Swaminathan Prasanna

K Gazeli

L Invernizzi

G Lombardi

C Lazzaroni
email: claudia.lazzaroni@lspm.cnrs.fr

A Remigy

X Aubert

Absolute N atom density measurement in a Ar/N 2 Micro Hollow Cathode Discharge jet by means of ns-Two-photon Absorption Laser Induced Fluorescence

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

A Remigy, X Aubert,

I. INTRODUCTION

Nitrogen is a crucial atom in many material deposition applications, from III-V nitride semiconductors such as GaN, AlGaN or InGaN [1][2][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 [START_REF] Singh | Materials Today: Proceedings[END_REF] . Although that these sources allow for large plasma volumes to be produced, they operate at a rather high power of at least few hundreds 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 attention [START_REF] Schoenbach | [END_REF]14 as they can be generated at much lower powers (1 W), 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 geometries of microplasmas, in which a hole of a few hundreds micrometers in diameter is drilled through an electrodedielectric-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 to 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 densities 17,18 (up to 10 22 m -3 ) and high density of N atoms (up to few 10 19 m -3 in the normal regime 19 ). Typically, the plasma volume generated by MHCD is confined in a micrometric 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 produced h-BN films over 2-inches 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 non intrusive techniques with high spatial resolution. The ground state of atomic nitrogen (2p 3 ) 4 S 0 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 2 normal regime in a gas mixture of argon (Ar) and molecular nitrogen (N 2 ). 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 section IV while section 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 Figure 1. It consists of an assembly of a 750 µm thick alumina (Al 2 O 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. 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 and visible in the photograph of Fig. 1.

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 measure the discharge current. Another voltage probe measures V I , i.e. 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 cov-ered 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 x and y axis vectors used to determine the position at which the measurements are done are represented in Fig. 1. To perform spatial measurements, the reactor is placed on a test bench as represented in Figure 2 (see next sections 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-ofsight through a borosilicate window.

Laser system

The ns-TALIF setup is represented in Fig. 2. The laser used is a tunable dye laser (SirahLasertechnik 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 β -barium borate (BBO) crystals process the dye laser beam in the Frequency Conversion Unit (FCU) to yield a threeharmonic 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 towards a 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 towards 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 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 and 600 µm long cylinder.

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 band-pass 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 & 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 reponse 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 mentionned before, impose 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 TM 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 ν l , the laser pulse energy E l , 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 This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. 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 .

PLEASE CITE THIS ARTICLE AS

Figure 3 shows the two excitation schemes used for Kr and N. In the following, the ground states of nitrogen (2p 3 ) 4 S 0 3/2 and krypton (4p 6 ) 1 S 0 are referred to as N and Kr respectively, while the laser-excited states of nitrogen (3p) 4 S 0 3/2 and krypton (5p') [3/2] 2 are denoted with N* and Kr* respectively. For nitrogen, the de-excitation to the states (2s) 4 P 0 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 nm 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 δ ν A = 2ν l -ν A where ν l and ν 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 the following 30 :

n N = η Kr η N T Kr A Kr,5p→5s T N 3 ∑ i=1 A N,i,3p→3s σ (2) Kr σ (2) N τ Kr * τ N * δ ν N =∞ δ ν N =-∞ dΨ N δ ν Kr =∞ δ ν Kr =-∞ dΨ Kr n Kr (1)
where η Kr and η 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→5s is the radiative decay rate (s -1 ) for the Kr 5p → 5s transition measured, A N,i,3p→3s is the radiative decay rate (s -1 ) of the i th radiative de-excitation process for the N 3p → 3s transition observed, σ the Kr* and N* states, respectively, in the conditions of our experiments. dΨ N and dΨ Kr are the ratio number of detected fluorescence photons during dt to the square number of laser photons for a given laser central frequency ν l (corresponding to an offset frequency δ ν A ). They are then integrated over the whole laser frequency domain.

