# An Optimized Graphene-Based Surface Plasmon Resonance Biosensor for Detecting SARS-CoV-2
## 3 Results and Discussions
### Optimization of Silver Thickness  
Figure 3a shows the SPR reflectance curves for varying silver thicknesses from 40 to 65 nm with PBS as the medium. The baseline configuration, Agbase (Sys\({}_{8}\) with 55 nm of silver in water), is included for comparison. As the silver thickness increases, the SPR dip shifts slightly and narrows, reflecting improved coupling with the evanescent field. However, there is a trade-off between narrowing the SPR dip and managing the attenuation and sensitivity, as excessive thickness can hinder light penetration into the metal layer.  
Figure 3: (**a**) SPR curves as a function of the angle of incidence ranging from 60\({}^{\circ}\) to 80\({}^{\circ}\), considering different silver thicknesses from 40 to 65 nm. Agbase denotes Sys\({}_{8}\) in water with an initial silver thickness of 55 nm. (**b**) Attenuation percentage, (**c**) FWHM, and (**d**) sensitivity enhancement percentage for all silver thicknesses tested.  
Figure 3b and Table S4 present the attenuation percentages for each silver thickness. A noticeable increase in attenuation occurs at higher silver thicknesses, particularly at 65 nm, where attenuation reaches 38.87%. The lowest attenuation is observed at 50 nm (0.43%), significantly reducing reflectance loss compared to thicker silver layers. This reduced attenuation at 50 nm suggests a more efficient SPR response, where the sensor maintains signal strength without excessive energy loss.  
The FWHM values, shown in Figure 3c and Table S4, indicate the sharpness of the SPR dip, with lower values reflecting sharper resonance and potentially higher signal-to-noise ratio. FWHM decreases as the silver thickness increases, with the lowest FWHM observed at 65 nm (1.64\({}^{\circ}\)). However, the trade-off at 65 nm is higher attenuation, which can impact sensitivity. At 50 nm, the FWHM is 2.24\({}^{\circ}\), balancing dip sharpness with manageable attenuation. This suggests that 50 nm provides an acceptable compromise, maintaining a defined resonance peak without the excessive broadening seen at lower thicknesses.  
Figure 3d and Table S4 illustrate the sensitivity enhancement for each silver thickness relative to Ag\({}_{\text{Base}}\). Figure S1 shows that sensitivity enhancement increases quasi-linearly with silver thickness, yet the whole improvement remains minimal, reaching a maximum of only 0.82% at 65 nm. At 50 nm, the sensitivity enhancement is 0.74%, offering a slight improvement over the baseline without the high attenuation and reduced FWHM associated with thicker layers. This minor increase in sensitivity suggests that thicker silver layers provide diminishing returns and that maximizing thickness beyond 50 nm is not cost-effective for practical applications.  
Based on the analysis of these metrics, a silver thickness of 50 nm is selected as the optimal configuration. This thickness provides the lowest attenuation (0.43%), a balanced FWHM (2.24\({}^{\circ}\)), and a manageable sensitivity enhancement (0.74%). This combination ensures that the sensor maintains a robust SPR response with minimized energy loss, sufficient dip sharpness, and acceptable sensitivity.