1 Introduction

An optical sensor is a sensing device which determines the desired quantity by measuring the change in refractive index, absorbance and fluorescence properties of analyte molecules (Wolfbeis 1991; Boisdé and Alan 1996). For the purpose of chemical and biomedical sensing, various optical methods like ellipsometry (Wang et al. 2003), spectroscopy (Rowe-Taitt et al. 2000), interferometry (Heideman et al. 1993) and surface plasmon resonance (SPR) (Homola 2003) have been used.

SPR is a widely preferred surface sensitive optical analysis technique which is capable of determining the properties of ultrathin films when full angular spectra are measured (Albers and Vikholm-Lundin 2011). SPR sensor can be classified on the basis of angular shift, wavelength, intensity, phase or polarization modulation (Homola and Marek 2006). In SPR sensors with angular modulation, surface plasmon (SP) is generated by the interaction between the incident transverse magnetic (TM) polarized light and the free electron in the metal surface. SP is actually the electronic density wave that propagates along the metal surface. The incident light resonantly couples with SP when the vector of an incident light matches with the wave vector of a surface plasmon wave (SPW). After that incident, an enormous electric-field can be observed which is referred to as surface plasmon resonance (SPR). Multiple angles of incidence of the light wave can be observed owing to the fluctuation of the strength of coupling between the incident wave and the SP. The angle of incidence because of the strongest coupling is measured and used as the sensor output. Refractive index of the sensing medium can be used to calibrate the sensor (Otto 1968; Kretschmann and Raether 1968; Matsubara et al. 1988). SPR based biosensor has gained huge popularity in the research field as it offers label-free and real-time detection technique for monitoring bio-molecular analysis. Application fields of SPR based biosensor are the detection of enzyme, environment, food safety (Homola 2003; Pumera 2011), antibody-antigen connection (Pei et al. 2000), DNA–DNA hybridization (Shushama et al. 2017) and so on. Due to having some limitations in Otto configuration, the modified SPR based on Kretschmann configuration is preferred (Kretschmann and Raether 1968). Al2O3 provides minimized loss in the performance of the biosensor because of its refractive index. Another property that contributes to the sensor improvement that is the uniformity of the Al2O3 layer (Sharma 2012).

The basic form of the Kretschmann configuration is a coupling prism and metal film. Silver, copper, aluminium, sodium and indium can be used as SPR active metal on the prism. Because of having the most practical nature with good resistance to oxidation and corrosion in different environment, stable and superior performance, gold is chosen over all other SPR materials (Shushama et al. 2017). Numerous technique based on particles in nanoscale can be utilized for the betterment of the sensor’s performance (Zhao 2006; Stewart et al. 2008). As Au layers have a limitation in absorbing biomolecules, so sensing layers can be introduced to enhance the sensitivity (Verma et al. 2015; Biednov et al. 2015). Recently, plenty of research works have been carried out using various layers for improved performance of the biosensor. Sensitivity increases as more biomolecules are absorbed. Mishra et al. (2015) used Si layer over the conventional Kretschmann configuration for better sensitivity. Ouyang et al. (2016) demonstrated the use of TMDC material MoS2 along with Si for further improvement in sensitivity, Rahman et al. (2018) showed the use of another TMDC material WS2 for better sensitivity, quality factor and detection accuracy.

Further improvement in the performance parameters than previous works can be attainable. Here we proposed a five-layer Kretschmann configuration based SPR biosensor model consisting of Al2O3 and WS2 layers and the number of layers are optimized in such a way to give out the best possible result.

2 Theoretical model and design consideration

Using five layers in the proposed model, SPR biosensor is analyzed. Figure 1 represents the configuration of the proposed biosensor. The excitation light of 633 nm wavelength is used for the SPR sensing. The TM-polarized light is incident on the one lateral side of the prism and reflected from another lateral side after reaching to the base. A photodetector is used to analyze that reflected light. Here, the proposed biosensor consists of Au layer, Al2O3 layer, transition metal di-chalcogenides WS2 and sensing layer.

