Effect of dielectric target properties on plasma surface ionization wave propagation

Surface ionization waves (SIWs) propagating along dielectric covered, grounded surfaces have been studied for various dielectric bulk and surface conditions; a dependence on the propagation velocity with respect to dielectric electrical thickness and near surface permittivity profiles are observed. SIWs generated by an atmospheric pressure plasma source are imaged interacting with planar dielectric surface. Surface wave velocity is obtained by tracking emission intensity as a function of time. Target dielectric thickness is varied from d=0.15−10 mm and dielectric constant is varied from ϵr=6.21−9.4 . The propagation of SIWs can be generally predicted by relating their velocity to the RC time constant of the circuit generated between the plasma and the dielectric surface, but it is found that this approximation breaks down for dielectric substrates of sufficient thickness and wave velocity becomes constant. The results show that wave velocity is stable and predictable for target thicknesses beyond a certain point determined by the permittivity of the target material. It is also shown that SIW propagation is strongly driven by the dielectric material near to the surface of the target in addition to the bulk material. The possible mechanisms driving these thickness dependent behaviors is discussed.


Introduction
The study of atmospheric pressure plasma jets (APPJ) has grown in recent years. Many of these plasma sources produce non-thermal plasmas (NTPs) that have advantageous features for specific applications. The interaction of NTPs with surfaces has found many applications in agriculture [1], surface modification [2], biomedical treatment [3,4], and catalysis * 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. [5][6][7]. NTPs are capable of simultaneously producing reactive species, charged particles, and strong UV photon irradiation [8][9][10]. Under the correct conditions, these sources are capable of producing stable and repeatable ionization waves that deliver NTP products to a target. These ionization waves have been extensively studied as micro-plasmas traveling in confined geometries [11,12] and as plumes in open air [13,14]. In open air, ionization wave fronts form trains of high velocity plasma packets, often referred to as plasma 'bullets', that have been observed propagating at velocities up to 2 × 10 5 m s −1 in noble gases [15,16].
As ionization waves generated by APPJs interact with a target material they can become surface ionization waves (SIWs) that propagate along the surface. While most works study the effect of the plasma on the surface, the surface can have tremendous impacts on the plasma SIW development. SIW have been shown to not propagate along conductive surfaces and surfaces with high dielectric constants (ϵ r > 20) [17]. Instead, when the ionization wave impacts conductive or high permittivity surfaces, a return stroke is generated and propagates back toward the plasma source [18]. Previous work by Viegas et al has shown that for low strength dielectrics (ϵ r < 20) the decay of the axial electric field in the target material allows for the radial field to drive the surface wave propagation [19]. The effect of grounding the target surface has also been studied and is shown to effect the formation and dynamics of SIWs [20,21].
In many of the above cited works it is common to relate the SIW velocity to the RC time constant τ of the circuit created between the plasma and dielectric substrate [19,21] where R is the resistance of the plasma and the sheath, C/A is the bulk capacitance per unit area of the target surface. d is the thickness of the dielectric target, ϵ r is the target relative permittivity, and V SIW is the SIW velocity along the target surface. This relation requires the assumption that the traditional formulation for capacitance is valid in these systems. Capacitance requires that all potential field lines be parallel and uniform as well as in a single direction perpendicular to the conducting boundary conditions. The limit to these assumptions and the implications on SIW propagation will be discussed in this work.
In regards to dielectric constant (ϵ r ), as permittivity increases so does the target capacitance and in turn the RC time. A longer RC time equates to a slowing of the rate at which charge can be delivered to the surface and therefore reduces the rate at which the SIW can propagate. This is evident in experimental work conducted by Yue et al where it is observed that when transitioning from a glass target of ϵ r = 4.9 to a water target with a dielectric constant ϵ r = 80 that the SIW propagation is not visible for the conductive surface and is greatly diminished for the water target [22]. It is also observed in numerical studies by Viegas et al where the target dielectric constant is varied from ϵ r = 1, 4, 20, 56, 80 and shows the spread of the SIW slowing with increasing dielectric constant [19].
The dielectric thickness is also an important part of the RC time. As the target surface thickness increases the capacitance of the target will decrease. This in turn equates to a lower RC time and therefore a more rapid rate of charge transfer to the surface. This extends to SIW velocity increasing as target thickness decreases. This relationship leads to a prediction that velocity of SIW should increase monotonically as the target dielectric gets thicker. Work studying the effect of target thickness is limited and narrow in scope. Guaitella and Sobota imaged a helium APPJ incident on glass targets 1, 2 and 4 mm thick at off normal incidence and noted that as target thickness increased, the discharge area shrunk and mean light intensity increased [21]. Adjacent work provide analytical solutions to SIW generated from sliding discharges showing that a SIW wave has a maximum speed at some thickness and then moves more slowly as thickness increases [23].
In this work, a nanosecond APPJ is used to generate plasma ionization waves for the study of SIW propagation. Helium is the working gas in this experiment. Experiments are configured to explore the effects of target thickness and dielectric permittivity on the propagation of SIW. Exploring SIW propagation for variable thickness with constant permittivity and variable target permittivity is considered. Variable permittivity targets are made by mixing differing materials in a single target configuration. The primary method for quantifying propagation characteristics is the SIW velocity. Experiments show that RC time predictions break down for thick dielectric targets and that the dielectric stack does not behave as a bulk capacitor. Proposed mechanisms for observed phenomena are discussed.
The experimental setup, diagnostics and analysis methods are described in section 2. Results and discussion for all experiments are in section 3, including SIW repeatability metrics. Concluding remarks are in section 4.

