrogen atom and $k_B$ the Boltzmann constant. With $T_g$ estimated to be of 470 K based on previous measurements on a similar source [23], we obtain $\Delta\lambda_D = 7$ pm.

* the Van der Waals broadening ($\Delta\lambda_{vdW}$) is caused by the collisions with perturbing particles with similar energy levels

as the emitting particle. It induces a Lorentzian profile and is expressed by [24, 25]:

$$ \Delta\lambda_{vdW} = 6.8 \times \frac{P_{Ar}}{T_g^{0.7}} + 2.4 \times \frac{P_{N_2}}{T_g^{0.7}} \quad (2) $$

with $P_{Ar}$ and $P_{N_2}$ the partial pressure of Ar and N₂, respectively, in Torr and $\Delta\lambda_{vdW}$ in pm.

* the Stark broadening ($\Delta\lambda_{Stark}$) is due to the interaction between the emitting atoms, ions and free electrons in the plasma, through the electric fields generated by these particles and it is expressed by [22]:

$$ \Delta\lambda_{Stark} = 4.7333 \times 200 \left( \frac{n_e}{10^{22}} \right)^{1/1.49} \quad (3) $$

with $n_e$ in m⁻³ and $\Delta\lambda_{Stark}$ in pm. The convolution of the above-described contributions leads to a Voigt profile of width $\Delta\lambda_{exp}$, which is measured experimentally. Figure 2 shows a typical $H_β$ line profile recorded and the associated Voigt fit used to determine $\Delta\lambda_{exp}$.

Subsequently, the value of the Stark broadening is calculated as follows [26]:

$$ \begin{gathered} \Delta\lambda_{Stark} = (\Delta\lambda_{exp}^{1.4} - \Delta\lambda_{DI}^{1.4})^{1/1.4} - \Delta\lambda_{vdW} \quad \text{with} \\ \Delta\lambda_{DI} = \sqrt{\Delta\lambda_{I}^{2} + \Delta\lambda_{D}^{2}}. \end{gathered} \quad (4) $$

The electron density is then linked to the Stark broadening $\Delta\lambda_{Stark}$ (in pm) through:

$$ n_e = 10^{22} \times \left( \frac{\Delta\lambda_{Stark}}{4.7333 \times 200} \right)^{1.49} \text{ m}^{-3}. \quad (5) $$

## 2.3. Fourier transform spectrometry vacuum ultra-violet absorption for N atom density determination

The N atom density determination was carried out with the VUV high-resolution FTS of the DESIRS (Dichroïsme
<figure><img src="image_110.png" /><figcaption>**Figure 2.** Normalized $H_β$ emission line spectrum (solid black) and corresponding Voigt fit (red dashed). Plasma conditions: hole diameter = 0.4 mm, P = 50 mbar, 0% N₂, $I_d$ = 1 mA.</figcaption></figure>

Et Spectroscopie par Interaction avec le Rayonnement Synchrotron) beamline at the SOLEIL synchrotron facility. The microplasma reactor was placed in the sample environment chamber of the FTS branch. The usual borosilicate windows were replaced with MgF₂ windows, transparent in the near VUV spectral range. The VUV Fourier transform spectroscopy (VUV FTS) setup is described in details in [27, 28]. This spectrometer covers the full VUV range down to 40 nm and allows for a very high spectral resolution to be achieved. It records the photo-absorption spectra over the full range, with a resolving power $\frac{\lambda}{\Delta\lambda}$ up to $1 \times 10^6$.

The N atom density is probed using the transition between the ground state ($2p^3 \ ^4S_{3/2}$) and the triplet state ($3s \ ^4P_{1/2,3/2,5/2}$) around 120 nm. The spectrometer yields the full convoluted transmission spectrum $T_C(\sigma')$ (with $\sigma'$ the wavenumber in cm$^{-1}$):

$$T_C(\sigma') = T_0(\sigma')[\Phi_I(\sigma' - \sigma) * T(\sigma)] \quad (6)$$

where $T_0(\sigma')$ is the transmission spectrum without absorbent, $\Phi_I(\sigma' - \sigma)$ the instrumental profile and $T(\sigma)$ the actual absorption spectrum of the sample. In the case of this spectrometer, the instrumental function is a sinc function $\Phi_I(\sigma' - \sigma) = \frac{\sin(\pi(\sigma' - \sigma))}{\pi(\sigma' - \sigma)}$, with a full width at half maximum (FWHM) $\Delta_I$ that is proportional to the sampling interval $\delta\sigma'$. In our case, $\Delta_I = 0.53 \text{ cm}^{-1}$. The raw data $T_C(\sigma')$ are first normalized to the baseline $T_0(\sigma')$ and deconvoluted from $\Phi_I(\sigma' - \sigma)$ to obtain the transmission spectrum, which, according to Beer-Lambert law, is equal to:

$$T(\sigma) = \exp[-\text{Abs}(\sigma)] = \exp[-k(\sigma) \cdot l_{\text{abs}}(N)] \quad (7)$$

with Abs($\sigma$) the absorbance, $l_{\text{abs}}(N)$ the absorption length for the N atoms considered here and $k(\sigma)$ the absorption coefficient. For a single line, between an upper level u and a lower level l, with a central transition wavenumber $\sigma_{ul}$, $k(\sigma)$ is given by [29]:

$$\begin{aligned} k(\sigma) &= k_0 \Phi(\sigma) \left( N_l - \frac{g_l}{g_u} N_u \right) \\ &= \frac{g_u}{g_l} \frac{1}{8\pi c \sigma_{ul}^2} A_{ul} \Phi(\sigma) \left( N_l - \frac{g_l}{g_u} N_u \right) \end{aligned} \quad (8)$$

with $g_u$ and $g_l$ the statistical weights of the upper and lower levels, $N_u$ and $N_l$ the corresponding population densities, c the speed of light, $A_{ul}$ the Einstein coefficient of the transition and $\Phi(\sigma)$ the normalized line profile. Because the gas temperature $T_g$, estimated to be of 470 K (0.05 eV), is much lower than the energy of the transition (10 eV), we can consider that $N_u \ll N_l$, which thus yields:

$$\text{Abs}(\sigma) = \frac{g_u}{g_l} \frac{1}{8\pi c \sigma_{ul}^2} A_{ul} \Phi(\sigma) N_l \cdot l_{\text{abs}}(N). \quad (9)$$

In the general case, the line profile $\Phi(\sigma)$ is a Voigt profile, i.e. the convolution of a Gaussian and a Lorentzian line profiles. The latter is related to the species lifetime and includes the pressure broadening (estimated to be of $0.01 \text{ cm}^{-1}$ in our conditions). The former reflects the thermal motion of the absorbent atoms, of mass M = 14, with a Doppler FWHM $\Delta\sigma_D = \sigma_{ul}\sqrt{8\ln(2)k_B T_g / Mc^2} = 0.35 \text{ cm}^{-1}$ at $T_g = 470$ K, assumed to be equal to the gas temperature because of the high collision rate.

Figure 3 shows the normalized, non deconvoluted transmission spectrum of the three transitions from the ground state of nitrogen ($2p^3 \ ^4S_{3/2}$) to the triplet state ($3s \ ^4P_{1/2,3/2,5/2}$), for the case of a 1 mm diameter hole, a gas mixture of 80% Ar and 20% N₂, a pressure of 30 mbar and a discharge current of 1 mA. Each line is individually fitted with a convolution of a sinc function and a Voigt profile, with fixed values for the instrumental function FWHM $\Delta_I$ and the Doppler broadening $\Delta\sigma_D$. In all of our experimental conditions, grazing the cathodic side, with percentages of N₂ as low as 1%, we faced a saturation of the absorption line. The line fitting was done only on the non-saturated wings of the Voigt profile, allowing us to still obtain a measurement but with less precision. Fitting each line individually grants us with a mean value and a standard error. The error on the column density $N_l \cdot l_{\text{abs}}(N)$, which is due to the signal-to-noise ratio obtained in each condition, can reach up to 20%, depending on the experimental conditions. This measurement is not affected by the reproducibility of the discharge since only one set of measurements has been performed, due to time constraints.

## 2.4. Tunable diode laser absorption spectroscopy for Ar* density determination

The determination of the Ar* density was carried out with an experimental setup based on that previously reported in [30] and illustrated in figure 4. The transition probed is the one at 811.531 nm between the metastable states ($4s \ ^3P_2$) and ($4p \ ^3D_3$) (transition referred as ($1s_5 \rightarrow 2p_9$) in Paschen's notation), using the commercial diode laser Toptica DL 100 DFB-L. The wavelength of the laser is adjusted between 811.501 and 811.561 nm to scan the entire line profile. This is done by modifying the operating current of the laser. The laser
<figure><img src="image_111.png" /><figcaption>Figure 3. Normalized, non deconvoluted, transmission spectrum of the N(2p³ ⁴S₃/₂ → 3s ⁴Pⱼ) triplet transition. Plasma conditions: hole diameter = 1 mm, grazing the anodic side, P = 30 mbar, 20% N₂, Iₐ = 1 mA.</figcaption></figure>

<figure><img src="image_112.png" /><figcaption>Figure 4. Experimental setup used for the determination of the Ar* density. PD = photodiode, ND filter = neutral density filter, IR filter = infra-red filter, BS = beam splitter.</figcaption></figure>

beam passes through an aperture and a neutral optical density (ND filter in figure 4) to sufficiently attenuate its intensity and avoid any saturation of the optical transition. The beam is then divided in two parts with a beam splitter: the first part passes through a low-pressure argon lamp used as a reference for the determination of the central wavelength of the transition, and the second part goes through the microplasma source. The beam probing the plasma is shaped by the aperture put before the reactor. Hence, the laser spot probing the medium is circular with a 1 mm diameter. After passing through the plasma, the laser beam is focused with a lens into a photodiode (PD2).

To record the absorbance of the plasma as a function of the laser wavelength, four signals are recorded for each plasma condition: the transmission T (laser ON, plasma ON), the plasma emission P (laser OFF, plasma ON), the laser emission L (laser ON, plasma OFF) and the background noise B (laser

OFF, plasma OFF). The absorbance (Abs) is then calculated as follows:

$$Abs(\lambda) = - \frac{T(\lambda) - P(\lambda)}{L(\lambda) - B(\lambda)}. \qquad (10)$$

As seen previously in section 2.3, the absorbance is related to the population density of the lower level through equation (9). However, instead of fitting the line profile, we directly used the integral of the absorbance:

$$N_l = \frac{g_l}{g_u} \frac{8\pi}{\lambda_{ul}^2} \frac{1}{A_{ul}l_{abs}(Ar^*)} \int Abs(\nu)d\nu \qquad (11)$$

with $\nu$ the frequency, $\lambda_{ul}$ the central wavelength of the line and given that the integral of the normalized line profile $\int \Phi(\nu)d\nu = 1$. This allows us to make no assumption on the
shape of the line profile. Each experience was repeated at least three times, yielding a standard deviation on the column density $N_l \cdot l_{abs}(Ar^*)$ between 20% and 50%, depending on the experimental conditions. The error increases with the percentage of $N_2$ in the discharge since the density of Ar* decreases and, consequently, the signal-to-noise ratio decreases as well. The reproducibility of the discharge from day to day is another source of error for this diagnostic.

## 2.5. 0D model

The experimental results obtained have been compared to those given by a 0D model of the discharge, yielding the volume averaged densities of species (including electrons), reaction rates and electron temperature. The model is based on a previous one [31, 32], upgraded with an adapted chemistry to study the Ar/N$_2$ gas mixture. 14 species are taken into consideration: ground-state argon atoms Ar, argon positive ions Ar$^+$, argon molecular ions Ar$_2^+$, metastable argon atoms Ar$^m$, resonant argon atoms Ar$^r$, excited argon atoms in the 4p state Ar$^{4p}$, ground-state molecular nitrogen N$_2$, electronically excited N$_2$ molecules (N$_2$(A)(A$^3\Sigma_u^+$), N$_2$(B)(B$^3\Pi_g$) and N$_2$(C)(C$^3\Pi_u$)), nitrogen atoms N, the positive nitrogen ions N$_2^+$ and N$_4^+$, and the electrons e. The Ar$^r$ includes the two resonant states $^1P_1$ and $^3P_1$, while the Ar$^m$ state includes both the $^3P_2$ (1s$_5$ in Paschen's notation) and the $^3P_0$ (1s$_3$ in Paschen's notation). We bring to the reader's attention that our absorption spectroscopy measurements relate to the density of metastable argon in the $^3P_2$ (1s$_5$) only. In the literature, the density ratio between the 1s$_5$ and 1s$_3$ states have been measured and found between 6.25 and 8.9 [33, 34], which gives an idea of the expected discrepancy between the experimental and the model results. On the basis of previous works [21, 23, 31, 35–44] in similar gas mixtures, we are considering 69 reactions in the plasma volume, gathered in table 1.

