## 5 Modeling and Simulating Si-SC Structures
### Modeling and Simulation of Si-SC with Patterned MLARC
This improvement is attributed to the combined effects of light trapping of the optimized cylindrical patterns and downshifting within the NQD layer. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & \multicolumn{4}{c}{**IQE (\%)**} & \multicolumn{4}{c}{**EQE (\%)**} \\ \hline
**Structure** & **350** & **550** & **750** & **350** & **550** & **750** \\ \hline Si-SC (no ARC) & 90.54 & 96.71 & 99.36 & 43.46 & 56.57 & 63.49 \\ \hline Si-SC with SiO\({}_{2}\)/NQD/LiF P-MLARC & 96.47 & 98.12 & 99.50 & 58.39 & 86.35 & 87.27 \\ \hline Si-SC with Si\({}_{3}\)N\({}_{4}\)/NQD/LiF P-MLARC & 95.95 & 97.80 & 99.41 & 64.62 & 94.96 & 95.08 \\ \hline \end{tabular}
\end{table} 
Table 7: IQE and EQE of Si-SC structures with patterned MLARCs of SiO\({}_{2}\)/NQD/LiF and Si\({}_{3}\)N\({}_{4}\)/NQD/LiF configurations. Figure 8: Sensitivity of \(J_{sc}\) to the pattern period at different geometric parameters, including patterns periodic (\(P\)) and radius (\(L\)) with \(L\)/\(P\) ratio = 0.32, for Si-SC structures with patterned MLARC configurations: SiO\({}_{2}\)/NQD/LiF and Si\({}_{3}\)N\({}_{4}\)/NQD/LiF. To evaluate the electrical performance of patterned MLARCs, J-V characteristics were simulated, as shown in Figure 9b. In addition, Table 8 summarizes the key electrical performance parameters for Si-SC structures with and without patterned MLARCs. The calculated \(J_{sc}\) values for the SiO\({}_{2}\)/NQD/LiF and Si\({}_{3}\)N\({}_{4}\)/NQD/LiF patterned MLARCs were 39.51 mA/cm\({}^{2}\) and 48.04 mA/cm\({}^{2}\), respectively, representing significant improvements over the continuous MLARC and SLARC configurations. The corresponding PCE values were 20.12% and 24.65%. Overall, the optimized patterned MLARC structures exhibited reduced reflectivity compared to their continuous counterparts, with the Si\({}_{3}\)N\({}_{4}\)/NQD/LiF configuration demonstrating superior performance. The introduction of periodic patterns led to enhanced light trapping and improved absorption, as evidenced by the increased IQE and EQE values. These findings were further corroborated by the electrical performance analysis, which revealed significant improvements in \(J_{sc}\) and PCE for the patterned MLARC structures. By correlating microscopic optical properties with macroscopic device performance, Table 9 presents a comparative overview of reflectivity, EQE, \(J_{sc}\), and PCE for different Si-SC structures. The results underscore the significant impact of ARC design on light absorption and charge carrier generation to optimize light management and enhance Si  
Figure 9: (a) Simulated reflectivity spectra and (b) current–voltage (J-V) characteristics for Si-SC structures with patterned MLARC of SiO\({}_{2}\)/NQD/LiF and Si\({}_{3}\)N\({}_{4}\)/NQD/LiF configurations. \begin{table}
\begin{tabular}{c c c c c} \hline
**Structure** & \(\mathbf{V_{oc}}\) **(V)** & \(\mathbf{J_{sc}}\) **(mA/cm\({}^{2}\))** & **FF** & **PCE (\%)** \\ \hline Si-SC (no ARC) & 0.59 & 25.18 & 0.82 & 12.27 \\ Si-SC with SiO\({}_{2}\)/NQD/LiF P-MLARC & 0.61 & 39.52 & 0.83 & 20.13 \\ Si-SC with Si\({}_{3}\)N\({}_{4}\)/NQD/LiF P-MLARC & 0.62 & 48.04 & 0.83 & 24.65 \\ \hline \end{tabular}
\end{table} 
Table 8: Electrical characteristics for Si-SC structures with patterned MLARC of SiO\({}_{2}\)/NQD/LiF and Si\({}_{3}\)N\({}_{4}\)/NQD/LiF configurations. SC performance. The enhanced performance of Si-SC with patterned MLARCs can be attributed to several factors:  
* Improved light trapping: The periodic patterns scatter incident light, increasing the optical path length within the active region and promoting multiple reflections, leading to enhanced light absorption. * Enhanced carrier generation: The NQD layer absorbs photons at shorter wavelengths and re-emits them at longer wavelengths through a downshifting process. These downshifted photons are more effectively absorbed by the semiconductor layer, resulting in increased carrier generation.