Fig. 1
figure 1

Schematic of experimental realization of WS2 and Al2O3 based SPR biosensor

Full size image

N-layer model is considered to obtain the expression for the reflected light. Transfer matrix method (TMM) and Fresnel equations based on that N-layer model are used to peruse the optical characteristics of multi-layers. The TMM is employed for a better understanding of the change in the reflectivity of SPR sensors. All layers are assumed to be stacked in parallel manner along the z-axis and the z-axis is considered to be perpendicular with the thickness dk of these layers. Other common features of any layers are dielectric constant ɛk, permeability μk and refractive index nk where suffix k represents the prism, Au metal, Al2O3, WS2, sample or the sensing medium. It is taken into account that each and every layer is uniform, isotropic and non-magnetic in nature. The boundary conditions for theoretical modelling is denoted by Z. Here, Z1 = 0 defines the tangential field of the first boundary and ZN-1 is considered for the last boundary (Zeng et al. 2015).

$$\left[ \begin{aligned} p_{1} \hfill \\ Q_{1} \hfill \\ \end{aligned} \right] = M\left[ \begin{aligned} P_{N - 1} \hfill \\ Q_{N - 1} \hfill \\ \end{aligned} \right]$$
(1)

where, P and Q are the tangential components of electrical and magnetic fields at the interface boundary of the layers. The characteristics matrix for the combined structure of the N-layer model of the sensor and for p-polarized light can be expressed by M.

$$M_{ij} = \left( {\prod_{K = 2}^{N - 1} M_{K} } \right) = \left[ \begin{aligned} M_{11} \,\,\,\,\,M_{12} \hfill \\ M_{21} \,\,\,\,\,M_{22} \hfill \\ \end{aligned} \right]$$
(2)

where K represents the Kth layer of the N-layered model (Wu et al. 2010).

Now Mk for the TMM waves of the incident light,

$$M_{K} = \left[\begin{array}{*{20}l} \cos \beta_{K} \,\,\,\,\,\,( - i\sin \beta_{K} /q_{K} ) \\ -iq_{K} \sin \beta_{K} \,\,\,\,\,\,\cos \beta_{K} \\ \end{array} \right]$$
(3)

Here, qk and \(\beta_{K}\) help to obtain the four elements M11, M12, M21 and M22 of the matrix M

$$q_{K} = \sqrt {\frac{{\mu_{K} }}{{e_{K} }}} \cos \theta_{K} = \frac{{\sqrt {(e_{K} - n_{1}^{2} \sin^{2} \theta_{1} )} }}{{e_{K} }}$$
(4)

and

$$\beta_{K} = \frac{{2\pi d_{K} }}{\lambda }\sqrt {(e_{K} - n_{1}^{2} \sin^{2} \theta_{1} )}$$
(5)

\(\theta_{1} = {\text{ incident angle for the first layer}}\).

Now the systematic complex reflection co-efficient (rp) for the combined N-layered structure is calculated by means of TMM for P-polarized light.

$$r_{p} = \frac{{(M_{11} + M_{12qN} )q_{1} - (M_{21} + M_{22qN} )}}{{(M_{11} + M_{12qN} )q_{1} + (M_{21} + M_{22qN} )}}$$
(6)

The corresponding reflectivity Rp for defined multilayer configuration is given by

$$R_{p} = \left| {r_{p} } \right|^{2}$$
(7)

3 Performance parameters of the SPR sensor

The main parameters on which the performance of the SPR biosensor depend are sensitivity, detection accuracy and the quality factor. For an efficient sensor, all these three parameters should be as high as possible (Pal et al. 2017). The sensitivity (S) is theoretically the ratio of the deviation in the resonance angle of incidence to the refractive index change of the sensing medium (Lin et al. 2016). The unit of the sensitivity is °/RIU.

$$S = \frac{\delta \theta }{{\Delta n_{s} }}$$
(8)

Detection accuracy (DA) is another important parameter which helps to determine the resolution of the SPR sensor. DA can be compared to the signal to noise ratio (SNR). The full width at a half maximum (FWHM) of the reflectance curve is necessary to calculate the DA. Low FWHM decreases the uncertainty in determination of the resonance dip and as a consequence, it increases the resolution of the sensor. Now, DA is actually the ratio of the deviation in resonance angle to the FWHM (Pal et al. 2017).

$$DA = \frac{{\theta_{res} }}{FWHM}_{{}}$$
(9)

Lastly, the Quality factor (Q) is the ratio of the sensitivity to the FWHM of the reflectance curve. The unit of the Q is RIU−1 (Rahman et al. 2018)

$$Q = \frac{S}{FWHM}$$
(10)

The proposed five-layer model is composed of BK7 prism, Au, Al203, WS2 and lastly the sensing medium.