In addition to the reactions listed in table 1, the ions and excited neutral species are also lost at the surfaces. For neutral species x, the diffusion flux rate to the surface is given by:

$$K_x = \left( \frac{\Lambda^2}{D_x} + \frac{2V(2 - \gamma_x)}{\gamma_x S v_x} \right)^{-1} \quad (12)$$

with $\Lambda = [(\pi/L)^2 + (2.405/R)^2]^{-1/2}$ the effective diffusion length, V/S the volume to surface ratio of the discharge, $\gamma_x$ the recombination coefficient and $v_x = (8k_B T_g / \pi m_x)^{1/2}$ the neutral atom mean velocity, where $m_x$ is the neutral atom mass. $D_x$ is the diffusion coefficient and it is inversely proportional to the pressure, such that at pressure P, temperature $T_g$, $D_x(P, T_g) = D_x(\text{atm. pressure, 300 K}) \times 1013/P \times (T_g/300)^{1.5}$. Ion losses at the surface are described with the ion flux for a positive ion i expressed as follows:

$$\Gamma_i = h_{Ri} u_{Bi} n_i \quad (13)$$

with $u_{Bi} = (eT_e/m_i)^{0.5}$ the Bohm velocity, where e is the elementary charge, $T_e$ the electronic temperature and $m_i$ the mass of ion i. $h_{Ri}$ is the edge-to-center density ratio calculated by:

$$h_{Ri} = \frac{\chi_{01} J_1(\chi_{01})}{R u_{Bi}} D_{ai} = \frac{\chi_{01} J_1(\chi_{01}) k_B T_i}{R u_{Bi} m_i \nu_i} \left( 1 + \frac{T_e}{T_i} \right) \quad (14)$$

where $\chi_{01} = 2.405$ is the first zero of the Bessel function $J_0$, $J_1(\chi_{01}) = 0.52$, $D_{ai}$ the ambipolar diffusion coefficient, $T_i$ the ion temperature equal to the gas temperature and $\nu_i$ the collision frequency. We use $\nu_i = n_g \sigma_i \bar{\nu}_i$ with $\sigma_i = 10^{-18} \text{ m}^2$ and $\bar{\nu}_i = (8k_B T_i / \pi m_i)^{1/2}$. All of the surface reactions considered and relevant parameters can be found in table 2. For every condition in the model, we use $T_g = 470 \text{ K}$, based on previous work [23].

The electron energy balance equation is:

$$\frac{d}{dt} \left( \frac{3}{2} n_e k_B T_e \right) = P_{\text{abs}} - P_{\text{loss}} \quad (15)$$

with $P_{\text{abs}}$ the absorbed power by the electrons and $P_{\text{loss}}$ the dissipated power by the electrons.

The expression of the absorbed power by the electrons is [39]:

$$P_{\text{abs}} = \frac{A}{S_C} (1 - \kappa) V_d \times I_d \quad (16)$$

with A the inner surface of the cathodic region ($A = 2\pi RL_{cath}$ with R the radius of the hole and $L_{cath}$ the cathode thickness), $S_C$ the surface through which the discharge current flows and $\kappa$ the fraction of the power dissipated by ions accelerated in the cathode sheath. The ratio $A/S_C$ and $\kappa$ are taken equal to 0.5 and 0.75, respectively, in our conditions.

Concerning the dissipated power by the electrons, we have used the formulation of the collisional energy loss proposed by Thorsteinsson and Gudmundsson [46], which includes the losses related to vibrational levels of nitrogen molecules and higher electronic levels of nitrogen atoms and molecules. The evolution of the collisional loss as a function of the electron temperature given in [46, 47] has been calculated assuming a Maxwellian electron energy distribution.

## 2.6. Probed areas and absorption lengths

In this section, we summarize the information gathered about the discharge through the different diagnostics and the 0D model. Figure 5 shows a scheme of the diagnostics performed, with the visible plasma delimited by the black dashed line. The 0D model computes the volume-averaged density of species over the cathodic area, delimited with the blue dashed line (in volume, it is a cylinder with the same diameter as the hole and the height of the cathode). This is the plasma region where most of the electric power is deposited [31] and, thus, where the densities are expected to be the highest.

The TDLAS measurements give the Ar* column density along the axis of the hole. Ar metastables are mainly created in the cathodic region (see blue dashed line in figure 5) by excitation by the energetic electrons, which are localized in this region, and are lost at the surface. Their concentration is, thus, localized in this region and, therefore, the absorption length has been estimated to be comparable to the hole radius (for example, $l_{abs}(Ar^*) = 200 \text{ µm}$ for a hole diameter of 400 µm).
<table><caption>**Table 1.** Reactions and corresponding reaction rates used in the 0D model. $T_e$ is the electronic temperature in eV, $T_e$ (K) the electronic temperature in K. The gas temperature $T_g$ is expressed in K as well. The reaction rates are in $m^3 s^{-1}$ for two-body reactions, in $m^6 s^{-1}$ for three-body reactions and in $s^{-1}$ for radiative decay.</caption><thead><tr><th>n</th><th>Reaction</th><th>Reaction rate</th><th>Reference</th></tr></thead><tbody><tr><td colspan="4">Electron impact ionization</td></tr><tr><td>R1</td><td>e + Ar → Ar<sup>+</sup> + e + e</td><td>2.34 × 10<sup>-14</sup> × T<sub>e</sub><sup>0.59</sup> × exp(-17.44/T<sub>e</sub>)</td><td>[35]</td></tr><tr><td>R2</td><td>e + Ar<sup>m</sup> → Ar<sup>+</sup> + e + e</td><td>6.8 × 10<sup>-15</sup> × T<sub>e</sub><sup>0.67</sup> × exp(-4.2/T<sub>e</sub>)</td><td>[35]</td></tr><tr><td>R3</td><td>e + Ar<sup>4p</sup> → Ar<sup>+</sup> + e + e</td><td>1.8 × 10<sup>-13</sup> × T<sub>e</sub><sup>0.61</sup> × exp(-2.61/T<sub>e</sub>)</td><td>[35]</td></tr><tr><td>R4</td><td>e + N<sub>2</sub> → N<sub>2</sub><sup>+</sup> + e + e</td><td>1.34 × 10<sup>-14</sup> × T<sub>e</sub><sup>0.7224</sup> × exp(-22.38/T<sub>e</sub>)</td><td>[36]</td></tr><tr><td colspan="4">Electron impact excitation and de-excitation</td></tr><tr><td>R5</td><td>e + Ar → Ar<sup>m</sup> + e</td><td>5 × 10<sup>-15</sup> × exp(-12.64/T<sub>e</sub>) + 1.4 × 10<sup>-15</sup> × exp(-12.42/T<sub>e</sub>)</td><td>[35]</td></tr><tr><td>R6</td><td>e + Ar → Ar<sup>r</sup> + e</td><td>1.9 × 10<sup>-15</sup> × exp(-12.6/T<sub>e</sub>) + 2.7 × 10<sup>-16</sup> × exp(-12.14/T<sub>e</sub>)</td><td>[35]</td></tr><tr><td>R7</td><td>e + Ar → Ar<sup>4p</sup> + e</td><td>2.1 × 10<sup>-14</sup> × exp(-13.13/T<sub>e</sub>)</td><td>[35]</td></tr><tr><td>R8</td><td>e + Ar<sup>m</sup> → Ar + e</td><td>4.3 × 10<sup>-16</sup> × T<sub>e</sub><sup>0.74</sup></td><td>[35]</td></tr><tr><td>R9</td><td>e + Ar<sup>m</sup> → Ar<sup>r</sup> + e</td><td>3.7 × 10<sup>-13</sup></td><td>[35]</td></tr><tr><td>R10</td><td>e + Ar<sup>m</sup> → Ar<sup>4p</sup> + e</td><td>8.9 × 10<sup>-13</sup> × T<sub>e</sub><sup>0.51</sup> × exp(-1.59/T<sub>e</sub>)</td><td>[35]</td></tr><tr><td>R11</td><td>e + Ar<sup>r</sup> → Ar + e</td><td>4.3 × 10<sup>-16</sup> × T<sub>e</sub><sup>0.74</sup></td><td>[35]</td></tr><tr><td>R12</td><td>e + Ar<sup>r</sup> → Ar<sup>m</sup> + e</td><td>9.1 × 10<sup>-13</sup></td><td>[35]</td></tr><tr><td>R13</td><td>e + Ar<sup>r</sup> → Ar<sup>4p</sup> + e</td><td>8.9 × 10<sup>-13</sup> × T<sub>e</sub><sup>0.51</sup> × exp(-1.59/T<sub>e</sub>)</td><td>[35]</td></tr><tr><td>R14</td><td>e + Ar<sup>4p</sup> → Ar<sup>r</sup> + e</td><td>3 × 10<sup>-13</sup> × T<sub>e</sub><sup>0.51</sup></td><td>[35]</td></tr><tr><td>R15</td><td>e + Ar<sup>4p</sup> → Ar<sup>m</sup> + e</td><td>3 × 10<sup>-13</sup> × T<sub>e</sub><sup>0.51</sup></td><td>[35]</td></tr><tr><td>R16</td><td>e + Ar<sup>4p</sup> → Ar + e</td><td>3.9 × 10<sup>-16</sup> × T<sub>e</sub><sup>0.71</sup></td><td>[35]</td></tr><tr><td>R17</td><td>e + Ar<sup>+</sup> → Ar<sup>m</sup></td><td>5.95 × 10<sup>-17</sup> × T<sub>e</sub><sup>0.5</sup></td><td>[35]</td></tr><tr><td>R18</td><td>e + e + Ar<sup>+</sup> → Ar<sup>m</sup> + e</td><td>5.6 × 10<sup>-39</sup> × T<sub>e</sub><sup>-4.5</sup></td><td>[23]</td></tr><tr><td>R19</td><td>e + Ar<sup>+</sup> → Ar<sup>m</sup> + Ar</td><td>5.4 × 10<sup>-14</sup> × T<sub>e</sub><sup>-2/3</sup></td><td>[31]</td></tr><tr><td>R20</td><td>e + e + N<sub>2</sub><sup>+</sup> → N<sub>2</sub> + e</td><td>5.651 × 10<sup>-39</sup> × T<sub>e</sub> (K)<sup>-0.8</sup></td><td>[37]</td></tr><tr><td>R21</td><td>e + N<sub>2</sub> → N + N + e</td><td>1.959 × 10<sup>-12</sup> × T<sub>e</sub> (K)<sup>-0.7</sup> × exp(-1.132 × 10<sup>5</sup>/T<sub>e</sub> (K))</td><td>[37]</td></tr><tr><td>R22</td><td>e + N<sub>2</sub><sup>+</sup> → N<sub>2</sub></td><td>4.8 × 10<sup>-13</sup> × T<sub>e</sub> (K)<sup>-0.5</sup></td><td>[38]</td></tr><tr><td colspan="4">Ion molecule reactions</td></tr><tr><td>R23</td><td>Ar<sup>+</sup> + Ar + Ar → Ar<sub>2</sub><sup>+</sup> + Ar</td><td>2.5 × 10<sup>-43</sup></td><td>[23]</td></tr><tr><td colspan="4">Neutral reactions: Penning ionization</td></tr><tr><td>R24</td><td>Ar<sup>m</sup> + Ar<sup>r</sup> → Ar + Ar<sup>+</sup> + e</td><td>2.1 × 10<sup>-15</sup></td><td>[35]</td></tr><tr><td>R25</td><td>Ar<sup>4p</sup> + Ar<sup>4p</sup> → Ar + Ar<sup>+</sup> + e</td><td>5 × 10<sup>-16</sup></td><td>[35]</td></tr><tr><td>R26</td><td>Ar<sup>m</sup> + Ar<sup>m</sup> → Ar + Ar<sup>+</sup> + e</td><td>6.4 × 10<sup>-16</sup></td><td>[35]</td></tr><tr><td colspan="4">Neutral reactions</td></tr><tr><td>R27</td><td>Ar + Ar<sup>m</sup> → Ar + Ar</td><td>2.1 × 10<sup>-21</sup></td><td>[35]</td></tr><tr><td>R28</td><td>Ar<sup>m</sup> + N<sub>2</sub> → N + N + Ar</td><td>3.6 × 10<sup>-17</sup></td><td>[21]</td></tr><tr><td>R29</td><td>Ar<sup>r</sup> + N<sub>2</sub> → N + N + Ar</td><td>3.6 × 10<sup>-17</sup></td><td>[21]</td></tr><tr><td colspan="4">Dissociative recombination</td></tr><tr><td>R30</td><td>e + e + N<sub>4</sub><sup>+</sup> → N<sub>2</sub> + N<sub>2</sub> + e</td><td>5.651 × 10<sup>-39</sup> × T<sub>e</sub> (K)<sup>-0.8</sup></td><td>[37]</td></tr><tr><td>R31</td><td>e + N<sub>2</sub><sup>+</sup> → N + N</td><td>4.8 × 10<sup>-13</sup> × (T<sub>e</sub> (K)/300)<sup>0.5</sup></td><td>[21]</td></tr><tr><td>R32</td><td>e + N<sub>4</sub><sup>+</sup> → N<sub>2</sub> + N<sub>2</sub></td><td>2 × 10<sup>-12</sup> × (T<sub>e</sub> (K)/300)<sup>0.5</sup></td><td>[21]</td></tr><tr><td colspan="4">Ion neutral reactions</td></tr><tr><td>R33</td><td>Ar<sup>+</sup> + N<sub>2</sub> → N<sub>2</sub><sup>+</sup> + Ar</td><td>4.45 × 10<sup>-16</sup></td><td>[21]</td></tr><tr><td>R34</td><td>Ar + N<sub>2</sub><sup>+</sup> → N<sub>2</sub> + Ar<sup>+</sup></td><td>2.81 × 10<sup>-16</sup></td><td>[21]</td></tr><tr><td>R35</td><td>N<sub>2</sub><sup>+</sup> + N<sub>2</sub> + Ar → N<sub>4</sub><sup>+</sup> + Ar</td><td>8.9 × 10<sup>-42</sup> × (Tg/300)<sup>-1.54</sup></td><td>[36]</td></tr><tr><td>R36</td><td>N<sub>4</sub><sup>+</sup> + N<sub>2</sub> → N<sub>2</sub><sup>+</sup> + N<sub>2</sub> + N<sub>2</sub></td><td>2.1 × 10<sup>-22</sup> × (Tg/121)<sup>-1.54</sup></td><td>[21]</td></tr><tr><td>R37</td><td>N<sub>2</sub><sup>+</sup> + N<sub>2</sub> + N<sub>2</sub> → N<sub>4</sub><sup>+</sup> + N<sub>2</sub></td><td>6.8 × 10<sup>-41</sup> × (Tg/300)<sup>1.64</sup></td><td>[21]</td></tr><tr><td>R38</td><td>N<sub>4</sub><sup>+</sup> + Ar → Ar<sup>+</sup> + N<sub>2</sub> + N<sub>2</sub></td><td>1 × 10<sup>-17</sup></td><td>[21]</td></tr><tr><td colspan="4">Radiation</td></tr><tr><td>R39</td><td>Ar<sup>r</sup> → Ar</td><td>1.77 × 10<sup>6</sup></td><td>[39]</td></tr><tr><td>R40</td><td>Ar<sup>4p</sup> → Ar<sup>m</sup></td><td>1.5 × 10<sup>7</sup></td><td>[35]</td></tr><tr><td>R41</td><td>Ar<sup>4p</sup> → Ar<sup>r</sup></td><td>1.5 × 10<sup>7</sup></td><td>[35]</td></tr></tbody></table>

