# Icing Mitigation by MEMS-Fabricated Surface Dielectric Barrier Discharge
## 3 Electrical Characterization
### SDBD Power  
The glass and FR-4 samples have the same thickness (500 um), a similar permittivity, see Table 1, and for both the discharge is ignited around 1.4 kV\({}_{\mathrm{rms}}\). Photos of the glass SDBD at different applied voltages, shown by Figure 6, demonstrate the expansion of the discharge area. The discharge started at electrode tips with a low luminosity. The luminosity of the spots increases with the voltage and the discharge expands around the electrode edges. The luminosity of the discharge is decreasing with the distance from the electrodes as it is typical for SDBDs (see, e.g., [PERSON] et. al [34]). The discharges occupy the whole area above the ground electrode at 2.8 kV\({}_{\mathrm{rms}}\). After that, a further increase of the voltage amplitude increases the luminosity of the discharge, however, the discharge area stays the same. More detailed photographs of the discharge can be found in Supplementary S8. The ignition of the discharges for the 150 um thick zirconia SDBD occurs slightly above 0.7 kV\({}_{\mathrm{rms}}\), with filaments randomly [42] distributed over the length of the high-voltage electrode, see Supplementary S9. The results of the power measurements are shown in Figures 7 and 8. The up and down cycle of the voltage-sweep were performed to visualize a possible degradation of the samples due to the erosion of either the electrodes or the dielectric. The power was scaled to the effective length of the high-voltage electrodes (L = 0.696 m) which was measured disregarding the microstructure as introduced by [PERSON] et al. [34]. The power of a freely expanding SDBD increases with a cubic behavior of the applied voltage (P \(\sim\) V\({}^{3}\)), see [43]. Considering Figure 6 the discharge expansion of the glass SDBD is limited by the dimensions of the ground electrode and as well as the neighboring high-voltage electrodes. Furthermore, starting from 2.8 kV\({}_{\mathrm{rms}}\) the power increases just linear with the applied voltage, similar to the volume dielectric barrier discharges [41]. A similar power voltage dependence is also obtained for the FR-4 sample and the measured values agree for both materials within the experimental errors. The dissipated power at the zirconia sample has a stronger dependency on the voltage due to the extremely thin dielectric with a higher dielectric constant [34; 40]. The power measurements in the capacitance configuration were straight forward for FR-4 and glass sample. The up- and down-cycle measurement were similar within the scope of the measurement accuracy. Both substrates have similar dielectric properties, see Table 1, and the power losses in the dielectric do not exceed 20%. Figure 6: SLR-camera images of the plasma expansion of the glass SDBD at different operating voltages. In the case for the 150 um zirconia sample, surprisingly, an electrical breakdown of the dielectric occurs at the capacitor configuration at voltages below 1 kV\({}_{\text{rms}}\). Presumably, due to the dielectric losses the substrate temperature increases and also the flowable silicone around the electrodes restricts the heat transfer to the environment which further heats the substrate. We assume that if a zirconia SDBD is operated for a longer period of time without external cooling, the following mechanism takes action. Dissipated power heats the dielectric. The electrical conductivity of the investigated dielectrics increases exponentially with the temperature [44; 45; 46]. Since the applied voltage is constant, the conductivity increase leads to an increase of the current and the dissipated power (P = UI), which again results in a growth of the temperature of the dielectric. The conductivity for zirconia [44] is about 3 orders of magnitudes higher than for glass [45]. At a reasonable local dielectric temperature of 350 \({}^{\circ}\)C zirconia already exhibits a conductivity comparable to drinking water. Therefore, at higher temperatures the conductance of zirconia is short-cutting the electrodes and destroying the SDBD.