3.1 Refractive index of various layers

In this proposed model BK7 prism is the first layer. Au film is the second layer with the thickness d2. The third layer is Al2O3 and its thickness is denoted by d3. WS2 is the fourth layer with the thickness d4. Each layer of WS2 is 0.8 nm (Lin et al. 2016). Now the refractive index of BK7 prism is nBK7.

$$n_{BK7} = \sqrt {\left( {\frac{{1.03961212\lambda^{2} }}{{\lambda^{2} - 0.00600069867}} + \frac{{0.231792344\lambda^{2} }}{{\lambda^{2} - 0.0200179144}} + \frac{{1.03961212\lambda^{2} }}{{\lambda^{2} - 103.560653}} + 1} \right)}$$
(11)

Here λ= Wavelength (µm) of the incident light = 633 nm.

According to Drude formula, the refractive index (nm) of Au metal (Shushama et al. 2017).

$$n_{m} = \sqrt {\left[ {1 - \frac{{\lambda^{2} \lambda_{C} }}{{\lambda_{P}^{2} (\lambda_{C} + i\lambda )}}} \right]}$$
(12)

where \(\lambda_{P} = {\text{plasma wavelength }} = \, 1.6826 \times 10^{ - 7} \;{\text{m}}\) \(\lambda_{C} = {\text{ collision wavelength }} = \, 8.9342 \times 10^{ - 6} \;{\text{m}}\)

Refractive index of the Al203 at 633 nm of wavelength is 1.7659 and WS2 is 4.89 + 0.314i. Refractive index of the sensing medium is 1.33 (Ouyang et al. 2017).

4 Result and discussion

In this paper, four structures are considered to evaluate the improvement done in the proposed model. (a) Structure no. 1 (Au = 47 nm, Al2O3 = 0 nm, WS2 = 0 nm), (b) Structure no. 2 (Au = 47 nm, Al2O3 = 6mn, WS2 = 0 nm, (c) Structure no. 3 (Au = 47 nm, Al2O3 = 0 nm, WS2 = 0.8 nm), (d) Structure no. 4 (Au = 47 nm, Al2O3 = 6 nm, WS2 = 0.8 nm). The range of the refractive index is taken 1.335 to 1.375. Change in RI of the sensing medium is responsible for the molecular binding. dn/dc depicts the slope of the RI (n) change of the solution in accordance with the change in concentration (c) of that solution. For HPS concentration minus cmc (cmcHPS = 1 × 10−4), it is shown that for 0.002 g/cm3 change in concentration, excellent linearity is shown when the range of RI is taken 1.335 to 1.3375 with 0.005 interval (Tumolo et al. 2004). This is the reason behind taking this specific range of RI from 1.335 to 1.375 in designing the proposed model.

Sensitivities for four classified structures have been plotted for the specified range of RI of the sensing medium in Fig. 2 It is seen that in structure no. 1 where Al2O3 and WS2 layers are absent then sensitivity increases from 130 to 158.89°/RIU for the change in the RI of the sensing medium from 1.335 to 1.375. In structure no. 2, after adding Al2O3, sensitivity increases from 150 to 200°/RIU. Later on structure no. 3, WS2 is added with the first structure keeping Al2O3 absent the obtained sensitivity range is 150–186.78°/RIU and it is comparatively lower than the structure 2. Finally, in the case of the proposed model presented by structure no. 4 where both Al2O3 and WS2 are present, a significant increase in the sensitivity is observed. For the change in RI from 1.335 to 1.375, the sensitivity changes from 180 to 211.11°/RIU and the highest sensitivity 227.50°/RIU is obtained at 1.37. That is why 1.37 is chosen for further analysis where the resonance angle shift is determined from the reflectivity curve.

Fig. 2
figure 2

Sensitivity versus refractive index of four structures

Full size image

In Fig. 3 Reflectivity versus angle of incidence is plotted for four individual structures above mentioned. Angle shift is administered by RI values 1.33 and 1.37 both. So, four structures individually exhibit reflectivity curves for refractive indices 1.33 and 1.37 respectively. At the RI value of 1.33, the sensor surfaces the basic initial point before the sensing starts and at 1.37 it corroborates the maximum sensitivity. For all four cases, ∆n has a constant value of 0.04. In Fig. 3a for first structure, \(\Delta \theta\) = 6.2° and the sensitivity (S) is 155°/RIU at 1.37. For the second structure in Fig. 3b, when ∆n is 0.04, we get \(\Delta \theta\) = 7.65° and S = 191.25°/RIU. Figure 3c represents the third structure where \(\Delta \theta\) = 7.25° and S = 181.25°/RIU. In Fig. 3d, for the fourth structure greatest angular shift (9.1°) is observed with the highest sensitivity (227.5°/RIU).