Plasma system
The experimental setup is divided into two primary systems, the plasma system and the dielectric target. A block diagram of the overall experiment is shown in figure 1. Following the setup the diagnostics and methods are given in section 2.3. The plasma system consists of an APPJ as identified in Jiang et al [24] The work presented here utilizes a nanosecond DC pulse of positive polarity for power delivery. Pulse width is set to 500 ns with 4.0 kV applied voltage. A 1 mm diameter tungsten electrode is nested within a 2 mm inner diameter quartz tube for primary gas flow. The working gas is helium delivered at a flow rate of 1 standard liter per minute. A copper ground ring sits outside of the quartz tube centered at the location of the electrode tip. The ground ring is 5.2 mm in height and is positioned 3.5 mm from the tip of the quartz tube.
Power is delivered by a Matsusada positive polarity high voltage power supply (AU-30P40). High voltage is gated using a DEI pulse generator (PVX-4110) driven by a BNC (model 575) delay generator. The source has a ballast resistor of 500 Ω at the source head. The source is mounted to a steel chamber to mitigate external air flows. The chamber is vented to prevent unwanted build-up of helium near the source and target.

Dielectric target
The dielectric target is configured to cover dielectric thicknesses ranging from 0.15 mm to 10 mm using different dielectric constants. Table 1 lists the material thicknesses and their relative dielectric constants. The dielectric material samples are 25 × 25 mm square cut panes. The dielectric slides used in this work were selected for their rigidity, smoothness, offthe-shelf readiness, and their low relative permittivity. It is known that for high dielectric constants that SIW propagation  is greatly diminished or is not visible [19,22]. Selecting dielectric constants far from ϵ ⩾ 50 ensures measurable variation in SIW propagation with varying permittivity. The target stage is 3D printed with a ground plane made of foil tape. Alignment pins on the stage guarantee that all glass layers are placed consistently. Both configurations are placed such that the gap between the source tip and dielectric surface is 10.5-11 mm. This gap is measured using the ICCD camera in observation mode and referencing known dimensions (figure 2). A three-axis adjustment stage is used to position the target and maintain constant source-to-target spacing for all thicknesses.
For glass materials used, the capacitance of a single thickness has been measured using an LCR meter (Keysight E4980A) and test stand (Keysight 16 451B) with a 5 mm diameter contacting electrode. The equation for a parallel plane capacitor is where ϵ 0 and ϵ r are vacuum permittivity and the relative dielectric constant, respectively. The area of the parallel conductors is A and the distance between the conductors is d. The error in the dielectric constants given is due to small gaps between the layers of material that trap air [25]. The presence of an air gap reduces the bulk average capacitance and needs to be taken into account. For these experiments the air gap is estimated to be g = 5 ± 3µm for all materials. For the thick dielectric samples of 1 mm thickness, the presence of this gap has minimal effect on the measured permittivity due to the air gap being far thinner than the sample. The error in the bulk averaged capacitance of each dielectric stack is listed and shown in figure 12 in section 3.5. For simplicity in describing the materials of interest, they will be referenced by their determined dielectric constant throughout this work. (ex. referring to a piece of sapphire data as ϵ = 9.4 sample)

