Introduction

Surface plasmon resonance phenomena occur optically, which achieves more excellent detection sensitivity [1]. Surface plasmons (SP) are free quantities of surface oscillations, obtained at the surface of a thin metallic film, the collective charge density oscillations propagate confined to the metallic dielectric interface. When the wave vector of an incident light couples with the wave vector of the evanescent wave, it is called a surface plasmon resonance (SPR) [2, 3]. The prism coupler used by Kretsch Amann’s ATR. In this configuration, the base of the prism is directly connected to the metal [4], but in otto’s configuration it used a very thin air gap between the prism and the film metal [5], for the purpose of exciting the surface plasmon. SPR sensors have received increasing attention due to their recent applications such as nanofibers and photonic crystal fiber [6, 7], solar cells [8], to detect specific bio-sensing [9, 10], used for detecting fat and melamine concentration milk [11]. Detection of chikungunya, virus dengue virus and diagnosis of novel coronavirus SARS-CoV-2 [12,13,14], designed for cancer cell detection [15, 16] biochemical interaction and detecting nano-objects in solution [17, 18] including medical diagnosis [19, 20], to detect disease in human teeth [21].

However, the SPR-based sensor is an excellent technique for sensing due to its important advantages such as high sensitivity, faster response, the dynamics of a reaction to follow in real time and the wide range of refractive index of the analyte [22,23,24]. Although SPR sensors use a variety of materials, recent research is interested in traditional transition metal dichalcogenides (TDM), because of their perfect electronic and optical properties. Recently, traditional (TDMs) have been intensively investigated theoretically and experimentally to demonstrate that some noble metals can form a layered structure with S and Se, of which PtSe2 is one of the most important properties, such as the largest band gap of (1,2 eV) for a monolayer of semiconductors, going from a bulk semi-metallic PtSe2 with zero band gap its strong interlayer interaction. On the other hand, the PtSe2 can also offers inertness to chemical agents and resilience to toxicity, making it a suitable material for sensing applications [25].

However, Silicon is getting more and more attention last 10 years due to its low cost. The addition of silicon in the structure SPR layer is capable of raising its sensitivity [26], Verma et al. used the silicon between the Gold and graphene layer in the SPR sensor was the highest sensitivity [27]. Ougang et al. have proposed the structure base for Silicon and TMDs on Gold film, and it was achieved with a more excellent sensitivity [28]. Rajeev et al. proposed SPRsensor-based Silicon and two-dimensional MXene (Ti3C2TX) to increase the sensitivity [29]. The employing of the Si nanomaterials has been theoretically improved the sensitivity [15]. PtSe2 over Ag and Au has demonstrated significant for improving sensitivity of sensor up to 162 deg/RIU and 265 deg/RIU, respectivity. Rahman et al. are designed a novel structure (Ag–PtSe2–WSe2) there sensitivity are 194 deg/RIU and 187 deg/RIU, respectively [30]. M. Mahabubur et al. have been proposed (Au–WSe2–PtSe2–BP) for improving the sensitivity up to 200 deg/RIU [31]. In this context of the present paper, we propose the traditional SPR biosensor schema based six layers on Silicon-PtSe2 coated biosensor. It was introduced in order to analyze and characterize some keys such as change of resonance angle θres, minimum reflectance (Rmin), FWHM, detection accuracy (DA), sensitivity (S) and FOM. We suggest a novel structure used numerical simulations of transfer matrix method (TMM); Here the architect-based Au/Si/Au/PtSe2 explored to improve its sensitivity.

It found a great advancement of the sensitivity of SPR by using the modified schema. These papers are presented as follows, the mathematical expression is in Sect. 2, the results and discussion are discussed in Sect. 3. Finally, the conclusion and necessary references are arranged at the end.

Mathematical background

This proposed structure is a modified Kretschmann model, as shown in Fig. 1. We used an SPRsensor using a multilayer composition consisting of a metal (Gold) film deposited at the base of the BK7 glass prism, silicon (Si) is attached with Gold. film, and the exterior of the silicon layer is also kept in direct contact with another metal layer. The biomolecular recognition element consists of the PtSe2 layer, which has a monolayer thickness of 0.375 nm [31].

