Surface DBD degradation in humid air, and a hybrid surface-volume DBD for robust plasma operation at high humidity

Surface dielectric barrier discharge performance deteriorates in humid air, with permanent and/or reversible degradation of its components. Plasma operation in a humid environment is unavoidable when humid air or water-containing materials are treated. Experimental and numerical results indicate that an electrically conductive thin film of water is responsible for ohmic dissipation and inhibited plasma ignition at high relative humidity. An alternative hybrid surface-volume dielectric barrier discharge design provides more stable and uniform plasma operation in high-humidity atmospheres.


Introduction
Atmospheric pressure plasma sources in ambient air have been widely studied in recent decades. In particular, the dielectric barrier discharge (DBD) is a practical and low-cost configuration, where radicals such as reactive oxygen and nitrogen species (RONS) are produced by the energetic electrons of the generated low temperature plasmas. A DBD generates plasma by means of a time-varying high voltage (several kVs) between two electrodes; the dielectric barrier is to prevent arcing between electrodes which could otherwise * Author to whom any correspondence should be addressed.
Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. occur following electrical breakdown of the gas. The DBD, which is usually a planar device, may generate the plasma in the volume of gas between opposing electrodes (volume dielectric barrier discharge, VDBD), or on the surface of a dielectric adjacent to the electrode edges (surface dielectric barrier discharge, SDBD). DBDs have found application in various fields and manufacturing processes, such as biological treatments [1]. In this case, the plasma treatment can be directly applied to biological samples, such as seeds or pathogens, which are included in the discharge setup, or indirectly by first treating water to generate plasma activated water (PAW), then using it in a second stage for the treatment of samples.
Many parameters influence the effectiveness of the treatment [2]. One of these is the relative humidity (RH), which is generally a component of the gas mixture, especially if the reactor chamber contains water (necessarily for PAW production) or water-containing materials (moistened seeds [3], agar, etc), with subsequent water evaporation, and water desorption from the inner walls. The presence of humid air can enhance the plasma generation of certain RONS and other radicals by introducing H 2 , with the consequent multitude of chemical reactions [4,5].
On the one hand, several applications aim at minimizing the operating RH: for example, O 3 production is hampered by humid air by providing additional ozone destruction mechanisms [6], quantified to be up to three times slower probably due to a change of chemical pathways [7]; the reactive thrust produced by DBD actuators is significantly reduced for RH = 70% [8]. Humidity management of surfaces is also a major concern for the reliability of electronic equipment [9,10].
On the other hand, higher RH levels above typical ambient values can be used to optimize the specific process under investigation: benzene decomposition is observed to reach an optimum in terms of efficiency for RH = 60% [11], the sterilization time of Bacillus atrophaeus spore is decreased to 15 min for RH = 90% instead of 60 min for RH = 60%-90% [12], the concentration of OH radicals is increased proportionally to RH for values higher than 35% [13], the remediation of naphthalene reaches an optimum for RH = 40%-60% [14], and 3 min exposure to air DBD plasma with 40%-90% RH leads to more than 2.3 times faster growth of Raphanus sativus L. [15] and a 56% increase in total seed weight of Arabidopsis thaliana [16]. Stable, humidity-proof SDBDs are therefore crucial for applications such as sterilization of microorganisms (bacteria, viruses and spores), treatment of plants, seeds [17], food, and PAW production, generally implying high humidity environments, which have great potential for industrial development.
These examples motivate the need for a reliable and uniform DBD plasma source whose long-term operation is robust at all RH values. However, high humidity can deteriorate the performance of a DBD, especially for SDBDs, by degrading the electrical characteristics of the plasma [5], and/or by causing damage to the DBD components which may be reversible or permanent.
SDBD performance in humid air (RH = 30%-85%) and DBD design improvements are investigated in this work, which is organized as follows: section 2 describes the DBDs under investigation and the experimental setup. Permanent degradation of the electrode and dielectric after continuous use in high humidity atmosphere is described in section 3.1. In section 3.2, operation at different levels of humidity is analyzed using Lissajous figures, equivalent circuits, and visual inspection of the plasma, with practical solutions for improved operation given in section 3.3. In section 4, the possible origin and consequences of a water film on the surface-activated SDBD are discussed, supported by numerical simulation. Novel surface-volume hybrid DBD (HDBD) versions are discussed in section 5, with one of these designs tested for a more robust operation in high humidity environments. The conclusions are given in section 6.

Experimental setup
Two initial designs of DBDs are investigated in this work, and both are tested in the same reactor setup.

Printed circuit board (PCB)-fingers SDBD
The first version of SDBD investigated, called 'PCB-fingers SDBD' is shown in figure 1(a), featuring a PCB with a disc of diameter 74 mm. The DBD dielectric is a 0.3 mmthick FR4 glass fiber plate used with no special cleaning procedure [9,10]. Both the top and bottom electrodes are made of 0.1 mm-thick Cu plating, treated with electroless nickel immersion gold (ENIG), resulting in a nickel plating to facilitate soldering, and a gold film coating intended to protect the copper electrodes against oxidation and corrosion. The highvoltage electrode is shaped in a connected array of 2 mm-wide, 2 mm-spaced flat fingers, whereas the ground electrode on the reverse side is a continuous ground plane.