ICCD imaging.
A Princeton Instruments PI-MAX3 ICCD camera is used to image the ionization wave interaction with the target dielectric. The lens used is a Nikon (AF-S Nikkor 18-55 mm) at a distance of 0.15 m from the jet source. Gate width is kept at 5 ns and the delay time-step is 5 ns. Images are taken over 2000 accumulations to average over noise in the system. Total elapsed time for imaging in the system is 200 ns. Figure 2 is the ICCD camera view of the source tip, dielectric target, and the target holder.

Electrical measurements.
The jet source has an integrated current probe (Pearson 510) and voltage is measured using a (Tektronix P6015A) high voltage probe, both connected to pickups on the plasma source. Current and voltage traces are collected with an 8 ps/pt resolution and averaged over 16 samples. There is a 0.66 ns delay between the voltage and the current measurement that is taken into account when determining pulse energy. Two separate measurements of current are taken for each experiment. The first is the total current when the gas is flowing and the plasma is ignited. The second is the displacement current when there is no gas flow and the plasma is extinguished. The difference between the total current and the displacement current is the true plasma current [26]. An example set of VI traces is given below in figure 3. The plasma current is much smaller than the total current due to the 500 Ω ballast resistor at the head of the source. Energy per pulse is calculated according to equation (3).
where t 1 and t 2 are the start and end times of a pulse event.

Post-Processing.
For each potential set-point of the conducted experiments (voltage, dielectric thickness, etc) there is a corresponding set of images that covers 200-250 ns of elapsed time of the ionization wave. This time covers ionization wave generation, propagation to the target, target impact, and propagation along the surface. Figure 4 shows the time evolution of the ionization wave as it transits from the source to the surface then propagates as an SIW. In order to capture the front edge of the propagation, a Matlab script is used for identifying the edges of the ionization wave event and tracking them as a function of time. Identification of the wave boundaries is accomplished using user functions 'subpixelEdges.m' and 'findlongestedge.m' to retain only the continuous boundary of the wave front [27]. The sensitivity of the boundary is adjusted until all images can be processed without changing any set-points. Once the edges are identified, the position data can be extracted and further processed. The output of the Matlab script is position as a function of time. The axial velocity is given by taking a linear fit of the data from IW initiation to IW impact ( figure 5(a)). The same process is also used to determine the radial velocity of the SIW ( figure 5(b)). Error for these linear fits is the standard error of the slope as calculated by the linear fit. The magnitude of the error is <10% for axial velocities and < 3% for SIW velocities, meaning that a linear fit is a good assumption for the region of study. The total elapsed time covered by a set of images is limited to the light intensity of the IW event. Peak intensity occurs when the IW impacts the surface and images are collected until the peak intensity falls too low for reliable analysis.

