## 3 Results and Discussion
### Optimization of the Fabrication Processes of Organic MIS Capacitors
This feature is contrary to the results shown in Figure 3a, in which the loss peak shifts to the low frequency regime when the positive gate voltage is increased. Such apparent decrease in the relaxation frequency is similar to the behavior of interface states reported for Si-based MOS capacitors [19; 20]. Hence, the equivalent circuit of the P3 HT MIS capacitor should include an array of series \(RC\) elements (\(R_{t}\), \(C_{t}\)) in parallel with \(C_{d}\) to account for the observed \(G\)/\(\omega\)-\(f\) characterisi  
Figure 2: Frequency dependences of the capacitance of the ITO/PI/P3 HT/Au MIS capacitors with (**a**) patterned and (**b**) unpatterned P3 HT films measured at various gate voltages. Another issue detrimental to the interface states in the organic MIS capacitors is the influence of unintended doping on organic semiconductor films. In particular, the electrical characteristics of P3 HT-based OFETs are well known to significantly suffer from hole doping to P3 HT films by O\({}_{2}\) and H\({}_{2}\)O in ambient air [25]; further, the density of the interface states in P3 HT MIS capacitors was found to depend on the dopant concentration [15]. Therefore, removing the dopants via the thermal annealing process is critical for the accurate determination of interface-state densities from organic MIS capacitors. In this work, we investigated the effect of thermal annealing on the dopant concentration by using capacitance-gate voltage (\(C\)-\(V_{G}\)) measurements of the P3 HT MIS capacitors with PI gate insulator. Figure 5a shows the variation in the \(C\)-\(V_{G}\) characteristics of the P3 HT MIS capacitor measured at 100 Hz before and after thermal annealing. In the experiment, the impedance characteristics of the MIS capacitors were measured at room temperature after thermal annealing at 100 \({}^{\circ}\)C for 1 h in a vacuum; this cycle was repeated five times (in the fifth cycle, the device was thoroughly annealed for 5 h). The dopant concentration in the P3 HT film can be determined using Schottky-Mott analysis [26] from the slopes of the \(1/C^{2}\)-\(V_{G}\) curves in the transition region between accumulation and depletion. The dopant concentration (\(N_{A}\)) is given as follows,  
\[N_{A}=2\bigg{[}q\varepsilon_{0}\varepsilon_{r}A^{2}\frac{d}{dV_{G}}\bigg{(} \frac{1}{C^{2}}\bigg{)}\bigg{]}^{-1}, \tag{2}\]  
where \(q\) is the elementary charge, \(\varepsilon_{0}\) is the permittivity of vacuum, \(\varepsilon_{r}\) is the relative permittivity of the semiconductor, and \(A\) is the active area of the MIS capacitor. Figure 4: (**a**) Equivalent circuits representing an ideal MIS capacitor and (**b**) a MIS capacitor with energetically distributed interface states. Figure 3: Frequency dependences of the conductance loss (\(G/\omega\)) of the ITO/PI/P3 HT/Au MIS capacitors with (**a**) patterned and (**b**) unpatterned P3 HT films measured at various gate voltages. Figure 5b shows \(1/C^{2}\)-\(V_{G}\) curves plotted from Figure 5a, and Table 1 summarizes the values of the dopant concentration for thermal annealing cycles estimated using Equation (2) by assuming \(\varepsilon_{r}=3\). The dopant concentration decreased dramatically after the first annealing cycle, and remained almost unchanged after the third annealing cycle, indicating that most dopants were removed from the P3 HT film. The dopant concentration after the fifth annealing cycle was \(1.4\times 10^{15}\) cm\({}^{-3}\), which is much lower than those reported for P3 HT MIS capacitors [15; 27]. These results suggest that the optimized device fabrication of the organic MIS capacitors enables the investigation of the influence of the gate insulator on the interface-state density via impedance measurements.