Perforated-disc SDBD
A second SDBD, called 'Perforated-disc SDBD' in figure 1(b), was designed both to overcome the material deterioration issues of the PCB-fingers SDBD described in section 3.1, as well as to be able to modify the SDBD into a hybrid surface-volume version that will be described in section 5. The high-voltage electrode is composed of a flat stainless steel mesh 1 mm thick, with electro-chemically perforated 2 mm square apertures, separated by 0.4 mm-wide steel. The dielectric is a 1 mm-thick, 81 mm-diameter alumina disc (Al 2 O 3 99.6% purity).

Reactor setup
The DBDs are tested in the cylindrical reactor of figure 1(c), and a schematic of the electrical circuit is depicted in figure 1(d). The high voltage power supply (Trek Model 615-10 [18]) generates a 1 kHz sinusoidal voltage in the range 1-14 kV peak-to-peak. A Teledyne Lecroy HDO6045 oscilloscope is used to monitor the DBD voltage V(t) measured by a 1000:1 HV probe HIvolt PHV 4-4171, and the voltage across the 33 nF polyester metallized film probe capacitor C p is measured with a 10:1 voltage probe Lecroy PP023. The capacitor voltage is used to measure the charge Q(t) of the time-integrated current to construct the Lissajous figures and obtain the DBD dissipated power [19]. The C p probe capacitance is two orders of magnitude higher than the DBD capacitance, so it acts as a virtual ground connection to the DBD. An example of the voltage waveform and the discharge current, as measured with the current monitor output I(t) of the power supply, is shown in figure 2. The V(t) and Q(t) waveforms are used to draw Lissajous figures; the I(t) waveform shown in figure 2 shows the overall capacitive response of the system, namely the ∼90 • shift between the voltage and current signal. During operation, the wires and the hygrometer probe pass through port 1. Port 2 is closed, port 3 is connected to the laboratory air extraction, and port 4 is connected to a source of humid air. (d) Schematic circuit showing the electrical diagnostics: voltage V(t) and charge Q(t) via voltage probes connected directly to the DBD, and current I(t) from the HV supply.
To exclude any spurious effects of humid air on the probe capacitor, the voltage probes, or the cables, the top surface of the DBD could be sealed off and independently exposed to humid air in an airtight enclosure; the experimental observations were unchanged, thus proving that the results are specifically related to the DBD electrode surface.
The electrode capacitance was also measured directly at the SDBD terminals using a vector impedance analyzer for low voltage without plasma in dry and humid conditions, thus cross-checking the values independently of the apparatus in figures 1(c) and (d).
The DBD surface temperature is monitored by a thermal camera FLIR E85, and detailed visual inspection of the PCBfingers SDBD is made after the experiments using an optical microscope. The RH level during the measurements could be controlled by two different methods: a HumidiKit (Incubator Warehouse) ultrasonic humidifier regulated to within ±10% by a hygrometer probe inside the reactor, or by a gas injection line mixing dry synthetic air with water-bubbled air using Bronkhorst flow-meters up to about 3000 sccm, monitored by a HM42 Vaisala HUMICAP ® humidity and temperature meter. There was no noticeable difference in the results using either humidifier method.

PCB-fingers SDBD performance in humid air
This section describes the performance and deterioration of the PCB-fingers SDBD when operated with 5 kV peak-to-peak at 1 kHz, for various values of RH. Experimental reproducibility was verified at least twice, and a new DBD was used for each experiment.

Irreversible degradation of the SDBD materials
Permanent physical damage and material degradation occurred after prolonged use of the SDBD in a humid environment. At an intermediate humidity level of 50%, after one hour of operation, several deteriorations were observed, in addition to a progressive reduction of the active plasma area. For example, extensive wear on the electrode edges becomes visible, with discoloration and the formation of rough edges and holes. The FR4 dielectric suffers a general whitening and takes on a blemished, or speckled, appearance shown in figure 3. These observations of long-term degradation of SDBD performance during plasma-seed experiments [2,17] were the original motivation for this investigation.  [10,20]. At the cathode, water and oxygen reduction can occur: such that (OH) − can then react with the metal or its oxide, forming salts that are soluble in water, thus corroding the electrode. At the anode, the electrode becomes oxidized, with release of hydrogen molecules and ions. Other oxidants which form in the plasma, including ozone and nitrogen oxides, can also aggravate the electrode corrosion. Surface streamers of SDBDs may directly damage the electrode, as observed in [21,22], thereby exposing the copper electrode below the compromised nickel-gold protection to oxidation. The electrodes can be protected by embedding them in the dielectric to avoid any direct contact with air and the plasma. This approach is applied in the diffuse coplanar surface barrier discharge technology proposed by ROPLASS [23], where the alternate grounded and HV electrodes are both covered by a 0.4 mm-thick layer of alumina. A much higher voltage in the range 12-30 kV peak-to-peak is necessary to reach breakdown in the air above the dielectric surface, requiring very high voltage supplies and oil cooling of the system.