Surface initial conditions
In order to ascertain whether the trends in SIW velocity are due strictly to changes in the target dielectric properties the stability of the ionization wave initiation and surface impact initial conditions is addressed. The consistency of ionization wave initiation is evaluated by observing the energy-per-pulse across a wide range of target thicknesses. Axial ionization wave velocity is tracked prior to SIW generation on the surface. A stable axial wave is expected to be repeatable and not vary with target thickness. Only the first 200 ns of the pulse is considered because this is the energy contained by the SIW during the time of imaging. Figure 6 shows that for the range of thickness covered there are no significant trends in power-per-pulse for a set voltage amplitude. There is a slight trend in decreasing energy with increasing thickness, but this is not seen to impact the results shown in later sections. This implies that ionization waves are generally initiated at the same E/N and power density. Figure 7 shows that for fixed gas flow rate and applied voltage the axial wave velocity does not deviate significantly with dielectric target thickness. The result is that changing the thickness of the target dielectric does not significantly affect the propagation characteristics of the axial ionization wave.
It is noted that the deviation in axial velocity magnitude is observed whenever the source is disassembled for cleaning or repair. This indicates that there is a degree of sensitivity to small changes that occur in electrode and grounding ring positions during the assembly process. The magnitude of pulse energy also changes as a result of the source assembly and maintenance process. That said it is accurate to say that an increase in pulse energy does result in an axial ionization wave of higher velocity. The effect of pulse energy on SIW propagation is not the focus of this work and as stated in section 2.1 the drive voltage is kept at 4 kV for all experiments. As with the mild trend with pulse energy, the SIW propagation results show no signs of being affected by these variations in the source assembly.
Controlling the gap distance from the target to the source tip is important for the consistency of the SIW initial condition. Reducing the gap would result in the dielectric target capacitance having a more significant effect on the energyper-pulse. Increasing the target distance would result in more energy being dissipated prior to ionization wave impact and reducing the distance the SIW spreads. For all results shown,    Another topic of note is the surface charging that occurs during the plasma surface interaction and the subsequent discharging that occurs over a much longer timescale than the offtime of the discharge. It is noted that the time between pulses is not sufficient for all surface charge to dissipate from the target dielectric or from the dielectric tube that the source is constructed with. The presence of lingering surface charge leads to a more consistent and repeatable discharge, often referred to as memory effects [28,29]. In this work the plasma is operated sufficiently long enough for the lingering charges to be at a steady state prior to each experiment. Figure 8 shows the results for the case where the permittivity of the target is constant as a function of thickness. A diagram of the stacking configuration is inset in figure 8. For thin targets there is a monotonic increase in SIW velocity as predicted by equation (1) that is most evident for the ϵ r = 6.21 material. For the material of dielectric constant ϵ r = 6.21 and ϵ r = 7.12 it can be seen that after some thickness (d = 1.65 mm and d = 3.0 mm, respectively) the velocity of the SIW plateaus to a constant value. In the case of ϵ r = 7.12 it is shown that this plateau in SIW velocity is present for thicknesses much greater than when the plateau is established. It is evident that for higher dielectric constant, the inflection point where SIW velocity becomes constant shifts to greater thickness. For ϵ r = 7.12 it is shown that the SIW velocity is not effected for thicknesses up to 10 mm. This is significant as it indicates that the SIW and the electric fields that accompany it are not effected by additional dielectric material after some transition point. It is also seen that as target permittivity increases, the SIW velocity decreases. This is in line with predictions made by the RC time relation.

SIW velocity
While the RC time constant predicts trends in SIW velocity for small thickness targets (< 2 mm for ϵ r = 6.21), the ability for RC time to predict SIW velocity breaks down as target thickness increases. This is most evident for the dielectric thickness but is also true for trends with permittivity. For thin dielectrics there is an ϵ −1 r dependence as predicted by equation (1), as the thickness increases this dependence becomes more linear in nature, indicating that the RC time prediction also breaks down for permittivity. This result establishes a transition point where for a fixed permittivity there is a limit at which additional material in a dielectric stack does not effect the propagation of SIWs. The mechanism for this behavior is discussed in section 3.5 with greater context given by other results.