Fig. 1
figure 1

Multilayer stack diagram of the biosensor based on Si and PtSe2

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The refractive index of the biological sample is considered to vary from 1.33 [32]. The BK7 glass prisms is characterized by the following dispersion relation (1) [33]:

$$ n_{p} = \sqrt {\frac{{1.03961212 \lambda^{2} }}{{\lambda^{2} - 0.00600069867}} + \frac{{0.231792344 \lambda^{2} }}{{\lambda^{2} - 0.0200179144}} + \frac{{1.03961212 \lambda^{2} }}{{\lambda^{2} - 103.560653}} + 1} $$
(1)

where λ the wavelength (µm).

The complex RI of Gold at different wavelengths can be calculated from the Drude-Lorentz model [34]:

$$ \varepsilon_{G} = 1 - \frac{{\lambda^{2} \lambda_{c} }}{{\lambda_{p}^{2} \left( {\lambda_{c} + i \lambda } \right)}} $$
(2)

Here \({\lambda }_{c}=2.4511\times {10}^{-5}m\) and \({\lambda }_{p}=1.6826\times {10}^{-7}m\) are the collusion and the plasma wavelength of Gold, respectively. The Silicon layer refractive index can be calculated using the following equation [35].

$$ n_{Si} = A + A_{1} e^{{ - \lambda t_{1} }} + A_{2} e^{{ - \lambda t_{2} }} $$
(3)

where: \(A=3.44904\), \({A}_{1}=2271.88813\), \({A}_{2}=3.39538\), \({t}_{1}=0.058304\) and \({t}_{2}=0.30384\) at λ wavelength in µm. The complex dielectric value of PtSe2 dependents on the thickness at wavelength of 633 nm, it is calculated using from the literature [36, 37].

We employ the matrix method to calculate the reflectance of the reflected light of the six-layer model. This matrix method is efficient and does not require any approximation. In this structure, all the layers are structured in the Z direction, each layer is characterized by the thickness (dk) and the constant optics of the metal and the dielectric. The relation between the tangential components of the electric field (E) and the tangential components of the magnetic fields (H) at the first and the final layer is given by [38].

$$ M = \mathop \prod \limits_{G = 2}^{G - 1} M_{G} = \left[ {\begin{array}{*{20}c} {M_{11} } & {M_{12} } \\ {M_{21} } & {M_{22} } \\ \end{array} } \right] $$
(4)
$$ M_{G} = \left[ {\begin{array}{*{20}c} {cos \delta_{G} } & {\frac{{ - sin \delta_{G} }}{{q_{G} }}} \\ { - i q_{G} sin \delta_{G} } & {cos \delta_{G} } \\ \end{array} } \right] $$
(5)

where ηG is the phase factor of the thin film and δG is the phase thickness and is determined as:

$$ q_{G} = \frac{{\sqrt {n_{G}^{2} - k_{G}^{2} - n_{p}^{2} sin^{2} \theta_{i} - 2 i n_{G} k_{G} } }}{{\varepsilon_{G} }} $$
(6)
$$ \delta_{G} = \frac{2\pi }{\lambda }d_{G} \sqrt {n_{G}^{2} - k_{G}^{2} - n_{p}^{2} sin^{2} \theta_{i} - 2 i n_{G} k_{G} } $$
(7)

θi is the angle of incidence, and nG,kG are constant optic of the complex refractive index and dG the thickness of the metal layer.

$$ r_{p} = \frac{{\left( {M_{11} + M_{12} q_{N} } \right) q_{1} - \left( { M_{21} + M_{22} q_{N} } \right)}}{{\left( {M_{11} + M_{12} q_{N} } \right)q_{1} + \left( { M_{21} + M_{22} q_{N} } \right)}} $$
(8)

The reflectance (R) is given by:

$$ R_{p} = \left| {r_{p} } \right|^{2} $$
(9)

