## 3 Results
smaller imaginary part of the refractive index, i.e., 333 deg/RIU with a 7 deg FWHM in comparison with 331 deg/RIU and 7.1 deg FWHM. Because the end goal is to maximize sensitivity, the discussion will be restricted to the structures that enhance it. From Table 2 it can be observed that the thin semiconductor's refractive index is 2.6 for the graphene, 2.62 for the MoS\({}_{2}\) and 2.66 for the WS\({}_{2}\). Among all materials that have been already utilized as top layers in SPR based sensors, BaTiO\({}_{3}\), having a refractive index of 2.405 [46], is the best candidate for this layer in the proposed sensor configurations. To verify if BaTiO\({}_{3}\) could really improve the sensing performance of the modified sensors, an additional set of optimizations was performed, to find the optimum thickness of the BaTiO\({}_{3}\) layer, using the same objectives and constraints as in the previous run. The convergence plots of layers and objectives can be found in Figure S3 and additional configurations together with the sensitivity and FWHM can be found in Figure S4 and Table S2 in Supplementary Information. The reflectivity curves of the most sensitive configurations containing BaTiO\({}_{3}\) can be seen in Figure 4.  
Table 3 demonstrates that the sensitivities obtained for all structures modified with BaTiO\({}_{3}\) are very close to those with the optimal refractive index, with the maximum difference in sensitivity being 9 deg/RIU for the configuration with MoS\({}_{2}\). Similarly, the FWHM values also change, and the FWHM value corresponding to MoS\({}_{2}\) with the optimal material refractive index is increased from 8.9 to 9.2 deg. The highest sensitivities, 330 deg/RIU and 325 deg/RIU, were obtained for the structures with graphene and WS\({}_{2}\), respectively. As in previous optimization studies, several solutions were found with a lower sensitivity of 200 deg/RIU, but with narrower reflectivity curves (<6 deg). Despite the enhanced performance of these structures, since the minimum level of reflectivity reaches a value of 5%, it is considered too high because of the inherent variations in the layer thickness during the fabrication process. Further, to eliminate the potential variations that could affect the sensor performance under realistic conditions, a new set of optimizations was performed, where the minimum level of reflectivity was introduced as an objective and constrained to be smaller than 1%. The reflectivity curves can be seen in Figure 5 and the performance determined for  
Figure 4: Reflectivity curves for the optimized structures containing the BaTiO\({}_{3}\) as a dielectric: black line shows the response for \(n=1.332\), the red line shows the response for \(n+\Delta n\) with \(\Delta n=0.005\). \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**L.N.**} & \multirow{2}{*}{**Material**} & \multicolumn{2}{c}{**Configuration**} & \multirow{2}{*}{**Sensitivity (deg/RIU)**} & \multirow{2}{*}{**FWHM (deg)**} \\  & & **Metal-Semic.–2D Mat.** & & \\ \hline
1 & Graphene & 40 nm–13 nm–1 L & 330 & 7.1 \\
2 & MoS\({}_{2}\) & 39 nm–11 nm–1 L & 249 & 9.2 \\
3 & WS\({}_{2}\) & 38 nm–11 nm–1 L & 325 & 8 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Optimized configurations with BaTiO\({}_{3}\) for which the sensitivity is enhanced. each configuration are presented in Table 4. In this case, there are three types of optimal configurations: one that improves sensitivity (black line), a second that narrows the FWHM (red line), and a third that minimizes the reflectivity level at resonance (blue line). The convergence plots of the layers and the objectives can be found in Figure S5. Additional configurations, together with the sensitivity and FWHM, can be found in Figure S3 and Table S6 in the Supplementary Information. From these results, it can be noted that adding the minimum level of reflectivity as an additional objective led to a slightly decreased sensitivity in comparison to the one obtained initially.