Varying dielectric constant
Another assumption made by relating SIW velocity to RC time is that capacitance per unit area depends on the thickness and permittivity of the entire stack. Where C from equation (1) is agnostic to the relative position of dielectrics in a heterogeneous target stack. This presents an opportunity to answer  whether there are additional interaction mechanisms influencing the SIW propagation. To investigate the effect of varying the average dielectric constant of the target, the thinner cover slips of ϵ r = 6.21 are stacked on top of a sapphire slide (ϵ r = 9.4) to build a total stack height of d = 1.90 mm and a final average dielectric constant of ϵ r = 7.88. Figure 9(a) shows a block diagram of the stacking configuration. The result is that as the substrate gets thicker, it is average dielectric constant will also decrease. As the dielectric constant reaches a final value and a final thickness it is expected that the SIW velocity will sit somewhere in between the trend-lines for the constituent material samples. The process is repeated so that in the second case the sapphire will sit on top of the dielectric stack while adding cover slips below. Figure 9(b) gives a diagram of this layout. In both cases the final stack thickness and average dielectric constant remain the same (ϵ r = 7.88 and d = 1.90 mm). What changes is the dielectric constant nearest to the target surface and facing the plasma. Figure 10 shows that the two cases do not have the same SIW trends. For the case where sapphire is on bottom (top shaded diamond markers), the final SIW velocity does not sit in between the ϵ r = 6.21 and ϵ r = 9.4 trend-lines as predicted.
Instead, the addition of the cover slips on top of the sapphire has led to the SIW velocity on the target converging to the cover slip trend. For the case where sapphire sits on top of the stack the SIW velocity is more closely aligned to the trend of the higher dielectric constant materials. The variation in SIW velocity between these two cases indicates that the SIW does not consider the dielectric target as a bulk average and has preference for the relative location of material that the average permittivity stack is comprised of, breaking the final assumption set by the RC time.
These results may also be affected by the fact that a different material is exposed to the plasma on each data set. The first being the cover glass and the second being the sapphire. A number of material effects other than dielectric constant have been observed to effect the charging of dielectric targets and (in effect) the SIW propagation. It is known from numerical work that secondary electron emission plays a large role in the propagation of SIW and the plasma morphology near the surface [30]. For the SIW interaction with dielectrics the source of secondary electrons is primarily due to ion and photon emission [31]. Vacuum ultraviolet (VUV) radiation can also greatly decrease plasma-induced surface charging of dielectric surfaces by temporarily increasing the local conductivity [32]. Potential effects of other plasma surface interactions will be discussed in more detail in section 3.5.

Near surface dependence
Revealing that there is a near-surface dependence on the makeup of the dielectric material stack means that the scale length of that dependence can be determined. To determine the thickness dependence of the dielectric near the surface an experiment similar to the one conducted in figure 10 is considered. In this case, a dielectric stack of fixed thickness is assembled with a starting configuration with the sapphire on top of a slide cover stack. Then, one slide cover at a time is moved to the top of the stack and the sapphire is systematically moved to the bottom of the stack. This preserves the bulk average dielectric constant while changing the location of the higher dielectric constant sapphire slide. Figure 11 shows the results of this study with an inset image describing the dielectric target configuration. It can be seen for both constant thickness cases that after some depth the position of the sapphire no longer effects the SIW velocity. The depth Figure 11. SIW velocity for a target stack where a Sapphire slide is placed progressively deeper into the stack by a distance x. Each trace is for a constant thickness d.
x of the sapphire in the stack needed to see this plateauing of SIW velocity is 0.6 mm for the 1.9 mm thickness study and 0.45 mm for the 3.1 mm thickness study. This establishes the scale length over which the SIW is affected by the permittivity'outlier' in the substrate. It is important to note the fidelity of this near-surface sensitivity is limited by the thickness of the dielectric slides used in the experiment. Thinner dielectric material would allow for higher spatial resolution of the transition to a plateauing of SIW velocity. The range provided by the two stacks in figure 11. gives a sense of scale to the near surface effect identified.
There is a deviation from the expected trend for the initial data point for both thicknesses. Where the SIW velocity was expected to decrease monotonically as the sapphire moves closer to the surface, the velocity instead increases when the sapphire sits on the top surface. At this time there is no strong evidence as to why this single deviation is seen. A discussion of possible contributions by additional material effects is presented in section 3.5.