Results and discussion

The optimization of sensitivity, detection accuracy and quality factor were considered as the main performance parameters of the excellent SPR sensor. The sensitivity (S) can be defined as the ratio of the change in the resonance angle (θSPR) to the change in the refractive index of the sensing region:

$$ S = \frac{{d\theta_{SPR} }}{{dn_{biosample} }} $$
(10)

The detection accuracy (DA) is a known as the ratio of the shift resonance angle (θSPR) to the full width at half maximum of the resonance plasmon curve as can be seen in the following relation:

$$ DA = \frac{1}{FWHM} $$
(11)

Another important parameter of interest is the figure of merit (FOM) that is determine as the ratio of the reflectance curve of sensitivity to the FWHM [39]:

$$ FOM = \frac{S}{FWHM} $$
(12)

Three schematic structure and their performance parameters of the SPR sensor reflectance curve for each structure as a function of the incident angle of sensing medium summarized in Table 1.

Table 1 Performance parameters of SPR sensor reflectance curve for different structure
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Figure 2a; show the movement of resonance angle is 1° with small increment in RI = 0.005 ford(Au) = 35 nm, d(Si) = 5 nm. It can see the calculated sensitivity from Eq. (10) of conventional sensor is 200°/RIU; after increasing thickness of Gold and decreasing thickness of silicon d(Au) = 60 nm, d(Si) = 3 nm in conventional SPR sensor. It can observe that the sensitivity achieved 206°/RIU shown in Fig. 2b.

Fig. 2
figure 2

Reflectance curve as a function of the incident angle for d(Au) = 35 nm, d(Si) = 5 nm (a) and d(Au) = 60 nm, d(Si) = 3 nm (b)

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Table 2; presents the values of minimum reflectance (Rmin), sensitivity (S), full width half maximum (FWHM), detection accuracy (DA), and figure of merit (FOM) at the wavelength 633 nm. the optimization thickness of Gold (Au), Silicon (Si) and the thickness of (PtSe2) at the illustrated in Fig. 3a–f. It can be observed from Table 2 that the high sensitivity and FOM of the two conventional structure Au/Si/Au/PtSe2 for combination (1) with thickness Au(35 nm)/Si(5 nm)/Au(5 nm)/PtSe2(2 nm), combination (2) and combination (3) Au(60 nm)/Si(5 nm)/Au(5 nm)/PtSe2(2 nm), for the best combination of SPR biosensor proposed is the structure having Au(60 nm)/Si(5 nm)/Au(5 nm)/PtSe2(2 nm) its property optimum highest sensitivity, optimum figure of merit 206°/RIU and 24.03 respectively. However, the sensitivity, Rmin and DA values for combination (1) are 200°/RIU, 0.025 and 0.082, respectively. It can be seen in Table 2; that when adding Si layer in the configuration Kretchmann without PtSe2 layer the sensitivity achieved 234°/RIU, this means adding Si layer on sandwich Gold is sufficient to increase the sensitivity enhancement, but biochemical detection needs to use Si and PtSe2 which greatly allow one to detect analyte.

Table 2 Performance parameter for optimized combination of Gold and Si thickness of proposed SPR
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Fig. 3
figure 3

Minimum reflectivity (Rmin) resonance angle (∆θres) as a function variation of the thickness of Gold for 2, 3.3, and 4.4 nm of PtSe2 at Si 3, 5, 7 nm

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In this work, the main aim was to optimize the thickness of (PtSe2), we plotted the change in resonance angle and the minimum reflectivity with various thickness of Silicon sheets (3, 5 and 7 nm) and the thickness of gold film (30, 35, 40, 45, 50 and 60 nm). Figure 3a–c and d–f show the simulation results of the (∆θres) and (Rmin) respectively.

From Fig. 3a–c we have compared its (∆θres), it found at the thickness of (PtSe2) equal to 2 nm the (∆θres) is as great as for 35 nm thickness of Gold and 5 nm thickness of Silicon (∆θres = 1°) and it can be seen from the plot is the highest that 60 nm thickness of Gold and 3 nm thickness of Silicon (∆θres = 1.03°).