(Continued.)
<table><caption>**Table 1.** (Continued.)</caption><thead><tr><th>n</th><th>Reaction</th><th>Reaction rate</th><th>Reference</th></tr></thead><tbody><tr><td colspan="4">Electronically excited states of N<sub>2</sub> reactions</td></tr><tr><td>R42</td><td>N + N + N<sub>2</sub> → N<sub>2</sub>(A) + N<sub>2</sub></td><td>1.7 × 10<sup>-45</sup></td><td>[40]</td></tr><tr><td>R43</td><td>N + N + N → N<sub>2</sub>(A) + N</td><td>1 × 10<sup>-44</sup></td><td>[40]</td></tr><tr><td>R44</td><td>N + N + N<sub>2</sub> → N<sub>2</sub>(B) + N<sub>2</sub></td><td>2.4 × 10<sup>-45</sup></td><td>[40]</td></tr><tr><td>R45</td><td>N + N + N → N<sub>2</sub>(B) + N</td><td>1.4 × 10<sup>-44</sup></td><td>[40]</td></tr><tr><td>R46</td><td>N<sub>2</sub>(A) + N → N<sub>2</sub> + N</td><td>2 × 10<sup>-18</sup></td><td>[40]</td></tr><tr><td>R47</td><td>N<sub>2</sub>(A) + N<sub>2</sub> → N<sub>2</sub> + N<sub>2</sub></td><td>3 × 10<sup>-22</sup></td><td>[40]</td></tr><tr><td>R48</td><td>N<sub>2</sub>(A) + N<sub>2</sub>(A) → N<sub>2</sub> + N<sub>2</sub>(C)</td><td>1.5 × 10<sup>-16</sup></td><td>[40]</td></tr><tr><td>R49</td><td>N<sub>2</sub>(A) + N<sub>2</sub>(A) → N<sub>2</sub> + N<sub>2</sub>(B)</td><td>3 × 10<sup>-16</sup></td><td>[40]</td></tr><tr><td>R50</td><td>N<sub>2</sub>(B) + N<sub>2</sub> → N<sub>2</sub> + N<sub>2</sub></td><td>3 × 10<sup>-17</sup></td><td>[40]</td></tr><tr><td>R51</td><td>N<sub>2</sub>(B) + N<sub>2</sub> → N<sub>2</sub>(A) + N<sub>2</sub></td><td>5 × 10<sup>-17</sup></td><td>[41]</td></tr><tr><td>R52</td><td>N<sub>2</sub>(B) → N<sub>2</sub>(A)</td><td>1.5 × 10<sup>5</sup></td><td>[41]</td></tr><tr><td>R53</td><td>N<sub>2</sub>(C) → N<sub>2</sub>(B)</td><td>3 × 10<sup>7</sup></td><td>[41]</td></tr><tr><td>R54</td><td>N<sub>2</sub>(C) + N<sub>2</sub> → N<sub>2</sub>(B) + N<sub>2</sub></td><td>3 × 10<sup>-17</sup></td><td>[41]</td></tr><tr><td>R55</td><td>N<sub>2</sub>(C) + N<sub>2</sub> → N<sub>2</sub>(A) + N<sub>2</sub></td><td>1.1 × 10<sup>-17</sup></td><td>[41]</td></tr><tr><td>R56</td><td>N<sub>2</sub> + Ar<sup>m</sup> → N<sub>2</sub>(C) + Ar</td><td>3.6 × 10<sup>-17</sup></td><td>[42]</td></tr><tr><td>R57</td><td>N<sub>2</sub>(A) + N<sub>2</sub>(A) → N<sub>4</sub><sup>+</sup> + e</td><td>1 × 10<sup>-19</sup></td><td>[43]</td></tr><tr><td>R58</td><td>N<sub>2</sub>(A) + N<sub>2</sub>(A) → N<sub>2</sub> + N + N</td><td>3 × 10<sup>-17</sup></td><td>[43]</td></tr><tr><td>R59</td><td>N<sub>2</sub>(A) → N<sub>2</sub></td><td>5 × 10<sup>-1</sup></td><td>[43]</td></tr><tr><td>R60</td><td>N<sub>2</sub>(B) + Ar → N<sub>2</sub>(A) + Ar</td><td>3 × 10<sup>-19</sup></td><td>[43]</td></tr><tr><td>R61</td><td>N<sub>2</sub> + Ar<sup>r</sup> → N<sub>2</sub>(C) + Ar</td><td>3.6 × 10<sup>-17</sup></td><td>[43]</td></tr><tr><td>R62</td><td>N<sub>2</sub>(C) + Ar → N<sub>2</sub>(B) + Ar</td><td>8 × 10<sup>-19</sup></td><td>[44]</td></tr><tr><td>R63</td><td>N<sub>2</sub>(A) + N<sub>2</sub>(A) → N<sub>2</sub>(A) + N<sub>2</sub>(B)</td><td>4 × 10<sup>-17</sup></td><td>[44]</td></tr><tr><td>R64</td><td>N<sub>2</sub>(A) + N<sub>2</sub>(A) → N<sub>2</sub>(A) + N<sub>2</sub>(C)</td><td>1.5 × 10<sup>-17</sup></td><td>[44]</td></tr><tr><td>R65</td><td>N<sub>2</sub>(C) + e → N<sub>2</sub>(B) + e</td><td>1.5 × 10<sup>-17</sup></td><td>[44]</td></tr><tr><td>R66</td><td>N<sub>2</sub>(B) + e → N<sub>2</sub>(A) + e</td><td>2 × 10<sup>-18</sup></td><td>[44]</td></tr><tr><td>R67</td><td>N<sub>2</sub>(A) + e → N<sub>2</sub> + e</td><td>2 × 10<sup>-18</sup></td><td>[44]</td></tr><tr><td>R68</td><td>N<sub>2</sub> + e → N<sub>2</sub>(B) + e</td><td>3 × 10<sup>-16</sup></td><td>[44]</td></tr><tr><td>R69</td><td>N<sub>2</sub> + e → N<sub>2</sub>(C) + e</td><td>3 × 10<sup>-16</sup></td><td>[44]</td></tr></tbody></table>

<table><caption>**Table 2.** Surface reactions and corresponding diffusion coefficients and reaction probabilities used in the 0D model.</caption><thead><tr><th>n</th><th>Reaction</th><th>D (m<sup>2</sup>s<sup>-1</sup>)</th><th>γ</th><th>Reference</th></tr></thead><tbody><tr><td>R70</td><td>Ar<sup>+</sup> → Ar</td><td></td><td></td><td>[45]</td></tr><tr><td>R71</td><td>Ar<sub>2</sub><sup>+</sup> → Ar + Ar</td><td></td><td></td><td>[45]</td></tr><tr><td>R72</td><td>N<sub>2</sub><sup>+</sup> → N<sub>2</sub></td><td></td><td></td><td>[45]</td></tr><tr><td>R73</td><td>N<sub>4</sub><sup>+</sup> → N<sub>2</sub> + N<sub>2</sub></td><td></td><td></td><td>[45]</td></tr><tr><td>R74</td><td>N → <sup>1</sup>&frasl;<sub>2</sub>N<sub>2</sub></td><td>9.41 × 10<sup>-5</sup></td><td>0.1</td><td>[46]</td></tr><tr><td>R75</td><td>N<sub>2</sub>(A) → N<sub>2</sub></td><td>5.47 × 10<sup>-5</sup></td><td>1</td><td>[43]</td></tr><tr><td>R76</td><td>N<sub>2</sub>(B) → N<sub>2</sub></td><td>5.47 × 10<sup>-5</sup></td><td>1</td><td>[43]</td></tr><tr><td>R77</td><td>N<sub>2</sub>(C) → N<sub>2</sub></td><td>5.47 × 10<sup>-5</sup></td><td>1</td><td>[43]</td></tr><tr><td>R78</td><td>Ar<sup>m</sup> → Ar</td><td>1.09 × 10<sup>-5</sup></td><td>1</td><td>[45]</td></tr><tr><td>R79</td><td>Ar<sup>r</sup> → Ar</td><td>1.09 × 10<sup>-5</sup></td><td>1</td><td>[45]</td></tr><tr><td>R80</td><td>Ar<sup>4p</sup> → Ar</td><td>1.09 × 10<sup>-5</sup></td><td>1</td><td>[45]</td></tr></tbody></table>

In what regards the OES, the light collected comes from the red crosshatched area. Hence, the electron density measured is the average density in this area.

The purple hatched rectangle shows the area over which the VUV FTS diagnostic probes for the N atom density. The VUV beam spot is a 2 by 3 mm rectangle, represented as plane in figure 5. The effective length of the volume probed by the laser spot is $l_{abs}(N)$, and has been estimated using a simple diffusion model. Indeed, in the Ar/N<sub>2</sub> gas mixture, the N atoms losses in the volume can only occur through three-body collisions

with N<sub>2</sub> molecules and Ar atoms with reaction coefficients of, respectively, $k_{N_2} = 8.27 \times 10^{-34} \times \exp(500/T_g(K))$ cm<sup>6</sup> s<sup>-1</sup> and $k_{Ar} = 0.05 \times k_{N_2}$ [21]. In our conditions, this results in a lifetime of about a minute and can be neglected. We, thus, resolve the diffusion equation, with no loss in the volume. The considered configuration is illustrated in figure 6(a) where half of the reactor is represented. The total radius of the reactor is 50 mm (L/2). The N atoms diffuse in the three dimensions, from the sphere of radius $R_0$ (i.e. the radius of the hole) where the density is assumed uniform and equal to $n_0$. The diffusion
<figure><img src="image_113.png" /><figcaption>**Figure 5.** Scheme of the areas probed by the different diagnostics, at scale, for a 0.4 mm diameter hole. The dotted black line shows the limits of the visible plasma. The blue dashed line shows the volume considered in the model. The red crosshatched area is the one over which the average electron density is measured, while the purple hatched area is the one probed by the VUV FTS (N atom density).</figcaption></figure>

<figure><img src="image_114.png" /><figcaption>**Figure 6.** (a) Schema of the diffusion of N atoms in the reactor. Half the cathodic chamber is represented. The hatched area represents the path of the VUV FTS laser beam. Geometric parameters used for the evaluation of $l_{abs}(N)$ are represented. (b) N atoms density as a function of the distance from the hole axis, as calculated by the spherical diffusion model.</figcaption></figure>

equation in spherical coordinates, in the stationary regime, is then written as:

$$ \Gamma(r) = -D \frac{\partial n(r)}{\partial r} \qquad (17) $$

where $\Gamma$ and $n$ are the flux and the density of N atoms, respectively, and $D$ is the diffusion coefficient (given in table 2).

The conservation equation for N atoms, when the recombination in the volume is neglected, can be expressed as follows:

$$ div \vec{\Gamma} = 0. \qquad (18) $$

Normalizing by $\Gamma_0 = \frac{n_0 D}{R_0}$ the flux at $r = R_0$ and solving the equation yields the following expression for the N atoms density as a function of the radial position $r$:

$$ n(r) = \frac{R_0 n_0}{r} \qquad (19) $$

which gives in cartesian coordinates:

$$ n(x, y, z) = \frac{R_0 n_0}{\sqrt{x^2 + y^2 + z^2}} \qquad (20) $$

The profile of the N atoms density found is plotted in figure 6(b). In order to determine the effective absorption length $l_{abs}(N)$, this density profile has to be integrated on the volume probed by the laser. For a given wavelength $\sigma$, the absorbance signal gathered by the FTS technique is:
$$
\begin{align}
\text{Abs}(\sigma) &= \frac{k(\sigma)}{x_0 y_0} \int_{d}^{d+x_0} \int_{-\frac{y_0}{2}}^{\frac{y_0}{2}} \int_{-\frac{L}{2}}^{\frac{L}{2}} n(x, y, z) dxdydz \nonumber \\
&= k(\sigma) n_0 \frac{R_0}{x_0 y_0} \int_{d}^{d+x_0} \int_{-\frac{y_0}{2}}^{\frac{y_0}{2}} \int_{-\frac{L}{2}}^{\frac{L}{2}} \frac{1}{\sqrt{x^2 + y^2 + z^2}} dxdydz \nonumber \\
&= k(\sigma) n_0 l_{\text{abs}}(N) \tag{21}
\end{align}
$$

where $x_0 = 2$ mm, $y_0 = 3$ mm and $L = 50$ mm are the dimensions of the volume probed by the laser beam and $d$ the distance between the edge of the hole and the laser beam, as defined in figure 6(a). The effective absorption length $l_{\text{abs}}(N)$ is then obtained by integrating numerically the triple integral and we get the following results for the three different hole radius considered in this study:

$$
\begin{align}
l_{\text{abs}}(N) &= 1.58 \text{ mm for } R_0 = 0.2 \text{ mm} \nonumber \\
&= 3.95 \text{ mm for } R_0 = 0.5 \text{ mm} \tag{22} \\
&= 7.90 \text{ mm for } R_0 = 1 \text{ mm}. \nonumber
\end{align}
$$

Using these values in equation (9), it yields $n_0$, the N atoms density at the frontier with the visible plasma, close to the area considered in the model.

