## 3 Results and Discussion
### Determination of the Interface States of MIS Capacitors with Different Polymer Gate Insulators
The \(G_{p}/\omega\)-\(f\) curve of the MIS capacitor with the PI gate insulator extracted from the measured impedance spectrum at a gate voltage of 0 V is shown in Figure 7a, in which the fitted curves using the three models are also indicated. It can be seen that the measured \(G_{p}/\omega\)-\(f\) curve is broader than the calculated curve using Equation (3), indicating that the interface states in the P3 HT MIS capacitors are energetically distributed [14; 15; 16; 18]. Moreover, we found that the statistical model  
Figure 6: (**a**) Equivalent circuit of a MIS capacitor with single-energy level interface states in depletion mode and (**b**) simplified version of (**a**). (**c**) Lumped parallel equivalent circuit of (**b**) or (**d**). (**d**) Equivalent circuit of a MIS capacitor with energetically distributed interface states. is in better agreement with the experimental curve than the continuum model. This suggests that the equivalent circuit model, which takes band-bending fluctuations into consideration, is appropriate to describe the impedance characteristics of P3 HT MIS capacitors. As shown in Figure 7b, the fitted \(G_{p}/\omega\)-\(f\) curves using the statistical model are in good agreement with the experimental curves obtained for different gate voltages: the energy distributions of interface-state densities can be determined using these curves. Figure 8 shows the densities of interface states above the valence band edge (\(E_{v}\)) in the P3 HT MIS capacitors with the different polymer insulators of PI, PVP, and PMSQ, calculated using the statistical model. The energy scale was determined by the conventional \(C\)-\(V\) method [30]. The energy level was calculated from the surface potential (\(\psi_{S}\)) at \(V_{G}\), which is given as follows  
\[E-E_{V}=\psi_{\mathrm{s}}(V_{G}\ )=\int_{V_{FB}}^{V_{G}}\biggl{(}1-\frac{C_{m}}{ C_{i}}\biggr{)}dv, \tag{8}\]  
where \(C_{m}\) is the capacitance at low frequency and \(V_{FB}\) is the flatband voltage. The value of \(V_{FB}\) was assumed to be \(-0.5\) V for all samples. In Figure 8, the density of interface states in P3 HT MIS capacitors is shown to be strongly affected by the type of polymer gate insulators; the density of interface states for P3 HT MIS capacitors with PMSQ insulators is relatively lower than that with other polymer insulators. To examine the influence of gate insulators on FET characteristics, bottom-gate/top-contact P3 HT FETs were fabricated on polymer gate insulators. In the FET devices, thin P3 HT films (\(\sim\)50 nm) were used. Their transfer characteristics (drain current (\(I_{D}\))-\(V_{G}\)) are shown in Figure 9; it can be seen that \(I_{D}\) and the subthreshold slope (SS) largely depend on the type of gate insulators. The field-effect mobilities and SS values of P3 HT FETs as well as the water contact angles on polymer insulators are summarized in Table 2. The table clearly illustrates the relationship between mobility, SS value, and the water contact angle. The mobility increases and the SS value decreases as the water contact angle on polymer insulators is increased. Moreover, the mobilities and SS values are closely correlated to the density of interface states shown in Figure 5:0 It is well known that the SS value is inversely proportional to the total density of interface states [31]. Therefore, based on the obtained results, the improvement in the mobility and SS value can be attributed to the decrease in the interface-state density. The difference in the interface-state densities in the P3 HT MIS capacitors with different polymer insulators is attributable to the difference in the surface energy of the gate insulators.