# Influence of pulsed gas injections on the stability of Townsend dielectric barrier discharges in nitrogen at atmospheric pressure

L Cacot, G Carnide, Myrtil L Kahn, H Caquineau, R Clergereaux, N Naudé, L Stafford

► To cite this version:

L Cacot, G Carnide, Myrtil L Kahn, H Caquineau, R Clergereaux, et al.. Influence of pulsed gas injections on the stability of Townsend dielectric barrier discharges in nitrogen at atmospheric pressure. Journal of Physics D: Applied Physics, 2022, 55 (44), pp.445204. 10.1088/1361-6463/ac8e78. hal-03775840

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Distributed under a Creative Commons Attribution 4.0 International License
Influence of pulsed gas injections on the stability of Townsend dielectric
barrier discharges in nitrogen at atmospheric pressure

L. Cacot ¹,³, G. Carnide ¹,², M. L. Kahn ², H. Caquineau ¹, R. Clergereaux ¹,
N. Naudé ¹* and L. Stafford ³†

¹LAPLACE, Université de Toulouse, CNRS, INPT, UPS, Toulouse, France

²LCC, CNRS (UPR 8241), Université de Toulouse, 205 route de Narbonne, 31077
Toulouse Cedex 4, France

³Département de physique, Université de Montréal, 1375 ave Thérèse-Lavoie-Roux,
Montréal, QC, H2V 0B3, Canada

Abstract

This work investigates the effects of pulsed nitrogen gas injections on the stability of
Townsend dielectric barrier discharges operated in continuous nitrogen gas flows at
atmospheric pressure. For single-pulse injections with pulse durations lower than the
continuous gas residence time (~50 ms), current-voltage characteristics reveal
homogeneous discharges with a single current peak per half-cycle of the applied voltage.
However, a sudden decrease of the discharge power over time combined with a temporary
transition from homogeneous to filamentary discharge is observed for longer pulses at
fixed pulsed gas flows and for higher pulsed gas flows at fixed pulse duration. In addition,
for multiple pulsed gas injections with repetition frequencies between 0.1 and 10 Hz,
discharge destabilisation increases with the number of pulses. Time-resolved optical

<footnote>* Electronic mail: nicolas.naude@laplace.univ-tlse.fr</footnote>

<footnote>† Electronic mail: luc.stafford@umontreal.ca</footnote>
emission spectroscopy reveals that, over the single pulse time scale, temporal variations of the emission intensities are longer than the expected residence times of the continuous and pulsed gas flows. Furthermore, a rise of oxygen impurities can be seen over both single and multiple-pulses time scales. Two-dimensional gas flow simulations reveal that pulsed injections introduce sharp and narrow temporal gas velocity profiles over the range of experimental conditions investigated, with no cumulative effects in the discharge cell from one pulse to the other. However, pulsed operation introduces significant changes in the neutral gas composition with time scales comparable to those revealed by electrical and optical diagnostics. In such conditions, the outgassing of impurities adsorbed on surfaces located upstream of the discharge cell plays a vital role in Townsend discharges' physics and characteristics.

**Keywords:** Dielectric Barrier Discharge, Townsend discharges, Current-voltage characteristics, Optical Emission Spectroscopy, Pulsed gas injection
# 1. Introduction

Non-equilibrium plasmas are routinely used in materials processing, for example, for thin film deposition and etching. For such applications, carrier and reactive gases are typically continuously injected in the plasma reactor [1,2]. For selected applications, however, pulsed gas injections are more appropriate to ensure the right set of populations of plasma-generated species [3–5]. For example, pulsed precursor injections are implemented when an additional control over deposition rate and nanostructure is required. For instance, $AlO_x$ thin film in a pulsed injection of $Al(CH_3)_3$ in an oxygen plasma tune from low-density after precursor injection (i.e. when the precursor concentration is high) to dense structure shortly after the injection (i.e when the precursor concentration is low) due to the impingement of plasma-generated ions and reactive oxygen species on the substrate surface [6]. In hybrid plasma deposition processes relying on plasma-enhanced chemical deposition (PECVD) and sputtering, pulsed precursor injections can prevent target poisoning and can be used for the deposition of multifunctional, nanocomposite coatings [7,8]. The pulsed carrier gas injections can also be synchronized with a pulsed power supply for discharge ignition and maintenance to precisely control the precursor dissociation and plasma-surface interactions during PECVD [9]. Nowadays, pulsed injections of the carrier, precursor, and reactive gases are also used in atomic layer deposition (ALD) and atomic layer etching (ALE) processes [10–12].

Compared to continuous gas flows, pulsed gas flows inevitably lead to temporal variations of the fundamental plasma properties. For example, in Tore Supra reactor used for fusion applications, the response of the scrape-off layer to a supersonic pulsed gas
injection has shown an increase in the plasma density and a decrease in plasma temperature
before returning to equilibrium after about 10 ms; in addition, the extent of such variations
is proportional to the total amount of gas injected into the plasma [13]. In a capacitively-
coupled, radio-frequency (RF) argon plasma at low pressure, Sadek et al. [14] have
reported cyclic evolutions of the electron temperature ($T_e$) and electron density ($n_e$)
following the pulsed injection of neutral gas density in an argon plasma. Cyclic evolutions
of $T_e$ and $n_e$ have also been reported by Garofano et al. [15] with pulsed injection of
hexamethyldisiloxane (HMDSO) in an argon plasma. In such conditions, variations of $T_e$
and $n_e$ are observed over multiple time scales: one linked to the pulsed injection of HMDSO
in the argon plasma and another due to the successive formation and disappearance of
nanoparticles in the dusty plasma [16,17].

