# Equivalent Electrical Circuit Modeling of CNT-Based Transparent Electrodes
## 4 Discussion  
In this paper, a review of the equivalent circuit-based models for the simulation of CNT networks like those established in CNT-based transparent conductive films was presented. Designing a CNT-based transparent electrode requires accounting for different parameters, such as the length, diameter and aspect ratio of the nanotubes, the CNT density, chirality, and doping, the presence of defects and impurities within the deposited film. All these factors affect the electrical behavior and the optical transparency of the conductive layer, thus contributing to the overall electrode performance. Having a reliable tool for the simulation of the electrical properties of the CNT-based conductive layer is indeed  
Figure 6: Schematic of the equivalent circuit modeling a composite CNTs/polymer material. The parallel impedance \(R_{res}\)-\(C_{res}\) represents the polymeric matrix. Each percolative path inside the CNT network is represented by a parallel branch like the one at the bottom, which includes the CNTs segment resistance. helpful for the design of a high-performing electrodes. Starting from the identification of percolation paths over two points of a CNT network, lumped-parameters equivalent electrical circuits can be developed to model the electrical properties of the CNT-based electrode. These circuits can then be used to account for the electrode properties in broader circuits that model complex devices featuring a CNT-based conductive layer. Starting from the distributed-parameters equivalent transmission line model of a single CNT, and passing by the lumped-parameter modeling of 2D, layered 2D, and 3D networks, the state of the art of CNT network modeling was described. The main features of the equivalent electrical circuit-based models described in this paper are summarized in Table 2 for comparison purposes. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multirow{2}{*}{**Outcome**} & \multirow{2}{*}{**Notes**} & \multirow{2}{*}{**CNT Metallic Resistance**} & \multirow{2}{*}{**Tunneling Resistance**} & \multirow{2}{*}{**Dynamic Elements**} & \multirow{2}{*}{**Solution Method**} & \multirow{2}{*}{**Outcome**} & \multirow{2}{*}{**Notes**} \\ \cline{5-8}  & & & & & & Kinetic & & CNT & Transmission \\  & & & & & inductance, & & frequency-dependent & & line model, \\  & & & & & electronic & analysis & computation & frequency- \\  & & & & & & & (theoretical) & dependent \\ \hline \multirow{5}{*}{**Method**} & \multirow{5}{*}{**Outcome**} & \multirow{5}{*}{**Outcome**} & \multirow{5}{*}{**Notes**} & \multirow{5}{*}{**CNT Metallic Resistance**} & \multirow{5}{*}{**Resistance**} & \multirow{5}{*}{**Dynamic Elements**} & \multirow{5}{*}{**Solution Method**} & \multirow{2}{*}{**Outcome**} & \multirow{2}{*}{**Notes**} \\  & & & & & & Kinetic & & CNT & & \\  & & & & & inductance, & & frequency-dependent & & line model, \\  & & & & & electronic & analysis & computation & frequency- \\  & & & & & & & (theoretical) & dependent \\ \hline \multirow{5}{*}{**Method**} & \multirow{5}{*}{**Outcome  
The modeling of CNT networks by means of 2D resistive networks is indicated to simulate the electrical conductivity of very thin films of free-standing nanotubes. To take into account the different percolation paths that can be established in thicker layers of nanotubes or in nanocomposites made by dispersing CNTs in a polymeric matrix, modeling by 3D networks is required. CNT/polymer composites are better modeled by resistive-capacitive networks that account for the frequency-dependent impedance of the material above the electrical percolation threshold caused by the insulating nature of the polymer. For this reason, the concept of \"best model\" depends both on the material characteristics and on the simulation objective.