Introduction

Surface plasmon resonance (SPR) is the one of the most powerful optical techniques used for medical diagnostics, enzyme and gaseous detection, and food safety [1,2,3,4,5,6,7,8]. This technique has been widely used for a quick and accurate detection of various physical and biochemical parameters. Most of the SPR-based sensor uses Kretschmann’s attenuated total reflection (ATR) method, in which the p-polarized incident light excites a surface plasmon wave (SPW) along the metal–dielectric interface on the thin metallic layer deposited on the base of an optical coupling prism [9]. The choice of metallic film is one of the crucial aspects in designing SPR-based applications. Usually gold (Au) is considered as the most suitable plasmonic material as it is highly resistive to oxidization, possesses better chemical stability, and provides higher sensitivity. Silver, on the other hand, shows better resolution whereas it oxidizes easily and possesses lesser sensitivity compared to Au. The bimetallic configuration of Au/Ag utilizes the advantages of both the metals and has been demonstrated in several works. It is noted that the usage of bimetallic film, though it improved the resolution of the sensor, its sensitivity seems not much improved [10,11,12,13]. Apart from Au and Ag, more metals have been identified for SPR sensing such as aluminum (Al), nickel (Ni), copper (Cu), and platinum (Pt), and each of these metals has their own advantages and disadvantages [14,15,16]. Recently, platinum has been identified as a potential SPR-active metal owing to its strong dependence of reflection coefficient on wavelength in the visible region of the spectrum, high reflecting property, inert, chemically stable with high melting point, and prolonged stability [17,18,19]. Shukla et al. theoretically analyzed the performance of the SPR sensor with platinum layer coated on optical fiber. They observed that the sensitivity of the sensor enhances linearly with the increase in the refractive index of the sensing medium for all thickness of platinum layer and for a given refractive index of the sensing medium [20]. Recently, black phosphorus (BP) is identified as one of the potential 2D materials [21] which gain rapid attention due to its widely tunable and direct bad gap, remarkable electrical and optical properties, and higher carrier mobility [22,23,24,25]. The BP also provides attractive physical, chemical, and mechanical anisotropic properties which make it a suitable candidate for high performance potential and chemical applications [26]. Srivastava et al. reported that implementation of double layer BP enhanced the sensitivity by 35% [27]. Recently, graphene, on the other hand, exhibits remarkable properties such as high charge carrier mobility which induces strong coupling at the interface between metal-graphene films [28]. Wu et al. reported that utilizing graphene layers enhanced the sensitivity by 25% compared with conventional gold–based SPR sensor [29]. Recently, many studies on enhancement of sensitivity of the SPR sensor upon utilizing graphene layers are attempted from numerical aspects [5, 30]. Furthermore, graphene is impermeable to gases such as oxygen and helium because the electron density of hexagonal rings is enough to prevent atoms and molecules from passing through the ring structure [31]. Hence, graphene can be used as a protective layer against oxidation of metals which is also found to improve the sensitivity of the sensor to a great extent [32]. Recently, SPR biosensors based on Blue P-TMDC-graphene heterostructure [33] and graphene-BaTiO3 nanosheets [34] have also been proposed.

In this paper, we have designed a new sensor configuration composed of Ag-Pt bi-metallic films sandwiched with 2D materials BP and graphene over Pt layer. Here, we report that ultra-high sensitivity of the SPR sensor can be realized upon suitable optimization of thickness of metal layers and no. of layers of BP and graphene. Here, it is noted that the proposed sensing configuration not only enhances sensitivity but also still keeps the FWHM of the resonance curve much smaller than the conventional sensor utilizing Au as plasmonic material and hence improved the resolution to a greater extent. Moreover, the top surface graphene coat not only protected the metal surface but also improved the biomolecular absorption through high surface to volume ratio and Pi conjugation structure.