Dielectric damage.
Hygroscopic materials absorb moisture and so are susceptible to alteration in a humid environment. Absorption of moisture into a hygroscopic material is a two-step process [24], namely, adsorption onto the surface followed by diffusion into the bulk [25]. In our particular case, adsorption is strongly enhanced by plasma surface activation as demonstrated in figure 4. The uncleaned, virgin FR4 is only mildly hydrophilic [10,26] as shown by the water droplet contact angle of Θ ≈ 60 • in figure 4(a), calculated using Θ = 2 tan −1 ( 2h/d ) , with h and d the height and the diameter of the drop on the surface, respectively [10]. However, after only a few minutes of exposure to SDBD plasma, the FR4 becomes strongly hydrophilic; a water drop placed on its surface is then observed to spread evenly, covering the whole width between the electrodes as shown in figure 4(b), with a contact angle too small to be measured. Such a strong increase in hydrophilicity indicates that a significant number of dielectric-surface polar groups were created by the plasma [27]. A similar effect of surface hydrophilic activation by DBD streamers has also been observed for polymethylmethacrylate (PMMA) polymer films [28].
The plasma activation of the FR4 surface can be explained by the breaking of the dielectric molecular bonds, for example, by the plasma energetic electrons. This can lead to the formation of dipoles on the surface of the dielectric, with a positive polarity outward and negative polarity inward that attracts polarized molecules such as water [27]. The contact angle behavior is similar to that of plasma-activated polyethylene terephthalate, where it is attributed to the formation of active OH surface groups, possibly indicating hydrogen bonding with water [29]. Also, the presence of water soluble impurities like salts or hygroscopic dust on uncleaned surfaces may cause formation of conductive aqueous layers at the deliquescence humidity which may lie below RH of ∼60% [9]. This efficient adsorption provides a ready source of surface moisture [10] which facilitates diffusion into the porous FR4 dielectric. The resultant absorption explains the whitening in figure 3 of the FR4, which, clearly, is a hygroscopic dielectric not suited for SDBD devices in humid air.
Irreversible damage to the dielectric could be avoided by choosing non-porous hydrophobic materials that do not become hydrophilic by plasma activation, nor are degraded by plasma exposure. FR4 absorbs 0.5% water by volume at room temperature and RH = 100% [24]; polyimide absorbs approximately twice as much water [30], whereas polypropylene tends to oxidize if heated [31], and polytetrafluoroethylene (PTFE) is degraded by plasma, as are many polymers and polymer coatings. Finally, high quality alumina (Al 2 O 3 ) and aluminum nitride appear to be the best candidates, not only for their dielectric properties and their immunity to moisture absorption, but also for their biological compatibility [32,33], although they are mildly hydrophilic. In fact, decomposition of epoxy resin could generate byproducts containing hydrocarbons (formaldehyde, formic acid or some cyanide-containing derivatives) that are bactericidal, and therefore more difficult to decouple from the possible sterilization effect of the plasma. We note that the choice of the dielectric might also affect the ignition voltage [34]. The alumina disc of the Perforateddisc SDBD (section 2.2) was verified to be hydrophilic [26] but much less activated by plasma operation than the FR4: after 30 min plasma operation, the contact angle of a water drop on the alumina remains almost the same, decreasing from Θ ≈ 60 • to ≈50 • , in sharp contrast to the FR4 in figure 4. Nevertheless, the weaker plasma activation of alumina's hydrophilicity does not prevent the formation of physisorbed water on the alumina surface. Photographs of the plasma visible emission at 5 kV peak-to-peak constant voltage after 30 min continuous plasma operation at relative humidities of (a) 36% ambient air; (b) 50% ambient air; (c) 71% using humidifier; and (d) 86% using humidifier.
By using alumina instead of FR4 for the dielectric, and a stainless steel mesh instead of the Cu-ENIG electrode, the Perforated disc SDBD suffered no material degradation throughout the whole campaign of measurements.

