## 3 Results and Discussion
### Initial CNT/Si Device Comparison
\begin{table}
\begin{tabular}{c c c} \hline  & **Fast-Filtered Films** & **Slow Gravity Filtered Films** \\ \hline PCE (\%) & **8.06** (7.21 \(\pm\) 0.84) & **9.64** (5.71 \(\pm\) 3.24) \\ \hline \(\text{J}_{\text{sc}}\) (mA cm\({}^{-2}\)) & **24.76** (22.26 \(\pm\) 1.33) & **27.46** (19.84 \(\pm\) 6.55) \\ \hline \(\text{V}_{\text{oc}}\) (V) & **0.532** (0.501 \(\pm\) 0.038) & **0.532** (0.495 \(\pm\) 0.044) \\ \hline FF & **0.66** (0.647 \(\pm\) 0.012) & **0.67** (0.554 \(\pm\) 0.172) \\ \hline Ideality & **2.34** (2.53 \(\pm\) 0.26) & **2.40** (2.89 \(\pm\) 0.71) \\ \hline \begin{tabular}{c} Saturated Current Density \\ (mA cm\({}^{-2}\)) \\ \end{tabular} & **0.00198** (0.005 \(\pm\) 0.003) & **0.0008** (0.025 \(\pm\) 0.033) \\ \hline \
\begin{tabular}{c} Series Resistance (\(\Omega\)) \\ \end{tabular} & **51.4** (53 \(\pm\) 1.66) & **50.5** (128 \(\pm\) 115) \\ \hline
\begin{tabular}{c} Shunt Resistance (\(\Omega\)) \\ \end{tabular} & **25,300** (10,456 \(\pm\) 12,857) & **17,200** (7665 \(\pm\) 6775) \\ \hline \end{tabular}
\end{table} 
Table 2: Solar device data for fast-filtered and slow-filtered films, bold text is the best-recorded result with the average and standard deviation in brackets. Figure 6: J/V properties for devices with 400 \(\mu\)L aliquot slow and fast-filtered arc-discharge SWCNT films. Where PCE is Percent Current Efficiency, \(\text{J}_{\text{sc}}\) is Short-Circuit Current Density, \(\text{V}_{\text{oc}}\) is Open Circuit Voltage, and FF is the Fill Factor. 550 nm and an experimental sheet resistance (Equation (1)), both of which have been achieved for the slow and fast arc-discharge SWCNT films. Equation (1): \(\sigma_{\text{dc}}\):\(\sigma_{\text{OP}}\) ratio equation. \[ \begin{split}\%_{\text{T}550}=(1+\frac{1}{2\text{K}_{\text{s}}}* \sqrt{\frac{\mu_{0}}{\epsilon_{0}}}*\frac{\sigma_{\text{OP}(550)}}{\sigma_{ \text{dc}}})^{-2}\\ \frac{\sigma_{\text{dc}}}{\sigma_{\text{OP}(550)}}=\frac{1}{2\text{ K}_{\text{s}}}*\frac{\sqrt{\frac{\mu_{0}}{\epsilon_{0}}}}{\Gamma^{-1/2}-1}\end{split}  \tag{1}\]  
where T is transmittance at 550 nm in this case, R\({}_{\text{s}}\) is the sheet resistance, \(\mu_{0}\) (\(4\pi\times 10^{-7}\) N A\({}^{-2}\)) is the free space permeability and \(\epsilon_{0}\) (\(8.854\times 10^{-12}\) C\({}^{2}\) N\({}^{-1}\) m\({}^{-2}\)) is the free space permittivity. Equation (1) shows that a high \(\sigma_{\text{dc}}\):\(\sigma_{\text{OP}}\) ratio will be produced for a film with low sheet resistance and high light transmittance. Thus, a higher \(\sigma_{\text{dc}}\):\(\sigma_{\text{OP}}\) ratio indicates a more optimal film for use in a CNT/Si device [43]. Table 3 shows that the \(\sigma_{\text{dc}}\):\(\sigma_{\text{OP}}\) ratio increases with treatment, indicating an improvement in overall film performance. This is expected as the treatment improves the film conductivity, the thionyl chloride doping also removes the VHS transitions visible in the 600-800 nm regions of the spectrum and thus reduces light absorbance (increasing transmittance). Overall, Table 3 also shows that the \(\sigma_{\text{dc}}\):\(\sigma_{\text{OP}}\) is higher for the fast-filtered films than for the slow-filtered films. This indicates that the fast-filtered films are superior for CNT/Si device use as their lower sheet resistance outweighs their increased light absorbance.