## 3 Results and Discussion  
### Optimization of the Fabrication Processes of Organic MIS Capacitors  
First, we describe the influence of the patterning of organic semiconductor films in the P3 HT MIS capacitors with crossed top and bottom electrodes on their impedance characteristics. Figure 2a shows the capacitance-frequency characteristics of the MIS capacitor with the P3 HT film patterned using O\({}_{2}\) plasma etching. The MIS capacitor with the patterned P3 HT film exhibits reasonable dependencies on frequency and gate voltage. In an ideal MIS diode with a \(p\)-type organic semiconductor, when the gate electrode is negatively biased, holes are injected from the top electrode and accumulate at the interface between the semiconductor and the gate insulator. This leads to the increase in the capacitance of the MIS capacitor, which approaches the capacitance of the gate insulator (\(C_{i}\)) when the frequency of the sinusoidal signal is extremely low because holes accumulate in the whole area of the semiconductor/gate insulator interface. At high frequencies, the injected holes do not follow the sinusoidal signal, leading to the depletion of the organic semiconductor film, which reduces the capacitance of the MIS capacitor. When the organic semiconductor films are completely depleted, the capacitance of the MIS capacitor (\(C\)) can be expressed by the series sum of a capacitance of semiconductor film (\(C_{S}\)) and \(C_{i}\); \(C=C_{S}C_{i}/(C_{S}+C_{i})\). The capacitance-frequency characteristics of the MIS capacitor fabricated without patterning P3 HT film are shown in Figure 2b. The capacitance of the MIS capacitor with the unpatterned P3 HT film increases with decreasing frequency, indicating an excess accumulation of holes at the semiconductor/gate insulator interface. It has been reported that holes injected from the top electrodes spread laterally across the semiconductor film to form an additional channel; this channel is responsible for the increase in the capacitance of the MIS capacitors in the low frequency regime [22; 23; 24]. To suppress such effects associated with lateral conduction along the semiconductor film, a circular top electrode surrounded by a concentric guard ring has been generally used in Si-based MOS capacitors [22] and organic MIS capacitors [13; 14; 15; 16; 18; 23]. Our experimental results demonstrate that the organic MIS capacitors with crossed top and bottom electrodes can be used for impedance measurements by patterning the organic semiconductor films using O\({}_{2}\) plasma etching. Figure 3a and b show the frequency dependence of the loss (conductance (\(G\))/mgler frequency (\(\omega\))) of the organic MIS capacitors with patterned and unpatterned P3 HT films, respectively. The conductance was determined by calculating the real part of admittance (\(Y\)) according to \(Y=G+j\omega C\). The figures indicate that the peripheral regions of the organic MIS capacitors significantly affect the position and magnitude of loss peaks. In Figure 3a, the peak position shifts to a higher frequency with increasing negative gate voltage. On the other hand, the response of an ideal MIS capacitor in the depletion mode can be described in the equivalent circuit shown in Figure 4a. In the figure, \(C_{i}\) represents the insulator capacitance, \(C_{d}\) represents the depletion capacitance, \(C_{b}\)\({}^{\prime}\) and \(R_{b}\)\({}^{\prime}\) represent the capacitance and resistance, respectively, of the bulk semiconductor, and \(R_{C}\) represents the contact resistance. The relaxation frequency (\(f_{R}\)) of the circuit is given by  
\[f_{R}=\frac{1}{2\pi R_{b}\ ^{\prime}(C^{\prime}+C_{b}\ ^{\prime})}=\frac{1}{2 \pi\tau}, \tag{1}\]  
where \(\tau\) is the relaxation time of the MIS capacitor and \(C^{\prime}\) represents the series sum of \(C_{i}\) and \(C_{d}\)[14; 15]. According to Equation (1), the relaxation frequency should increase when the positive gate voltage is increased because it leads to an increase in the depletion width and hence decreases in \(C^{\prime}\).