The effect of airflow on the space-time distribution of filaments in dielectric barrier
discharge (DBD) at atmospheric pressure has also been investigated [18]. It is found that
modification of the gas flow rate changes the breakdown positions and morphology of
discharge filaments, a feature linked to the combined effect of electric field and airflow on
particle distribution [19,20]. While the filamentary regime of DBDs is more common, there
has been significant interest in the so-called “homogeneous” regime of DBDs characterized
by the absence of micro-discharges and a relatively spatially homogeneous light emission
over the whole inter-electrode gap [21,22]. Of note, such micro-discharges in the
filamentary regime of DBDs imply high-energy input localized over small surface areas
such that their presence can be highly problematic for materials processing applications
[23,24]. On the other hand, homogeneous discharges can typically be obtained through
judicious control of the voltage and current waveforms and the choice of the appropriate
carrier and reactive gases [25].

A handful of studies have reported the development and use of homogeneous DBDs for advanced surface engineering applications (see, for example, [26–35]). However, most of them implement continuous gas flows (carrier and precursor gases). This work aims to examine the effects of pulsed gas injections on the stability of homogeneous DBDs operated with a continuous laminar gas flow. To study the disturbances related to a pulsed injection, experiments are carried out with the injection of gas only, without precursors. The experiments are done in the specific case of a low-density Townsend discharge obtained in a plane-to-plane configuration with N₂ for both the continuous and pulsed gas injections. As reported by many authors, this Townsend discharge is typically characterized by ion density ~10¹⁰ cm⁻³, electron density ~10⁷ cm⁻³, electron temperature ~5 eV, neutral gas temperature ~300 K, and power density in the ~1 W.cm⁻² [21,36]. Such Townsend discharges are relevant for the deposition of functional, nanostructured coatings on a variety of surfaces, including heat-sensitive materials [26–29,32,33,37–40]. Depending on the pulsed gas injection conditions, spatially-resolved current-voltage characteristics and time-resolved optical emission spectroscopy measurements reveal peculiar discharge behaviors following single and multiple pulsed gas injections.

**2. Experimental set-up and diagnostics**

The experimental setup used in this work was described in detail elsewhere
[29,32,41]. The plane-to-plane DBD cell is housed in an enclosed metallic chamber
(volume below 100 cm³) to carry out experiments in a controlled pressure and atmosphere.
As shown in Figure 1 (a), the gas pipes (continuous and pulsed flows, see below) and DBD
cell are connected in a gas mixing chamber. Downstream of the DBD, the system is linked
to the vacuum system. Prior to each experiment, the chamber is pumped down to a pressure
of 10⁻³ mbar to reduce any contamination. The gas gap is then filled up to atmospheric
pressure by a continuous flow of N₂ (99.999% purity) at 1 L.min⁻¹. The discharge cell
consists of two parallel alumina plates separated by a 1 mm gap. One side of alumina plates
is painted with a 3 cm×3 cm conductive silver paste acting as a metallic electrode. To
collect spatially-resolved electrical measurements along the gas flow lines, the ground
electrode is formed of three equal-size metalized strips; this feature is shown in Figure 1
(a) [42]. Here, the middle strip is separated by 400 µm from its neighbors.
<figure><img src="image_2.png" /><figcaption>Figure 1: (a) Schematics of the experimental set-up with the multi-strip ground electrode for spatially-resolved electrical measurements; upstream of the DBD cell, the gas pipes for continuous and pulsed nitrogen gas flows arrive in a mixing chamber, (b) typical current-voltage characteristics of a Townsend discharge in N₂ at 1 kHz with a continuous gas flow.</figcaption></figure>

A power supply providing a low-frequency sinusoidal voltage signal (1 kHz) is connected to a linear power amplifier whose output is linked to the primary winding of a step-up transformer. The discharge cell is connected to the secondary winding of the transformer. A 13 kV peak-to-peak voltage is applied to the electrodes and is measured by
a high-voltage probe (Tektronix P6015A). The outputs of the three strips of the ground electrode are connected to three 330 Ω resistors to gather the corresponding currents. The applied voltage and measured currents of each zone are displayed on an oscilloscope (Teledyne Lecroy WaveSurfer 3024, 200 MHz bandwidth).