Theory

The structure of the proposed SPR biosensor is given in Fig. 1 which consists of a multilayer (six layers) structure. Keeping in mind the widely used prism required for momentum match, the first layer is of BK7 prism. The second layer is an optimized thickness of 40-nm thickness of silver which is deposited on the base of the coupling prism. The third and fourth layers are BP and 15-nm thickness of platinum. The fifth layer is considered as graphene followed by a sensing layer. TM-polarized light, wavelength of 633 nm, is used at one face of the prism and is assumed to be collected from the other face with proper optics. The dispersion of prism is considered as [35]

$${n_{{\text{BK7}}}} = {\left( {\frac{{1.03961212{\lambda^2}}}{{{\lambda^2} - 0.00600069867}} + \frac{{0.231792344{\lambda^2}}}{{{\lambda^2} - 0.0200179144}} + \frac{{1.03961212{\lambda^2}}}{{{\lambda^2} - 103.560653}} + 1} \right)^{1/2}}$$
(1)
Fig. 1
figure 1

Schematic diagram of the proposed SPR biosensor

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where λ is the wavelength of incident light in micrometers.

The wavelength dependence dielectric constant of silver is calculated using Drude-Lorentz formula, given by

$${\varepsilon_m}(\lambda ) = {\varepsilon_{mr}} + {\varepsilon_{mi}} = 1 - \frac{{{\lambda^2}{\lambda_c}}}{{\lambda_p^2({\lambda_c} + i\lambda )}}$$
(2)

where \({\lambda_p}\) = 1.4541 × 10−7 m and \({\lambda_c}\) = 1.7614 × 10−5 m. Here, \({\lambda_p}\) and \({\lambda_c}\) are the plasma and collision wavelength of silver (Ag), respectively [32]. The third layer is BP whose refractive index is n3 = 3.5 + 0.01i at λ = 633 nm, and the thickness of BP is calculated as d3 = V × 0.53 nm [36], where the number of BP layer is indicated by V. The fourth layer is platinum (Pt) layer, and its dielectric constant is calculated according to the Drude model as given in Eq. (3), with \({\lambda_p}\) = 2.415 × 10−7 m and \({\lambda_c}\) = 1.795 × 10−5 m [37]. The fifth layer is made of graphene, and its refractive index (n5) is calculated as

$${n_5} = 3.0 + i\frac{{C_1}}{3}\lambda$$
(3)

where the constant C1 ≈ 5.446\({\upmu }{{\text{m}}^{ - 1}}\) [38].

The sixth layer is the sensing medium whose refractive index is assumed to change in the range of 1.33 to 1.35 as such a change is usually attributed for the detection of biomolecules. In order to theoretically evaluate the amplitude of the reflection coefficient for p-polarized incident beam for the system with multilayer structure stacked along the z-axis, several methods including N-layer matrix method [39, 40], admittance loci method [41], and S matrix method [42] are proposed. As the N-layer matrix method is very accurate as it contains no approximation, here, we proposed to use the N-layer matrix method to evaluate the performance of the proposed sensor configuration, and such method has also been adopted for similar SPR sensor configuration proposed recently [43]. In the N-layer matrix method, the tangential fields at the boundary Z = Z1 = 0 are related to those at the final boundary Z = ZN−1 by

$$\left[ {\frac{{U_1}}{{V_1}}} \right] = M\left[ {\frac{{{U_{N - 1}}}}{{{V_{N - 1}}}}} \right]$$
(4)

where U1, and V1 are the tangential components of the magnetic and electric fields of the first layer, and UN−1 and VN−1 are the tangential components of the magnetic and electric fields of the Nth layer. M is the characteristic matrix for the proposed structure and for p-polarized light; it is given by

$$M = \mathop \Pi \limits_{k = 2}^{N - 1} {M_k} = \left[ {\begin{array}{*{20}{c}} {{M_{11}}}&{{M_{12}}} \\ {{M_{21}}}&{{M_{22}}} \end{array}} \right]$$
(5)

with

$${M_k} = \left[ {\begin{array}{*{20}{c}} {\cos {\beta_k}}&{\frac{{ - i\sin {\beta_k}}}{{q_k}}} \\ { - i{q_k}\sin {\beta_k}}&{\cos {\beta_k}} \end{array}} \right]$$
(6)

where

$${q_k} = {\left( {\frac{{\mu_k}}{{\varepsilon_k}}} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}}\cos {\theta_k} = \frac{{{{\left( {{\varepsilon_k} - n_1^2{{\sin }^2}{\theta_1}} \right)}^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}}}}{{\varepsilon_k}}$$

and

$${\beta_k} = \frac{2\pi }{\lambda }{n_k}\cos {\theta_k}\left( {{z_k} - {z_{k - 1}}} \right) = \frac{{2\pi {d_k}}}{\lambda }{\left( {{\varepsilon_k} - n_1^2{{\sin }^2}{\theta_1}} \right)^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}}}$$