Bisceglia et al 30 refer to equation 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(δ ν A )d(δ ν A ), g(δ ν A ) being the statistical overlap factor between the atom absorption line and the normalized laser line. Thus, the product g(δ ν A )d(δ ν 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) ∆ν l and ∆ν A respectively, and can be expressed by:

g(δ ν A )d(δ ν A ) = dΨ A δ ν A =∞ δ ν A =-∞ dΨ A = 4 ln 2/π ∆ν e f f A e -4 ln 2 δ ν A ∆ν e f f A 2 d(ν A ) (2)
where

∆ν e f f A = 2∆ν 2 l + ∆ν 2
A 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 literature (1.06 pm in 31 and 1.53 pm in 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 δ ν A =∞ δ ν A =-∞ dΨ A can be measured only once to determine the value of g(δ ν A ). The density of N atoms can then be determined using a single laser shot at the central frequency ν A , according to the equation 30 :

n N = η Kr η N T Kr A Kr,5p→5s T N 3 ∑ i=1 A N,i,3p→3s σ (2) Kr σ (2) N τ Kr * τ N * dΨ N dΨ Kr g(δ ν Kr ) g(δ ν N ) n Kr (3)
The calculation of the uncertainty on the density of nitrogen is done using the propagation of uncertainties of the independent variables 30,[START_REF] Venkateshan | Mechanical Measurements[END_REF] . In the following, this will be referred to as the total uncertainty. It takes into account all of the uncertainty sources, as calculated in 30 . The most significant uncertainty comes from the poor knowledge of the ratio of the two-photon absorption cross-sections σ 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→5s and A N,i,3p→3s ), as well as the transmittance of the optics (T Kr and T N ) and the sensitivity of the photomultiplier (η Kr and η N ) for which the error is gathered from the manufacturer data-sheets. On the opposite, the TALIF integrals (dΨ N and dΨ Kr ), the fluorescence lifetimes (τ Kr * and τ N * ) and the FWHM (∆ν A ) used for the determination of g(δ ν 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 as the repeatability uncertainty.

B. TALIF measurements validity verification

The hereinabove discussion and the validity of the equation (3) on the determination of the N atoms density, relies 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 is too high, such as photo-ionization, photo-dissociation and stimulated emission 27,[START_REF] Döbele | [END_REF] .

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 versus the laser energy. When This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. the two-photon laser absorption dominates over the other phenomena, the PD factor has a value of about 2.

PLEASE CITE THIS ARTICLE AS

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-atoms interaction is dominated by the two-photon absorption and, thus, equation (3) can be used for the determination of the absolute density of N atoms in the discharge in this laser energy range.

C. Fluorescence lifetime and quenching rate

From equation (3), one can see that the precise knowledge of the radiative lifetimes τ Kr * and τ 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 atoms density. Some of the data are available in the literature referring to pure nitrogen environments, but the quenching coefficient of N* in an Ar/N 2 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 [START_REF] Kramida | Published: NIST Atomic Spectra Database (ver. 5.9)[END_REF] , 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 τ Kr * is equal to the radiative lifetime of the Kr* state.

For nitrogen atom, Figure 5 where A N,i,3p→3s is the Einstein coefficient of the i th radiative de-excitation process.

-the quenching rate Q of N* atoms by both N 2 molecules and Ar atoms.

Hence, the effective decay rate 1/τ N * is expressed by:

1 τ N * = 1 τ r,N * + k q N 2 [N 2 ] + k q Ar [Ar] = 1 τ r,N * + P × 10 -4 k B T × k q N 2 x N 2 + k q Ar (1 -x N 2 ) (4)
where k q N 2 and k q Ar are the quenching rates of N* by N 2 and Ar, respectively, in cm 3 .s -1 , [N 2 ] and [Ar] are the densities of N 2 an 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 N 2 in the gas mixture. τ N * and τ r,N * are expressed in s. Figure 6 shows the corresponding Stern-Volmer plots ( 1 τ N * in s -1 as a function of P in mbar) for different fractions of N 2 in the gas mixture (x N 2 ).

The Stern-Volmer plot yields τ r,N * which is the inverse of the intercept in equation ( 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, e.g., 24.04 ns computed from the value of A N,i,3p→3s recommended by the NIST database [START_REF] Kramida | Published: NIST Atomic Spectra Database (ver. 5.9)[END_REF] , and 29.6 ns from 29 . Using our measurements at x N 2 = 1 in Fig. 6, we determined the quenching rate of N* by N 2 , k q N 2 = 7.55 (± 0.3) ×10 -11 cm 3 .s -1 , which is ≈1.8 and ≈1.1 times higher than the values of 4.1×10 -11 cm 3 .s -1 and 6.7×10 -11 cm 3 .s -1 reported in references 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 q Ar = 5.0 (± 1.6) ×10 -11 cm 3 .s -1 . In contrast with k q N 2 , we did not find any published value of k q Ar in the literature to compare it with our result. 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 This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. outside of the margin of error. The pressure limit then depends on the gas mixture as illustrated in Fig. 6: at 100% N 2 , measurements can be made up to 65 mbar while at 20% N 2 the critical pressure increases up to 110 mbar.