Typical current-voltage characteristics of the Townsend discharge in N₂ at atmospheric pressure are presented in Figure 1 (b). Two specific features can be seen for all zones: i) the sinusoidal portion linked to the displacement current and thus to time variations of the applied voltage, and ii) the broad peak associated to the discharge current in a homogeneous Townsend discharge [43–45]. To obtain a homogeneous discharge rather than a filamentary discharge formed of narrow discharge channels randomly distributed in time and space [46], a Townsend (rather than streamer) breakdown is required [21]. This condition implies a preionization of the gas but also a discharge ionization slow enough to avoid a fast avalanche development. This can be achieved through the presence of long-lived species from one half-cycle of the applied voltage to the other; this effect is commonly referred to as the “memory effect”. In the specific case of N₂ discharges, long-lived metastable N₂(A) states are not only involved in volume Penning ionization at low electric fields [47], but they can also induce secondary electron emission following their interaction with charged dielectric surfaces [48]. Over the range of experimental conditions examined, the very first discharges are typically filamentary and then become homogeneous due to the onset of memory effects linked to the formation of long-lived metastable N₂(A) states [47,49].
In addition to the continuous gas flow, pulsed gas injection is realized using an Atokit injection system commercialized by Kemstream. The gas pulses are led to the discharge cell through a 60 cm long stainless-steel pipe with a 4 mm inner diameter. The pulsed gas is chosen identical to the continuous discharge gas (N₂, 99.999% purity). Several injection parameters can be controlled, including the gas opening time (pulse duration), the pulse injection frequency, and the gas pressure upstream of the pulsed injection device (upstream pressure, P<sub>U</sub>, Figure 1(a)). To maintain atmospheric-pressure conditions with both the continuous and pulsed gas flows, the pressure in the plasma chamber (P<sub>C</sub>) recorded at the output of the DBD cell is set to atmospheric pressure using a controlled valve (MKS 248D) placed upstream of the pumping system (see Figure 1(c)). Here, the applied voltage is synchronized with the pulsed gas injection using the Transistor-Transistor-Logic (TTL) output of the injection control unit.

To determine the total amount of gas injected per pulse, the chamber pressure (P<sub>C</sub>) is recorded without the continuous gas flow, and the inlet valve of the pumping system closed (see Figure 1(a)). The corresponding pressure rise after each pulse is shown in Figure 2(a) for different gas opening time values and upstream pressure values.
<figure><img src="image_3.png" /><figcaption>Figure 2: (a) Pressure variation (ΔP) inside the closed chamber as a function of the gas opening time (t<sub>gas</sub>) for various upstream pressures (P<sub>U</sub>). Straight lines correspond to linear fits. (b) Instantaneous pulsed gas flow (Q) as a function of gas opening time for various upstream pressures (P<sub>U</sub>). Lines are to guide the eye only.</figcaption></figure>

As shown in Figure 2(a), the pressure rise increases linearly with the gas opening time. In addition, the rate of increase is steeper for the large upstream pressures due to the largest pressure gradient between the pulse injector and the chamber. Based on these results, the instantaneous gas flow Q during each pulse can be defined as

$$Q(L.s^{-1}) = A \frac{\Delta p (mbar)}{t_{gas}(s)} \quad (1)$$

where Δp and t<sub>gas</sub> are the pressure variation and the gas opening time, respectively. By recording the pressure rise as a function of time inside the closed chamber with a known continuous gas flow, a calibration curve (not shown) can be obtained to find the constant A (L.mbar<sup>-1</sup>). The corresponding instantaneous gas flow for each pulse are presented in Figure 2(b) for various gas opening times and upstream pressures. For a fixed P<sub>U</sub>, Figure 2(b) shows that Q remains constant regardless of the gas opening time: this confirms that the quantity of gas injected during the gas opening time only depends on the upstream
pressure. For the short gas opening times (5 ms and below), the opening and closing times
of the valve inside the injection control unit become comparable to the injection time.
Hence, in such cases, slightly lower *Q* values are observed in Figure 2(b).

Optical emission spectroscopy (OES) measurements are realized using an optical
fiber with the tip placed along the middle portion of the discharge. The signal is transferred
to a high-resolution monochromator (Acton SP-2500) equipped with an intensified charged
coupled device (iCCD) camera (Princeton Instruments PI-MAX3). OES measurements are
synchronized with the pulse injections using the TTL output of the injection control unit.
A typical OES spectrum of the Townsend discharge in N₂ at atmospheric pressure is
displayed in Figure 3 (same conditions as in Figure 1 (b)).

<figure><img src="image_4.png" /><figcaption>Figure 3: Typical optical emission spectrum of a Townsend discharge in a continuous nitrogen flow.</figcaption></figure>
As can be seen in Figure 3, discharge emission is dominated by the Second Positive System (SPS) of N₂, the Herman Infrared system (HIR) of N₂, and the O(¹S)N₂ band. Here, the excited N₂(C), N₂(C''), and O(¹S)N₂ states giving rise to the observed emission bands are mostly populated according to the following reaction schemes [49–51]:

$$N_2(X) + e^- \rightarrow N_2(C) + e^- \qquad (2)$$

$$N_2(A) + N_2(A) \rightarrow N_2(C'') + N_2(X) \qquad (3)$$

$$\begin{cases} O(^3P) + N_2(A) \rightarrow O(^1S) + N_2(X) \\ O(^1S) + 2N_2(X) \rightarrow O(^1S)N_2 + N_2(X) \end{cases} \qquad (4)$$

Based on Equations (2) and (3), the emission intensity of the SPS is typically linked to the electron population [52], whereas the emission intensity of the HIR is ascribed to the square of the population of metastable N₂(A) states [53]. As for the O(¹S)N₂ excimer emission, Equation (4) reveals that it can be related to both N₂(A) and oxygen impurities [49–51]. In presence of low oxygen concentrations into Townsend N₂ discharges, it is worth highlighting that X. Lin et al. [54] have recently shown that associative ionization reaction N(²P) + O(³P) → NO⁺ + e⁻ can be the dominant process involved in the memory effect.

