## 2 Materials and Methods  
The configuration of the SPR sensor emerged from the classical Kretchmann configuration (prism-metallic layer-sensing medium), where two additional layers, a thin semiconductor layer and a graphene/TMDC (MoS2 or WS2) monolayer, were stacked on top of the metallic layer, as shown in Figure 1.  
The material for the coupling prism was borosilicate-crown glass (BK7) with a refractive index calculated using the following equation:  
\[n^{2}-1=\frac{1.03961212\lambda^{2}}{\lambda^{2}-0.0060069867}+\frac{0.23179234 4\lambda^{2}}{\lambda^{2}-0.0200179144}+\frac{1.01046945\lambda^{2}}{\lambda^{2 }-103.560653} \tag{1}\]  
where \(\lambda\) is the incidence wavelength expressed in \(\mu\)m, and the dispersion parameters were taken from [35]. The layers were stacked on top of each other in the z-direction and dimensions for all layers in the x and y directions are considered infinite. The complex refractive index of the silver layer was calculated using the following equation [36]:  
\[\widetilde{n}_{Ag}=\sqrt{1-\frac{\lambda^{2}\lambda_{c}}{\lambda_{p}^{2}( \lambda_{c}+i\lambda)}} \tag{2}\]  
where \(\lambda\) is the incident radiation wavelength in \(\mu\)m, \(\lambda_{c}\) and \(\lambda_{p}\) are the collision and plasma wavelengths that have the values 1.7614 \(\times\) 10\({}^{-5}\) m and 1.4541 \(\times\) 10\({}^{-7}\) m, respectively. The graphene monolayer thickness was considered 0.34 nm and the complex refractive index was computed with the following equation [37]:  
\[\widetilde{n}_{Graphene}=3+\frac{iC_{1}\lambda}{3} \tag{3}\]  
where \(C_{1}\) has a value of 5.446 \(\mu\)m\({}^{-1}\). The optical parameters and the thickness of one monolayer of TMDC are 5.0805 + 1.1724i and 0.65 nm for MoS2 [24], and 4.8937 + 0.3123i and 0.8 nm for WS2 [24], respectively. Figure 1: The proposed sensor configurations. The last layer from the configuration is the region where the biomolecular interactions (adsorption, DNA hybridization, etc.) take place, even though in an SPR classic configuration this layer is called the'sensing medium'. The sensing medium's refractive index varied from 1.332 to 1.337 with a change of 0.005 RI (refractive index units). It is worth mentioning that two approximations were made: (i) the quantum effects between graphene/TMDC monolayers were neglected, and, (ii) when more than two graphene/TMDC monolayers were stacked on top of each other the complex refractive index of the overall layer was considered the same as the one for one monolayer but with an increased thickness (N \(\times\) monolayer thickness) [38]. The SPR sensor's response depends on two damping processes [39]: (i) the leakage radiation due to the interference phenomena resulting from the multiple interfaces, and (ii) the absorption loss due to the energy transfer between the incident photons and the metallic layer phonons. A resonant energy transfer between incident radiation and surface plasmon polaritons (SPPs) appears by varying the angle of incidence, and, as a result, the resonance is seen as a sharp drop in reflectivity levels. Considering a classic three layer configuration, the equation for the resonance condition gives the angle at which the SPP wave is coupled with the incident radiation:  
\[k_{0}n_{p}\sin\theta=k_{0}\sqrt{\frac{\varepsilon_{s}\varepsilon_{m}}{ \varepsilon_{d}+\varepsilon_{m}}} \tag{4}\]  
where \(k_{0}\) is the incident light wavevector, \(n_{p}\) is the prism's refractive index, \(\theta\) is the incidence radiation angle, and \(\varepsilon_{s,m}\) represents the dielectric constants of the semiconductor and metal, respectively. The left-hand side of the equation is the propagation vector of light in the prism, whilst the right-hand side is the propagation vector of SPP from the metallic interface.