PLEASE CITE THIS ARTICLE AS

IV. RESULTS AND DISCUSSION

For a clearer representation of our results, both the total and repeatability uncertainty can be considered in this paper. In section 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 ev-ery 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 atoms 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 Remigy et al. 19 . Both works refer to the performance of parametric studies of the N atom density versus the gas mixture and pressure. This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. 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 Figure 7. In Fig. 7, TALIF measurements are done 4 mm away from the plasma (purple circle) to avoid reflections of the laser radiation on the MHCD surface, while the FTS VUV measurements were performed at the cathodic expansion (blue square) 19 .

PLEASE CITE THIS ARTICLE AS

Influence of the gas mixture

Figure 8 shows the densities of N atoms as a function of the percentage of N 2 into the Ar/N 2 gas mixture, measured with the TALIF method. FTS VUV measurements from 19 are plotted as well for comparison. With both methods, we note a similar trend: the N atoms density increases with the percentage of N 2 , but not linearly as one would expect from the increase of N 2 concentration only. This trend can be explained by the fact that at low N 2 percentages, the electron density is high 19 while the electron temperature is only slightly lower than at higher N 2 percentages (2 eV at 50% N 2 compared to 1.5 eV at 0% N 2 , i.e., pure Ar according to [START_REF] Kasri | Développement de sources microplasma en mélange N2/Ar pour la production d'azote atomique en vue d'une application aux procédés de dépôt de nitrure[END_REF] ) and can fairly efficiently dissociate the few present N 2 molecules (with a dissociation degree up to 1%). The electron -ion dissociative recombination reaction N + 2 + e → N + N is the main production path of N atoms 19 because of the efficient charge transfer from the ion Ar + to N 2 (Ar + + N 2 → N + 2 + Ar) [START_REF] Kang | [END_REF] . When the percentage of N 2 increases, the electron density drops as well as the dissociation rate. However, the N 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 N 2 in the Ar/N 2 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 d = 1 mA. TALIF measurements are plotted with the total uncertainty. atoms density does not decrease because more N 2 is added and a decent dissociation rate is maintained thanks to the contribution of argon metastable atoms which can dissociate N 2 molecules 43 . Using TALIF, we were able to make one more measurement in a pure N 2 discharge, which was not possible by FTS VUV. The measured N atoms density was higher than those obtained in all Ar/N 2 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) N 2 (X 1 Σ + g , v) by electron impact, and collisions of N 2 molecules that are excited in various electronic and vibrational states 44 . 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 that Ar atoms are not completely detrimental to a nitrogen discharge. This shall be further discussed in section 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 atoms density displays a profile which decreases with respect to the radial position r, according to the equation 19 :

n N (r) = R 0 n 0 r ( 5
)
with R 0 the radius of the hole and n 0 the N atoms density at r = R 0 (blue square in Fig. 7). The FTS VUV measure-This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. ments estimate n 0 at R 0 = 0.2 mm. Using equation ( 5), we can estimate this density as well from the density measured by TALIF at r = 4 mm, as follows: n 0 (TALIF) = n N (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.

PLEASE CITE THIS ARTICLE AS

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 n 0 (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 N 2 (A 3

Σ + u ) + N 2 (A 3 Σ + u ) → N 2 (X 1 Σ + g ) + 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 [START_REF] Kang | [END_REF] .

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, i.e., using the configuration of Fig. ??b where the valve between the two chambers is closed. For simplicity, the pressure in the high pressure (upstream) chamber is denoted P 1 and that in the low pressure (downstream) chamber, where a plasma jet is formed, is denoted P 2 (P 1 > P 2 ). The 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. ??b.