# 3. Electrical characterization of the discharge

## 3.1. Townsend discharge with a single pulsed gas injection

Current-voltage characteristics are used to analyze Townsend discharge with a single pulsed gas injection; Figure 4(a) to Figure 4(c) report the absolute value of the maximum current at each half period of the applied voltage for the entrance, middle, and
exit zones of the DBD cell. The results are shown at two gas opening times (10 ms, Figure 4(b) and 100 ms, Figure 4(c)) for $P_U=2$ bar. For all experiments, the controlled valve of the pumping system is fixed to $P_C=1$ bar to maintain atmospheric-pressure conditions in the DBD cell with pulsed gas injections. Values without pulsed gas injections (continuous gas flow only, Figure 4(a)) are also presented. For all conditions, the discharge current is very low ($< 0.5$ mA); as reported in the literature [45], this is due to the ionization level not being high enough, which agrees with the behavior of the Townsend discharge in $N_2$. Furthermore, the maximum current at the entrance of the DBD cell is systematically lower than in the two other zones. A similar feature for continuous gas flows was reported by other authors [49, 54, 55]. In such conditions, the discharge first ignites at the exit, and the population of long-lived metastable $N_2(A)$ states rises between the entrance and the exit; this leads to a lower breakdown voltage and thus to a higher discharge current for the same amplitude of the applied voltage near the exit [49].
<figure><img src="image_5.png" /><figcaption>Figure 4: Absolute value of the maximum current at the entrance, middle and exit positions for each half-period of the applied voltage: (a) without pulsed gas injection (continuous gas flow only), (b) with a pulsed gas injection for a pulse duration of 10 ms, and (c) with a pulsed gas injection for a pulse duration of 100 ms. Selected current-voltage characteristics for 100 ms injection: (d) homogeneous Townsend discharge at 0.042 s (○) and (e) filamentary discharge at 0.143 s (Δ). Here, the upstream pressure on the injection control unit is fixed to 2 bar.</figcaption></figure>

Figure 4(a) further shows that regardless of the position along the gas flow lines, the absolute value of the maximum current without pulse (continuous gas flow only) remains constant over time. On one hand, for $t_{gas}=10$ ms, i.e. for pulse durations shorter than the residence time of the continuous gas flow (~50 ms), Figure 4(b) indicates that the maximum current oscillates after the pulsed gas injection up to about 100 ms and then stabilizes. This applies particularly at the entrance position, where the memory effect is weaker [49]. On the other hand, for longer pulse durations (for example, $t_{gas}=100$ ms), Figure 4(c) reveals that the maximum current sharply increases after the pulse end and then
oscillates before progressively returning to steady-state values. Such current variation for
a pulse duration of 100 ms is linked to the formation of micro-discharges and a temporary
transition from the homogeneous to filamentary discharge regime [56]. This can be
confirmed by the set of current-voltage characteristics presented in Figure 4(d) and Figure
4(e) for t<sub>gas</sub>=100 ms. At 42 ms after the pulsed gas injection, Figure 4(d) shows that the
discharge remains in the homogenous regime but exhibits a small rise in the breakdown
voltage and a slight decrease of the maximum current with respect to the ones observed for
continuous gas flow only. In contrast, at 143 ms after the pulsed gas injection, Figure 4(e)
reveals that the discharge transits to a filamentary regime characterized by narrow
discharge channels randomly distributed in time and space [57]. In such conditions, the
maximum current significantly varies over very short time scales and can even reach the
saturation limit of the oscilloscope.

Discharge destabilization can also be analyzed from the time evolution of the power absorbed or dissipated by electrons in the discharge. Directly obtained from current-voltage characteristics in homogenous discharges [58], the results are presented in Figure 5 for several gas opening times (2, 10, 50 and 100 ms) for P<sub>U</sub>=2 bar. Here, all discharge power measurements are collected on the middle electrode (similar features with different values are observed for the entrance and exit zones [55]). While the discharge power remains constant for continuous gas flows in agreement with the evolution of the absolute value of the maximum current (Figure 4(a)), two features can be seen in Figure 5 for pulsed gas flows: i) the power remains almost constant up to 10 ms after the beginning of the pulse and then ii) depending on the gas opening time, the power in the homogeneous regime
decreases down to the discharge power with only a continuous gas injection and a transition
towards the filamentary regime may occur (Figure 5(c) and (d)) for the longer durations
(50 and 100 ms).

<figure><img src="image_6.png" /></figure>

Figure 5: Discharge power (collected on the middle electrode) for various tgas: (a) 2 ms, (b) 10 ms, (c)50 ms and (d)100 ms. Here, PU is fixed to 2 bar. In the red zones, due to oscilloscope saturation in the filamentary regime, the power cannot adequately be calculated from current-voltage characteristics. A small drop is always observed for the first data point (only a few discharges in the 1-2 ms time scale); such a feature can be linked to the transition from filamentary to homogeneous discharge regime due to the time required for the buildup of the memory effect [47,49].

For P<sub>U</sub>=2 bar, the instantaneous gas flow was estimated to 32 L.min<sup>-1</sup> regardless of
the gas opening time (see Figure 2). Considering the dimensions of the inlet tube, assuming
that the gas flow is identical at the outlet of the pulsed injector and throughout the whole
system, the pulsed gas can be expected to reach the DBD cell after around 10 ms. Hence,
the slight drop in power observed around 10 ms for all conditions can be linked to the
sudden arrival of the pulsed gas in the discharge zone. Such a decrease of the discharge power is consistent with a reduction of the discharge current observed over selected time frames in Figure 4(d). For 2 ms (Figure 5(a)) and 10 ms (Figure 5(b)), the pulse duration and the total amount of gas injected per pulse are such that the discharge remains in the homogeneous regime. For injections over longer time scales (50 ms, see Figure 5(c)), and 100 ms, Figure 5(d)) and thus for larger amounts of gas injected per pulse, however, the discharge becomes filamentary over selected time frames. For example, for 50 and 100 ms gas opening times, this occurs for about 50 and 100 ms, respectively.