Reversible degradation of the plasma performance
The photographs in figures 5(a)-(d) show the plasma visible emission for different humidities at 5 kV peak-to-peak constant voltage. Figure 5(a) shows the bright discharge obtained in nominally-dry ambient air at RH = 36%.
The dimmer emission observed in figure 5(b), for ambient air at a higher humidity of RH = 50%, results from a progressive light reduction after 30 min of operation. When the SDBD is used in dry air after one hour of use at RH = 50%, ignition cannot be re-established in the dark regions of the SDBD. This is consistent with the irreversible damage discussed in section 3.1.
The images in figures 5(c) and (d), for RH > 70%, characterize the weak emission during the whole experiment, causing no apparent damage to the SDBD materials after one hour operation. In this case, plasma ignition does partially recover if the SDBD is subsequently operated in dry conditions. In view of the deterioration due to water in section 3.1, we hypothesize that this reversible degradation at such high humidity is due to the appearance of a water film on the SDBD in humid air that is preventing plasma ignition, thus protecting the SDBD from any plasma damage. The evidence for a conducting water film is investigated in the following.
The Lissajous figures for each value of RH are reported in figure 6(a). At the lowest RH of 36%, for which the plasma is well established, the Lissajous rhomboid-like form is characteristic of the classical DBD plasma cycle [19]. However, for increasing RH and diminishing plasma emission, the Lissajous figures become more elliptical. The area within each Lissajous figure equals the total dissipated energy per cycle [19] and the corresponding time-averaged power of the discharges is shown in figure 6(b). The power is highest in dry ambient air at RH = 36%, falls to about half that value at 50% humidity, but increases for higher humidity levels. The lack of visible plasma emission in the discharge pictures of figures 5(c) and (d) suggests that, at high RH, the electrical power is dissipated by some additional mechanism as well as through any residual plasma discharge. One possibility is ohmic losses, perhaps due to a resistive water film, as discussed below and in section 4.
To further investigate the effect of humidity on the SDBD electrical parameters, the Lissajous figures are now compared for a range of voltage amplitudes at low and high RH. Figure 7(a) shows the measurements in dry conditions, where breakdown and plasma occur at 5 kV peak-to-peak. Below this voltage, there is no ignition and the Lissajous figures all lie very close to a straight line whose gradient is the SDBD electrode capacitance, C = Q/V = 423 pF in this case; the vector impedance analyzer similarly measures 430 pF. In absence of plasma, the dry SDBD therefore behaves like an ideal, lossless capacitor because the virgin FR4 dielectric has an estimated resistance of ∼15 GΩ (see appendix).
In contrast, figure 7(b) shows the Lissajous figures measured at high humidity, RH = 80%, for which no breakdown occurs, even at 5 kV. Compared to the straight lines in figure 7(a), the Lissajous figures are all transformed into ellipses which are still characteristic of a capacitor, but now with ohmic losses. This is demonstrated below by analysis of an equivalent circuit of a capacitance C with a parallel resistance R, as shown in the inset of figure 7(b).
For an AC voltage V(t) = V 0 sin (ωt), with V 0 a constant amplitude, and ω = 2π f the angular frequency ( f = 1 kHz), the total current in the equivalent circuit is which can be integrated to obtain the time-dependent charge: whose time average is zero as observed in all of the Lissajous figures. Generally, the work done, W, by the power supply to move the charge Q(t) through a voltage cycle is W =¸Q dV, which is the enclosed area of a Lissajous figure [19], hence the time-averaged power is the energy multiplied by the frequency, P = Wf. In the present case of analytical expressions for Q(t) and V(t), the Lissajous figure enclosed area can be directly calculated by substitution to obtain so P = Wf = V 2 0 /(2R) is the time-averaged ohmic power dissipation, as expected by inspection of the equivalent circuit in figure 7(b).
The calculated ellipses Q(V) give excellent fits to the Lissajous measurements in figure 7(b). The fitted values are in the range R = 1.5-2.3 MΩ and C = 517-588 pF [35]. Note that R is now about 10 4 times smaller than the 15 GΩ resistance of the dry FR4 dielectric (a new SDBD was used for each experiment, so FR4 degradation is not responsible for the reduced resistance). The measured powers are equal to V 2 0 /(2R). These results are consistent with ohmic power dissipation, without plasma, at the high humidity of 80% RH. The fitted values for C are about 30% higher than the dry dielectric capacitance of figure 7(a), confirming the increase in capacitance reported in [36]. Similar degradation of the plasma is also found for the Perforated-disc SDBD with alumina dielectric, even though there is no deterioration of the materials. All of these experimental measurements are explained in appendix by an equivalent circuit analysis involving a resistive film on the dielectric.
The concept of ohmic power dissipation due to a water film on a hydrophilic SDBD surface in humid air is developed quantitatively by numerical simulation in section 4.1.

Practical solutions for stable, uniform SDBD plasma in high humidity atmosphere
This section is concerned with solving the problem of plasma partial extinction in high RH (70%-80%) when using the PCB-fingers SDBD. The issues of suitable SDBD materials to avoid irreversible damage of FR4 were addressed in the previous section 3.1.
External heating of the SDBD surface, for example, by a hot plate behind the grounded electrode, enhances water evaporation from the dielectric surface and reduces the local RH in the vicinity of the SDBD. For RH 75 ± 2% as measured in the reactor volume by the in situ humidity probe, the plasma emission over the DBD surface is partially recovered at 49 • C in figure 8(b), while it is fully recovered over the whole surface of the device at 71 • C in figure 8(d). The corresponding Lissajous figures in figure 8(e) change from an elliptical shape (consistent with ohmic dissipation) at 30 • C without external heating, to a rhomboid-like shape resembling operation in dry air at 71 • C (consistent with plasma dissipation). These observations are consistent with the formation of a water film playing a key role in extinguishing the humid air plasma. Heating concurs with the recommended practice of keeping PCB materials warm to protect them from damage in humid air [9], and also reduces the absorption of water, limiting electrode corrosion. However, strong heating of the DBD is incompatible with some applications, being detrimental for ozone generation by promoting discharge poisoning [37], as well as for most biological specimens, for instance, affecting seed germination by causing heat shock [38].
Higher DBD voltage increases the region of active plasma by enlarging the air volume where the breakdown electric field is attained. This solution was tested at 82% RH, operating the DBD for 17 min at 5 kV (no ignition) and 6 kV (plasma recovered). After 30 min operation, similar surface temperatures of 35 • C and 44 • C were measured, respectively, by an infrared camera. The main mechanism heating the dielectric is plasma heating of the ambient gas, which then heats the surface of the dielectric by conduction and convection [39].
Ultrasonic drying could conceivably be used to enhance water evaporation from the SDBD surface similarly to a humidifier where mist is ejected from a water surface by ultrasound [40]. However, a preliminary test with the SDBD on a 28 kHz ultrasound transducer was not effective; possibly because the applied frequency was too low, since typical frequencies for water atomization are closer to MHz [41] (the higher the frequency, the smaller the mist droplets).