### 3. Results and discussion

As a reminder, in this study, the discharge current was maintained at 1 mA for every condition and the gas temperature was assumed to be at $T_g = 470$ K. The range of parameters covered for the measurement of the density of Ar*, e and N may differ due to the time and diagnostic constraints. The input data of the model ($V_d$, $I_d$, P, %N₂, Hole diameter) are those gathered experimentally.

#### 3.1. Effect of the hole diameter

The first parameter studied was the hole diameter. Figure 7 shows the evolution of the N atom and Ar* densities, as a function of the hole diameter. The densities show a clear decrease when the hole diameter increases. At 0% N₂, the corresponding discharge voltage $V_d$ remains constant independently of the hole diameter, around 250 V. At 1% N₂, however, the discharge voltage increases with the hole diameter, from 700 V at 0.4 mm to 800 V at 2 mm, following the Paschen curve, and, thus, showing that the chemistry of the plasma changes drastically, even with very few N₂ admixed, as it is well documented in the literature [21, 33, 48]. The discharge power ($I_d \times V_d$) increases thus slightly with the hole diameter. However, the corresponding power density (($I_d \times V_d$)/V, V being the volume of the hole) inside the holes, plotted in figure 7 in blue squares, decreases. This leads to a less energetic plasma and lower excited species densities, explaining the trends observed in figure 7 for Ar* and N atoms. In this study, the electron density has not been measured as a function of the hole diameter. Nonetheless, the decrease of the electron density with the increase of the hole diameter has been previously reported.

For example, in helium in [49, 50], where, under the same conditions, the electron density becomes 1.5 times lower when the diameter increases from 0.3 to 1 mm. To optimize the dissociation of N₂ and the production of N atoms, a smaller hole diameter is thus desired, but this effect is limited by the recombination at the wall and by the constraints of the application (for instance, the gas flux through the hole for deposition processes).

#### 3.2. Effect of the gas pressure

Figure 8 shows the evolution of the N atom density, the Ar* density and the electron density as a function of the gas pressure in the reactor. In figure 8(a), one can observe that the density of N atoms increases with the pressure both in the model (solid black line) and in the experiments (purple dots). There is a reasonable agreement between the experiments and the model but this latter overestimates the N atoms density. The density of any species is expected to increase linearly with the pressure, without a modification of the production and loss scheme. However, figure 8(b) seems to show that the production and loss scheme changes. Indeed, in figure 8(b), we observe a decrease of the density of Ar* with the pressure predicted both by the experiments and the model. Figure 8(c) shows that the measured electron density increases slightly on the considered pressure range. The model does not deviate too much, with a small increase between 30 and 50 mbar, and a slight decrease between 50 and 80 mbar. Therefore, it seems that, at a higher pressure, the production of N atoms increases, consuming possibly Ar* through the reaction $Ar^m + N_2 \rightarrow N + N + Ar$ (R28), while the gain-loss balance of electrons remains similar.

To better understand these trends, we plotted in figure 9 the calculated relative contribution of the non-negligible processes of production of N atoms and loss of Ar* at 10% N₂. In figure 9(a), we can see that the model predicts that reaction R28 is the main production path of N atoms over the pressure range considered. We can observe that the contributions of the electron processes $e + N_2 \rightarrow N + N + e$ (R21) and $e + N_2^+ \rightarrow N + N$ (R31) are almost constant in the considered pressure range, which is consistent with the evolution of the electron density predicted by the model in figure 8(c). On the other hand, the contribution of $N_2(A) + N_2(A) \rightarrow N_2 + N + N$ (R58) is increasing with the pressure, explaining partially the increase of the N atoms density in figure 8(a). In figure 9(b), we can see that the model predicts a decrease with the pressure of the contribution to the loss of Ar* of the electron-impact reaction $e + Ar^m \rightarrow Ar^{4p} + e$ (R10) and a constant contribution of $e + Ar^m \rightarrow Ar^r + e$ (R9), while the contributions of R28 and R56 (which are superimposed) increase. It is, however, worth noting that R10 is not an effective loss process of Ar* since the produced Ar* rapidly decay back to the Ar* state through reaction R40.

To obtain a maximum N atom production, one should increase the gas pressure in the reactor. However, this will also lead to an increased breakdown voltage and thus an appropriate power supply is needed to provide higher electric power.
<figure><img src="image_115.png" /><figcaption>**Figure 7.** Experimental densities of (a) N atoms (purples circles) and (b) Ar\* (red circles), and associated power densities in the hole (blue squares) for three hole diameters. P = 50 mbar, I\_d = 1 mA.</figcaption></figure>

<figure><img src="image_116.png" /><figcaption>**Figure 8.** Experimental densities of (a) N atoms, (b) Ar\* and (c) e as a function of the gas pressure. The corresponding calculated densities are also plotted (solid lines). Hole diameter = 0.4 mm, I\_d = 1 mA.</figcaption></figure>

### 3.3. *Effect of the gas mixture*

Figure 10 represents the densities of N atoms, Ar\* and e as a function of the percentage of N₂ into the gas mixture. When adding N₂ in the gas mixture, the density of N atoms greatly increases (figure 10(a)), but not linearly as it would

be expected from the effect of the added N₂ only. The 0D model depicts a different trend, with a maximum of density reached around 10% of N₂. At the same time, the density of Ar\* decreases (figure 10(b)), but, again, not linearly as it would be expected from the removal of Ar in the gas mixture. This suggests a modification of the dominating production paths of
<figure><img src="image_117.png" /><figcaption>**Figure 9.** Calculated relative contributions of the non-negligible processes of (a) N atom production and (b) Ar<sup>m</sup> loss, as a function of the gas pressure. Hole diameter = 0.4 mm, *I*<sub>d</sub> = 1 mA, 10% N<sub>2</sub>.</figcaption></figure>

<figure><img src="image_118.png" /><figcaption>**Figure 10.** Experimental densities of (a) N atoms, (b) Ar\* and (c) e as a function of the percentage of N<sub>2</sub> in the gas mixture. The corresponding calculated densities are also plotted (solid lines). Hole diameter = 0.4 mm, *P* = 50 mbar, *I*<sub>d</sub> = 1 mA.</figcaption></figure>

N atoms. In figure 10(c), we can see that the measured electron density remains almost constant between 0% and 20% of N<sub>2</sub>, and then drops by one order of magnitude between 20% and 40% of N<sub>2</sub>. Beyond this percentage, we reach the detection limit of the method. The experimental decrease of

the electron density is well captured by the model but not the plateau between 0% and 20% of N<sub>2</sub>.

To better understand how the production scheme of N atoms is modified by the content of N<sub>2</sub> in the gas mixture, figure 11 shows the calculated relative contributions of the
<figure><img src="image_119.png" /><figcaption>**Figure 11.** Calculated relative contributions of the non-negligible processes of (a) N atom production and (b) Ar<sup>m</sup> loss, as a function of the percentage of N<sub>2</sub> in the gas mixture. Hole diameter = 0.4 mm, P = 50 mbar, I<sub>d</sub> = 1 mA.</figcaption></figure>

non-negligible production processes of N atoms and loss pro-
cesses of Ar<sup>m</sup>. In figure 11(a), we can see that, at very low N<sub>2</sub>
percentages, the dissociative electron-ion recombination with
N<sub>2</sub><sup>+</sup> (R31) is the main production path of N atoms. The contri-
bution of R31 decreases rapidly when few more N<sub>2</sub> is added
(4% of N<sub>2</sub> has already a drastic effect). This decrease is related
to the drastic drop of the electron density shown in figure 10(c).
The dissociation of N<sub>2</sub> by the metastable argon atoms then
becomes dominant between 5% and 55% of N<sub>2</sub> through reac-
tion Ar<sup>m</sup> + N<sub>2</sub> → N + N + Ar (R28). This matches the exper-
imental data of figure 10(b) where the density of Ar<sup>m</sup> drops
when more N<sub>2</sub> is added. The contribution of the dissociation
of N<sub>2</sub> by the electrons through e + N<sub>2</sub> → N + N + e (R21)
becomes comparable to R28 around 55% of N<sub>2</sub> and then dom-
inant at higher N<sub>2</sub> fraction. As displayed in figure 11(b), at
low N<sub>2</sub> fraction, the metastable argon atoms are mainly lost
through the electron-impact reactions e + Ar<sup>m</sup> → Ar<sup>r</sup> + e (R9)
and e + Ar<sup>m</sup> → Ar<sup>4p</sup> + e (R10). Then, as the electron dens-
ity decreases, the contribution of these two reactions decreases
and, between 30% and 40% of N<sub>2</sub>, becomes comparable to the
contribution of the quenching reactions R28 and N<sub>2</sub> + Ar<sup>m</sup>
→ N<sub>2</sub>(C) + Ar (R56), which are the dominant loss processes
of Ar<sup>m</sup> at high N<sub>2</sub> fraction. The increase of the N<sub>2</sub>(C) vibra-
tional temperature that is expected from R56 has been meas-
ured by our team in a similar discharge [51]. The decrease
of both the electron and Ar<sup>*</sup> densities is the reason why the
model predicts a decrease of the N atoms density when the N<sub>2</sub>
percentage increases (see figure 10(a)), which is not observed
experimentally.

Concerning the density of Ar* presented in figure 10(b), its
decrease is well captured by the model for N₂ fractions higher
than 10%, but it is not the case for the strong experimental
variation of the density at low N₂. Moreover, the values of the
density predicted by the model are slightly higher than those
experimentally measured, as it is also the case for the atomic
nitrogen density. This overestimation of the densities by the
global model can be partially explained by the fact that the
electron energy distribution function (EEDF) is considered as
Maxwellian, which is a reasonable hypothesis in pure argon,
but it has been recently shown in the literature that the EEDF

in Ar/N₂ mixture is not a 'Maxwellian-like', exhibiting rather
a strong depress at high excitation energy [52].

3.4. N₂ dissociation rate

As the absolute density of N atoms is an important para-
meter for many applications, it is interesting to visualize
the efficiency of our discharge at dissociating N₂ molecules.
Figure 12 sums up the evolution of the dissociation rate of N₂
as a function of the gas mixture and the pressure. The dissoci-
ation rate is defined as N<sub>N</sub>/2N<sub>N2</sub>. The evolution of the dissociation
rate with the gas pressure and mixture does not change when
the hole diameter varies. Hence, only the values for the lowest
diameter (0.4 mm), where the dissociation is the greatest, have
been plotted.

The measured dissociation rate reaches a few 0.1%, which
is lower than what is found in the literature, with dissociation
rates of a few percents [53], up to 10% [18]. Dissociation could
be further optimized using a pulsed discharge, as it has been
shown to yield greater electronic densities [15]. Note that the
experimental decrease of the dissociation rate with the N₂ frac-
tion is well captured by the global model. The larger calcu-
lated dissociation rate is related to the larger N atoms density
predicted by the model compared to that measured by FTS
absorption.

In figure 12(a), one can observe that the N₂ dissociation rate
rapidly drops when more N₂ is added to the discharge, from
0.73% to 0.06%. However, we have seen in section 3.3 that
this does not translate into a decrease of the N atom density
since more N₂ is added. We have seen that the dissociation of
N₂ by Ar* (R28), which is dominant between 5% and 55% of
N₂ in the gas mixture, and by electrons (R21), which is dom-
inant at high N₂ fraction, allow a decent dissociation rate to
be maintained and a greater N atom density to be achieved
(figure 10(a)). However, R28 does not seem to be efficient
at low N₂ percentage, as the question was raised in [54], and
is negligible compared to the dissociative electron-ion recom-
bination (R31) in our study. In the model, the contribution of
(R28) and (R21) is counterbalanced by the decrease of the
<figure><img src="image_120.png" /><figcaption>**Figure 12.** Experimental dissociation rates (blue circle) and the corresponding calculated rates (solid line) as a function of (a) the gas mixture (at *P* = 50 mbar) and (b) the gas pressure (at 20% N₂). Hole diameter = 0.4 mm, *I*<sub>d</sub> = 1 mA.</figcaption></figure>

electron and Ar\* densities beyond 10% of N₂, leading to a decrease of the N atom density, but this is not measured experimentally. As a perspective, a more detailed study above 80% of N₂ would be very interesting to verify if a drop of the N atoms density appears and find the optimal amount of argon admixture in a nitrogen discharge.

Figures 12(a) and (b) show that the effect of the pressure on the N₂ dissociation rate is much lower than the effect of the gas mixture. However, we can see that the experimental dissociation rate remains constant between 30 and 50 mbar, before slightly increasing at 80 mbar. This is due to the fact that the N atom density increases faster than the increase of N₂ density due to the pressure increase. It should be checked if this effect persists at different N₂ percentages in the gas mixture, when other N atom production reaction dominate.

To optimize the production of N atoms, the experimental data show that a high pressure and high percentage of N₂ is desirable. Nonetheless, we have also noticed that in these conditions, the discharge is less stable and requires a higher electric power from the power supply to operate. This influence the final operating parameters chosen for different applications.

## 4. Conclusion

In this paper, a MHCD was thoroughly studied by coupling advanced experiments with a 0D volume-averaged model. This study is a step toward the implementation of this plasma source in PECVD reactors and the optimization of the production of nitrogen atoms for nitride deposition on large surfaces. Although the plasma is generated in a small hole, it was demonstrated that it is possible to increase the plasma volume and, thus, the deposition area by: (i) arranging several MHCDs in arrays and (ii) putting a third electrode few centimeters away from the MHCD structure to expand the discharge from the holes to the polarizable substrate [1, 51]. The reactive species for the deposition process (in particular nitrogen atoms) are produced in the MHCD hole and that is why it is necessary to understand the fundamental physics of the discharge in this region to optimize the process.

