# Equivalent Electrical Circuit Modeling of CNT-Based Transparent Electrodes
## 4 Discussion
To choose the most suitable modeling technique for the simulation of a certain application, it is necessary to answer some fundamental questions:  
* _Is the thickness of the CNT-based conductive layer small enough to assume that the CNT network is planar and the percolative paths are all lying on the conduction plane?_ If so, a 2D network model will give sufficiently accurate results with a small complexity and low computational effort. Otherwise, if the layer thickness is not negligible, a better accuracy can be obtained by modeling a 3D network. * _Is the quantity of interest frequency-dependent?_ If the CNT-based material is meant to work in a dynamic regime, e.g., in harmonic or switching conditions, depending on the frequency of interest it could be necessary to include the modeling of the capacitive behavior. * _Is the CNT network dispersed inside a material that contributes to determining the quantity of interest in a non-negligible way?_ This could be, for example, the case of CNT-based nanocomposites used for sensing applications, in which the mechanical and thermal properties of the hosting polymer must be taken into account to predict the material response to the input quantity. * _Are the CNTs mostly metallic, semiconducting, or mixed?_ Conduction between metallic CNTs happens easily, with the carriers experimenting a low junction resistance. Conduction between metallic and semiconducting CNTs, on the contrary, is hindered by a high potential barrier that determines a high value for the junction resistance. In this case, the tunneling resistance related to the conduction between nanotubes becomes dominant with respect to the nanotube resistance, which is related to the conduction along a single nanotube. For this reason, the information about the nature of the CNTs helps in determining if one of the two contributions to the total resistance can be neglected. Furthermore, in the case of mostly semiconducting nanotubes, it should be considered to include the modeling of the density of states in the resistance computation. * _Are there experimental data available?_ If so, it could be useful to implement a model including fitting parameters that can be tuned to match the experiment results. In this way, the simulated quantities should be more reliable, but not applicable to other materials. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multirow{2}{*}{**Methods**} & \multirow{2}{*}{**Methods**} & **CNT Metallic** & **Tunneling** & **Dynamics** & **Solution** & **Outcome** & **Notes** \\  & & & **Resistance** & **Resistance** & **Elements** & **Method** & **Outcome** & **Notes** \\ \hline \multirow{2}{*}{**Methods**} & \multirow{2}{*}{**Methods**} & \multirow{2}{*}{Fixed value of conductivity\(\sigma_{n}\) = 2 x 10\({}^{6}\) a.u. for rods and \(\sigma_{m}\) = 2 a.u. for insulating matrix} & \multirow{2}{*}{No} & \multirow{2}{*}{Franke-Lob algorithm for RRNs} & Computation of the electrical conductivity of 2D CNT films (theoretical) & Zero-width \\  & & & & & & \\ \hline \hline \end{tabular} n.a. stands for “non-applicable”.  
\end{table} 
Table 2: _Cont._In this review, models accounting for the tube segment resistance, the tunneling resistance, the density of states and the charge transport were described and reviewed, highlighting strengths and weaknesses of each, in the view of providing guidance in the choice of the best-performing technique depending on the application under examination, in terms of trade-off between accuracy and complexity. Conceptualization, M.L.M. and P.L. ; writing--original draft preparation, M.L.M. ; writing--review and editing, P.L. and V.T. ; supervision, P.L. All authors have read and agreed to the published version of the manuscript. This research was partially supported by FARB founding of the University of Salerno and from the European Union's Horizon 2020 research and innovation programme under grant agreement GrapheneCore3 No 881603. Not applicable. The authors declare no conflict of interest.