## 3 Results and Discussion
### Concentration and Calibration Study  
After measuring the Raman far-field spectra and optimizing the experimental parameters, we performed a concentration-dependent SERS study by dropping different concentrations of the S protein on the surface of the substrate. Each spectrum displayed in Figure 5a is obtained by averaging three spectra recorded from three positions of the substrate's surface. We observed an interesting change in the bands of the Raman spectra by decreasing the concentration, e.g., Raman bands are similar for the concentrations of \(10^{-6}\) M and \(10^{-7}\) M. However, the situation changes after varying the concentration between \(10^{-8}\) M and \(10^{-10}\) M, where the spectra are similar, see Figure 5a. The Raman bands' intensity decreases in both features, whereas their broadness decreases. The latter is due to the interaction between the proteins that become weaker by decreasing their number. This change in the conformational structure of the S protein is expected when the number of protein by a surface unit changes. In fact, the S protein has a big size and by increasing the concentration, a broadness and a shift of the Raman bands can be observed [39]. This change was also observed for the RBD protein published in our previous work [22]. All the spectra in Figure 5a show most of the relevant peaks displayed in Figure 4 such as tyrosine (Tyr), glutamic acid (Glu), tryptophan (Trp), phenylalanine (Phe), C-N and C-C protein stretching, C-H rocking, and C-H stretching of glycoproteins located at 640 cm\({}^{-1}\), 876 cm\({}^{-1}\), 889 cm\({}^{-1}\), 1005 cm\({}^{-1}\), 1033 cm\({}^{-1}\), 1050 cm\({}^{-1}\), 1377 cm\({}^{-1}\), and 1460 cm\({}^{-1}\), respectively. At low concentration, a peak located at 1600 cm\({}^{-1}\) assigned to amino acids (Tyr, Phe, Trp) or \(\gamma_{\text{as}}\) (COOH) is observed [36; 40]. The observed modes are present in all the concentrations. In addition, the observed modes were also observed in the concentration-dependent study performed on RBD proteins in our previous work, see Figure 5a [22] where the spectra are very similar. The electrodynamical properties of the functional groups of amino acids are very sensitive to the interaction with a metallic surface such as gold and silver. The latter  
Figure 4: Far-field Raman spectra of **(a)** RBD, and **(b)** S. For both proteins, the most relevant vibrational bands are cysteine (Cys), histidine (His), tyrosine (Tyr), glutamic acid (Glu), tryptophan (Trp), phenylalanine (Phe), C-N and C-C protein stretching, C-H rocking, and C-H stretching of glycoproteins located at 526 cm\({}^{-1}\), 640 cm\({}^{-1}\), 876 cm\({}^{-1}\), 889 cm\({}^{-1}\), 1005 cm\({}^{-1}\), 1033 cm\({}^{-1}\), 1050 cm\({}^{-1}\), 1377 cm\({}^{-1}\), and 1460 cm\({}^{-1}\), respectively. Laser wavelength 632.8 nm, using CaF\({}_{2}\) substrate and 150 s integration time.  
explains the increase and the decrease of the band intensities relative to those observed in the far-field spectra [40]. Figure 5b,c show a linear dependence between the Raman intensity and the concentration of the S protein and RBD, respectively. The intensity was calculated by integrating under the Raman bands, confirming the linear response property and sensitivity of our biosensor. The intensity of SERS on RBD, in Figure 5c, were taken from our previous work [22] where we integrated it under the Raman spectra. If we compare between the two slopes in Figure 5b,c, we conclude that we can detect the S protein at four times lower concentrations than RBD. This could be attributed to the size of the S protein compared to the RBD. This confirms that our method of detection is four times more sensitive for the S protein than the RBD.