Fig. 3
figure 3

Reflectivity versus angle of incidence a structure no. 1 b structure no. 2 c structure no. 3 d structure no. 4

Full size image

Because of the change in the RI of the sensing medium, the change in the resonance angle can be found which is denoted by θres. In Fig. 4 we have plotted the resonance angles versus the RI for previously mentioned four structures. The same RI range (1.33 to 1.375) is employed here. Highest resonance angle range from 76.20° to 85.5° is perceived for the structure no. 4. Maximum resonance angle 85.7° is manifested by 1.37. This outcome reinforces the reliability of the proposed model using Au, Al2O3, WS2.

Fig. 4
figure 4

Resonance angle versus refractive index for four structures

Full size image

Table 1 summarizes the overall result obtained from all four structures. It is clearly shown that structure no. 4 gives the highest sensitivity of 227.5°/RIU. On the contrary, structure no. 1 gives the maximum value for quality factor and detection accuracy respectively 31 and 1.24 with the lowest sensitivity of 155°/RIU. As sensitivity is a very important parameter for a biosensor and lower sensitivity is not desirable, so the structure no. 4 is considered as the most optimized one.

Table 1 Summarization of overall result for four structures
Full size table

Layers in this configuration are optimized very cautiously. For having the main focus on designing a highly sensitive SPR biosensor, sensitivity has been the most prominent factor to be considered while optimizing.

In Fig. 5a the width of Au layer is optimized and the maximum sensitivity 227.5°/RIU is discerned at 47 nm. The optimization of Au layer has been simulated for a width range from 40 to 65 nm.Sensitivity gradually increases up to 47 nm but afterwards it decreases which underlies the rationalization of elected width of Au layer at 47 nm. Figure 5b illustrates the change in sensitivity by changing the thickness of WS2 layer. It attributes that valid positive sensitivity can be acquired by only monolayer or bilayer WS2 and so Fig. 5c reveals the reflectivity curve for these two valid cases. Monolayer of WS2 is scored for giving highest the sensitivity with thickness of 0.8 nm. In Fig. 5d it is realized that at six layers of Al2O3 highest sensitivity can be achieved. Figure 5e exposes how reflectivity curves are shifted because of changing the number of Al2O3 layers. In MATLAB simulation each Al2O3 layer is considered as 1 nm, consequently the optimized thickness of the concerning layer is set at 6 nm.

Fig. 5
figure 5

a Sensitivity versus width of the Au layer. b Sensitivity versus WS2 layer. c Reflectivity versus angle of incidence of WS2. d Sensitivity versus Al2O3 layer. e Reflectivity versus angle of incidence of Al2O3

Full size image

Eventually, it is realized that by increasing the number of WS2 layers negative invalid sensitivity can be detected which is not acceptable. That is why the number Al2O3 layer is varied instead of WS2 layer. In afterwards simulation, the number of Al2O3 layers is varied considering two different cases. In the first case, the number of Al2O3 layers are varied keeping the WS2 layer absent and the corresponding values of the parameters are listed below in Table 2. In the second case, no of the Al2O3 layers are varied keeping a monolayer of WS2 and corresponding results are summarized in Table 3. Here the reason behind taking only one layer of WS2 is that after optimizing it is found that monolayer of WS2 gives the highest sensitivity. When two sets of values from Tables 2 and 3 are compared with each other, it is found that without WS2 layer, seven layers of Al2O3 gives the highest values for sensitivity, quality factor and detection accuracy. But with a monolayer of WS2, six layers of Al2O3 gives the best possible values for all three parameters.

Table 2 Al2O3 layers are varied keeping the WS2 layer absent
Full size table
Table 3 Al2O3 layers are varied keeping a monolayer of WS2
Full size table

Table 4 shows a comparison among the previous reported results and the proposed models respectively. The comparison result substantiates that among the all results, the proposed model has the highest sensitivity and quality factor.

Table 4 Sensitivity comparison of different reported prism based SPR biosensors
Full size table

5 Conclusion

Our proposed five-layer prism-based SPR biosensor model using Au, Al2O3 and WS2 exhibits the improved sensitivity, quality factor and detection accuracy. The thickness of all layers are optimized to get the best possible result. Refractive indices of each layer for 633 nm wavelength are given as input in the MATLAB code for the simulation. Layer optimization is mainly done on the basis of sensitivity and angular shift. Several simulations have been carried out by changing the thickness of each layer in the MATLAB code to accomplish the most satisfactory outcome. In angular modulation mode due to the optical properties of the layers used in the biosensor highest sensitivity of 227.50°/RIU is achieved. The maximum value of the other two performance parameters e.g. the quality factor and the detection accuracy are respectively 28.26 RIU−1 and 1.1123.