Local enhancement of electron heating and neutral species generation in radio-frequency micro-atmospheric pressure plasma jets: the effects of structured electrode topologies

The effects of structured electrode topologies on He/O2 radio frequency micro-atmospheric pressure plasma jets driven at 13.56 MHz are investigated by a combination of 2D fluid simulations and experiments. Good qualitative agreement is found between the computational and experimental results for the 2D spatio-temporally resolved dynamics of energetic electrons measured by phase resolved optical emission spectroscopy, 2D spatially resolved helium metastable densities measured by tunable diode laser absorption spectroscopy and 2D spatially resolved atomic oxygen densities measured by two photon absorption laser induced fluorescence. The presence of rectangular trenches of specific dimensions inside the electrodes is found to cause a local increase of the electron power absorption inside and above/below these surface structures. This method of controlling the electron energy distribution function via tailored surface topologies leads to a local increase of the metastable and atomic oxygen densities. A linear combination of trenches along the direction of the gas flow is found to result in an increase of the atomic oxygen density in the effluent, depending linearly on the number of trenches. These findings are explained by an enhanced Ohmic electric field inside each trench, originating from (a) the low electron density, and, consequently, the low plasma conductivity inside the trenches, and (b) the presence of a current focusing effect as a result of the electrode topology.


Introduction
Radio-frequency (RF) driven micro-atmospheric pressure plasma jets (µAPPJs) have gained considerable scientific attention in the last decades due to their various industrial applications [1][2][3][4][5][6]. The primary fields where such jets are utilized are surface manufacturing (sterilization, surface functionalization, nanomaterial synthesis) [7][8][9][10][11][12] and plasma biology/medicine (wound healing, cancer treatment) [13][14][15][16][17][18], mainly due to the high generation rate of certain reactive radicals, such as reactive oxygen and nitrogen species [19][20][21][22]. Optimizing and controlling the generation of such species is of paramount importance in applications. This can be achieved by controlling the electron energy distribution function (EEDF), since radicals are primarily created through electron impact collision processes. One possible way is provided by voltage waveform tailoring (VWT), where using multiple harmonics of a fundamental frequency to tailor the shape of the driving voltage waveform can control the spatio-temporal electron power absorption dynamics and, thus, the generation of certain neutral species, e.g. helium metastables or atomic oxygen, as reported in [23][24][25][26][27]. This control is achieved through the peculiar voltage waveform shape, which leads to a fast sheath expansion/collapse, and thus a restricted spatiotemporal region of enhanced electron power absorption, which significantly contributes to the generation of reactive species through electron impact collision processes. VWT in µAPPJs is based on previous studies at low pressures where this technology was used to control charged particle distribution functions including electrons and ions [28][29][30][31][32][33].
Such spatio-temporal regions of enhanced electron power absorption dynamics can not only be realized by voltage waveform tailoring. In low pressure discharges, using structured electrodes, similar effects have been achieved, which have been investigated both experimentally and computationally [34][35][36][37][38][39]. The main physical mechanism leading to the increased electron power absorption within such trenches is the acceleration of (bulk as well as secondary) electrons by the sheath electric field. In some cases these electrons are 'trapped' within the trench, by moving back-and-forth between the trench walls, thereby contributing to an increased excitation/ionization rate in this region. Due to the resemblance with the corresponding phenomenon in hollow cathode discharges, this mechanism goes by the name of RF hollow cathode effect [40][41][42]. If the trench width is large enough to allow electrons to penetrate into such structures during the local sheath collapse, electrons will be accelerated horizontally inside the trench by the expanding sheaths at the trench sidewalls and, at low pressure, can bounce between the simultaneously expanding sheaths at both sidewalls. This electron bounce-resonance heating [43] can lead to the generation of highly energetic electrons inside such a trench, which are pushed out of the trench by the vertical expansion of the sheath at the bottom of the structure. Moreover, at low pressure a cross-firing of energetic electron beams can happen above the trench due to the expanding sheaths at the edges of the trench orifice [35,38].
However, as shown in e.g. [44,45], the mechanisms underlying electron power absorption are fundamentally different in low and atmospheric pressure discharges. Contrary to low pressure discharges, where electrons are accelerated by the sheath electric field, and, due to their non-local kinetics can have a high energy over a wide spatial region, at atmospheric pressure, the Ohmic electric field originating from collisions is of fundamental importance. Based on these differences, the fundamental mechanisms how structured electrodes affect the electron power absorption dynamics are expected to be different at low and high neutral gas pressures.
