# Charge Carrier Distribution in Low-Voltage Dual-Gate Organic Thin-Film Transistors
## 3 Results and Discussion  
Transfer characteristics in the saturation regime and output characteristics of the OTFTs were shown in Figure 2. Transfer characteristics in the linear regime obtained from experimental and numerical simulation were shown in Figure 3. The simulated characteristics were similar to the experimental. Channel width (\(W\)) and length (\(L\)) was 740 \(\upmu\)m and 7 \(\upmu\)m, respectively. Capacitance per unit area was 21 nF/cm\({}^{2}\). The electrical properties such as mobility in saturation (\(\mu_{\rm sat}\)) and linear regime (\(\mu_{\rm lin}\)), threshold voltage (\(V_{\rm TH}\)), on-current (\(I_{\rm ON}\)) and subthreshold slope (\(SS\)) were summarized at Table 2. At \(V_{\rm DS}=-5\) V, \(I_{\rm ON}\) for the BG, TG, and DG devices was 0.23 \(\pm\) 0.04 \(\upmu\)A, 1.5 \(\pm\) 0.2 \(\upmu\)A, and 1.9 \(\pm\) 0.2 \(\upmu\)A, respectively. \(SS\) for the BG, TG, and DG devices was 0.5 \(\pm\) 0.3 V/dec, 1.5 \(\pm\) 1.0 V/dec, and 0.3 \(\pm\) 0.1 V/dec, respectively. The higher \(I_{\rm ON}\) and steeper \(SS\) were obtained: the result is consistent with that from previously reported [5; 6]. Furthermore, for the DG devices, saturation (\(V_{\rm DS}=-5\) V) and linear (\(V_{\rm DS}=-0.1\) V) mobility was 0.05 \(\pm\) 0.013 cm\({}^{2}\)/Vs and 0.047 \(\pm\) 0.013 cm\({}^{2}\)/Vs, respectively. The mobility for the DG devices was also better than those of the single-gate devices. On the whole, the DG devices exhibited better electrical properties. To elucidate the origin of better switching characteristics of the DG device, charge carrier distribution in the organic semiconducting layer was displayed in Figure 4. Spatial \(x\)-axis and \(y\)-axis were defined as Figure 4a, where the origin was set to be the crossing point of middle of the channel and the line along the bottom-dielectric/semiconductor interface. Free hole densities as a function of \(y\)-axis at \(V_{\rm GS}=1\) V (off state) and \(V_{\rm GS}=-2\) V (on state) were shown in Figure 4b,c. \(V_{\rm DS}=-0.1\) V in all \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Channel width & 732 \(\upmu\)m & Temperature & 300 K \\ \hline Channel length & 6.73 \(\upmu\)m & \begin{tabular}{c} Work function of source, drain \\ and gate electrodes \\ \end{tabular} & 4.6 eV \\ \hline Channel thickness & 10 nm & Ionization energy of semiconductor & 5.0 eV \\ \hline Dielectric constant of insulator, \(\varepsilon_{\rm i}\) & 3.38\(\varepsilon_{0}\) & The effective density of states in the valence band, \(D_{\rm v}\) & 1.6 \(\times\) 10\({}^{20}\) cm\({}^{-3}\) \\ \hline Dielectric constant of semiconductor, \(\varepsilon_{\rm s}\) & 4\(\varepsilon_{0}\) & \
\begin{tabular}{c} •[\(E_{\rm t}\)] \\ \end{tabular} &
\begin{tabular}{c} •[\(E_{\rm v}-E_{\rm t}\)] \\ \end{tabular} & 3 \(\times\) 10\({}^{18}\) cm\({}^{-3}\) \\ \hline Dielectric thickness & 140 nm & Density of trap states, \(D_{\rm t}\) & 3 \(\times\) 10\({}^{18}\) cm\({}^{-3}\) \\ \hline Mobility along the channel, \(\mu_{\rm x}\) & 0.24 cm\({}^{2}\)/Vs & Average energy of trap states, \(E_{\rm t}\) & 0.15 eV \\ \hline Mobility perpendicular to the channel, \(\mu_{\rm y}\) & 0.048 cm\({}^{2}\)/Vs & Carrier density in the neutral state, \(n_{0}\) & 3 \(\times\) 10\({}^{23}\) cm\({}^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters Used in the finite element method (FEM) Simulation. three device simulations. For the single-gate devices, the carrier density at the side of the gate electrode could be controlled in the range of 6.2 \(\times\) 10\({}^{20}\)-2.5 \(\times\) 10\({}^{23}\) m\({}^{-3}\). Nevertheless, the carrier density at the opposite side of the gate electrode was hardly controlled (2.1 \(\times\) 10\({}^{21}\)-5.5 \(\times\) 10\({}^{22}\) m\({}^{-3}\)). On the other hand, for the DG system, the carrier density over the entire region in the channel could be controlled in the wider range of 4.8 \(\times\) 10\({}^{18}\)-3.8 \(\times\) 10\({}^{23}\) m\({}^{-3}\).