## 3.2. Townsend discharge with multiple pulsed gas injections

Based on the data displayed in Figure 5, it seems that for single-pulse injections of N₂, the transition from homogeneous to filamentary discharge only occurs when the pulse durations become comparable to the residence time of the continuous gas flow (~50 ms). However, based on the results presented in Figure 2, such a trend with the pulsed gas opening time could also be linked to the total amount of gas injected per pulse. Hence, for longer pulse durations, it seems that the gas from the pulsed injection could no longer be entirely evacuated over the time scale of the continuous gas flow, suggesting a rise in the population of gaseous species. This aspect can be further examined by “multiple” pulsed injection experiments realized in the specific case of 5 injections with a gas opening time of 10 ms and $P_U=2$ bar; the results for the discharge power as a function of time are displayed in Figure 6. For the specific set of injection conditions presented in Figure 6, the discharge modification becomes more prominent for successive pulsed gas injections, suggesting an accumulation effect from one pulse to the other. More specifically, the
decrease of the discharge power after each pulse rises with the number of pulses such that the discharge transits from the homogeneous to the filamentary regime after several pulsed gas injections.

<figure><img src="image_7.png" /><figcaption>Figure 6: Discharge power for $t_{gas}$= 10 ms, 2 bar. The data are plotted over two-time scales: on a linear scale after multiple pulsed gas injections (left) and on a log scale after each pulsed gas injection (right). The same colour code is used in both cases: black-first pulse, red-second pulse, blue-third pulse, green-fourth pulse and purple-fifth pulse.</figcaption></figure>

Based on the results in Figure 6, discharge destabilization should be more prominent for larger amounts of gas injected per pulse for a given value of $t_{gas}$. This aspect can be examined by plotting the discharge power variation over time for several values of the upstream pressure $P_U$, i.e. for different instantaneous flows of the pulsed gas injection (see Figure 2); the results are reported in Figure 7.
<figure><img src="image_8.png" /><figcaption>Figure 7: Discharge power for $t_{gas}$= 10 ms and several upstream pressure values: (a) 1.5 and (b) 2.5 bar. The data are plotted over two-time scales: on a linear scale after multiple pulsed gas injections (left) and on a log scale after each pulsed gas injection (right). The same color code is used in both cases: black-first pulse, red-second pulse, blue-third pulse, green-fourth pulse and purple-fifth pulse.</figcaption></figure>

Figure 7 reveals that the slight drop in discharge power linked to the sudden arrival of the pulsed gas occurs earlier at 2.5 bar (~80 ms) than at 1.5 bar (~130 ms). Based on the results presented in Figure 2, such behavior is consistent with the corresponding rise in the instantaneous pulsed gas flow for $t_{gas}$=10 ms, going from about 24 L.min⁻¹ at 1.5 bar to about 41 L.min⁻¹ at 2 bar. Figure 7 also shows that the extent of the discharge destabilization rises with $P_U$. More specifically, while the discharge remains in the homogeneous regime up to at least 5 pulses for $P_U$=1.5 bar (Figure 7 (a)), the discharge destabilization intensifies with the number of pulses for $P_U$=2.5 bar (Figure 7 (b)). Such behavior is very good agreement with a cumulative effect of the pulsed gas injection on the stability of Townsend discharge. Discharge modification is more prominent for larger amounts of gas injected per pulse, and thus for longer pulses at fixed instantaneous pulsed
gas flows (Figure 5) or higher instantaneous pulsed gas flows at fixed pulsed duration (Figure 7). Of note, it can be seen from the set of data presented in Figure 6 and Figure 7 that the transition from the homogeneous to the filamentary discharge regime occurs when the discharge power reaches a critical value around 0.3 W.

A similar cumulative effect can be seen by varying the pulsed injection frequency for $t_{gas}= 10$ ms and $P_U =2$ bar (Figure 8). After the first pulse, the same decrease of the discharge power at 10 ms is observed for 0.1 Hz (Figure 8 (a)), 1 Hz (Figure 6), and 10 Hz (Figure 8 (b)); this trend is consistent with the fixed value of the instantaneous pulsed gas flow (32 L.min⁻¹, Figure 2). After such a temporary drop, the discharge power increases back to the value achieved without any pulsed gas injection. Depending on the injection frequency, two distinct trends can be seen: i) if the injection period (1/f) is long enough to retrieve power values higher than the critical one, the discharge will remain or go back to a homogeneous discharge regime, and ii) if not enough time is provided to the discharge before a subsequent pulse, the power does not increase back to the critical value and the discharge will remain filamentary.
<figure><img src="image_9.png" /><figcaption>Figure 8: Discharge power for $t_{gas}$= 10 ms at (a) 0.1 Hz and (b) 10 Hz injection frequency. The data are plotted over two-time scales: on a linear scale after multiple pulsed gas injections (left) and on a log scale after each pulsed gas injection (right). The same color code is used in both cases: black-first pulse, red-second pulse, blue-third pulse, green-fourth pulse and purple-fifth pulse.</figcaption></figure>