The MHCD was ignited by a DC power supply and operated in the normal regime, in an Ar/N₂ gas mixture. In various experimental conditions, the densities of Ar\* and N atoms were determined by absorption spectroscopy (TDLAS and FTS VUV measurements, respectively) and the electron density was obtained by means of high-resolution OES. Coupled with a 0D model, these results allow for a better comprehension of the multiple processes involved in the atomic nitrogen production in the MHCD and how it could be optimized to provide efficient nitrogen plasma sources for thin nitride film deposition at lower temperature than conventional CVD. The comparison between the experimental results and the 0D model shows a reasonable agreement with well-captured trends for the different densities but with calculated values of atomic nitrogen and argon metastable atoms densities higher than those given by the experiments. This can be partially explained by the fact that the EEDF is considered as Maxwellian, which is a reasonable hypothesis in pure argon, but it has been recently shown in the literature that the EEDF in Ar/N₂ mixture is not a 'Maxwellian-like', exhibiting rather a strong depress at high excitation energy.

We have found that a smaller hole of the MHCD increases the densities of species, by increasing the power density in the hole. In nitrogen-containing gas mixtures, the applied power to the MHCD is lowered by using a smaller hole, but the power density still rises as well as the density of excited species. It is possible to produce more N atoms by working at a higher pressure, while the Ar\* atoms are lost, which could indicate that Ar\* is consumed by the dissociation of N₂. A study of the influence of the gas mixture showed that Ar\* compensates the drop of the electron density in gas mixtures between 5% and 55% of N₂, maintaining some dissociation and yielding a still increasing density of N atoms thanks to the added N₂. A complementary study is needed to check if this effect is maintained for Ar/N₂ gas mixtures with more than 80% of N₂.

## Data availability statement

All data that support the findings of this study are included within the article (and any supplementary files).
## Acknowledgments

This work was supported by the French Research National Agency (ANR) through the DESYNIB Project (ANR-16-CE08-0004 JCJC) and the Labex SEAM. The authors would like to thank Pascal Chabert and Olivier Guaitella for useful discussions on this work.

## ORCID iDs

Alice Remigy https://orcid.org/0000-0003-2743-2981

Kristaq Gazeli https://orcid.org/0000-0002-5479-0373

João Santos Sousa https://orcid.org/0000-0002-6438-7940

Nelson De Oliveira https://orcid.org/0000-0001-7828-7206

Claudia Lazzaroni https://orcid.org/0000-0003-0966-560X

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# Absolute N-atom density measurement in an Ar/N₂ micro-hollow cathode discharge jet by means of ns-two-photon absorption laser-induced fluorescence

Cite as: Phys. Plasmas **29**, 113508 (2022); doi: 10.1063/5.0110318

Submitted: 15 July 2022 · Accepted: 11 October 2022 ·

Published Online: 8 November 2022

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A. Remigy, X. Aubert, S. Prasanna, K. Gazeli, L. Invernizzi, G. Lombardi, and C. Lazzaroni<sup>a)</sup>

## AFFILIATIONS

Laboratoire des Sciences des Procédés et des Matériaux, LSPM, CNRS, Université Sorbonne Paris Nord, UPR 3407, F-93430, Villetaneuse, France

<sup>a)</sup>Author to whom correspondence should be addressed: claudia.lazzaroni@lspm.cnrs.fr

## ABSTRACT

In this work, nanosecond two-photon absorption laser-induced fluorescence (TALIF) is used to probe the absolute density of nitrogen atoms in a plasma generated using a micro-hollow cathode discharge (MHCD). The MHCD is operated in the normal regime, and the plasma is ignited in an Ar/N₂ gas mixture. First, we study a MHCD configuration having the same pressure (50 mbar) on both sides of the electrodes. A good agreement is found between the density of N atoms measured using TALIF in this work and previous measurements using vacuum ultraviolet Fourier transform absorption spectroscopy. Then, we introduce a pressure differential between the two electrodes of the MHCD, creating a plasma jet. The influence of the discharge current, the percentage of N₂ in the gas mixture, and pressures on both sides of the MHCD is studied. The current has a small impact on the N-atom density. Furthermore, an optimal N-atom density is found at around 95% of N₂ in the discharge. Finally, we demonstrate that the pressure has a different impact depending on the side of the MHCD: the density of N atoms is much more sensitive to the change of the pressure in the low-pressure side when compared to the pressure change in the high-pressure side. This could be due to several competing phenomena: gas residence time in the cathodic region, recirculation, or recombination of the N atoms at the wall. This study contributes to the optimization of MHCD as an efficient N-atom source for material deposition applications.

Published under an exclusive license by AIP Publishing. https://doi.org/10.1063/5.0110318

## I. INTRODUCTION

Nitrogen is a crucial atom in many material deposition applications, from III-V nitride semiconductors such as GaN, AlGaN, or InGaN,¹⁻³ used in microelectronics and photonics,⁴,⁵ to nitrogen-doped diamond and NV centers for quantum application,⁶ and hexagonal boron nitride (h-BN) as a substrate for graphene-based technologies.⁷,⁸ Synthesis of such materials requires sources of nitrogen (N) atoms that can produce high densities over large surfaces, most of the time at low pressure to promote surface mobility at the substrate where the growth occurs. To do so, many different plasma configurations have been used, for instance, microwave plasma,⁹ inductively coupled plasma,¹⁰ ECR plasma,¹¹ or radio frequency plasma.¹² Although that these sources allow for large plasma volumes to be produced, they operate at a rather high power of at least few hundred watts. On the opposite, microplasmas, which are usually defined as plasmas with at least one dimension

lower than 1 mm, have attracted a lot of attention¹³,¹⁴ as they can be generated at much lower powers (1 W), and provide high electron density and, thus, rich chemical reactivity, while maintaining the plasma volume at the microscale level. Micro-hollow cathode discharges (MHCD) represent a particular geometry of microplasmas, in which a hole of a few hundred micrometers in diameter is drilled through an electrode–dielectric–electrode structure.¹⁵ When supplied with a simple DC power, a plasma ignites in the hole and can be sustained in different regimes depending on the discharge current.¹⁶ At low current (typically 0.1–0.5 mA), even if the discharge is DC power driven, an unstable and oscillating regime appears (self-pulsing regime), which leads to pulsed discharge voltage and current signals. At higher current (>1 mA), however, the plasma becomes stable, with continuous voltage and current, and it expands on the cathodic surface (normal regime). This plasma source has been shown to produce high electron densities¹⁷,¹⁸
(up to $10^{22} m^{-3}$) and high density of N atoms (up to few $10^{19} m^{-3}$ in the normal regime¹⁹). Typically, the plasma volume generated by MHCD is confined in a micro-metric hole. To implement it in applications requiring large plasma volumes, it is possible to achieve the generation of a large afterglow discharge, which makes the MHCD a versatile plasma source. The plasma volume of MHCDs can be extended using different techniques: creating a plasma jet,²⁰ using an array of MHCDs,²¹ and even using a third electrode to expand the plasma outside the hole, which is known as the micro-cathode sustained discharge (MCSD).²²,²³ The latter solution has been successfully used to produce h-BN films over 2-in.-diameter substrates.²⁴ When targeting nitride deposition, precise measurements of the N atoms density in these discharges are needed. However, the characterization of such plasmas is challenging due to their small dimensions, which demands nonintrusive techniques with high spatial resolution. The ground state of atomic nitrogen ($2p^3$) $^4S_{3/2}$ is only accessible in the vacuum ultraviolet (VUV) range, which can be probed using absorption spectroscopy, but it requires a UV radiation source and vacuum environment. To circumvent the need for VUV facilities, two-photon absorption laser-induced fluorescence (TALIF) was introduced and successfully used to probe the density of N atoms in various plasma sources.²⁵,²⁶ TALIF is a highly sensitive technique with a very good spatial and temporal resolution.

In this paper, we report on TALIF measurements of the N atoms density in a MHCD-generated plasma operated in the normal regime in a gas mixture of argon (Ar) and molecular nitrogen ($N_2$). The addition of small quantities of argon to the discharge may enhance the dissociation of $N_2$ and increases the lifespan of the MHCD device. The MHCD is first studied without a pressure differential, to compare with a previous study of the N atoms density performed using absorption spectroscopy.¹⁹ We then introduce a pressure differential to increase the plasma volume, which is useful when targeting an application of the MHCD source in material deposition. Here, we study the impact of the introduction of this pressure differential on the production of N atoms. The impact of the gas mixture, the discharge current, and

variation of the pressure differential on the production and propagation of N atoms is also studied. Section II describes the plasma reactor and the TALIF experimental setup used to characterize it. Section III explains the methodology used to perform quantitative measurements of the N atoms absolute density in the plasma. The parametric study and discussion are presented in Sec. IV, while Sec. V closes the paper with the conclusion.

## II. EXPERIMENTAL SETUP

### A. Plasma source

A scheme of the MHCD studied in this work is illustrated in Fig. 1(a). It consists of an assembly of a 750-µm-thick alumina ($Al_2O_3$) dielectric plate, in between two 100-µm-thick molybdenum (Mo) electrodes. This assembly is glued with a heat-resistant epoxy glue, and then, laser pierced with a 400-µm-diameter hole. The source is placed at the junction of the two chambers of a reactor, as represented in Fig. 1(b). A pipe with a valve links the two chambers, allowing them to operate either at the same pressure (when the valve is open), or with a pressure differential (when the valve is closed). Using two gas flowmeters, an Ar/$N_2$ gas mixture is injected in the upstream chamber, and a primary pump with a manual valve is installed in the downstream chamber. The pressure of both chambers can be regulated by adjusting the gas fluxes delivered by the flowmeters and the pumping using the manual valve.

To ignite the plasma, a negative DC power supply (0–2000 V) is used. A negative high voltage is applied to the cathode in the upstream chamber, while the anode (downstream chamber) is grounded. When a pressure differential is set between the two chambers, a plasma jet appears on the anodic side, as depicted in Fig. 1(b) and visible in the photograph of Fig. 1(c).

A ballast resistor $R_b = 480 kΩ$ is connected between the power source and the cathode to limit the discharge current $I_d$. The discharge voltage $V_d$ is monitored using a voltage probe placed after $R_b$. Between the anode and the ground, a small resistor $R_m = 180 Ω$ is used to

<figure><img src="image_124.png" /><figcaption>**FIG. 1.** Scheme of (a) the MHCD configuration and (b) the reactor used in the experiments. $R_b = 480 kΩ$, $R_m = 180 Ω$, HV = High Voltage. The cathode is on the left, where a negative high voltage is applied and the anode, on the right, is grounded. (c) Photograph of the plasma jet. Conditions: 80% $N_2$, $I_d = 1.6 mA$, $P_1 = 30$, $P_2 = 10 mbar$, gas flux = 36 sccm.</figcaption></figure>
measure the discharge current. Another voltage probe measures $V_b$ that is, the voltage across $R_{m}$, which can then be used to calculate the corresponding discharge current. The pair ($V_{d}$, $I_{d}$) is defined by the plasma conditions and, thus, $V_{d}$ and $I_{d}$ cannot be set independently. In this study, we use the current $I_{d}$ as a reference and the corresponding discharge voltage $V_{d}$ is defined by the plasma conditions. In the range of electrical conditions covered here, the MHCD is operating in the normal regime with continuous discharge current and voltage signals.

## B. TALIF diagnostic setup

The density of N atoms produced by the plasma source investigated in this study is evaluated using a ns-TALIF setup, described hereafter, and applied in a large range of plasma conditions. The $\bar{x}$ and $\bar{y}$ axis vectors used to determine the position at which the measurements are done are represented in Fig. 1(b). To perform spatial measurements, the reactor is placed on a test bench as represented in Fig. 2 (see Secs. II B 1 and II B 2 for a more detailed description). The reactor is equipped with two fused silica windows, providing a 90% transmission at 205 nm, so that the laser radiation can reach the plasma. The fluorescence is collected perpendicularly to the laser line-of-sight through a borosilicate window.

### 1. Laser system

The ns-TALIF setup is represented in Fig. 2. The laser used is a tunable dye laser (Sirah Lasertechnik Cobra-Stretch) pumped by the

second harmonic of a 500 mJ/pulse Nd:YAG laser (Spectra Physics Quanta-Ray Lab-Series 170–01). The Nd:YAG laser pulses at 10 Hz and provides a pulse with a width of 7 ns measured by means of the photodiode PD1. Two $\beta$-barium borate (BBO) crystals process the dye laser beam in the frequency conversion unit (FCU) to yield a three-harmonic laser beam. These harmonics are separated using two fused silica Pellin–Broca prisms, to spatially select the third harmonic, which is used in our experiments. Its wavelength can be tuned between 204 and 207 nm, and has a typical energy of 2.5 mJ/pulse. The visible harmonic of the beam coming out of the FCU is directed toward an iodine cell ($I_2$ cell). The laser wavelength is systematically calibrated using the known absorption profile of the cell as a function of the laser wavelength. The UV-C beam obtained is directed toward the reactor using a periscope and focused at the center of the reactor using a 35 cm-focal length lens. When exiting the reactor, the laser beam is collimated onto a calorimeter (Coherent J-10MB-LE), which is connected to an oscilloscope (Lecroy WaveJet 354-A, 500 MHz, 2 GS/s) in order to record the laser energy. It was verified that the absorption of the laser by the plasma is negligible beforehand, with no difference on the energy measured with and without plasma. That is due to the small cross section of the two-photon absorption process. More so than the plasma, the optical windows of the reactor do absorb a part of the laser radiation. The energy of the laser beam in the reactor is calculated from the energy measured outside the reactor by considering the transmittance of the optical windows. The laser focal spot size can be calculated from its wavelength and the characteristics of the optics.²⁷ With a beam diameter before the lens of 5 mm, the minimum waist of

<figure><img src="image_125.png" /><figcaption>FIG. 2. Experimental setup of the TALIF measurements. Solid lines represent laser radiation, dashed lines represent electric signals, and dotted lines represent fluorescence emission. FCU: frequency conversion unit.</figcaption></figure>
the laser is calculated to be of 5 µm. The Rayleigh length is 300 µm. The volume of interaction between the laser and the plasma, from which the fluorescence is coming, can be approximated by a 14-µm-diameter cylinder and a 600-µm-long cylinder.