Spatial mapping

Figure 10 shows the evolution of the N atoms density as a function of the axial (y) and radial (x) position in the downstream chamber. In Fig. 10, the density of N atoms remains almost constant along the jet axis: it decreases by only 16% over 35 mm. Fig. 10 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 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 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 deposited 46 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 atoms losses in the volume, in an Ar/N 2 mixture, originate in three-body collisions with Ar atoms and N 2 molecules. The reaction rates of these reactions (8.27 × 10 -34 × exp(500/T g (K)) cm 6 s -1 for N 2 and half as This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. much for Ar 43 ; T g is the gas temperature) being very small, with a resulting lifetime of about 1 minute, the N atoms 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 of the N atoms density measured along the y axis can likely be explained by the mixing of the plasma jet with the ambient gas in the low pressure chamber.

PLEASE CITE THIS ARTICLE AS

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.

Effect of the discharge current

Figure 11 depicts the evolution of the N atoms density as a function of the discharge current. The density increases by about 30% with a discharge current increases 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 of the discharge current will also induce an increase of the surface of the cathodic expansion, to provide the additional electrons needed. These two phenomena, the increase of the discharge current and the increase of 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 [START_REF] Lazzaroni | Etude théorique et expérimentale d'une micro décharge à cathode creuse à pression intermédiaire dans l'argon[END_REF] . The limited effect of the discharge current on the electron density has been measured previously in a similar discharge in pure argon [START_REF] Lazzaroni | Etude théorique et expérimentale d'une micro décharge à cathode creuse à pression intermédiaire dans l'argon[END_REF] . This explain the slight effect on the density of excited species, such as N atoms, which is shown in Fig. 11.

Effect of the gas mixture

Figure 12 shows the evolution of the N atoms density in the plasma jet as a function of the gas mixture. The density increases sharply as the N 2 percentage in the gas mixture increases from 10 to 20% and then increases slower between 20 and 80 % of N 2 . A maximum density seems to be reached around 95 % of N 2 before going slightly down at 100% N 2 (i.e., pure nitrogen discharge). We notice that this tendency is the same as the one measured without a pressure differential in section IV A 1, suggesting This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset. that the chemistry involved is very similar. Indeed, as discussed in section 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 data obtained here at high N 2 percentages, between 90 % and 100 %, reveal 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 N 2 start playing an important role. For instance, the metastable pooling dissociation reaction N 2 (A 3 Σ + u ) + N 2 (A 3 Σ + u ) → N 2 (X 1 Σ + g ) + N + N has been shown to gain in importance 19,[START_REF] Kang | [END_REF] , although it is not a very efficient source of N atoms. The kinetics of the N 2 (A 3 Σ + u ) and the other electronically excited states N 2 (B 3 Π g ) and N 2 (C 3 Π u ) was shown to be coupled in a collisional-radiative loop with main exit channels producing vibrational states of N 2 30,[START_REF] Guerra | [END_REF] . Vibrational states and the vibrational ladder phenomena are known to be a significant production channel for N atoms in pure N 2 discharge 51 . 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 N 2 (A 3 Σ + u ) 52 , N 2 (B 3 Π g ) and especially N 2 (C 3 Π u ) 53 , fueling the collisional-radiative loop mentioned before. This loop may then lead to the production of vibrational states of N 2 followed by production of N atoms. Another production channel that argon addition may enhance is the electron-ion dissociative recombination reaction, i.e. N +

PLEASE CITE THIS ARTICLE AS

2 + e → N + N. Indeed, the ion charge transfer Ar + + N 2 → N + 2 + Ar is very efficient 54 and an increase in the N + 2 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 discharge 55 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 N 2 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 (P 1 = 50 mbar). With the same current and same gas mixture, the density measured in the jet (P 1 = 50 mbar and P 2 = 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% N 2 , P = 50 mbar, the density on the cathodic side, without a jet, inside the hole is around 1.5×10 20 m -3 (see Fig. 8) while it is of 2.5×10 18 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 the next two sections, we explore the influence of the pressures: (i) the lower pressure P 2 , in the chamber where the jet is formed, and (ii) the higher pressure P 1 , at the cathodic side of the MHCD.

Effect of the lower pressure

Figure 13 shows the evolution of the N atoms density as a function of the lower pressure P 2 . The upper pressure is fixed at P 1 = 50 mbar; the gas flux injected and the strength of the pumping are adapted to obtain different pressures P 2 . The density of N atoms, measured 4 mm downstream of the MHCD in the jet, is 4 times higher when P 2 is increased by a factor of 10. This could be due to the fact that the higher P 2 is the more time the gas mixture spends in the cathodic region where excited species are created.