The effect of structured electrodes on the electron power absorption dynamics at atmospheric pressure has, to the knowledge of the authors, not yet been investigated. In this paper we investigate this experimentally as well as computationally, using a variety of experimental plasma diagnostics and a fluid-based plasma simulation, nonPDPSIM [46,47], to access several important plasma parameters with high spatial and temporal resolution. The main goal of this work is to gain a qualitative understanding of the effects of tailored boundary surface topologies on the electron heating dynamics and to provide one possible approach to control the reactive species generation by customized boundary surfaces. We show, that by using a structured electrode, the electron power absorption can be enhanced locally in the region of the trenches, which then leads to an increased radical generation rate. Based on the simulation and experimental results, which are in qualitative agreement, we explain the underlying physical mechanisms leading to the observed spatio-temporal electron power absorption dynamics.
The paper is structured as follows: section 2 gives a description of the experimental as well as computational methods used in this study; in section 3 the results are discussed, and finally, in section 4 conclusions are drawn.

Description of the experimental setup and simulation model
The jet used in this investigation is based on the COST reference micro plasma jet [48]. The photo of the electrode configuration of the jet used in experiments is shown in figure 1(a), while the schematic of the simulation domain as well as that of the electrode configuration are shown in figures 1(b) and (c), respectively.
Compared to the standard COST jet design, the electrode geometry has been modified for this work in the following way: for our base case investigations, both electrodes have five trenches of 0.5 mm width and 1 mm depth. The distance between two consecutive trenches is 5 mm (x-direction, see figure 1(c)). Such trench geometries and dimensions ensure that the plasma can penetrate into these surface structures, while their width remains sufficiently small to ensure an efficient local enhancement of plasma parameters. Just like in the standard jet configuration, the electrodes are 1 mm thick and 1 mm apart. Together with the quartz glass plates glued to the sides of the electrodes, this results in a 1 mm × 1 mm × 30 mm discharge channel (plus the volume of the trenches). The electrode material is stainless steel.
The working gas is He with an admixture of O 2 . The gas flow is chosen so that most reactive species are carried outside the jet efficiently, but it does not lead to unstable discharges, e.g. it does not lead to turbulence caused by a too fast flow. Considering the feature size of the COST jet, the He gas flow rate is set at 1 slm [24,25,44,49], whereas the O 2 flow is fixed at 5×10 −3 slm.
The experimental diagnostic methods used in this work are phase resolved optical emission spectroscopy to track highly energetic electrons in space and time, two-photon absorption laser-induced fluorescence (TALIF) to measure atomic oxygen densities, and tunable diode laser absorption spectroscopy to measure helium metastable densities. All diagnostics yield two-dimensionally resolved data of the respective plasma parameters. The x-direction along the gas flow and the ydirection perpendicular to the electrode surface are resolved. The application of these techniques at the COST jet has already been described in [50], including references regarding the details and underlying principles of the diagnostic methods.
In the simulation (cf figure 1(b)) the whole domain has a grounded outer wall. The electrodes and the outer wall are separated by dielectrics with a relative permittivity of ϵ r = 4, since in the experiments, the electrodes are enclosed by quartz glass. Gases are mixed in the zone at the left side of the jet, where the separation between the two electrodes is 5 mm. The discharge cannot be ignited in the gas mixing region at typical voltages used to drive this kind of plasma jet. The side chamber on the right is used to resolve the effluent. The simulations are performed using the computational platform nonPDPSIM developed by Mark Kushner and co-workers [46,47]. It is a two-dimensional fluid dynamics code that can handle multiple particle species.
In the simulation, the continuity equation is solved for the charged species, using the drift-diffusion approximation. In order to account for some effects of kinetic origin in case of electrons, a zero-dimensional Boltzmann equation is solved (using a 2-term approximation) within a certain time interval, in order to provide an energy distribution function for the electrons. The rate constants for chemical reactions in the source and loss terms (which depend on the electron temperature), as well as the electron transport coefficients, are then tabulated as a function of the mean electron energy, where the latter is obtained from solving the electron energy conservation equation.
Neutral species are described by a compressible Navier-Stokes equation. Finally, the electric field (based on the electrostatic approximation) is generated by solving Poisson's equation. The code uses an unstructured grid mesh, and is appropriate for the simulation of weakly ionized plasmas at high/intermediate pressure. The code design and its applications were discussed in detail in previous works [46,47].