## 2. Fluorescence collection system

Once excited by the laser, the N atom will de-excite emitting a fluorescence signal that is collected by means of a gated photomultiplier tube (PMT; Hamamatsu H11526-20-NF). The fluorescence is imaged onto a slit fixed in front of the PMT using a 10-cm-focal-length lens in a 4f configuration (see Fig. 2). A 600-µm horizontal slit limits the background noise, and a bandpass filter selects the appropriate wavelength range of the fluorescence. This configuration allows for a better TALIF signal-to-noise ratio (SNR) to be achieved by limiting the background noise collected by the PMT. Because the size of the collection optic is much larger than that of the laser spot size, the spatial resolution of the technique is determined by the laser spot size.

To synchronize the laser pulse that induces the fluorescence with the gated PMT, the system is triggered using the visible part of the dye laser beam. It is directed onto a Thorlabs SM05PD2A photo-diode (PD1 in Fig. 2), which is connected to a Rohde and Schwartz RTO 1044 oscilloscope (4 GHz, 20 GS/s). The oscilloscope then produces a 1 ms signal, long enough to trigger a multi-function I/O device (National Instruments USB 6343, 1 MHz, 500 kS/s). This is used because the ns signal from the laser would have been too short. In turn, the device generates the triggers for the PMT. Taking in consideration the response time of all the devices and the length of the cables, the global response time of the system is of about 200 ns. This latter, in addition to the 1 ms signal mentioned before, imposes that two laser pulses are necessary to perform TALIF measurements. The first pulse triggers the collection system, and the second one generates the fluorescence signal that is actually recorded. The appropriate delay is thus imposed between the triggering laser shot and the 5 µs gate of the PMT.

The control of the whole platform, including the laser and collection system, as well as the signal acquisition and data processing, is done using a dedicated LabVIEW™ program. For each measurement, by changing the laser frequency, we scan the absorption line around its central frequency (206.67 nm for nitrogen and 204.13 nm for krypton). At each laser frequency, we record the time-resolved fluorescence signal generated by the laser radiation at frequency $v_b$, the laser pulse energy $E_b$, and the iodine fluorescence signal, which is needed for wavelength calibration.

# III. DETERMINATION OF THE ABSOLUTE N-ATOM DENSITY USING ns-TALIF

## A. N atoms density calibration using krypton gas

To perform quantitative measurements of atomic densities using TALIF, a calibration technique using a noble gas, which was first introduced by Goehlich et al.,²⁸ has been widely used in the literature.

This method is based on the comparison of TALIF measurements performed in a noble gas with a known density, and those referring to an atomic species of interest. The TALIF excitation schemes of those two species must be as close as possible in terms of laser excitation and emitted fluorescence wavelengths. In this way, there is a negligible difference between the laser setup and fluorescence collection optics

between the two measurements. In the case of N atoms, krypton (Kr) gas is well suited and typically used for calibration purposes.²⁹,³⁰,⁶²

Figure 3 shows the two excitation schemes used for Kr and N. In the following, the ground states of nitrogen (2p³)⁴S⁰ and krypton (4p⁶)¹S₀ are referred to as N and Kr, respectively, while the laser-excited states of nitrogen (3p)⁴S⁰ and krypton (5p') [3/2]₂ are denoted with N⁺ and Kr⁺, respectively. For nitrogen, the de-excitation to the states (2s)⁴P⁰ and 1/2;3/2;5/2 produces three fluorescence lines at 742.364, 744.230, and 746.831 nm that are all collected by the PMT. The de-excitation of Kr⁺ to the state (5s) [3/2]₁ produces two lines at 587.09 and 826.32 nm, with a known ratio between them. We used the line at 587.09 nm to capture the fluorescence signal of Kr, since the 826.32 nm line may contain radiation emanating from other excited states. In the case where the laser-atom interaction is dominated by the two-photon absorption, the density of the N⁺ (or Kr⁺) state is related to the offset frequency $\delta v_A = 2v_l - v_A$, where $v_l$ and $v_A$ are the laser central frequency and the absorption line central frequency for an atom A = N or Kr, respectively.

The relation between the known density of krypton $n_{Kr}$ and the density of the ground state of atomic nitrogen $n_N$ is as follows:³⁰

$$n_N = \frac{\eta_{Kr}}{\eta_N} \frac{T_{Kr} A_{Kr,5p \to 5s}}{T_N \sum_{i=1}^{3} A_{N,i,3p \to 3s}} \frac{\sigma_{Kr}^{(2)} \tau_{Kr^+}}{\sigma_N^{(2)} \tau_{N^+}} \frac{\int_{\delta v_N = -\infty}^{\delta v_N = \infty} d\Psi_N}{\int_{\delta v_{Kr} = -\infty}^{\delta v_{Kr} = \infty} d\Psi_{Kr}} n_{Kr}, \quad (1)$$

where $\eta_{Kr}$ and $\eta_N$ are the sensitivity of the PMT over the spectral range of the fluorescence signal of krypton and nitrogen, respectively; $T_{Kr}$ and $T_N$ are the transmittance of the optics used for collecting the fluorescence signal of krypton and nitrogen, respectively; $A_{Kr,5p \to 5s}$ is the radiative decay rate (s⁻¹) for the Kr 5p → 5s transition measured; $A_{N,i,3p \to 3s}$ is the radiative decay rate (s⁻¹) of the i-th radiative de-excitation process for the N 3p → 3s transition observed; $\sigma_{Kr}^{(2)}$ and $\sigma_N^{(2)}$ are the two-photon excitation cross section (m⁴); and $\tau_{Kr^+}$ and $\tau_{N^+}$ are the fluorescence decay times, that is, the lifetimes of the Kr⁺ and N⁺ states, respectively, in the conditions of our experiments. d $\Psi_N$ and d $\Psi_{Kr}$ are the ratio number of detected fluorescence photons during dt

<figure><img src="image_126.png" /><figcaption>FIG. 3. Two-photon excitation and fluorescence scheme of nitrogen and krypton atom.</figcaption></figure>
to the square number of laser photons for a given laser central frequency $\nu_l$ (corresponding to an offset frequency $\delta\nu_A$). They are then integrated over the whole laser frequency domain.

Bisceglia et al.³⁰ refer to Eq. (1) as the full excitation method (FEM) since it requires recording the full line profile for each density measurement, which takes a significant amount of time (70 points are needed to properly resolve the line profile). To reduce the acquisition time, Bisceglia et al.³⁰ suggest to experimentally determine the factor $g(\delta\nu_A)d(\delta\nu_A)$, $g(\delta\nu_A)$ being the statistical overlap factor between the atom absorption line and the normalized laser line. Thus, the product $g(\delta\nu_A)d(\delta\nu_A)$ represents the fraction of the laser energy that is actually used to excite the atoms, and its integral over the line is equal to 1. It depends on the line profiles of the laser and the absorption, which are both Gaussian in our case with full width at half maximum (FWHM) $\Delta\nu_l$ and $\Delta\nu_A$, respectively, and can be expressed by

$$g(\delta\nu_A)d(\delta\nu_A) = \frac{d\Psi_A}{\int_{\delta\nu_A=-\infty}^{\delta\nu_A=\infty} d\Psi_A} = \frac{\sqrt{4\ln 2/\pi} e^{-4\ln 2} \left(\frac{\nu_A}{\Delta\nu_A^{\text{eff}}}\right)^2}{\Delta\nu_A^{\text{eff}}} d(\nu_A), \quad (2)$$

where $\Delta\nu_A^{\text{eff}} = \sqrt{2\Delta\nu_l^2 + \Delta\nu_A^2}$ is the effective FWHM experimentally obtained from the line profile. We measured this effective FWHM over a wide range of plasma conditions, and it was found to be of about 9.6 pm with a standard variation of only 0.8 pm. This is due to the fact that the effective broadening is largely dominated by the laser broadening, typically of 8 pm,³⁰ which is much larger than what is reported in the literature (1.06 pm in Ref. 31 and 1.53 pm in Ref. 32).

This result means that we can accurately use the peak excitation method (PEM) described by Bisceglia et al.³⁰ The full line profile and its integration $\int_{\delta\nu_A=-\infty}^{\delta\nu_A=\infty} d\Psi_A$ can be measured only once to determine the value of $g(\delta\nu_A)$. The density of N atoms can then be determined using a single laser shot at the central frequency $\nu_A$, according to the equation³⁰

$$n_N = \frac{\eta_{Kr}}{\eta_N} \frac{T_{Kr} A_{Kr,5p \to 5s}}{T_N \sum_{i=1}^{3} A_{N,i,3p \to 3s}} \frac{\sigma_{Kr}^{(2)} \tau_{Kr^*}}{\sigma_N^{(2)} \tau_{N^*}} \frac{d\Psi_N}{d\Psi_{Kr}} \frac{g(\delta\nu_{Kr})}{g(\delta\nu_N)} n_{Kr}. \quad (3)$$

The calculation of the uncertainty on the density of nitrogen is done using the propagation of uncertainties of the independent variables.³⁰,³³ In the following, this will be referred to as the total uncertainty. It takes into account all of the uncertainty sources, as calculated in Ref. 30. The most significant uncertainty comes from the poor knowledge of the ratio of the two-photon absorption cross sections $\sigma_{Kr}^{(2)}/\sigma_N^{(2)}$, which leads to an error of about 60% on the absolute density of the N atoms.

Nonetheless, it is worth noticing that the total uncertainty can be divided into two contributions: a systematic and a random uncertainty. Sources of a systematic error on the absolute density determination are the ratio of the two-photon absorption cross sections mentioned above, the Einstein coefficients ($A_{Kr,5p \to 5s}$ and $A_{N,i,3p \to 3s}$), and the transmittance of the optics ($T_{Kr}$ and $T_N$) and the sensitivity of the photomultiplier ($\eta_{Kr}$ and $\eta_N$) for which the error is gathered from the manufacturer data sheets. On the opposite, the TALIF integrals

($d\Psi_N$ and $d\Psi_{Kr}$), the fluorescence lifetimes ($\tau_{Kr^*}$ and $\tau_{N^*}$), and the FWHM ($\Delta\nu_A$) used for the determination of $g(\delta\nu_A)$ are all sources of a random error. The repeatability of the discharge will also contribute to this random uncertainty on the measured density of N atoms. The random uncertainty can be estimated by repeating the same measurement several times. In this work, it is found to be of up to 30%, the worst cases being when the discharge is the most unstable and the density the lowest. In the following, it is referred to as the repeatability uncertainty.

## B. TALIF measurements validity verification

The hereinabove discussion and the validity of Eq. (3) on the determination of the N atoms density rely on the assumption that the laser-atom interaction is dominated by the two-photon laser absorption. Several phenomena can occur if the laser instantaneous and local power density are too high, such as photo-ionization, photo-dissociation, and stimulated emission.²⁷,³⁴

To make sure that these conditions are fulfilled, one can use the power dependence (PD) factor.³⁵ The PD factor is the slope obtained from the linear fit of the log-log plot of the integral of the TALIF signal vs the laser energy. When the two-photon laser absorption dominates over the other phenomena, the PD factor has a value of about 2.

In this work, we varied the laser energy using neutral density filters placed on the path of the laser beam, before the reactor, and measured the corresponding TALIF signal. Figure 4 shows the log-log plot of the integral of the TALIF signal as a function of the laser energy, for both Kr and N atoms. The corresponding linear fits are also plotted giving a PD factor of 1.91 for Kr and 2.03 for N. It shows that the laser-atom interaction is dominated by the two-photon absorption and, thus, Eq. (3) can be used for the determination of the absolute density of N atoms in the discharge in this laser energy range.

<figure><img src="image_127.png" /><figcaption>FIG. 4. Time-integrated TALIF signal as a function of the laser energy for Kr (red circles) and N (blue squares) along with associated linear fits. Error bars are obtained from the non-linear fitting procedure used to calculate the integral of the TALIF signal.³⁰</figcaption></figure>
<figure><img src="image_128.png" /><figcaption>FIG. 5. Sample raw PMT signal (solid blue) in V as a function of time (s) and associated fit used to integrate the signal (dashed red). Plasma conditions: P = 50 mbar in both chambers, 80% N₂/20% Ar, I<sub>d</sub> = 1 mA.</figcaption></figure>

### C. Fluorescence lifetime and quenching rate

From Eq. (3), one can see that the precise knowledge of the radiative lifetimes $\tau_{Kr^*}$ and $\tau_{N^*}$ of the excited states Kr* and N*, respectively, as well as the associated quenching coefficients, is critical for reliable quantitative measurements of the N atom density. Some of the data are available in the literature referring to pure nitrogen environments, but the quenching coefficient of N* in an Ar/N₂ mixture is not measured, which motivated our study. The accurate measurement of the N* atoms lifetime is limited by the duration of our laser pulse, which is 7 ns long. Indeed, TALIF measurements are difficult in conditions where the fluorescence lifetime is shorter than the laser pulse duration. In this case, the use of picosecond or femtosecond lasers can be a better solution.²⁷,³⁶,³⁷

For the krypton gas, we performed calibration measurements at a pressure of 1 mbar and measured a lifetime of 30.3 ± 1.8 ns. This value is higher than 28.5 ns, which is the one obtained when computing the Kr* radiative lifetime from the Einstein coefficient recommended by the NIST database,³⁸ but lower than 34.1 ns,²⁹ which is traditionally used in various TALIF diagnostics. At 1 mbar, we can thus consider the quenching of the Kr* atom to be negligible and the fluorescence decay time $\tau_{Kr^*}$ is equal to the radiative lifetime of the Kr* state.

For nitrogen atom, Fig. 5 shows a typical fluorescence signal. Fitting the exponential decay of the PMT signal yields the time

constant $\tau_{N^*}$ of the fluorescence decay, that is, the decay of the population of the upper state N*.

