# Graphene-Based Grid Patterns Fabricated via Direct Ink Writing for Flexible Transparent Electrodes
## 3 Results and Discussions
### Characterization of Graphene Film Fabricated by DIW
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline  & & & & & & & & & & & \\ \cline{2-10}  & **1** & **3** & **5** & **7** & **9** & **11** & **13** & **15** & **17** & **19** \\ \hline
**G-0** & 0.98 \(\pm\) 0.05 & 1.25 \(\pm\) 0.10 & 1.57 \(\pm\) 0.10 & 3.39 \(\pm\) 0.10 & 5.82 \(\pm\) 0.15 & 6.96 \(\pm\) 0.15 & 8.19 \(\pm\) 0.15 & 10.30 \(\pm\) 0.20 & 11.52 \(\pm\) 0.20 & 12.83 \(\pm\) 0.20 \\
**G-10** & 0.52 \(\pm\) 0.05 & 1.02 \(\pm\) 0.05 & 1.36 \(\pm\) 0.10 & 1.82 \(\pm\) 0.10 & 2.34 \(\pm\) 0.10 & 2.86 \(\pm\) 0.10 & 3.38 \(\pm\) 0.10 & 4.00 \(\pm\) 0.10 & 4.52 \(\pm\) 0.15 & 4.96 \(\pm\) 0.15 \\
**G-20** & 0.63 \(\pm\) 0.05 & 0.92 \(\pm\) 0.05 & 1.33 \(\pm\) 0.10 & 1.87 \(\pm\) 0.10 & 2.67 \(\pm\) 0.10 & 2.94 \(\pm\) 0.10 & 3.47 \(\pm\) 0.10 & 3.83 \(\pm\) 0.10 & 4.23 \(\pm\) 0.15 & 4.87 \(\pm\) 0.15 \\
**G-30** & 0.62 \(\pm\) 0.05 & 0.92 \(\pm\) 0.05 & 1.33 \(\pm\) 0.10 & 1.82 \(\pm\) 0.10 & 2.60 \(\pm\) 0.10 & 2.86 \(\pm\) 0.10 & 3.38 \(\pm\) 0.10 & 3.60 \(\pm\) 0.10 & 4.02 \(\pm\) 0.15 & 4.38 \(\pm\) 0.15 \\ \hline \end{tabular}
\end{table} 
Table 1: Thickness (\(\mu\)m) of graphene films with different numbers of layers. Figure 3: (**a**) Surface and (**b**) cross-sectional SEM images of **G-20**; (**c**) cross-sectional SEM image of **G-0**; (**d**) the average thickness of **G-0**, **G-10**, **G-20**, and **G-30** with 15 deposited layers; (**e,f**) the typical step meter results of **G-0** and **G-20**. To better evaluate the electrical property of graphene films fabricated by DIW, the electrical conductivity of each film was calculated according to the following equation:  
\[\sigma=\frac{1}{\rho} \tag{1}\]  
where \(\sigma\) is the conductivity in S/m and \(\rho\) is the resistivity in \(\Omega\cdot\)m. The resistivity can be calculated according to the following equation:  
\[\rho=\frac{R\cdot S}{L}=Rs\cdot w \tag{2}\]  
where Rs (\(\Omega/\)sq) is the sheet resistance and w (m) is the average thickness of each graphene film. The values of w and Rs for **G-0**, **G-10**, **G-20** and **G-30** with different numbers of layers are listed in Tables 1 and 2, respectively, and were used to calculate the conductivity. The calculated electrical conductivities of each graphene film with different numbers of layers are presented in Figure 4. It is obvious that using the water/ethanol mixture solvent led to a higher electrical conductivity, and the best performance was achieved by **G-20**. The highest conductivity of 5.22 \(\times\) 10\({}^{5}\) S/m was obtained after depositing 15 layers. This value is among the highest conductivities reported in other studies [30; 31; 32; 33]. The main reason for the high conductivity obtained by **G-20** can be attributed to the improved graphene flakes alignment using the water/ethanol mixture solvent. When >15 layers of graphene flakes were deposited, the electrical conductivity decreased. Considering the requirements for sheet resistance of GFTEs and the fabrication period/cost, 15 layers were deposited to fabricate the GFTEs in our study.