Here, θ and λ represent angle and wavelength of the incident light. The proposed model consists of six layers, and hence, N = 6. Thus, transfer matrices are calculated in accordance with Eq. (6), and the corresponding amplitude reflection coefficient (rp) is given as

$${r_p} = \frac{{\left( {{M_{11}} + {M_{12}}{q_N}} \right){q_1} - \left( {{M_{21}} + {M_{22}}{q_N}} \right)}}{{\left( {{M_{11}} + {M_{12}}{q_N}} \right){q_1} + \left( {{M_{21}} + {M_{22}}{q_N}} \right)}}$$
(7)

In the above equation, q1 and qN correspond to the BK7 substrate and the sensing layer, respectively, and finally, the reflectivity (Rp) can be given as

$${R_p} = {\left| {r_p} \right|^2}$$
(8)

Sensitivity of the SPR biosensor is measured as the small change in the refractive index \(\left(\Delta {n}_{s}\right)\) of the analyte with the change in resonance condition in the reflectance curve (\(\Delta {\theta_{{\text{res}}}}\)); therefore, the sensitivity is given by

$$S = \frac{{\Delta {\theta_{{\text{res}}}}}}{{\Delta {n_s}}}$$
(9)

The other prominance parameters of the SPR sensors are quality factor (Q) and signal-to-noise ratio (SNR); these parameters should be high for the good sensors. SNR is defined as the ratio of resonance angle shift (\(\Delta {\theta_{{\text{res}}}}\)) and the full width at half maxima (FWHM) (\(\Delta {\theta_{0.5}}\)) of the reflectance curve,

$$SNR = \frac{{\Delta {\theta_{{\text{res}}}}}}{{\Delta {\theta_{0.5}}}}$$
(10)

The quality factor (Q) is given by

$$Q = \frac{S}{{\Delta {\theta_{0.5}}}}$$
(11)

where,

S(θ) — sensitivity of the SPR biosensor

\(\Delta {\theta_{0.5}}\) — FWHM of the SPR curve

Results and Discussions

In the proposed work, we numerically analyzed the performance of the new SPR sensor configuration (Ag-BP-Pt-graphene) using the transfer matrix method. The condition of minimum reflectance (Rmin) close to zero ensures coupling of maximum energy of incident TM polarized light with the surface plasmon, and it is necessary for the design of any SPR sensor to have improvised sensitivity and resolution [44,45,46]. In order to ensure such a condition, here we fixed one such possible configuration with thicknesses of Ag as 40 nm and Pt as 15 nm. Figure 2a shows the reflectance curve plotted corresponding to the change in RI (refractive index) of the sensing medium from 1.330 to 1.335 (\(\Delta {n_s}\) = 0.005) in the absence of BP and graphene (V = 0 and L = 0). As can be clearly seen from Fig. 2a that the shift in the resonance angle is measured as ∆θ = 1.21°, and the corresponding sensitivity calculated as per Eq. (9) is 240.76°/RIU. Figure 2b and c show that upon introducing a single layer of either BP or graphene (V = 1 and L = 0 or V = 0 and L = 1) improved the shift in resonance angle as ∆θ = 1.26°, and the corresponding sensitivity is calculated as 252.23°/RIU. Hence, it is to be noted that the addition of either the monolayer of graphene or BP is found to have the same effect on the sensitivity of the sensor. However, it is further noted from Fig. 2d that for the proposed sensor configuration with the inclusion of both monolayer of BP and graphene (V = 1 and L = 1), the shift in the resonance curve is found to be significantly improved as ∆θ = 1.38° due to the different values of the dielectric constant of the materials which fulfill the resonance condition at different angles. The corresponding sensitivity is found to have much improved as 275.15°/RIU. As the sensitivity enhancement depends on the absorption of incident light in the different layers, the proposed configuration with single layers of BP and graphene shows better absorption and, hence, exhibits much improvement in the sensitivity compared with traditional structure [47].

