# An Optimized Graphene-Based Surface Plasmon Resonance Biosensor for Detecting SARS-CoV-2
## 3 Results and Discussions
### Optimization of the Number of Graphene Layers  
To determine the optimal configuration, we analyze the sensor's performance with one to six graphene layers. Figure 5 and Table S6 summarize these results, while Figure S3 shows the sensitivity enhancement trend. Figure 4: (**a**) SPR curves as a function of the angle of incidence ranging from 65\({}^{\circ}\) to 90\({}^{\circ}\), considering different silicon nitride thicknesses from 5 to 20 nm. \(S_{3}\)N\({}_{4,\text{base}}\) denotes Sys\({}_{8}\) in water with the optimized silver thickness of 50 nm and initial silicon nitride thickness of 5 nm. (**b**) Attenuation percentage, (**c**) FWHM, and (**d**) sensitivity enhancement percentage for all silicon nitride thickness tested. Figure 5a presents the SPR reflectance curves as the number of graphene layers increases. As more graphene layers are added, the SPR dip shifts to higher angles and broadens, indicating greater interaction with the evanescent field. However, excessive broadening with multiple layers reduces the dip sharpness, which critically impacts sensor precision. The single-layer graphene configuration (L1) maintains a distinct SPR dip at approximately 82\({}^{\circ}\), balancing sensitivity and dip sharpness. Figure 5b and Table 56 display the attenuation percentages for each configuration. Attenuation rises sharply as the graphene layers increase, with a notable jump to 66.15% at six layers. Single-layer graphene (L1) has the lowest attenuation at 8.30%, indicating minimal reflectance loss and efficient SPR response. This low attenuation with single-layer graphene suggests that it supports a strong SPR signal while retaining energy, crucial for maximizing signal-to-noise ratios. The FWHM values, shown in Figure 5c and Table 56, increase as the graphene layer count rises. At one layer, the FWHM is 4.99\({}^{\circ}\), which is within an acceptable range for achieving a sharp resonance. With additional layers, FWHM increases significantly, reaching 9.58\({}^{\circ}\) at five layers and 13.8\({}^{\circ}\) at six layers, indicating a substantial loss in resonance sharpness. Maintaining a sharp resonance is critical for high-precision detection, and single-layer graphene offers an optimal balance between sensitivity and FWHM. Figure 5: (**a**) SPR curves as a function of the angle of incidence ranging from 65\({}^{\circ}\) to 90\({}^{\circ}\), increasing the number of graphene layers. L1 base denotes Sys8 in water with the optimized silver thickness of 50 nm, the optimized silicon nitride thickness of 15 nm, and the initial one-layer graphene system. (**b**) Attenuation percentage, (**c**) FWHM, and (**d**) sensitivity enhancement percentage for all number of graphene layers tested. Sensitivity enhancement, displayed in Figure 5d and Table S6, increases linearly up to four layers, with a maximum of 3.27% at five layers. However, beyond four layers, sensitivity enhancement plateaus and even begins to decrease slightly. Single-layer graphene (L1) provides a sensitivity enhancement of 1.28%, which is lower than configurations with multiple layers but is balanced by the advantages of lower attenuation and narrower FWHM. Figure S3 highlights this quasi-linear trend, indicating that while additional graphene layers initially improve sensitivity, they also introduce diminishing returns and adverse effects on attenuation and FWHM at higher counts. To stress again, single-layer graphene (L1) is selected as the optimal configuration. This choice is justified by the following considerations:  
* The low attenuation of single-layer graphene minimizes signal loss, ensuring a strong SPR response. * With a manageable FWHM, single-layer graphene maintains a sharp resonance dip, balancing precision and sensitivity. * Although sensitivity enhancement is higher with more layers, as reported in [25], the improvement with single-layer graphene is acceptable, especially given the diminishing returns and high attenuation observed with additional layers.