Effect of the higher pressure

Figure 14 shows the evolution of the N atoms density as a function of the higher pressure P 1 . The lower pressure is fixed at P 2 = 2 mbar; the gas flux injected and the strength of the pumping are adapted to obtain different pressures P 1 . The density of N atoms, measured 4 mm downstream of the MHCD in the jet, is decreasing when P 1 increases. However, the density value is a lot less sensitive to variations of P 1 than it is to variations of P 2 : the density only decreases by 30% This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

PLEASE CITE THIS ARTICLE AS

N atoms density as a function of the residence time in the cathodic region

As discussed in the previous sections, the dominant phenomenon which could explain the different trends of the measured N atom density might be the residence time in the cathodic region, which varies with ∆P, and would prevent the plasma from reaching the stationary regime before it is thrust outside the cathodic region. Using the commercial software Ansys Fluent TM , we were able to perform Computational Fluid Dynamics (CFD) simulation, i.e. 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 sections IV B 4 and IV B 5 are then plotted as a function of this parameter.

Figure 15 shows the N atoms 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 P 2 = 2 mbar (constant) and P 1 variable from 30 to 110 mbar. Although P 1 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 P 1 = 50 mbar and P 1 = 70 mbar, respectively, while varying P 2 from 1 to 10 mbar. We observe that although This is the author's peer reviewed, accepted manuscript. However, the online version of record will be different from this version once it has been copyedited and typeset.

PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0110318

the change of P 2 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 P 1 . The role of the residence time seems to be negligible even if for a constant P 2 (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 of 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 P 1 and we did not find in 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 P 2 having a larger influence on the jet turbulences than the pressure P 1 , thus having a higher impact on the N atoms density. These pressures may also have an impact on the N atoms 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/N 2 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 towards 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 N 2 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 of 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% N 2 and 4% of argon admixture, a pressure in the high pressure chamber of 30 mbar and 10 mbar in the low pressure chamber. 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.

3 FIG. 1 .

 31 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 mbar, P 2 = 10 mbar, gas flux = 36 sccm.

FIG. 2 .

 2 FIG. 2. Experimental set-up of the TALIF measurements. Solid lines represent laser radiation, dashed lines represent electric signals and dotted lines represent fluorescence emission. FCU : Frequency Conversion Unit.

( 2 )

 2 FIG.3. Two-photon excitation and fluorescence scheme of nitrogen and krypton atom.

( 2 )

 2 Kr /σ(2) N which leads to an error of about 60% on the absolute density of the N atoms.

  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 signal30 .

  shows a typical fluorescence signal. Fitting the exponential decay of the PMT signal yields the time constant τ N * of the fluorescence decay, i.e. the decay of the population of the upper state N*. The effective time constant for the fluorescence τ N * is a result of two factors: -the natural radiative de-excitation of the excited level, with a time constant τ r,N * =

  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% N 2 /20% Ar, I d = 1 mA.

  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).

  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% N 2 in Ar/N 2 , I d = 1 mA. TALIF measurements are plotted with the total uncertainty.

  FIG. 10. Experimental densities of N atoms as a function of the position (a) along the jet axis y, on the hole axis of symmetry (x = 0 mm) and (b) along the radial direction x, at y = 15 mm. 20% N 2 in Ar/N 2 , I d = 1.6 mA, P 1 = 50 mbar, P 2 = 1 mbar, gas flux = 40 sccm. Data points are plotted with the repeatability uncertainty.

FIG. 11 .

 11 FIG. 11. Experimental densities of N atoms as a function of the discharge current. 10% N 2 in Ar/N 2 , P 1 = 50 mbar, P 2 = 1 mbar, gas flux = 100 sccm. Plotted with the repeatability uncertainty.

  FIG. 12. Experimental densities of N atoms as a function of the percentage of N 2 in the Ar/N 2 gas mixture. I d = 1.6 mA, P 1 = 50 mbar, P 2 = 1 mbar, gas flux = 100 sccm. Data points are plotted with the repeatability uncertainty.

  FIG. 13. Experimental densities of N atoms as a function of the gas pressure in the low pressure chamber. 100% N 2 , I d = 1.6 mA, P 1 = 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.

ACKNOWLEDGMENTS

This work is supported by the French Research National Agency (ANR) through the DESYNIB project (ANR-16-CE08-0004 JCJC). The authors would like to thank Gérard Bauville for the fabrication of the MHCD devices used for this study. . . . .

DATA AVAILABILITY STATEMENT

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