The possible physical origin of water film on the dielectric at high humidity
The above observations show indirect evidence for a water film being responsible for SDBD extinction at high RH > 60%. The water film cannot be due to spontaneous condensation from the humid air because the dew point, corresponding to RH = 100%, was not reached in these experiments. Instead, surface hydration due to physisorption on a hydrophilic dielectric surface (whether FR4 or alumina in the present case) can account for an adsorbed layer of water [27]. In physisorption, multiple monolayers of absorbate (water) form on an absorbent (the dielectric surface) for vapor pressure far below the saturated vapor pressure, whereas the number of condensed water clusters in the humid air remains negligible. According to Brunauer et al [42], this difference is explained by surface tension considerations: in the gas phase the large free surface energy of small clusters makes their formation improbable except near to the dew point. On the other hand, in surface adsorption, the effective 'liquid surface' is practically complete after the first monolayer has been adsorbed, so that during the formation of successive layers, hardly any surface tension has to be overcome.
The number of physisorbed monolayers can be estimated using, for example, the BET isotherm theory [9,42] where the maximum possible number of monolayers is given by 1/(1 − RH) for hydrophilic surfaces. For example, at RH = 75% in figure 8, the maximum number of monolayers is 4, in qualitative agreement with Monte Carlo molecular simulations [43]. This would seem to be much too thin (∼1 nm) to form an electrically-conducting water film; however, even as few as three monolayers (RH > 66%) are, surprisingly, already sufficient to exhibit significant surface electrical conductivity [9,44,45]. The thin film conductivity enhancement factor, relative to bulk water [44], is shown to be as high as 10 5 , and could be due to conduction along a polarized HOHHO − layer, by tunneling via dipole resonances [46]. The influence of RH on surface dielectric properties can be characterized  [58] by ellipsometry, with indication of saturation and water layer formation above 80% RH on TiO 2 [47]. Note that the proposed explanation for the experimental observations in this work involves only the sheet resistance, R □ , of the hypothetical water film. As shown in appendix, R □ = 1/(σd) in units of (Ω per square), where σ (Ω −1 m −1 ) is the effective electrical conductivity, and d (m) is the film thickness. Consequently, only the product of σ and d is required-in the absence of independent measurement of either parameter-and the BET isotherm estimate of ∼1 nm is a lower limit for d.