Fig. 2
figure 2

Reflection intensity as a function of incident angle with a V = 0 and L = 0, b V = 1 and L = 0, c V = 0 and L = 1, and d V = 1 and L = 1

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Figure 3a shows the shift in dip of the SPR curve corresponding to the change in RI of the sensing medium in the range of 1.330 to 1.350. It is noted that, without BP and graphene (M = 0 and L = 0), the shift in the dip varies from 76.18 to 81.0°, whereas it increased from 76.75 to 82.4° for the configuration with the inclusion of the monolayer of BP (V = 1 and L = 0) which is due to a strong dispersion of BP around the incident wavelength. It is also noted that further increases in ∆θ around 76.96 to 82.4° are obtained for the configuration with the monolayer of graphene (V = 0 and L = 1) which shows better absorption property of graphene over BP. However, for the configuration with the inclusion of both BP and graphene (V = 1 and L = 1) layers, the shift in the resonance curve dip is found to have improved very much from 78.65 to 85.58° which is due to the combined effect of both the layers. Figure 3b shows the variation of sensitivity of the proposed sensor with respect to the refractive index of the sensing medium by keeping the other parameter the same as before. We observed that for the configuration without BP and graphene layers, the sensitivity increased from 206.29 to 332.48°/RIU (V = 0 and L = 0). However, in the inclusion of BP (V = 1 and L = 0), the sensitivity is found to vary from 217.83 to 378.34°/RIU, whereas an addition of the monolayer of graphene without BP (V = 0 and L = 1) enhances the sensitivity from 229.29 to 389.8°/RIU. It is also noted that for the configuration considered with the inclusion of both monolayers of BP and graphene (V = 1 and L = 1), further improved the sensitivity from 252.2 to 435.6°/RIU, which is due to the combined effect of both the 2D materials as the dispersion variation is different for both BP and graphene which results in a modified effective index around the wavelength of operation. Here, we concluded that the addition of BP and graphene layers can significantly improve the sensitivity of the proposed biosensor compared with the conventional gold–based SPR structure [47].

Fig. 3
figure 3

a Change in resonance shift, b sensitivity corresponding to the change in RI of the sensing medium from 1.330 to 1.335

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Furthermore, we optimized the no. of graphene and BP layers required to achieve the best performance of the proposed sensor. Figure 4a shows the reflection spectra versus the angle of incidence obtained for a monolayer of graphene with increasing number of black phosphorus (BP) layers for Ag = 40 nm and Pt = 15 nm. It is noted from Fig. 4a that the increasing number of BP layers largely shifts the reflectance dip as the resonance condition is satisfied at a higher angle and, hence, improved the sensitivity, which is due to higher mobility of charge carriers and higher absorption efficiency of BP [48]. We also observed that similar shift in resonance curve is also noted for the addition of graphene layers as shown in Fig. 4b and found to be larger than the addition of BP layers owing to the large real part of dielectric constant of graphene.

Fig. 4
figure 4

Reflection intensity as the function of incident angle a different layers of black phosphorus (BP) with monolayers of graphene, b different layers of graphene with monolayer of BP

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It is also noted from both Fig. 4a and b that increasing either the no. of BP and graphene layers not only generates larger shift in resonance dip but also makes the resonance curve wider and shifts the Rmin to higher values. Such an increase in FWHM of the spectral curve is due to the decrease of the propagation velocity of SP waves in 2D materials which results in damping [49]. The increase in Rmin is due to the saturation in absorption of incident light energy and the increase of electron loss [50,51,52]. It is also noted that widening of resonance curve and increase in Rmin are higher for graphene due to its large imaginary part of dielectric constant when compared to BP. This means arbitrarily increasing either BP or graphene layers makes the SPR curve broader, and it is more difficult to measure near the resonance angle, thereby affecting the accuracy of the measurement. Thus, we can conclude that one cannot arbitrarily increase the number of BP and graphene layers as an attempt to improve the sensitivity of the sensor.

