# An Optimized Graphene-Based Surface Plasmon Resonance Biosensor for Detecting SARS-CoV-2
## 2 Materials and Methods  
### Biosensor Architecture and Initial Parameters  
The architecture of the proposed biosensor and the initial configuration parameters are presented in Figure 1 and Tables S1 and S2. This multilayer SPR biosensor is designed to detect SARS-CoV-2 by leveraging the unique properties of various materials in a layered configuration. The performance of this sensor is enhanced by incorporating graphene and silicon nitride layers between the metal substrate (silver) and the functionalization layer, which specifically targets SARS-CoV-2 viral components. Figure 1 points out the difference between the basic [20] and multilayer configurations. The basic SPR sensor configuration (Figure 1, left) consists solely of a BK-7 prism and a silver (Ag) layer, with water acting as the sensing medium. The resonance angle (\(\theta\)) in this simple configuration is highly sensitive to changes in the refractive index of the medium but lacks specificity and sensitivity for biomolecular interactions. In contrast, the proposed multilayer configuration (Figure 1, right) integrates additional layers, i.e., silicon nitride (Si\({}_{3}\)N\({}_{4}\)), graphene, and a thiol-tethered single-stranded DNA (ssDNA) layer. This architecture is designed to enhance the interaction between the evanescent field generated by SPR and the target analyte (SARS-CoV-2), thereby improving detection sensitivity and specificity [21].  
Table S1 lists the systems analyzed in this study, covering a range of configurations from the basic SPR sensor to more complex multilayer systems. The simplest configurations (Sys\({}_{0}\) and Sys\({}_{1}\)) consist of the prism/silver structure with water (H\({}_{2}\)O) and phosphate-buffered saline (PBS) solution, respectively, as sensing media. These configurations serve as baseline systems for comparison, allowing for the evaluation of performance improvements introduced by multilayer design. The remaining configurations (Sys\({}_{2}\) to Sys\({}_{9}\)) include sequential additions of Si\({}_{3}\)N\({}_{4}\), graphene, and ssDNA, building towards the complete multilayer configuration (Sys\({}_{9}\)) of prism/silver/silicon nitride/graphene/ssDNA/PBS. The inclusion of PBS in the medium is essential, as it reflects the experimental preparation conditions for SARS-CoV-2 at different concentrations [19]. It is expected that PBS will serve to maintain pH stability and simulate physiological conditions, which are critical for maintaining viral structure during detection.  
Table S2 provides the initial parameters used to configure each layer of the biosensor, with values sourced from prior research [22; 23; 24; 25]. The BK-7 prism (refractive index 1.5151) serves as the substrate for SPR excitation, while the silver layer (thickness 55.0 nm, refractive index 0.056253 + 4.2760i) is optimized to facilitate strong plasmon resonance. Silicon nitride (Si\({}_{3}\)N\({}_{4}\)), with a refractive index of 2.0394 and a thickness of 5.0 nm, is applied as a dielectric layer to enhance the evanescent field without excessive damping. The graphene layer, deposited at 0.34 nm thickness, exhibits a refractive index of 2.7611 + 1.6987i, which enhances light-matter interactions at the sensor interface. Finally, the functional layer, comprising thiol-tethered ssDNA with a refractive index of 1.462 and a thickness of 3.20 nm, is designed to capture SARS-CoV-2 with high specificity through molecular recognition interactions [26].