It has also been shown that nonPDPSIM can successfully be used to simulate the COST jet [44] and other kinds of micro plasma jets [51][52][53][54][55][56] on a qualitative level. It has been shown that the electron power absorption mode observed experimentally can be reproduced by the simulation, if higher voltages are used. The latter stems from the fact, that not all kinetic effects are captured, in particular Penning ionization. Electrons created by this process can reach energies that increase the highenergy tail of the EEDF, which the 2-term approximation cannot capture. Thus, sources will be underestimated, and this is the reason why higher voltages are needed for a good agreement between simulations and experiment.
The charged species considered in this work include electrons (e − ), positive ions (O 2 + , O + , He + ), and negative ions . Ground state neutral species include He, O 2 , O, O 3 , while the following excited states are considered: , and He * (which is an ensemble of He(2 3 S) and He(2 1 S)). For He atom-electron collision processes, cross sections for one elastic [57], three excitation [57, 58] and one ionization [57] processes are used. For collision processes between electrons and O 2 molecules, cross sections proposed by Gudmundsson et al [59] are used. Collisions between electrons and other neutral species are neglected, due to the low densities of the latter species (at least one order of magnitude lower compared to that of oxygen). Rate constants of reactions between heavy species (ions and neutrals) are based on Turner [60]. The chemical reaction list and surface loss probability of neutral species are those given in [50].
For the electrode surface model, the ion induced secondary electron emission coefficients are set to 0.05, 0.1 and 0.2 for O 2 + , O + , He + , respectively . This specific set of secondary electron emission coefficients was found to reproduce experimental results (i.e. the electron power absorption mode) in previous works [44]. The secondary electron emission induced by negative ions is negligible, since negative ions are trapped by the plasma potential and can hardly reach the surfaces. Electrons have a probability of 0.5 to be reflected once they arrive at the surfaces. 50% of electron impact helium excitations are assumed to generate He * [61].
The discharge is driven by a sinusoidal voltage waveform with a frequency of 13.56 MHz. Two voltage amplitudes are used in the simulation: 650 V and 850 V. In the experiment 350 V and 520 V are used. As discussed in detail in [44], the simulation results can only be compared qualitatively to the experimental findings and higher voltages must be used in the simulation as compared to the experiment. This was explained by the limitations of the fluid dynamical simulation approach caused by neglecting electron kinetic effects (see the description of the simulation above). Most of the unstructured mesh is located inside the discharge domain (highlighted in orange in figure 1(b)). The size of the mesh is identical inside and outside the trenches.

Results
In this section, we discuss the effects of trenches on the generation of energetic electrons as well as selected neutral species based on experimental and simulation results. Figure 2 shows photos of the operating jet at voltage amplitudes of 350 V (a) and 520 V (b). Local enhancements of the light emission intensity can be seen near and within the trenches at both voltages. The discharges are almost symmetric with respect to the center of the gap between the two electrodes. Outside the trenches, where the two electrodes are plain-parallel, the local light emission intensity maxima increase in the high voltage amplitude case. Inside and in between the trenches (vertical direction) regions of high light emission can be seen. These regions reach deeper into the trenches in case of higher voltage. The reason for this trend as a function of voltage amplitude will be discussed below. Figure 3 shows the spatio-temporally resolved He(3 3 S) electron impact excitation rate from the ground state (with an energy threshold of 22.7 eV) obtained from simulations at voltage amplitudes of 650 V and 850 V outside the trench (a), (b) and inside the trench (c), (d), respectively. The positions in the x-direction, i.e. along the direction of the gas flow inside the jet, correspond to the vertical black dashed lines in figure 1(c).
In the region outside the trench (i.e. in the gap without trenches, region (i), cf figure 1(c)), in the low voltage case (panel (a)), electrons are accelerated by the bulk drift electric field at times of high RF current due to the low conductivity induced by frequent collisions at atmospheric pressure [45]. The excitation rate is strong in the plasma bulk during sheath expansion. This mode is known as Ω-mode [61]. As the voltage amplitude is increased to 850 V (panel (c)), the majority of energetic electrons is generated near the sheaths by the enhanced electric field, when the respective sheath expands to its maximum. Those electrons mainly originate from Penning ionization, and partially from secondary electron emission induced by ions bombarding the electrodes. This leads to the increased excitation rates shown in panel (c) observed at the times of maximum sheath voltage within each RF period. This mode is known as Penning-mode [61].