As mentioned previously, through selective control of the operating conditions, $N_2$ discharges can be homogeneous due to the presence of long-lived species from one half-cycle of the applied voltage to the other. Involved in the production of seed electrons at low electric fields [47,49], any factor leading to a net loss of metastable $N_2(A)$ states would no longer ensure conditions for homogeneous discharge formation [21]. Hence, the Townsend breakdown would be replaced by a streamer breakdown, and the discharge would transit to a filamentary regime. This is typically accompanied by an increase in the breakdown voltage [21]; this feature is consistent with the data presented in Figure 4(d). One of the phenomena leading to a net metastable loss in $N_2$ discharges is the quenching of $N_2(A)$ states by gas-phase collisions [21]. Hence, additional gas-phase species arising
from the pulsed gas injections and the cumulative effect can play an important role on the
populations of N₂(A) states and, thus on the stability of Townsend discharges. In particular,
the set of current-voltage characteristics for single and multiple injections have shown that
gas accumulation can be linked to many possible routes: (i) pulse durations longer than the
residence time of the continuous gas flow at fixed instantaneous pulsed gas flows,
(ii) larger instantaneous pulsed gas flows at fixed pulsed duration, and (iii) multiple pulsed
injections with repetition frequencies between 0.1 and 10 Hz. In line with this discussion,
any significant change of the neutral gas composition, for example, in the presence of
impurities or precursors used for materials processing, could modify the discharge stability;
we will return to this point later.

**3.3. Optical emission spectroscopy of the discharge**

Optical emission spectroscopy (OES) is used to examine in more detail the stability
of Townsend N₂ discharges with pulsed gas injections. Here, the gas tubes and discharge
chamber are flushed more than 10 times with nitrogen before the experiment to ensure a
minimal contribution from outgassing and thus from impurities emanating from surfaces
[60]. In such conditions, it is found that the homogeneous discharge regime can be
maintained over a larger number of pulses than in the previous set of less standardized
experiments (Figure 6, Figure 7, and Figure 8). Figure 9 presents the time evolution of the
discharge power and selected emission intensities for 10 pulsed gas injections. Here, the
gas opening time, upstream pressure, and injection frequency are fixed to 10 ms, 2 bar, and
1 Hz, respectively. Values for a Townsend discharge with a continuous flow of nitrogen
are also shown for comparison.
<figure><img src="image_10.png" /><figcaption>Figure 9: (a) Discharge power with and without gas injection. Evolution of the emission intensity of (b) N₂ SPS, (c) N₂ HIR, (d) O(¹S)N₂, (e) N₂ SPS/Power and (f) O(¹S)N₂/(N₂HIR)⁰.⁵. Here, the gas opening time, upstream pressure, and injection frequency are fixed to 10 ms, 2 bar, and 1 Hz, respectively.</figcaption></figure>
As highlighted in the previous section, Figure 9 (a) indicates that the discharge power decreases sharply with the pulsed gas injection but returns to a pre-defined value after each perturbation. After several injections, however, the power continues to decrease without returning to the value before perturbation. A similar trend is observed in Figure 9 (b) for the emission intensity of the SPS of N₂ linked to the N₂(C) state [61]. From Equation 1, N₂(C) is mainly populated by electron-impact collisions on ground state N₂(X). Therefore, the similar trend in the time evolution of the discharge power and N₂ SPS emission intensity over time can partially be linked to temporal variations of the electron density (linked to the discharge power). In this framework, the N₂(C) emission intensity is divided by the discharge power to analyze the time evolution of N₂(X) with pulsed gas injection; the results are presented in Figure 9 (e). While no significant change can be seen for the first few pulses, a slight decrease occurs following each additional pulse with an accumulative effect for a larger number of pulses. It is important to note that additional gas or any change in the gas composition can induce temporal modification of the collisional quenching of emitting N₂(C) states [21,62]: hence, the behavior observed in Figure 9 (e) can result from time variations of both N₂(X) and optical efficiency of N₂(C)-to-N₂(B) transitions (due, for example, to the incorporation of impurities, see below).

As for the N₂ HIR emission (see Figure 9 (c)), it monotonously decreases with time. For a large number of pulses, a decrease can also be seen on the time frame of each single pulse. Based on Equation (2), such short and long-time scale diminutions are a signature of N₂(A) losses [61]. In Figure 9 (d), the time evolution of the emission intensity from the O(¹S) N₂ system presents two features. First, between the first and the fourth injection, the
emission intensity globally increases with a return to the pre-defined value before the next
pulse. Based on Equation (3), two parameters can result in an increase in O(¹S)N₂ emission:
i) an increase of the population of N₂(A) states and ii) an increase in the population of
oxygen O(³P) state [61,63]. Since the emission intensity of N₂ HIR linked to the population
of N₂(A) either remains either constant or shows the opposite trend in the first 4 seconds
of the experiment (Figure 9 (c)), the increase in O(¹S)N₂ most likely arises from an increase
in the number density of oxygen atoms. This can be confirmed in Figure 9 (f) by the ratio
of the emission intensity of O(¹S) N₂ over the square root of the emission intensity of the
N₂ HIR system; this ratio is directly linked to the evolution of oxygen species. Second, after
the fifth pulse, the emission intensity decreases drastically for both N₂ HIR and O(¹S)N₂;
such trend can be explained by the net loss of N₂(A) due to the expected quenching by
oxygen species [59].