Similarly, Fig. 3d–f shows the minimum reflectivity curves for different thickness of (Gold) with optimized thickness of layer (PtSe2), and for Fig. 3e at 35 nm thickness of Gold and with 632 nm wavelength, it can be observed from these plots that minimum reflectivity is lower for this case and for Fig. 3d at 60 nm thickness of Gold, it is clear that the minimum reflectivity is still very highest (Rmin = 0.60) which indicates that the SPR in this structure is not strong and the sensing medium is not very remarkable. For a perfect biosensor, (∆θres) should be high, but at the moment (Rmin) should be minimum.

From Fig. 4, the result shows that change of sensitivity. First, the sensitivity is quasi linear decreasing with the lowest thickness (PtSe2).

Fig. 4
figure 4

The sensitivity as a function thickness of Gold and different thicknesses of PtSe2with a d(Si) = 2 nm, b d(Si) = 5 nm and c d(Si) = 7 nm a wave length 632.8 nm

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The Fig. 4a shows, the sensitivity varies at 60 nm thickness of Gold to S = 206°/RIU with thickness of d(PtSe2) = 2 nm at S = 142°/RIU with thickness of d(PtSe2) = 4.4 nm. We may therefore conclude that the sensitivity is best at the lowest (PtSe2) thickness. Secondly, the result illustrates that the sensitivity increased with increasing of gold thickness at 3 nm thickness of Silicon and at the thickness of d(PtSe2) = 2 nm.

We can achieve for Fig. 4b at d(PtSe2) = 2 nm the sensitivity increase at the maximum d(Au) = 35 nm equal to 200°/RIU and then decreases.

Another important parameter for study a SPR biosensor is detection accuracy (DA), it is highest for lower thickness (PtSe2), we can see for Fig. 5a the (DA)increase with increase of thickness of Gold at d(PtSe2) = 2 nm. From Fig. 5b show the (DA) increase for maximum and started to decrease.

Fig. 5
figure 5

The DA as a function thickness of Gold d(Si) = 3 nm (a) and d(Si) = 5 nm (b)

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We calculated the FOM by the formula FOM = S/FWHM. From this, we can get the FOM increase with the increase of thickness of Gold showing a Fig. 6a. For Fig. 6b the FOM decrease with the increase of thickness of (PtSe2).

Fig. 6
figure 6

The FOM as a function thickness of Gold d(Si) = 3 nm (a) and d(Si) = 5 nm (b)

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Table 3; shows the comparison among the enhancement of the proposed SPR sensor with another existing SPR sensor in the literature, and has information on the sensitivity, minimum reflectance, and quality factor at the 633  nm wavelength.

Table 3 Comparison of proposed work with another existing sensor
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Conclusion

In this study, we have theoretically investigated a novel SPR biosensor using (with insertion of) a Silicon layer and PtSe2 layer of the conventional structure to obtain better performances. In this proposed SPR biosensor working on the visible light region by using the transfer matrix method. The structure is based on six layers, in which first is a low refractive index BK7as the coupling prism and insertion the silicon layer and PtSe2 layer between two gold films. The changes of different architect parameters are improving the sensitivity. It found that the change of resonance angle decreases on increasing the thickness of PtSe2. and the present analysis also represents that the FWHM decreases up to the extent due to which the quality factor and detection accuracy improve enormously. The result demonstrated that the maximum sensitivity as high as 200°/RIU with figure of merit (FOM) 16.43 RUI−1can achieved with structure is designed for gold (35 nm), Silicon (5 nm) and PtSe2 (2 nm), where the highest sensitivity 206°/RIU can be obtained for Gold (60 nm), Silicon (3 nm) and PtSe2 (2 nm). Additionally, the maximum figure of merit (FOM) is 16.43 RUI−1. It is expected that the novel structure may be very much useful in different fields of biosensing and optical sensing application.