As seen in figure 2, the presence of the trenches can lead to a local enhancement of the electron power absorption dynamics (which manifests itself in the higher excitation rates as compared to the plan parallel electrode case). Consequently, inside the trench (panels (b), (d)) the excitation rates are higher than those outside the trench. The vertical dashed black lines in figure 3 indicate times of high excitation within each RF period. In panel (a) and outside the trenches, these maxima correspond to a time when the sheath expansion is fastest. As seen in panels (b), (d), inside the trench, the excitation maxima occur several nanoseconds later than the time of fast sheath expansion. Similarly, the horizontal white dashed lines in panels (b), (d) indicate the positions of the planar electrodes without trenches. It can be seen, that the excitation maxima occur deeper inside the trench at the high voltage amplitude.
To understand the reasons for the local enhancement of the electron power absorption dynamics and the time delay of the excitation maximum inside the trench with respect to the maximum that occurs outside the trenches at the time of fast sheath expansion, figure 4 shows 2D profiles of the computationally obtained He(3 3 S) excitation rate (first row), the corresponding emission strengths obtained from experiments (second row), the electron density, n e (third row, simulation), the absolute value of the y-component of the electron flux density, |Γ e,y | (fourth row, simulation) and the absolute value of the y-component of the electric field, |E y | (fifth row, simulation) for the four different time instances indicated by the vertical dashed lines in figures 3(a) and (b). The voltage amplitude is 650 V in the simulations and 350 V in the experiments. The color scale for the excitation rate is saturated so that patterns outside the trench are visible. The emission intensities are normalized to the maximum value of the four panels. The result of the simulations (first row) and that of the experiment (second row) show good agreement. As shown in the panels of the first row, the maxima of the excitation rate are located inside the trenches. During the first half of the RF period (i.e. between 0 and ≈ 37 ns), electrons move from the top to the bottom due to the RF electric field. As twice the sheath width is smaller than the width of the trench, electrons can penetrate into the trench. As the sheath of the top boundary expands, inside the trench electrons are pushed together by the expanding sheaths at the two side walls as well as of the top boundary of the top trench, leading to a 'focusing effect' of the conduction current density, i.e. a spatial position inside the trench (indicated by the white dashed arrows in figure 4(d1)), where the electron conduction current density is particularly high and much higher compared to regions outside the trench. This focused conduction current density needs to be driven by a high local Ohmic electric field (see last row of figure 4). This enhanced electric field occurs inside the top trench in regions of significant electron density close to the trench orifice and, thus, accelerates electrons to high energies at this position, so that they can excite ground state helium atoms via collisions. At 8 ns and 15 ns the electric field is much higher compared to the field at the trench at the opposite (bottom) electrode, where the sheath is collapsing and the current focusing effect does not happen at this time within the RF period. The high local electric field inside the trench during the local sheath expansion phase is further enhanced by the low conductivity inside the trench caused by the low local electron density as compared to the electron density in the plasma bulk. When the electron cloud moves outside the trench, the electron flux profile broadens laterally as electrons are no longer confined by the sidewall sheaths. As the electron density and, thus, the conductivity increase towards the bulk center, the electric field decreases.
For the second half of the RF period, an enhanced excitation is induced in the bottom trench during the phase of local sheath expansion, as seen in panels (a3), (a4). As mentioned above, the maximal excitation rates inside the trench (15 ns and 52 ns) occur several nanoseconds later than the maximum outside the trench (8 ns and 44 ns), cf figure 3. This is caused by the decreased electron density inside the trench. This leads to a lower conductivity inside compared to outside the trench, which explains the enhanced Ohmic electric field inside the trench, that can effectively increase the electron energy, as shown in panels (e2), (e4) at 15 ns and 52 ns, respectively. This (Ohmic) electric field has to be high, since, due to the current focusing effect, a high current has to be driven inside the trench. As a consequence of the more Ohmic behavior of the plasma inside compared to outside the trench, the excitation maximum occurs with a delay inside the trench, as shown in figures 3(a) and (b). Figure 5 shows  the excitation rates are dominant close to the boundaries due to electrons from Penning ionization and secondary electrons accelerated by the strong electric field in the sheaths when the sheaths are fully expanded at 21 ns and 59 ns, i.e. the plasma is operated in a different mode outside the trenches compared to the lower voltage scenario discussed before. Therefore, the excitation maximum occurs later outside the trench as compared to the lower voltage scenario and also later as compared to the excitation maximum inside the trench. Inside the trench, the excitation rates occur deeper in the trench at high voltage compared to the lower voltage case, cf figure 4. Electrons can move deeper into the trench as shown in the third and fourth rows of figure 5 due to the higher power input and the resulting higher plasma density as well as smaller sheath widths. The focusing effect of the electron conduction current inside the trench can be clearly seen at 14 ns and 50 ns in panels 5(d1), (d3), inducing a locally enhanced electric field (panels (e1), (e3)) that accelerates electrons. The strong excitation rates close to the downstream (right) corners of the trenches in figures 5(a2), (b2) and (a4), (b4) are a result of the depleted neutral gas density and, consequently, the decreased number of collisional processes (elastic and inelastic ones with low threshold energy), electrons undergo in this region. Thus, electrons can gain more energy by acceleration in the RF electric field over one mean free path to participate in inelastic collisional processes with a higher threshold energy, such as the excitation of He to metastable niveaus, which is discussed in the following.