Numerical simulations
To have a better physical understanding of the effects of humidity on the operation of a SDBD without plasma, i.e. below the voltage threshold for ignition, two-dimensional time-dependent numerical simulations are performed using the Dynamic Electric Currents Equations of COMSOL ® [48]. The module computes the electro-quasistatic [49] solution to current conservation at each time-step: where J = σE is the conduction current density, E the electric field intensity, ρ the free electric charge density, D = ϵ 0 ϵ r E the electric displacement field, and V the electric potential. The conductivity is assumed to be constant and uniform. ∂ ∂t = iω for a time harmonic solution. The values of the relative permittivity ϵ r and the electrical conductivity σ are taken from the material properties in table 1. Deionized water conductivity, 5 × 10 −6 Ω −1 m −1 , has been considered here, keeping in mind that tap water with much higher conductivity (σ = 5 × 10 −3 -5 × 10 −2 Ω −1 m −1 ) might be more appropriate for the laboratory ambient conditions [50]. The effective conductivity of the water film could also depend on the formation mechanism of the monolayers, depending on how ions or impurities on the uncleaned surfaces are incorporated.
The possibility that the measured ohmic losses are due to the electrical conductivity of humid air is excluded by the simulations, because there is no observable change in the results even for a humid air conductivity several orders of magnitude higher than 10 −14 Ω −1 m −1 for humid air in table 1. A full treatment of the DBD operation would need a model of the SDBD plasma itself [60,61], which is beyond the scope and requirement of this work, especially if plasma chemistry of humid air [4] and the surface physics of physisorption and chemisorption were also to be included. Surface ionization waves associated with DBD plasma are very sensitive to the dielectric surface properties [61], so it can be expected that SDBD plasma ignition would be affected by a surface water film. Lichtenberg figures are a related phenomenon of electrostatic discharges on dielectric surfaces, which can be suppressed under high humidity (RH = 90%) conditions [62].
The model geometry shown in figure 9 features the main components of the PCB-fingers SDBD, namely the 100 µmthick top electrode, the 300 µm-thick FR4 dielectric, and the ground electrode as the bottom boundary. Due to the spatial resolution limitation of the numerical model, in order to investigate high humidity RH ≈ 80%, a 1 µm-thick representative water layer (assumed uniform) is included on the FR4 and electrode surfaces as shown in the inset. Its effective conductivity is scaled with respect to the bulk-water value given in table 1 to yield the required sheet resistance R □ = 1/(σd). A sinusoidal signal V(t) = V 0 sin (2π f t) is applied to the HVelectrode, with f the applied frequency of 1 kHz as in the experiments. Periodic boundary conditions are applied at the left and right walls of the system, and the top boundary is an insulator, as depicted in figure 9. The parameters evolve over several AC periods to give a converged E-field distribution and a symmetrical current trace with zero time-averaged charge, the same as for the experimental Lissajous figures.
To account for the 3D fringing field effects of the real DBD and to align the 2D numerical electrostatic calculation with the experimental value for dry capacitance, the 2D domain depth (out of the plane) is adjusted to 1.35 m. This corresponds approximately to the ∼1.1 m physical length of the PCB-fingers HV electrode. Numerical simulations at 2.5 kV pp (below the experimental voltage for plasma ignition) are performed with and without a water film, time-integrating the simulated electrode current to produce the corresponding Lissajous figures which are compared with experimental measurements in figure 10.
A reasonable compromise for the capacitance (the ratio is underestimated by 12%) and ohmic power (overestimated by 30%) is obtained for a water film sheet resistance of 6.7 GΩ per square. Note that the experimentally-observed increase in capacitance and the ohmic dissipated power are both accounted for by adjusting the single variable of the sheet resistance, thus supporting the interpretation of a water film at high humidity. The sheet resistance is only a factor 3 higher than estimated in the semi-qualitative equivalent circuit model in appendix. To put the sheet resistance into context: if the film has the minimum thickness of 1 nm predicted by the BET isotherm model, then the water film conductivity is enhanced by a factor 3 × 10 4 relative to deionized water, or by only a factor 3 relative to tap water. We note that even if deionized water was initially used, its conductivity would increase in the presence of plasma-generated chemicals such as nitrogen oxides, therefore the deionized water conductivity in table 1 is most likely underestimating the actual value.
A thin conducting water layer covering the surfaces of the SDBD components would reduce the electric field strength during the period of the applied AC voltage, thereby inhibiting plasma ignition. For example, if we consider the extreme limiting case of a thin metal layer covering the dielectric surface, this would lead to an equipotential surface, reducing the surface electric field above the dielectric to zero.
For a quantitative study of the E-field strength, 2D simulations were performed at 5 kV pp , at which no ignition is observed experimentally in humid conditions, as discussed in section 3.2. A zoom of the 2D electric field pattern near to the electrode edge is shown in figure 11 for a range of water film sheet resistance. To better visualize the electric field strength variation, a qualitative ignition region is shown by indicating the maximum spatial extent of the 3 kV mm −1 electric field breakdown limit in dry air. The ignition region is seen to decrease for lower water sheet resistance, down to the value of 2 GΩ per square, where the ignition region almost vanishes, due to a partial 'short-circuit' effect by the water film. For the 1 µm-thick simulated water film, scaled by 10 3 relative to a 1 nm thin film, this corresponds to a conductivity enhancement factor of 10 5 when compared with σ = 5 × 10 −6 S m −1 in table 1 for bulk deionized water. This appears to be consistent with the observed lack of ignition in high humidity, and with the enhanced conductivity of a few water mono-layers as observed by Guckenberger et al [44], up to five orders of magnitude higher than the bulk value.

Hybrid surface-volume DBD, the HDBD
The experimental and numerical results discussed in sections 3 and 4 show how SDBD performance can be degraded by the presence of an thin water layer with an enhanced electrical conductivity which is a consequence of high humidity. To optimize the design of a DBD to be more robust in a humid environment, a hybrid combination of a surface and volume DBD can be envisaged. The proposed HDBD shown in figure 12(c) can be seen either as a narrow-gap VDBD, figure 12(a), with an open, flat-mesh electrode; or equivalently, as a SDBD, figure 12(b), with the patterned electrode raised above the dielectric surface. The HDBD is more robust as a plasma source than the SDBD because the high voltage electrode is physically separated from the dielectric surface: the electric field occurs across an air gap, thus guaranteeing breakdown into an air plasma, even in presence of a highlyconducting surface film on the dielectric.
The concept of simultaneous volume and surface DBD operation is demonstrated by Kettlitz et al [63] using timeresolved imaging of a single discharge between one wire of a mesh and a counter-electrode in ambient dry air for a 0.5 mm gap. The plasma of a HDBD generates reactive radicals which diffuse into the space beyond the mesh electrode. This represents an indirect plasma source, because the plasma charged particles and electric fields remain mostly confined between the mesh and the plane electrode.
Another hybrid-type solution is a wire array with ceramic tubes around metal wires arranged as a planar surface source, introduced by Kitazaki et al [15,16,64,65]. This is a wireto-wire VDBD array arranged as a plane surface source with alternate HV/ground wires. The dielectric barrier is composed of individual ceramic tubes around each wire, instead of using a single ceramic plate for the whole HDBD. The wire-to-wire arrays are relatively transparent to the passage of plasma radicals from both sides of the quasi-planar source, but are possibly more mechanically fragile than the mesh-to-plate design of the Perforated-disc HDBD.