The effective time constant for the fluorescence $\tau_{N^*}$ is a result of two factors:

* The natural radiative de-excitation of the excited level, with a time constant $\tau_{r,N^*} = \frac{1}{\sum_{i=1}^{3} A_{N,i,3p \to 3s}}$, where $A_{N,i,3p \to 3s}$ is the Einstein coefficient of the i-th radiative de-excitation process.

* The quenching rate Q of N* atoms by both N₂ molecules and Ar atoms.

Hence, the effective decay rate $1/\tau_{N^*}$ is expressed by

$$ \frac{1}{\tau_{N^*}} = \frac{1}{\tau_{r,N^*}} + k_{qN_2} [N_2] + k_{qAr} [Ar] \\ = \frac{1}{\tau_{r,N^*}} + P \times \frac{10^{-4}}{k_B T} \times [k_{qN_2} x_{N_2} + k_{qAr} (1 - x_{N_2})], \quad (4) $$

where $k_{qN_2}$ and $k_{qAr}$ are the quenching rates of N* by N₂ and Ar, respectively, in cm³ s⁻¹; [N₂] and [Ar] are the densities of N₂ and Ar, respectively, in cm⁻³; P is the pressure in mbar; $k_B$ the Boltzmann constant in J K⁻¹; T the gas temperature in K; and $x_{N_2}$ the fraction of N₂ in the gas mixture. $\tau_{N^*}$ and $\tau_{r,N^*}$ are expressed in s. Figure 6 shows the corresponding Stern–Volmer plots ($\frac{1}{\tau_{N^*}}$ in s⁻¹ as a function of P in mbar) for different fractions of N₂ in the gas mixture ($x_{N_2}$).

The Stern–Volmer plot yields $\tau_{r,N^*}$, which is the inverse of the intercept in Eq. (4) for any gas mixture. Based on the results of Fig. 6, the radiative lifetime of N* is found equal to 26.4 ± 1.2 ns, which is consistent with published values in the literature, for example, 24.04 ns computed from the value of $A_{N,i,3p \to 3s}$ recommended by the NIST database,³⁸ and 29.6 ns from Ref. 29. Using our measurements at $x_{N_2} = 1$ in Fig. 6, we determined the quenching rate of N* by N₂, $k_{qN_2} = 7.55$ (±0.3) × 10⁻¹¹ cm³ s⁻¹, which is ≈1.8 and ≈1.1 times higher than the values of 4.1 × 10⁻¹¹ cm³ s⁻¹ and 6.7 × 10⁻¹¹ cm³ s⁻¹ reported in Refs. 29 and 39, respectively. Finally, our experiments at $x_{N_2} = 0.2$ and 0.5 in Fig. 6 and another experiment performed at $x_{N_2} = 0.8$ (not presented in this paper) yield the quenching rate of N* by Ar, $k_{qAr} = 5.0$ (±1.6) × 10⁻¹¹ cm³ s⁻¹. In contrast with $k_{qN_2}$, we did not find any published value of $k_{qAr}$ in the literature to compare it with our result.

<figure><img src="image_129.png" /><figcaption>FIG. 6. Stern-Volmer plots of N* for different Ar/N₂ gas mixtures. Red circles: $x_{N_2} = 1$. Purple triangles: $x_{N_2} = 0.5$. Blue diamonds: $x_{N_2} = 0.2$. The corresponding linear fits are plotted as well using solid red, and dotted purple and dashed blue lines, respectively. The upper dashed black horizontal line represents the inverse of the laser pulse width. The lower dashed black horizontal line represents the inverse of a 9 ns effective lifetime, which is the minimum lifetime for which TALIF measurements can be performed.</figcaption></figure>
The lifetime measurements from Fig. 6 define the maximum pressure at which the absolute N-atom density can be measured for each gas mixture. We chose to limit our measurements to effective lifetimes higher than 9 ns, in order to be outside of the margin of error. The pressure limit then depends on the gas mixture as illustrated in Fig. 6: at 100% N₂, measurements can be made up to 65 mbar, while at 20% N₂, the critical pressure increases up to 110 mbar.

#### IV. RESULTS AND DISCUSSION

For a clearer representation of our results, both the total and repeatability uncertainty can be considered in this paper. In Sec. IV A, where we compare the absolute N-atom density measured by two different techniques, the total uncertainty is used. However, for the rest of the results section, where we compare different TALIF measurements between them, the total uncertainty is less relevant since it is the same for every measurement. Thus, the repeatability uncertainty is used to better identify relevant trends.

##### A. Without pressure differential: Absorption spectroscopy and TALIF comparison

In this section, we compare the measurements of the N atom density performed using TALIF (this work) and the high-resolution Fourier transform spectrometer (FTS) in vacuum ultra violet (VUV) of the DESIRS Beamline at SOLEIL synchrotron.⁴⁰ The latter results are reported by Remigij et al.¹⁹ Both works refer to the performance of parametric studies of the N-atom density vs the gas mixture and pressure.

For the measurements presented in this section, the valve is opened and both chambers are at the same pressure. Our experiments were focused on the cathodic side of the discharge, in front of the MHCD hole as illustrated in Fig. 7. In Fig. 7, TALIF measurements are done 4 mm away from the plasma (purple circle) to avoid reflections

<figure><img src="image_130.png" /><figcaption>FIG. 7. Scheme of plasma configuration without a pressure differential between the two chambers indicating the location of the N-atom density measurement by means of TALIF (purple circle) and FTS VUV (blue square).</figcaption></figure>

of the laser radiation on the MHCD surface, while the FTS VUV measurements were performed at the cathodic expansion (blue square).¹⁹

##### 1. Influence of the gas mixture

Figure 8 shows the densities of N atoms as a function of the percentage of N₂ into the Ar/N₂ gas mixture, measured with the TALIF method. FTS VUV measurements from Ref. 19 are plotted as well for comparison. With both methods, we note a similar trend: the N atom density increases with the percentage of N₂, but not linearly as one would expect from the increase in N₂ concentration only. This trend can be explained by the fact that at low N₂ percentages, the electron density is high,¹⁹ while the electron temperature is only slightly lower than at higher N₂ percentages (2 eV at 50% N₂ compared to 1.5 eV at 0% N₂, i.e., pure Ar according to Ref. 41) and can fairly efficiently dissociate the few present N₂ molecules (with a dissociation degree up to 1%). The electron-ion dissociative recombination reaction N₂⁺ + e⁻ → N⁺N is the main production path of N atoms¹⁹ because of the efficient charge transfer from the ion Ar⁺ to N₂ (Ar⁺ + N₂ → N₂⁺ + Ar).⁴²

When the percentage of N₂ increases, the electron density drops as well as the dissociation rate. However, the N atom density does not decrease because more N₂ is added and a decent dissociation rate is maintained thanks to the contribution of argon metastable atoms, which can dissociate N₂ molecules.⁴³

Using TALIF, we were able to make one more measurement in a pure N₂ discharge, which was not possible by FTS VUV. The measured N atom density was higher than those obtained in all Ar/N₂ mixtures. In pure nitrogen, it has been shown that the production of N atoms may occur through several processes, which can be summed up in two categories: dissociation of the ground state molecules (at different vibrational levels, v) N₂(X¹Σ⁺g, v) by electron impact, and collisions of N₂ molecules that are excited in various electronic and vibrational states.¹⁴ While it is difficult to estimate the dominant dissociative processes in our case, since we are not aware of the existence of an extensive model of our peculiar discharge in nitrogen, it is possible

<figure><img src="image_131.png" /><figcaption>FIG. 8. Experimental densities of N atoms measured by FTS VUV (blue squares)¹⁹ and TALIF (purple circles; this work) as a function of the percentage of N₂ in the Ar/N₂ gas mixture. The black dashed line represents the TALIF measurements corrected to take into account the fact that the two techniques are performed at different locations. Conditions: P = 50 mbar in both chambers, I<sub>d</sub> = 1 mA. TALIF measurements are plotted with the total uncertainty.</figcaption></figure>
<figure><img src="image_132.png" /><figcaption>FIG. 9. Experimental densities of N atoms by FTS VUV (blue squares)¹⁹ and TALIF (purple circles; this work) as a function of the pressure. The black dashed line represents the TALIF measurements corrected to take into account the fact that the two techniques are performed at different locations. Conditions: without pressure difference between the chambers, 20% N₂ in Ar/N₂, I_d = 1 mA. TALIF measurements are plotted with the total uncertainty.</figcaption></figure>

that Ar atoms are not completely detrimental to a nitrogen discharge. This shall be further discussed in Sec. IV B 3 hereafter.

From Fig. 8, although the trends obtained with the two techniques are very similar, we notice a great difference in the absolute value of the N-atom density measured (more than one order of magnitude). It can be easily explained by the difference of the location at which the density is measured. Indeed, the N atom density displays a profile, which decreases with respect to the radial position r, according to the equation¹⁹

$$n_N(r) = \frac{R_0 n_0}{r} \qquad (5)$$

with R₀ the radius of the hole and n₀ the N atoms density at r = R₀ (blue square in Fig. 7). The FTS VUV measurements estimate n₀ at

R₀ = 0.2 mm. Using Eq. (5), we can estimate this density as well from the density measured by TALIF at r = 4 mm, as follows: n₀(TALIF) = nₙ(r = 4 mm) × (4 mm/0.2 mm). This estimation has been plotted in Fig. 8 with a dashed line, and it matches very well the FTS VUV measurements.

## 2. Influence of the pressure

Figure 9 illustrates the density of N atoms as a function of the gas pressure, measured with TALIF (purple circles) and FTS VUV (blue squares). The density n₀(TALIF), estimated as explained before, is plotted with a dashed line. As it can be seen, it matches well the FTS VUV measurements, although a discrepancy exists for a pressure of 80 mbar. This could be due to the fact that the discharge is less stable at higher pressure and the FTS VUV measurement at 80 mbar was only done once, and is thus less reliable.

Nevertheless, the evolution of the N atoms density with the pressure is similar with both techniques and the density increases with an increased pressure. This trend shows that the production process of N atoms varies with the pressure as it was shown using a 0D (volume-averaged) global model of the discharge.¹⁹ It is mostly due to the increased contribution from the metastable pooling dissociation reaction N₂(A³Σ⁺) + N₂(A³Σ⁺) → N₂(X¹Σ⁺) + N + N. Based on other studies, it seems that this process becomes more and more significant when the pressure is increased, for example, from 20 to 200 mTorr in an ICP discharge.⁴²

## B. With pressure differential: TALIF measurements of the N atoms density in a MHCD jet

In this section, we present the measurements performed with a pressure differential between the two chambers, that is, using the configuration of Fig. 1(b) where the valve between the two chambers is closed. For simplicity, the pressure in the high-pressure (upstream) chamber is denoted P₁ and that in the low-pressure (downstream) chamber, where a plasma jet is formed, is denoted P₂ (P₁ > P₂). The

<figure><img src="image_133.png" /><figcaption>FIG. 10. Experimental densities of N atoms as a function of the position (a) along the jet axis $\vec{y}$, on the hole axis of symmetry (x = 0 mm) and (b) along the radial direction $\vec{x}$, at y = 15 mm. 20% N₂ in Ar/N₂, I_d = 1.6 mA, P₁ = 50, P₂ = 1 mbar, gas flux = 40 sccm. Data points are plotted with the repeatability uncertainty.</figcaption></figure>
cathode of the MHCD is found in the high-pressure chamber, while the anode in the low-pressure chamber. The position of the TALIF measurements is located based on the coordinate system of Fig. 1(b).

## 1. Spatial mapping

Figure 10 shows the evolution of the N atom density as a function of the axial (y) and radial (x) position in the downstream chamber. In Fig. 10(a), the density of N atoms remains almost constant along the jet axis: it decreases by only 16% over 35 mm. Fig. 10(b) shows however that the density drops as we move away from the jet axis (x = 0), being two times lower at x = 20 mm. This decrease could be overcome using an array of holes, with MHCDs working in parallel.²¹ In comparison with the case of a MHCD without a jet, we can see that there are N atoms over a long distance along the jet axis. It is unlikely that N atoms are produced directly inside the jet. Indeed, the structure of the electric field is peculiar in the MHCD.⁴⁵ The potential difference is mainly localized in the annular cathode sheath involving a strong radial electric field (along the axis $\vec{x}$ illustrated in Fig. 1) in this region. The electrons emitted at the cathode are accelerated in the cathode sheath by this strong electric field. Out of this region, in the so-called positive column, the electric field lines are found on the axial direction (along the axis $\vec{y}$ illustrated in Fig. 1) having a much weaker magnitude. Thus, the electrons are accelerated from the cathodic region to the anode where they are collected. The motion of the electrons is induced by the electric force and not by the pressure gradient, which drastically decreases the possibility to have electrons outside of the hole on the anodic side in our configuration. Hence, it is most likely that the N atoms are produced in the cathodic region, where most the electric power is deposited⁴⁶ and then either diffuse in the cathodic chamber (in the case where there is no pressure differential), or are transported along the anodic chamber due to the pressure differential. This is especially interesting for atomic nitrogen deposition purposes: the N atoms are produced inside the MHCD hole, which, besides the fact that it is very compact (only 1 mm long), allows for a transport of active species over several centimeters in the downstream chamber. It should be noted that due to the small diameter of the reactor window, we were not able to perform more measurements along the jet axis.

The N atom losses in the volume, in an Ar/N₂ mixture, originate in three-body collisions with Ar atoms and N₂ molecules. The reaction rates of these reactions [$8.27 \times 10^{-34} \times \exp(500/T_g(K)) \text{ cm}^6 \text{ s}^{-1}$ for N₂ and half as much for Ar;⁴³ $T_g$ is the gas temperature] being very small, with a resulting lifetime of about 1 min, and the N atom losses in the volume can be neglected. Thus, we expect the diffusion profile of N atoms to be resulting from fluid phenomena and the decrease in the N atoms density measured along the $\vec{y}$ axis can likely be explained by the mixing of the plasma jet with the ambient gas in the low-pressure chamber.

