## 5 Modeling and Simulating Si-SC Structures
### Modeling and Simulation of Si-SC with Patterned MLARC  
To investigate the potential of patterned MLARCs, the SiO\({}_{2}\)/NQD/LiF and Si\({}_{3}\)N\({}_{4}\)/NQD/ LiF configurations were simulated using Lumerical FDTD. As shown in Figure 8, the geometric parameters, including layer thicknesses (\(d\)), period (\(P\)), and radius (\(L\)) of the cylindrical patterns, were optimized. The Lumerical FDTD simulation tool was employed to simulate these structures, with periodic boundary conditions applied in the \(x\) and \(y\) directions to mimic an infinite array of patterns, while light propagation was modeled along the \(z\)-axis. The optimization of patterned MLARCs involved a systematic variation of the period (\(P\)) of the cylindrical patterns, while maintaining a constant \(L/P\) ratio of approximately 0.32. This approach allowed for an assessment of the impact of pattern periodicity on the overall device performance. By simulating Si-SC structures with varying \(P\) values within the range of 250 nm to 600 nm, the sensitivity of \(J_{sc}\) to the pattern period was investigated. As depicted in Figure 8, \(J_{sc}\) initially increases with increasing \(P\), reaching a maximum value at \begin{table}
\begin{tabular}{c c c c c} \hline \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 C-MLARC & 0.61 & 34.10 & 0.83 & 17.26 \\ Si-SC with Si\({}_{3}\)N\({}_{4}\)/NQD/LiF C-MLARC & 0.61 & 35.54 & 0.83 & 18.02 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Electrical characteristics for Si-SC structures with and without continuous MLARC of SiO\({}_{2}\)/NQD/LiF and Si\({}_{3}\)N\({}_{4}\)/NQD/LiF configurations. Figure 7: **(a)** Simulated reflectivity spectra and (b) current–voltage (J-V) characteristics for Si-SC structures with continuous MLARC of SiO\({}_{2}\)/NQD/LiF and Si\({}_{3}\)N\({}_{4}\)/NQD/LiF configurations. an optimal period before decreasing at larger \(P\) values. This behavior indicates the existence of an optimal pattern periodicity that maximizes light trapping and carrier generation. The observed trend can be attributed to the interplay between light scattering, diffraction, and interference effects within the patterned structure. At smaller periods, light scattering is less efficient, leading to reduced light trapping. Conversely, at larger periods, excessive light scattering can occur, resulting in increased reflection losses. The optimal period represents a balance between these competing effects, maximizing light absorption and minimizing reflection. By conducting a parametric study across a range of \(d\), \(P\), and \(L\) values, through rigorous optimization, the following \(d\) values were determined: 80 nm SiO\({}_{2}\), 40 nm NQD, and 60 nm LiF for the SiO\({}_{2}\)/NQD/LiF configuration; 60 nm Si\({}_{3}\)N\({}_{4}\), 60 nm NQD, and 60 nm LiF for the Si\({}_{3}\)N\({}_{4}\)/NQD/LiF configuration. The cylindrical patterns of NQD and LiF layers were optimized with (\(P\)) of 550 nm and (\(L\)) of 175 nm. The optimization analysis identified the optimal geometric parameters of the pattern for each MLARC configuration, providing valuable insights for the design of high-performance Si-SCs. Figure 9a presents the reflectivity spectra of the patterned MLARC configurations. Both structures exhibited significantly reduced reflectivity compared to their continuous counterparts, particularly in the visible and near-infrared regions. The Si\({}_{3}\)N\({}_{4}\)/NQD/LiF configuration demonstrated superior light trapping capabilities, achieving a minimum reflectivity of 5% at 550 nm. The impact of patterned MLARCs on carrier generation was assessed through IQE and EQE calculations. Table 7 presents the results, indicating a substantial enhancement in EQE for both configurations compared to the SLARC and continuous MLARC counterparts.