HDBD numerical simulations
To clarify how the 2D electric field profiles are affected by introducing a 0.2 mm air gap in the HDBD design, numerical simulations similar to those in figure 11 are shown in figure 13 for the Perforated-disc SDBD geometry of figure 1(b). The  Schematics of (a) a volume DBD with a single dielectric barrier, where the plasma and its products are confined to the narrow gap between the electrodes; (b) a surface DBD with flat finger electrodes where the plasma is susceptible to partial extinction in high humidity; and (c) a raised mesh-to-plate hybrid DBD, which combines the robust air-gap plasma of the VDBD with the open geometry of the SDBD plasma source. The hybrid discharge shape mimics the combined forms of the VDBD filament and the SDBD pancake plasma [63]. The electrodes are shown in cross-section for only two electrode elements, with arbitrary ground or high voltage connection, in each diagram.
ignition region of the dry SDBD, figure 13(a), is significantly diminished by the presence of the water film in figure 13(c). In contrast, almost no influence of the water film is observed when the Perforated-disc is raised by 0.2 mm to form the HDBD configuration in figures 13(b) and (d). This is because the HDBD electric field is principally perpendicular to the surface, and therefore unaffected by the film conductivity. In contrast, the SDBD electrode is in electrical contact with the film; its electric field lies partly along the surface and is thus susceptible to a partial short-circuit by the film as shown in figures 11(d) and 13(c).

HDBD experimental measurements
Experimentally, the HDBD configuration is simply achieved by inserting a 0.2 mm thick PEEK-dielectric spacer ring under the circumference of the Perforated-disc SDBD. This raises the electrode mesh above the dielectric surface, thus breaking electrical contact with any surface film of water. The plasma visible light emission, partly obscured underneath the mesh of the HDBD, is shown in figures 14(a) and (b) for 35% and 85% RH respectively. The corresponding Lissajous figures are given in figure 14(c). For voltages even higher than 6 kV the plasma spreads out to fill the area on the dielectric between the mesh wires. In contrast to SDBDs, the plasma ignition of the HDBD is not inhibited by the high humidity, and the plasma is uniform (insofar as the mesh is planar) in both dry and humid conditions. The only remaining influence of a surface water film on the HDBD can be seen in the wider Lissajous figure, with 30% higher total power dissipated at 85% RH, attributed to ohmic losses in the water film caused by the plasma current when it spreads across the dielectric surface [61,63].

Conclusions
The performance of a SDBD made of printed circuit copper electrodes on FR4 dielectric was investigated at various levels of RH. At intermediate humidity (RH = 50%), a gradual extinction of the plasma region occurs over hours, due to a deterioration of the SDBD materials from plasma chemical reactions with water. At higher humidity (70%-85%), plasma ignition is inhibited over parts of the surface, and the plasma visible emission is faint even though the input power level is maintained. Ohmic power loss persists for voltages below the ignition threshold. Plasma performance is restored at high humidity by heating the SDBD. These experiments, taken together with equivalent circuit analysis of Lissajous figures and numerical simulation of the SDBD electric field, suggest that a thin water film with enhanced sheet resistance on hydrophilic FR4 inhibits the plasma performance in a high humidity environment. To further confirm this scenario, complementary measurements could be envisaged in future works: optical emission of the OH(A-X) band should be affected by the presence of a conducting water sheet [66], incorporation of water on the upper level of the dielectric surface would affect the time evolution of attenuated total reflection-Fourier transform infrared spectroscopy spectra [67], and electric field variations could be assessed by the emission bands ratio of N 2 second positive system and N + 2 first negative system intensities [68]. A HDBD is proposed as a combination of a surface and a volume DBD by interposing a 0.2 mm air gap between a perforated electrode and the dielectric, thus breaking any contact with the water film on the dielectric surface. The HDBD shows a more robust performance at high humidity in terms of plasma emission intensity, uniformity, and ignition reliability, because the electric field in air is not diminished by a resistive water film on the dielectric surface. Material deterioration is eliminated by using alumina instead of FR4, and by replacing the copper electrode with a stainless steel perforated disc.

Data availability statement
The data cannot be made publicly available upon publication because they are not available in a format that is sufficiently accessible or reusable by other researchers. The data that support the findings of this study are available upon reasonable request from the authors.

Acknowledgment
The authors wish to acknowledge the support of the SPC technical team.