Through a more detailed look at a single pulsed injection (over 1 s), it can be noticed
in Figure 9 (e) and Figure 9 (f) that the rate of change in N₂(X) (and/or optical efficiency)
and O(³P) populations is very slow considering the expected residence time of gas-phase
species in the DBD cell. With an instantaneous gas flow around 32 L.min⁻¹ (see Figure 2),
the corresponding gas residence time can be estimated to 2 ms. In addition to the pulsed
gas injections, there is a continuous flow of nitrogen characterized by a residence time of
about 50 ms. As can be seen in Figure 9, the more prominent variations of the N₂(X) (and/or
optical efficiency) and O(³P) populations occur halfway along the gas injection period, i.e.
0.5 s. This result suggests other mechanisms occurring over much longer time scales than
those linked to continuous and pulsed nitrogen gas flows.
**4. Discussion**

Further characterization of the pulsed gas flow channel can be realized using the set of data presented in Figure 2. As can be seen in **Erreur ! Source du renvoi introuvable.**, regardless of the gas opening time, the instantaneous gas flow, *Q*, increases with the pressure difference between the upstream and the chamber pressures, *P*<sub>U</sub>-*P*<sub>C</sub> (*P*<sub>C</sub> being set to atmospheric pressure). Assuming a linear variation (Hagen-Poiseuille equation in a laminar gas flow [64]), the proportionality constant corresponds to the so-called fluid conductance. From the set of data presented in **Erreur ! Source du renvoi introuvable.**, the gas conductance can be estimated to 5×10<sup>-9</sup> m<sup>3</sup>.Pa<sup>-1</sup>.s<sup>-1</sup>. However, the significant departure from the linear trend displayed in **Erreur ! Source du renvoi introuvable.** suggests that the Hagen-Poiseuille equation is not suitable. Two hypotheses can be made to interpret this non-linearity, either a transition from laminar to turbulent gas flow or the head losses due to the specific gas flow channel [64].

<figure><img src="image_11.png" /><figcaption>Figure 10: Correlation between the instantaneous pulsed gas flow *Q* and the pressure difference between the pulse injector and the chamber *P*<sub>U</sub>-*P*<sub>C</sub> for various gas opening times.</figcaption></figure>
To analyze the possible transition from laminar to turbulent gas flow, the Reynolds number, $Re = \frac{\rho.U.D}{\mu}$, where $\rho$ is the mass density, $U$ is the gas speed, $D$ is the characteristic dimension of the system, and $\mu$ is the dynamic viscosity, was calculated. Over the range of experimental conditions investigated, Re rises from about 35 for the continuous gas flow of 1 L.min⁻¹ to more than 1000 for an instantaneous gas flow of 32 L.min⁻¹; this result is consistent with an instantaneous transition from laminar to an intermittent flow regime over the time scale of the pulsed gas injection [64]. However, filamentation appears on time scales much longer than the pulse duration and not necessarily after the first injection. Furthermore, the extent of discharge destabilization varies with the injection frequency. Since these aspects are unrelated to Reynold’s number and thus to a change in the gas flow regime, other issues must be involved, most likely singular head losses from the inlet pipe to the gas mixing chamber and then to the DBD cell (see Figure 1).

To understand the pulsed gas injection behavior over the range of experimental conditions investigated, 2D simulations are done using COMSOL Multiphysics [65] Here, simulations are performed along the discharge axis, with the mixing chamber allowing a coupling between the inlet gas pipes (continuous and pulsed gas flows) and the DBD cell. The injection conditions simulated by COMSOL are as determined experimentally, i.e. a continuous flow rate of 1 L.min⁻¹ and a pulsed injection of 10 ms at 0.1 Hz (instantaneous flow rate of 32 L.min⁻¹). Figure 11 (a) shows the time-resolved gas velocity calculated at the center of the inter-electrode gap. As expected, the gas velocity sharply rises and then drastically decreases after each pulsed injection. No accumulation can be seen from one
pulse to the other. Hence, the gas flow in the DBD cell does not seem to be modified out
of the time scale of the instantaneous pulsed gas flow.

<figure><img src="image_12.png" /><figcaption>Figure 11: (a) Gas velocity profile obtained from COMSOL simulations at the centre of the inter-electrodes space. 2D mapping of the gas flow lines at (b) 3.09 (Time 1, before the 10-ms pulse), (c) 3.11 (Time 2, after the 10ms pulse) and (d) 3.20 seconds (Time 3, 10 ms after the 10ms pulse). The injection conditions simulated by Comsol are as follows: a continuous flow rate of 1 L.min⁻¹ and a pulsed injection of 10 ms at 0.1 Hz (instantaneous flow rate of 32 L.min⁻¹).</figcaption></figure>