Discussion
As previously stated, the assumption of relating SIW velocity to RC time relies mainly on the description of capacitance in a parallel plate and the assumptions that are contained. Capacitance requires that all potential field lines be parallel and uniform as well as in a single direction perpendicular to the conducting boundary conditions. Ionization waves incident with surfaces do not exist with uniform, 1D electric fields. Instead, SIW propagate in the presence of both axial and radial electric fields. Viegas et al (2018) determines these field components and their temporal development for an SIW [33]. The following analysis is informed from the results of this work and work done by Viegas et al.
Radial electric fields are being generated from two sources. One is from volume charge gradients between the plasma SIW and the region ahead of the discharge. The second is due to a surface charge gradient across the area in front of the discharge to the area below the discharge where surface charge has built up. Axial electric fields are generated by both volume and surface charge in relation to the ground plane.
Results from figures 8 and 11 establish that there are two transition points of interest. The first is due to bulk dielectric thickness while the second is due to near-surface sensitivity to dielectric make-up. Each depth can be related to a separate component of the electric fields present in SIW propagation.
For dielectrics where the SIW propagation is still affected by changes in target thickness it can be said that this is due to the component of the field that penetrates deepest into the dielectric target. The component of the field most likely to penetrate deeply into the dielectric is the axial field. The axial field is responsible for the force that draws and deposits surface charge. In cases where the SIW is no longer affected by thickness but is shown to be sensitive to the proximity of a permittivity 'outlier' (figure 11), this is the result of a field component that does not penetrate as deeply into the substrate. This corresponds to the radial electric field which leads the ionization front of the SIW, moving the volume charge along the surface.
The combination of these two depth dependent fields then provides an explanation to the plateauing of SIW visible in figure 8. For thin dielectrics the RC time approximation acts as a reasonable predictor for SIW velocity as a function of thickness and permittivity. As the ground plane is moved further away and additional dielectric material is added, the well constrained nature of the field lines that allow for the RC time assumption to predict behavior breaks down as less of the axial field is constrained by the ground plane. This reduces the magnitude of the axial field and simultaneously reduces the rate of charge transfer to the dielectric surface. Meanwhile the radial field generated by volume charge is unchanged and continues to promote radial propagation of the ionization front. The reduction in the rate of charge transfer is balanced by the radial fields promoting SIW propagation and produces the thicknessindependent SIW velocity observed.
The relationship of the two transition points to SIW propagation identified in this work can be described as a piecewise function which depends on dielectric thickness d, the bulk average dielectric constant ϵ, and the distribution dependent dielectric constant ϵ(x). Where x denotes the location of a permittivity outlier in a dielectric stack. Equation (4) is given as where d 1 is determined by the transition from 0.45 mm to 0.6 mm revealed in figure 11 and d 2 is determined by the plateau point for a thick dielectric in figure 8. Equation (4) establishes that when varying target thickness the SIW dependencies on dielectric constant and thickness change. In the case of thin targets the SIW velocity has a strong dependence on dielectric constant as a function of position. This behavior is seen in figure 11. At an intermediate thickness the near surface behavior remains but is accompanied by the SIW responding as a bulk average dielectric constant. This is visible in the transition to a velocity plateau in figure 11 where each total thickness has a different bulk average dielectric constant. For very thick dielectric stacks the near surface and bulk average effects remain but we see that after the transition point d 2 in figure 8 the SIW velocity is no longer dependent on changing thickness and becomes constant for a fixed permittivity. Figure 12 shows surface wave velocity as a function of capacitance per unit area. If SIW velocity trends solely with dielectric constant, it is expected that the trends of all materials and material stacks should collapse along the same curve. It can be seen in figure 12 that as reduced capacitance increases the velocity trends for each data set collapse toward a single line. As reduced capacitance gets smaller it can be seen that the trends diverge and do not align with capacitance per unit area as would be expected if this were the primary predictor of SIW velocity. This is in line with the RC time approximation of equation (1) breaking down and becoming a poor predictor of SIW propagation.
The introduction of error in the air gap between the layers of dielectric and the dielectric constants themselves gives the horizontal error for figure 12. Percent error for the ϵ = 6.21 material is the largest at 16.98%. This is due to the ratio of air gap to sample thickness being higher than the other materials. The ϵ = 7.12 and ϵ = 9.4 materials have horizontal percent errors of 3.34% and 2.19%, respectively. In the case of experimental data represented by figure 10 the error changes linearly from 0% to 10.46% as layers of thin dielectric are added.
In using a variety of materials it is not just their relative permittivity that can impact the propagation of SIW. Material effects to consider include secondary electron emission, dielectric loss tangent, surface roughness, and VUV radiation to name a few. As these physical interactions generate more electrons the ionization source term for the SIW is enhanced, generating more free charge and increasing SIW propagation velocity. Previous work has shown that a high population of electrons exist near the surface as a result of secondary electron emission and that SIW propagation is greatly affected by secondary electron emission [30]. In this work, material thickness and permittivity is controlled and examined. The effects of additional material properties is not a focus of this work and should be the focus of future work.

