## 3 Results and Discussion
### Discharge Characteristics
Since the capacitance is so high between the two short-gap electrodes on the surface of the both-side dielectric layer, a high displacement current is expected even before the ignition with an operation voltage less than the \(V_{f}\). At the breakdown, the plasma current that is due to the filamentary channels of the microdischarges is added to the displacement current; however, the plasma current is restricted by the dielectric layer and the current will not rise abruptly. Thus, at the \(V_{f}\), the slightly increasing current slope reflects the plasma generation. Under the special operating conditions, usually those of a low-pressure operation, the _glow mode_ is present [42; 43]. The latter cases of the I-V characteristics have been analyzed regarding the usual discharge-tube experiments, including the DBD structure with the gases of a low pressure that is approximately several tens of Torr [44; 45; 46; 47]. At the breakdown voltage, the electron avalanche is accompanied by the Townsend discharge, which is the abrupt current increase followed by the normal glow in terms of the I-V characteristics. Regarding the DBD experiments of Figures 3-5, however, the representation of the filamentary mode of the streamer channel is shown in Figure 6.  
Figure 6 shows the I-V curves of each dielectric sample listed in Table 1 with respect to the discharge experiment shown in Figure 2. Figure 6a shows the graph of the solid plates and Figure 6 (b) shows the graph of the flexible films. For the electrode structure in Figure 2 with the thickness of each dielectric listed in Table 1, the capacitance was measured using the LCR-821 LCR meter (GW Instek, Taiwan), and the following results were given: (alumina, glass, quartz) = (2.40, 2.20, 1.70 pF), and (PI, GP, PP) = (2.55, 2.32, 1.70 pF). The firing voltage (\(V_{f}\)) is represented in the graph of Figure 6. For the \(V_{f}\), the voltage was selected upon the initial observation of the plasma with the naked eye. For all the solid plates and flexible polymer films, the larger \(C\) values correspond to the greater reductions of the firing voltage and the plasma current. For the analysis of the I-V graphs of Figure 6, the equivalent circuit is presented in Table 1.0 Two circuit paths were used for the I-V measurement, as follows: One is the capacitor (\(C_{o}\)) circuit between the electrodes of the upper and lower plates, and the other is the circuit connecting the dielectric-layer capacitance (\(C_{1}\)) and the plasma resistance (\(R_{p}\)). The equivalent circuit shown in Figure 7 is composed of a parallel connection with two circuits. The impedance (\(Z\)) of the two parallel circuits is as follows [48; 49]:  
Table 1.1  
The slope of the I-V curve in Figure 6 corresponds to the \(11/Z1\) of Equation (1). Assuming the sufficient largeness of the \(R_{p}\) (\(R_{p}>11/\omega C_{1}\) 1), and without considering the imaginary capacitance, the slope of the I-V curve is as follows:  
Table 1.2  
Table 1.3 Current–voltage (I–V) graphs for the solid plates (**a**) and polymer films (**b**). In the I-V curve of Figure 6, the slope tends to change slightly before and after the discharge. The slope slightly increased after the discharge. This finding means the slope of Equation (2) increased as the \(R_{p}\) decreased due to the post-discharge current increase. Using Equation (2) with the reactance of the \(C_{o}\), the \(R_{p}\) was calculated for the slope value of the I-V curve in Figure 6 for each dielectric sample. The reactance (\(X_{o}=1/\omega C_{o}\)) with the LCR-meter-measured \(C_{o}\) values was calculated as follows: (alumina, glass, quartz) = (1.84, 1.90, 2.47 M\(\Omega\)) and (PI, GP, PP) = (1.78, 1.87, 2.47 M\(\Omega\)). Using the \(X_{o}\), the \(R_{p}\) before and after the discharge was calculated by the comparison of the slope of the I-V curve in Figure 6 with the \(11/Z\,\)I of Equation (3).