In order to understand this effect in detail, 2D profiles of the gas temperature, T gas (a), the helium density, n He (b), and the molecular oxygen density, n O2 (c), at a voltage amplitude of 850 V obtained from simulations are shown in figure 6. Gas heating is strong inside the trench. The higher gas temperature in the bottom trench is caused by the grounded walls in the simulation model leading to a weakly asymmetric discharge due to the capacitive coupling of the RF driven (bottom) electrode to the grounded wall and the corresponding displacement current, cf figure 1(b). Since the pressure is kept constant at all positions in the simulation, the enhanced gas temperature (increased from 320 K in the bulk to 350 K in the bottom trench) inside the trenches leads to a decrease of the neutral gas densities of He and O 2 , according to the ideal gas law. The decrease of the He density can be fully explained by the temperature rise (hence the 10% decrease in figure 6(b)), while for the molecular oxygen density additional electron impact processes (e.g. dissociation of molecular oxygen) lead to an  enhanced depletion (with a degree of dissociation of approximately 10%) due to the enhanced electron heating dynamics. The gas velocity is small close to the surface due to the nonslip boundary condition. From the high temperature region gas with a lower density is swept alongside the gas stream, thereby decreasing the neutral gas density near the trench corner in the downstream region, as shown in panels (b), (c). As the mean free path in atomic oxygen, generated by electron impact dissociation of O 2 , is larger than in molecular oxygen (mainly due to the lack of a high number of inelastic processes with a relatively low threshold energy, such as rotational and vibrational excitations), and as O 2 is efficiently converted into atomic oxygen in the trench regions, electrons can gain more energy in regions of depleted molecular oxygen density, because they can be accelerated by the RF electric field over a longer mean free path. Overall, these mechanisms explain the excitation maxima at the trench corners in the downstream region of each trench.
As a consequence of the change in the electron heating dynamics induced by the structured electrodes, reactive neutral species generations, which are closely related to electron impact collisions within the discharge volume, also change The experimental and simulation results are in qualitative agreement. The differences in the absolute density could stem from both the experiment and the simulation model. In the simulation, the fully kinetic behavior of the species is not considered. In the experiment, the spatial resolution of the measurement can lead to a lower density due to the averaging procedure. A strong local enhancement of the helium metastable density is induced inside and above/ below each trench due to the increased local Ohmic electric field as a consequence of the low electron density and the current focusing effect. In the high voltage case, the helium metastable density reaches deeper into the trench and also becomes noticeable near the downstream corner. Outside the trench, the densities change from central-peak to dual-peak profiles as the voltage amplitude is increased, resulting from the transition of the electron heating dynamics. The density profiles are almost identical for each trench, due to the very fast relevant reaction rates compared to the influence of the gas flow. Figure 8 shows the 2D profiles of the time-averaged atomic oxygen densities obtained from TALIF measurements at a voltage amplitude of 350 V (a), 520 V (b), and the corresponding simulated atomic oxygen densities at a voltage amplitude of 650 V (c) and 850 V (d). The results are taken near the middle trench, while the atomic oxygen densities inside the trench cannot be determined by TALIF measurements, since it was not possible to direct the laser beam into the trenches. A strong local enhancement of the atomic oxygen densities is induced inside the trenches. In the low voltage case (panels (a), (c)), the density distribution outside the trenches increases along the direction of the gas flow. At high voltage, a noticeable local enhancement of the atomic oxygen densities near the entrance of both trenches can be observed from experiments ( figure 8(b)) and simulations (figure 8(d)) (due to the decreased background gas density near the corner at the downstream side, and the high Ohmic electric field in the trench), while the densities near the center of the gap between the two electrodes do not change appreciably along the flow direction, as shown in panels (b) and (d).
