# Nonvolatile Organic Floating-Gate Memory Using N2200 as Charge-Trapping Layer
## 2 Device Structure and Physical Models
### Physical Models  
In p-channel OFETM, the carrier transport mechanism is influenced by the temperature, electric field, organic semiconductor channel, hole traps between the electrode and gate dielectric layer, etc. [36]. The carrier transport of N2200 FG-OFETM is simulated by solving the Poisson equation, the carrier continuity equation, and the hole drift diffusion equation [37; 38]. The physical models employed in the experiment are as follows:  
\[\
abla(\varepsilon_{0}\varepsilon_{\mathrm{S}}\
abla\varphi)=q(n-p+N_{\mathrm{ t}}-P_{\mathrm{t}}) \tag{1}\]  
\[\
abla\cdot J_{\mathrm{p}}=q(G-R) \tag{2}\]  
\[J_{\mathrm{p}}=q\mu_{\mathrm{p}}E_{\mathrm{P}}-qD_{\mathrm{p}}\
abla_{\mathrm{P}} \tag{3}\]  
\[D_{\mathrm{p}}=\mu_{\mathrm{p}}\frac{K_{0}T_{L}}{q} \tag{4}\]  
where \(\varphi\) is the electrostatic potential, \(N_{\mathrm{t}}\) and \(P_{\mathrm{t}}\) are the density of trapped electrons and holes, respectively, and \(n\) and \(p\) are the concentrations of electrons and holes. \(J_{\mathrm{p}}\) is the hole current density, \(G\) indicates the rate of hole production, which is considerably affected by the hole potential barrier, and \(R\) is the recombination rate. \(E_{\mathrm{p}}\) represents the electric \begin{table}
\begin{tabular}{l l l} \hline \hline
**Parameter** & **Symbol** & **Value** \\ \hline Channel length & \(L/\mathrm{\mu m}\) & 80 \\ Channel width & \(W/\mathrm{\mu m}\) & 1000 \\ Thickness of source and drain electrodes & \(S_{\mathrm{T}}\), \(D_{\mathrm{T}}/\mathrm{nm}\) & 50 \\ Thickness of organic semiconductor & \(T_{\mathrm{S}}/\mathrm{nm}\) & 40 \\ Thickness of tunneling insulator & \(T_{\mathrm{T}}/\mathrm{nm}\) & 6, 8, 10, 12, 14 \\ Thickness of FG & \(T_{\mathrm{F}}/\mathrm{nm}\) & 18 \\ Thickness of gate insulator & \(T_{\mathrm{OX}}/\mathrm{nm}\) & 90 \\ Dielectric constant of gate insulator (PMMA) & \(\varepsilon_{\mathrm{S}}\) & 3.0 \\ Dielectric constant of FG layer (N2200) & \(\varepsilon_{\mathrm{S}}\) & 3.5 \\ Work function (Cu) & \(W_{\mathrm{F}}/\mathrm{eV}\) & 4.65–4.70 \\ Active layer band gap width (pentacene) & \(E_{\mathrm{g}}/\mathrm{eV}\) & 1.8–2.2 \\ Band gap width of FG layer (N2200) & \(E_{\mathrm{g}}/\mathrm{eV}\) & 3.3–3.6 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Physical and structural parameters used for device simulation. Figure 1: Schematic diagram of device structure. field strength. \(D_{\text{P}}\) is the hole diffusion coefficient. According to Einstein Equation (4), \(J_{\text{P}}\) is expressed as  
\[J_{\text{P}}=q\mu_{\text{P}}\cdot\left(E_{\text{P}}-\frac{K_{0}T_{\text{L}}}{q} \cdot\
abla_{\text{P}}\right) \tag{5}\]  
where \(K_{0}\) is the Boltzmann constant, \(T_{\text{L}}\) represents the lattice temperature (300 K), and \(\mu_{\text{P}}\) is the Poole-Frenkel mobility [39]. \[\mu_{\text{P}}=\mu_{\text{P0}}\exp\left[-\frac{E_{\text{h0}}}{K_{0}T}+\left( \frac{\beta}{k_{0}T_{\text{L}}}-\gamma\right)\sqrt{E}\right] \tag{6}\]  
In this model, \(\mu_{\text{P0}}\) represents the low-field mobility, \(E_{\text{h0}}\) signifies the activation energy of the hole (\(E=0\)) of 0.018 eV (\(E=0\)), \(\beta\) is the Poole-Frenkel hole factor, and \(\gamma\) is the fitting parameter. In order to obtain good simulation results, the contact between the electrode and the organic semiconductor was defined as the Schottky barrier. Furthermore, the hot carrier injection and Fower-Nordheim (FN) tunneling models were used to simulate the injection of holes from the channel into the FG layer, as well as their release from the FG layer into the channel after P/E operations.