Appendix. Equivalent circuit for the SDBD with a resistive water film
The schematic and T-section circuit in figure 15 bring physical insight into how a surface resistive film strongly reduces the parallel equivalent resistance R, and modestly increases the equivalent capacitance C in figure 7(b), relative to the dry conditions in figure 7(a). In figure 15, each half of the water film is represented by a single microstrip T-section, 1 mm long. The inductive impedance of this short, low frequency (1 kHz) microstrip is negligible compared to its series resistance. By symmetry, the lateral current i through the water film is zero at the film center, hence the overall circuit can be summarized as in figure 16. Finally, the parallel elements C and R of the overall equivalent circuit of the inset in figure 7(b) are found by a combination using the transformation of series-to-parallel circuits [69], to give: Quantitative estimates can now be made for the dry and humid cases, using the PCB-fingers SDBD properties in section 2.1 and table 1. The total effective electrode length (out of the plane) is L ≈ 1 m, width w = 2 mm, FR4 dielectric thickness D = 0.3 mm with ϵ r = 4.5 and conductivity σ FR4 = 10 −11 Ω −1 m −1 .
For the dry SDBD in figure 7(a), the parallel-plate estimate of the electrode capacitance is C pcb = ϵ 0 ϵ r wL/D ≈ 266 pF; this is less than the 423 pF measured in figure 7(a) and confirmed by the vector impedance analyzer, because the significant contribution from fringing fields is neglected here. The dielectric resistance in parallel with C pcb (not shown in figure 15) is R pcb = D/(σ FR4 wL) ≈ 15 GΩ, which is effectively an insulator, as expected for a dielectric. Therefore, the equivalent circuit for the dry SDBD in figure 7(a) is simply the capacitance C pcb .
For the humid SDBD in figure 7(b), the equations (A1)-(A3) apply. The water film lateral resistance, R wf in figure 15, is R wf = w/(σLd) = R □ w/L, where d is the water film thickness, σ the water conductivity, and R □ = 1/(σd) is the water film sheet resistance in units of (Ω per square). For a preliminary estimate of R □ we consider the BET isotherm [42] estimate of d ∼ 1 nm in section 4, with the conductivity of de-ionized water in table 1 enhanced [44] by a factor 10 5 . Thus, R □ ≈ 2 GΩ per square, hence R wf ≈ 4 MΩ, and q ≈ 1.2 using (A3). Finally, the calculated equivalent circuit values in figure 7(b) show a ∼50% increase in capacitance from 266 pF to C ≈ 420 pF using (A1), and R ≈ 1.2 MΩ using (A2), in rough agreement with the experimental values in figure 7(b).
The agreement could be improved by taking into account fringing fields for C pcb , and by adjusting the assumed value for R □ , but the fringing fields can only be calculated by numerical simulation. Nevertheless, this equivalent circuit model demonstrates the observed modest increase (∼30%) in capacitance C from figures 7(a) to (b), and, especially, a very strongly reduced parallel resistance R from 15 GΩ down to ∼1 MΩ, due to a water film.
An advantage of this analytical approach is that it is easy to evaluate the two limiting cases of R wf → ∞ (q → 0) for the dry SDBD, and R wf → 0 (q → ∞) for the 'metal film' limit of a perfectly-conducting water film. Substitution into (A1)-(A3) gives the R, C values for the two limits: dry : C → C pcb , R → ∞; metal : C → 2C pcb , R → ∞, hence 1 ⩽ C/C pcb ⩽ 2. (A4) A moment's consideration of figure 15 shows that the SDBD capacitance does indeed double in passing from the dry limit to the 'metal' limit (fringing fields are ignored in this simple model), and also that the equivalent resistance R → ∞ because there is no ohmic power dissipation in the water film for both limits. Clearly, there must be an intermediate value of the water film resistance R wf for which the parallel equivalent resistance R is a minimum. Using (A2), and setting ∂R/∂R wf = 0, the minimum equivalent resistance R is found to occur at q = 1, which is, in fact, close to the value calculated above. Serendipitously, the experimental parameters are therefore close to the minimum R condition, which also corresponds to the maximum ohmic power loss. If the operating frequency had been much higher or much lower than 1 kHz, or if the humidity had always been less than RH ∼ 80%, then power dissipation due to a water film might not have been observed at all. Finally, note that the equivalent circuit model cannot accurately account for the spatially-distributed resistance and capacitance of the water film, and neglects the capacitive contribution from fringing fields. Hence the numerical simulation in section 4.1 is necessary for a quantitative estimation of the impedance given in figure 10, and for calculations of the electric field spatial distribution in figure 11 Figure 15. The T-section equivalent circuit represents a water film on the PCB-fingers SDBD in figure 1(a). Bottom: cross-section showing a w = 2 mm-wide copper electrode flanked by a surface water film on each side. Top: the equivalent circuit of the central element is shown in red. C pcb is the capacitance of each w = 2 mm-wide section of the dielectric (thickness D = 0.3 mm) to ground, and R wf is the lateral total resistance of the w = 2 mm-wide water film of thickness d. For the double T-section description of the water film, C pcb is split into two parallel halves, and R wf is split into four equal series resistances, assuming a uniform water film. I is the capacitive current from the electrode to ground; i is the current conducted laterally across the water film, and via the water film capacitance to ground.