Since the efficient generation of radical species is of utmost importance in the jet, to which the presence of trenches greatly contributes, the question arises, whether, by increasing the number of trenches, the atomic oxygen density in the effluent can be enhanced. In figure 9 the timeaveraged atomic oxygen density for the whole discharge volume as well as the effluent obtained from simulations at a voltage amplitude of 850 V is shown for different numbers of trenches.
For the planar electrode case, the atomic oxygen density reaches its maximum near the nozzle in the discharge volume, due to the comparable rates between the relevant reactions and the gas flow, and decays in the effluent. The presence of the structured electrodes can locally enhance the atomic oxygen density significantly, leading to the highest density inside the trench instead of the nozzle. In real applications, reactive species densities near the nozzle are usually expected to be controlled for surface treatments. The time-averaged atomic oxygen densities near the nozzle taken at the position highlighted by the black dot in figure 9 for different numbers of trenches are shown in figure 10. The density has an approximately linearly increasing trend as a function of the number of trenches. This enhancement is ultimately caused by the transport of atomic oxygen out of the trench regions, that act as strong local sources of these species, into the effluent. The more such source regions exist within a given discharge volume, the higher the atomic oxygen density in the effluent will be. We note, that the presence of atomic oxygen recombination in the volume between the electrodes is included in a self-consistent manner in the simulation [44].
Thus, a potential way of increasing the reactive oxygen density near the nozzle can be the increase of the number of trenches in the jet. However, as seen in figure 10, the increase is not very sharp, i.e. there is a factor of ≈2 between the case with 8 trenches and the one without trenches.
Based on these results, a more promising plasma source design for enhancing the atomic oxygen density in the effluent might be a jet, where the original nozzle is closed and instead the trench bottom/top surfaces are opened and used as nozzles. In this way the strong atomic oxygen sources would be located in direct vicinity of the nozzles and their transport into the effluent should be efficient. Moreover, much larger substrate surface areas could be treated uniformly based on this array-like arrangement. This new reactor design is planned to be explored in the future.

Conclusions
In this paper the effects of a structured electrode topology on RF micro-atmospheric pressure plasma jets driven by sinusoidal voltage waveforms at two voltage amplitudes have been investigated by experiments and simulations. We have included symmetric rectangular trenches into both electrodes of the jet, each being 0.5 mm in width and 1 mm in depth. Local enhancements in the electron impact excitation rates, the helium metastable densities, as well as the atomic oxygen densities have been observed inside and above/below the trenches from both simulations based on a fluid description and from multiple experimental diagnostics. The electron heating dynamics outside the trench are similar to that in discharges with two planar electrodes. Outside the trench the electron impact helium excitation rates are strong when the sheath is expanding at the low voltage amplitude, while they become significant when the sheath is fully expanded at the high voltage amplitude due to a mode transition from the Ω-to the Penning-mode induced by increasing the driving voltage amplitude. Inside the trenches, the electron impact helium excitation rates are strongly enhanced due to a focusing effect of the electron conduction current and the correspondingly strong local drift electric field, and the low conductivity in that region due to the decreased electron density inside the trenches as compared to the bulk region. This effect also contributes to the fact that these enhanced excitation rates inside the trench occur a few nanoseconds later compared to the time when sheath expansion is fastest. The electron flux is focused inside the trench, but broadens outside the trench. In the high voltage case, a strong excitation rate is induced near the downstream corner of the trench as well, due to the spatiotemporal distribution of the neutral gas densities.
As a result of the change in the electron heating dynamics induced by the presence of the trenches, the helium metastable density and the atomic oxygen densities are enhanced significantly inside and above/below the trenches, which has been observed from both simulations and experiments. The atomic oxygen densities near the nozzle increase as a function of the number of trenches. It might be possible to increase the reactive species densities close to the nozzle by increasing the length of the jet, as well as the number of the trenches. Since (at optimal gas flow) the oxygen density shows an asymptotic behavior (see [62]), increasing the length makes now big difference, but trenches may allow higher gas flows or molecular oxygen admixtures to achieve higher atomic oxygen densities. This may be observed in further studies. The current work only aims for a qualitative understanding of the observed phenomena and the underlying behavior of electron power absorption dynamics. However, further investigations may include effects of other parameters (e.g. gas flow, feature size/shape of the trench, etc).

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.