For this reason, and a clearer study of the influence of other parameters on the production of N atoms, only the measurements performed at x = 0 and y = 4 mm are presented in the following.

## 2. Effect of the discharge current

Figure 11 depicts the evolution of the N atom density as a function of the discharge current. The density increases by about 30% with a discharge current increase from 1 to 2 mA. For a MHCD working in the normal regime, the discharge voltage is constant, even if the

discharge current increases.⁴⁷,⁴⁸ The increase in the discharge current will also induce an increase in the surface of the cathodic expansion, to provide the additional electrons needed. These two phenomena, the increase in the discharge current and the increase in the cathodic expansion surface, have opposite effects on the current density. Indeed, the ratio of the discharge current to the surface on which it is collected involves an almost constant current density.⁴⁹ The limited effect of the discharge current on the electron density has been measured previously in a similar discharge in pure argon.⁴⁹ This explains the slight effect on the density of excited species, such as N atoms, which is shown in Fig. 11.

<figure><img src="image_134.png" /><figcaption>FIG. 11. Experimental densities of N atoms as a function of the discharge current. 10% N₂ in Ar/N₂, P₁ = 50, P₂ = 1 mbar, gas flux = 100 sccm. Plotted with the repeatability uncertainty.</figcaption></figure>

## 3. Effect of the gas mixture

Figure 12 shows the evolution of the N atom density in the plasma jet as a function of the gas mixture. The density increases sharply as the N₂ percentage in the gas mixture increases from 10% to

<figure><img src="image_135.png" /><figcaption>FIG. 12. Experimental densities of N atoms as a function of the percentage of N₂ in the Ar/N₂ gas mixture. $I_d$ = 1.6 mA, P₁ = 50, P₂ = 1 mbar, gas flux = 100 sccm. Data points are plotted with the repeatability uncertainty.</figcaption></figure>
20% and then increases slower between 20% and 80% of N₂. A maximum density seems to be reached around 95% of N₂ before going slightly down at 100% N₂ (i.e., pure nitrogen discharge).

We notice that this tendency is the same as the one measured without a pressure differential in Sec. IV A 1, suggesting that the chemistry involved is very similar. Indeed, as discussed in Sec. IV B 1, the production of excited species seems to happen very similarly inside the hole in both cases, and only the way they are transported to the location of the measurement differs.

The supplementary material obtained here at high N₂ percentages, between 90% and 100%, reveals a maximum, which may indicate that there are some advantages of adding small argon admixtures in a nitrogen discharge, although their effect on the N-atom density increase is moderate. At higher pressures, electronically excited states of N₂ start playing an important role. For instance, the metastable pooling dissociation reaction N₂(A³Σ⁺u) + N₂(A³Σ⁺u) → N₂(X¹Σ⁺g) + N + N has been shown to gain in importance,¹⁹,⁴² although it is not a very efficient source of N atoms. The kinetics of the N₂(A³Σ⁺u) and the other electronically excited states N₂(B³Πg) and N₂(C³Πu) was shown to be coupled in a collisional-radiative loop with main exit channels producing vibrational states of N₂.³⁰,⁵⁰ Vibrational states and the vibrational ladder phenomena are known to be a significant production channel for N atoms in pure N₂ discharge.⁵¹,⁶⁰,⁶¹

This phenomenon may still be significant in nitrogen plasmas with small amounts of argon. When added in small admixtures, Ar atoms may produce electronic states such as N₂ (A³Σ⁺u),⁵² N₂ (B³Πg), and especially N₂ (C³Πu),⁵³ fueling the collisional-radiative loop mentioned before. This loop may then lead to the production of vibrational states of N₂ followed by production of N atoms.

Another production channel that argon addition may enhance is the electron-ion dissociative recombination reaction, that is, N₂⁺ + e⁻ → N + N. Indeed, the ion charge transfer Ar⁺ + N₂ → N₂⁺ + Ar is very efficient⁵⁴ and an increase in the N₂⁺ density could translate in an increased production of N atoms. In the literature, it was also found that argon admixture has a limited impact on the electronic temperature in the discharge⁵⁵ and, thus, will not negatively impact the efficiency of the electron-ion dissociative recombination reaction.

Finally, argon admixture also allows for the discharge to be operated at a lower injected power.

Even though the evolution of the N atoms density with the percentage of N₂ is similar with and without a pressure differential, we notice a great discrepancy in the absolute density of N atoms measured. Given that the cathodic region is the place where most of the power is deposited, hence where excited species are produced, one may think that the pressure on the cathodic side will be the one impacting the production in the hole, even with a pressure differential. We, thus, compared results without a pressure differential at 50 mbar in both chambers and results with a pressure differential at 50 mbar in the cathodic chamber (P₁ = 50 mbar). With the same current and same gas mixture, the density measured in the jet (P₁ = 50 mbar and P₂ = 1 mbar) is about 60 times lower than that estimated in the cathodic region without the jet (both chambers at P = 50 mbar). For instance, at 1 mA, 10% N₂, P = 50 mbar, the density on the cathodic side, without a jet, inside the hole is around 1.5 × 10²⁰ m⁻³ (see Fig. 8), while it is of 2.5 × 10¹⁸ m⁻³ inside the jet (see Fig. 11). This difference can be partially explained by the transport of the plasma and mixing with surrounding gas when entering the low-pressure

chamber. The recombination of N atoms on the walls of the hole could be another explanation, as well as the fact that the gas spends less time in the cathodic region.

In Secs. IV B 4 and IV B 5, we explore the influence of the pressures: (i) the lower pressure P₂, in the chamber where the jet is formed, and (ii) the higher pressure P₁, at the cathodic side of the MHCD.

### 4. Effect of the lower pressure

Figure 13 shows the evolution of the N atoms density as a function of the lower pressure P₂. The upper pressure is fixed at P₁ = 50 mbar; the gas flux injected and the strength of the pumping are adapted to obtain different pressures P₂. The density of N atoms, measured 4 mm downstream of the MHCD in the jet, is 4 times higher when P₂ is increased by a factor of 10. This could be due to the fact that the higher P₂ is the more time the gas mixture spends in the cathodic region where excited species are created.

### 5. Effect of the higher pressure

Figure 14 shows the evolution of the N atoms density as a function of the higher pressure P₁. The lower pressure is fixed at P₂ = 2 mbar; the gas flux injected and the strength of the pumping are adapted to obtain different pressures P₁. The density of N atoms, measured 4 mm downstream of the MHCD in the jet, is decreasing when P₁ increases. However, the density value is a lot less sensitive to variations of P₁ than it is to variations of P₂: the density only decreases by 30% over a range of pressure of 80 mbar. The same kind of phenomenon could explain the evolution of the N atoms density as a function of P₁ and P₂, since in both cases, the density decreases when the pressure differential (ΔP = P₁ − P₂) increases.

### 6. N atom density as a function of the residence time in the cathodic region

As discussed Secs. IV B 4 and IV B 5, the dominant phenomenon, which could explain the different trends of the measured N-atom

<figure><img src="image_136.png" /><figcaption>FIG. 13. Experimental densities of N atoms as a function of the gas pressure in the low-pressure chamber. 100% N₂, I₀ = 1.6 mA, P₁ = 50 mbar, gas flux and strength of the pumping adapted to regulate the pressure (between 34 and 36 sccm). Data points are plotted with the repeatability uncertainty.</figcaption></figure>
<figure><img src="image_137.png" /><figcaption>FIG. 14. Experimental densities of N atoms as a function of the gas pressure in the high-pressure chamber. 100% N₂, *I*<sub>d</sub> = 1.6 mA, P₂ = 2 mbar, gas flux and strength of the pumping adapted to regulate the pressure (between 20 and 80 sccm). Data points are plotted with the repeatability uncertainty.</figcaption></figure>

density, might be the residence time in the cathodic region, which varies with ΔP, and would prevent the plasma from reaching the stationary regime before it is thrusted outside the cathodic region. Using the commercial software Ansys Fluent™, we were able to perform computational fluid dynamics (CFD) simulation, that is, without plasma, and compute the velocity profile of the gas inside the hole and estimate its residence time in the cathodic region (100 μm long). Measurements from Secs. IV B 4 and IV B 5 are then plotted as a function of this parameter.

Figure 15 shows the N atom density as a function of the gas residence time in the cathodic region. We first notice that there is no general correlation of the density variation with the residence time. To try to elucidate the role of the residence time, we plotted with different

symbols, three groups of measurements performed with one of the two pressures constant, the other being variable.

Circles are measurements referring to P₂=2 mbar (constant) and P₁ variable from 30 to 110 mbar. Although P₁ variation has a great incidence on the residence time, we notice that the effect on the N atoms density is small, with a slight density increase between a residence time of 0.62 and 0.77 μs. Squares and triangles represent groups of measurements performed at P₁=50 mbar and P₁=70 mbar, respectively, while varying P₂ from 1 to 10 mbar. We observe that although the change of P₂ has a very small impact on the residence time, its effect on the N atoms density production is much larger when compared to that of P₁.

The role of the residence time seems to be negligible even if for a constant P₂ (circles in Fig. 15) its influence is probably compensated by an increased N atom production at higher pressures in the cathodic region,¹⁹ which could compensate the decrease in the density at lower residence times. In the literature, MHCD jets are usually operated at atmospheric pressure,⁵⁶ and in most cases, the jet moves out of the cathodic side of the MHCD.⁵⁷,⁵⁸ Furthermore, MHCD setups driven by pulsed power supplies can be found.⁵⁹ In these conditions, the pressure on the two sides of the MHCD cannot be controlled independently as it is the case in our configuration. With the lower pressure put equal to the atmospheric one, the analog to a variation of the higher pressure is a change of the gas flux. However, this only corresponds to a variation of the higher pressure P₁ and we did not find in the literature a jet where the lower pressure can be varied. Giuliani *et al*.⁵⁹ showed that turbulences in the plasma plume highly influence the plasma inside the hole due to the cooling of the gas, which was also suggested by Pei *et al*.⁵⁶ This could also be happening in our conditions, with the pressure P₂ having a larger influence on the jet turbulences than the pressure P₁, thus having a higher impact on the N atom density. These pressures may also have an impact on the N atom recombination in the hole, and hence on their density in the plume.

V. CONCLUSION

Measurements of the N-atom density in a MHCD operated in an Ar/N₂ gas mixture have been performed using the TALIF technique.

First, with the MHCD operating with the same gas pressure on both sides (chambers), we reproduced a previous study conducted using VUV absorption spectroscopy. The results of the two techniques are very coherent, with differences that can be easily explained with a simple diffusion model.

The end target of our group being to be able to use the MHCD as a nitrogen source for deposition processes, a pressure differential was introduced between the two sides of the MHCD. It creates a plasma jet toward the lower pressure chamber, which can transport N atoms relatively over long distances (few centimeters), while the region in which they are initially created is only 1 mm long. A study of the influence of the percentages of Ar and N₂ in the gas mixture showed that a few percent of argon admixed in a nitrogen can very slightly increase the density of N atoms produced (an increase in 5% of the density is measured when 4% of Ar is added, compared to pure nitrogen). The chemistry involved is similar to the case without the plasma jet. The optimum conditions to maximize the density of N atoms produced are with a gas mixture of 96% N₂ and 4% of argon admixture, a pressure in the high-pressure chamber of 30 and 10 mbar in the low-pressure chamber.

<figure><img src="image_138.png" /><figcaption>FIG. 15. Experimental densities of N atoms as a function of the residence time in the cathodic region. Circles are with P₂ = 2 mbar and P₁ varying. Squares are with P₁ = 50 mbar and P₂ varying. Triangles are with P₁ = 70 mbar and P₂ varying. 100% N₂, I_d = 1.6 mA, P₁ = 30–110, P₂ = 1–10 mbar, gas flux and strength of the pumping adapted to regulate the pressures. Data points are plotted with the repeat-ability uncertainty.</figcaption></figure>
The generation of the jet seems to have effects that are linked to fluid dynamics. We studied the influence of the pressure variation on both sides of the MHCD: the lower pressure $P_2$ has a much more distinct effect on the density of N atoms measured 4 mm downstream of the hole on its axis. On the opposite, the effect of the higher pressure $P_1$ is rather small. This difference on the impact of the two pressures is probably related to three main phenomena: (i) the modification of the time spent in the cathodic region where most of the power is deposited, (ii) the recombination of N atoms on the sides of the hole and (iii) the turbulences in the plasma jet.

## ACKNOWLEDGMENTS

This work was supported by the French Research National Agency (ANR) through the DESYNIB Project (No. ANR-16-CE08-0004 JCJC). The authors would like to thank Gérard Bauville for the fabrication of the MHCD devices used for this study.

## AUTHOR DECLARATIONS

### Conflict of Interest

The authors have no conflicts to disclose.

## Author Contributions

**Alice Remigy:** Conceptualization (equal); Data curation (lead); Formal analysis (equal); Investigation (lead); Methodology (equal); Visualization (lead); Writing – original draft (lead); Writing – review & editing (supporting). **Xavier AUBERT:** Conceptualization (equal); Methodology (equal); Supervision (supporting); Validation (equal); Writing – review & editing (supporting). **Swaminathan Prasanna:** Conceptualization (equal); Formal analysis (supporting); Methodology (equal); Software (lead); Supervision (supporting); Validation (equal); Writing – review & editing (supporting). **Kristaq Gazeli:** Formal analysis (equal); Supervision (supporting); Validation (equal); Writing – review & editing (equal). **Laurent Invernizzi:** Validation (supporting); Writing – review & editing (equal). **Guillaume Lombardi:** Conceptualization (equal); Funding acquisition (equal); Project administration (equal); Resources (equal); Supervision (lead); Writing – review & editing (equal). **Claudia Lazzaroni:** Conceptualization (equal); Funding acquisition (equal); Project administration (lead); Supervision (lead); Validation (supporting); Writing – review & editing (equal).

## DATA AVAILABILITY

The data that support the findings of this study are available within the article.

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