Figure 11 b), c) and d) show 2D mappings of the gas velocity before the fourth
10-ms pulse (b, Time 1 (3.09 s) in a), after the fourth 10-ms pulse (c, Time 2 (3.19 s) in a),
and 1 ms after the fourth 10-ms pulse (d, Time 3 (3.20 s) in a). In all cases, the gas velocity
profile with respect to height in the interelectrode space remains parabolic. This behavior
is consistent with the low Womersley number (from 0.2 to 2 between 0.1 and 10 Hz). In
such conditions, the frequency of pulsations is sufficiently low that a parabolic velocity
profile (Hagen-Poiseuille equation [64]) has time to develop during each cycle, and the
flow remains nearly in phase with the instantaneous pressure gradient pressure gradient [66]. However, it can be seen in Figure 11 b), c) and d) that pulsed gas injection introduces recirculations in the gas mixing chamber located upstream of the DBD cell. In addition, these recirculations remain from one pulse to the other (for example, from the end of one pulse shown in Figure 11 d) to the onset of another pulse as in Figure 11 b)). In such cases, one readily observe much longer gas residence time in the mixing chamber than in the DBD cell. Therefore, with impurities continuously outgassing from chamber walls, one can assume an accumulation of impurities in the mixing chamber between each pulse and a progressive release of such impurities in the discharge.

This possible change in the neutral gas composition is considered by introducing in COMSOL simulations a constant oxygen desorption rate from the walls of the mixing chamber. Here the flux is estimated to $10^{-5}$ mol/m$^2$s to produce an oxygen molar fraction in the discharge zone of a few ppm. While such a feature does not significantly impact gas flow lines, Figure 12 a) reveals that it introduces a significant temporal variation of the relative oxygen content. Clearly, a sudden rise in the oxygen molar fraction occurs after each pulse, with a shape similar to the one of the gas velocity. However, while the gas velocity linked to the pulsed injection rapidly returns to the value of the continuous gas flow, a second rise in the oxygen content with much slower decay occurs between each pulse. An accumulation from one pulse to the other can also be seen. As highlighted in Figure 12 b), c), and d), such variations characterized by much longer time scales than those linked to pulsed and continuous gas flow are directly linked to surface outgassing and recirculations in the gas mixing chamber.
<figure><img src="image_13.png" /><figcaption>Figure 12: Oxygen molar content obtained from COMSOL simulations at the centre of the inter-electrodes space. 2D mapping of the oxygen content at (b) 3.09 (Time 1, before the 10-ms pulse), (c) 3.11 (Time 2, after the 10-ms pulse) and (d) 3.20 seconds (Time 3, 10 ms after the 10-ms pulse). The injection conditions simulated by Comsol are as follows: a continuous flow rate of 1 L.min⁻¹, a pulsed injection of 10 ms at 0.1 Hz (instantaneous flow rate of 32 L.min⁻¹), and an oxygen desorption rate from the chamber wall of 10⁻⁵ mol/m².s. In (a), the gas velocity is also shown for comparison.</figcaption></figure>

Of note, the behaviors presented in Figure 12 are comparable to the one of the O(³P), and the opposite to the one of the N₂(A) observed by time-resolved optical emission spectroscopy (Figure 9). Hence, the incorporation of oxygen impurities through surface outgassing and recirculations in the gas mixing chamber can contribute to N₂(A) losses and thus to a discharge destabilization, in excellent agreement with the experiments for both single pulse and multiple pulses (Figure 4, Figure 5, Figure 7, Figure 8). Several studies have examined the influence of oxygen impurities on the fundamental properties of DBD operated in N₂. For a low amount of oxygen (up to a few tens of ppm), the power rises with the oxygen addition. However, the opposite trend is observed at higher oxygen content [49]. In addition, high oxygen content leads to a transition from the homogeneous to the
filamentary discharge regime. This set of results is again consistent with the electrical and
optical characteristics presented for single pulse and multiple pulses.

**5. Conclusion**

The objective of this work was to understand the behavior of Townsend DBD
operated in a homogeneous regime following pulsed gas injection. Time-resolved
discharge power measurements coupled with OES analysis have been realized over single
and multiple pulsed injections of nitrogen in a continuous laminar nitrogen gas flow. The
effects on discharge stability of three main pulsed injection parameters have been analyzed:
i) gas opening time (pulse duration), ii) instantaneous pulsed gas flow (through
modification of the upstream pressure P<sub>U</sub>), and iii) pulse repetition frequency. For single
pulsed gas injection, discharge power measurements revealed that gas opening times longer
than 50 ms yield to a filamentary discharge regime. For larger amounts of gas injected per
pulse and successive pulsed gas injections, transition from homogeneous to filamentary
also occurred. In such conditions, OES revealed an increase of nitrogen and oxygen species
leading to a significant loss of metastable N<sub>2</sub>(A) species and hence of the memory effect,
which is essential to obtain a Townsend discharge.

Over the range of experimental conditions investigated characterized by high
instantaneous gas flows due to pulsed injection in a continuous gas flow, it was found that
surface outgassing and gas recirculations in the gas mixing chamber located upstream of
the DBD cell can induce oxygen impurities in the discharge over much longer time scales
than the ones expected from the instantaneous and continuous gas flows. However, it can
be expected that such features are directly linked to the dimension and shape of the system,
in particular of the gas mixing chamber. As will be demonstrated in forthcoming papers,
the operation of Townsend discharges in pulsed gas flow regimes show interest for several
applications, in particular for the deposition of multifunctional thin films.

Acknowledgments

This work was financially supported by the Université Toulouse III - Paul-Sabatier
and Direction des Relations Internationales of the Université de Montréal through their
contributions to the Québec-France International Research Network on Nanomatériaux
Multifonctionnels Contrôlés (IRN-NMC).

**Data availability statement**

The data are available from the corresponding author upon request.
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