Based on the above analysis, to optimize the number of BP and graphene layers, we calculated the sensitivity for the BP and graphene layers. Figure 5 shows the minimum reflectance (Rmin) and sensitivity corresponding to the number of graphene layers with a monolayer of BP for the configuration Ag = 40 nm and Pt = 15 nm. It is clearly observed that the sensitivity of the proposed configuration increased till increase of the number of graphene layers as four, and then it starts to decrease. This is because of increase of minimum reflectance (Rmin) from the 4th layer onwards as it reduces the absorption of light, i.e., optical energy losses occurred due to the increasing number of graphene layers. Hence, for the proposed configuration, we optimized the no. of graphene layers as 4 for the best performance. The Rmin and sensitivity obtained for the optimized graphene layer (L = 4) are 0.0336 and 401°/RIU respectively. Figure 6 shows the variation of Rmin and sensitivity versus number of BP layers with optimized no. layers of graphene (L = 4). From Fig. 6, it is noted that the sensitivity of the proposed sensor improved till the addition of the 2nd layer of BP, and it is found to start decreasing sharply. This suggests that we just need to choose V = 2 for getting a maximum sensitivity for sensing applications. It is observed that after optimization of BP and graphene layers (V = 2 and L = 4), the sensitivity of the proposed biosensor improved very much as 412°/RIU and can still keep the FWHM value as 5.731°. The signal-to-noise ratio (SNR) and quality factor (Q) are calculated using Eqs. (10–11) and are found to be as 0.36°−1 and 71.88 RIU−1, respectively. Furthermore, to have a better insight into the electric field distribution at different layers in the proposed multilayered system, the normalized electric field distribution of SP wave at different layers is plotted and is shown in Fig. 7. It is noted from Fig. 7 that the Ag layer enhances the electric field and shows a peak at the Ag-BP interface. The field intensity falls in the BP layers and further gets much enhanced in the platinum (Pt) layer which shows the excitation of SPs at this interface. It is noted that an addition of graphene layer further increases the field intensity which reaches its maximum at the interface of the graphene-sensing medium and decays exponentially in the sensing medium. This enhanced probing field close to the graphene layer with long probing depth is highly sensitive to biomolecular interaction throughout the penetrating depth. Such an enhanced probing evanescent field increases the interaction volume and hence maximize the sensitivity of the sensor [40, 53].

Fig. 5
figure 5

Minimum reflectance and sensitivity as functions of number of graphene layers (L)

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Fig. 6
figure 6

Minimum reflectance and sensitivity as a function of number of BP layers (V)

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Fig. 7
figure 7

Normalized electric field distribution of SP wave in the proposed SPR sensor

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Finally, we concluded that the proposed sensor with the configuration of 40-nm thickness of Ag, with two layers of BP, 10 nm of platinum (Pt), and four layers of graphene over Pt can enhance the sensitivity as high as 412°/RIU with FWHM of 5.731°. The signal-to-noise ratio and quality factor values are noted as 0.36°−1 and 71.88 RIU−1, respectively. The FWHM obtained here is nearly close to the Au–Ag bimetallic film–based SPR sensor; however, the sensitivity achieved is found to be much higher [54]. Some of the relevant works and its sensitivity have been compared in Table 1. We expect on the basis of the enhanced performance of sensitivity and lower FWHM of the SPR curve, the proposed sensor will have better performance in the chemical and biological applications.

Table 1 Comparison among proposed biosensors with other existing biosensors
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Conclusion

In this paper, we theoretically proposed an SPR sensor configuration sandwiching BP layers between silver- and graphene-coated platinum in the Kretschmann setup. We observed that, by properly optimizing the structure of the sensor, sensitivity can be enhanced as high as 412°/RIU and can still keep the FWHM of the resonance curve as small as 5.731°. We also noted that the sensitivity can be tuned and controlled by changing the number of layers of BP and graphene. We expect that such a proposed configuration exhibiting enhanced sensitivity and lower FWHM will find potential applications in food safety, chemical examination, and biological detection.