Conclusion
In this work, a nanosecond DC APPJ is used to produce ionization waves incident on a planar surface to study the propagation of SIW. SIW velocities are determined for dielectric targets of varying thickness and permittivity. It is assumed that the RC time constant of the plasma-surface reaction can qualitatively predict the trajectory of SIW velocity related to target thickness and dielectric constant. This predictive capability breaks down for dielectric thicknesses beyond some thickness where the SIW velocity no longer responds to changes in thickness.
The work reveals two transition thicknesses relating to SIW propagation. The first indicates that for thick targets (d > 1.9 mm @ ϵ r = 6.21) there is a, not previously documented, plateau beyond which the dielectric thickness no longer effects the SIW velocity. The second transition region shows that the velocity of the SIW is sensitive to the near-surface make-up of the dielectric (d = 0.45 − 0.6 mm). Where in this region, the SIW velocity responds to the relative position of an implanted high permittivity material only up to the above thickness range.
Though the experimental conditions are well controlled, effects relating to additional plasma-surface interactions are not controllable given the nature of the experiment. Variability in SIW velocity effects relating to the source design and assembly are also noted and are not of serious impact in this work.
In application, the knowledge of these thickness dependent regions allows for SIW velocity to be tuned, or made more stable, by the careful selection of dielectric constant and material thickness. This work shows that small changes in target thickness and dielectric constant can alter SIW velocity by a factor of two or greater. The results of this work may impact systems with complex interfaces that incorporate various thicknesses and electrical properties.
Additional work is needed to more closely analyze the underlying mechanisms defined in this work and better understand the role that secondary electron emission and other material properties play in SIW propagation, a task well suited to a validated numerical model. Targets of very small thickness (d < 0.6 mm) are also of high interest, as the near-surface sensitivity and bulk effects are both at play. Future work should include the use of thinner dielectric layers or bulk materials with incremental thicknesses more finely resolved than shown here. This would enable more precise examination of the transition regions outlined in this work.

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