Zinc sulfide, silicon dioxide, and black phosphorus based ultra-sensitive surface plasmon biosensor

The optical biosensor is the emerging research area in the field of bio-photonics. The black phosphorus zinc sulfide-based hybrid configuration is suitable for implementing and analyzing ultrasensitive biosensors. Ag/Zinc sulfide/silicon dioxide/black phosphorus-based biosensor has been implemented in the proposed work using the modified Kretschmann configuration. The sensitivity improvement of the designed SPR sensor is analyzed in the different arrangements of the layers. The thickness of the layers of all the materials has been optimized. The thickness of the Ag metal layer is optimized and taken as 45 nm. The sensitivity and quality factor measured here is as high as 664.6∘/RIU\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$664.6^\circ {\text{/RIU}}$$\end{document} and 200 at 1.37 refractive index with the P-polarized light source of 633nm\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$633\;{\text{nm}}$$\end{document} wavelength. The proposed biosensor confirms tremendous sensitivity, detection accuracy, and quality factor growth compared with the traditional SPR sensors. Zinc sulfide has multiple applications in the sensing fields, like sensors based on UV rays, lasers, and gas.


Introduction
The surface plasmon resonance is a condition that exists when a P polarized wave is an incident on the interface of a metal and dielectric material through a coupling prism. Some part of incident light penetrates into the metal layer, generally known as an evanescent wave, causing excitation of the free electrons, which finally produces surface plasmon performance parameters like sensitivity, the figure of merit (FoM), detection accuracy (DA) change is limited using Ag alone in the SPR designs can be improved by using 2D material. In sensing applications, the commonly used 2D materials are graphene (Mohanty et al. 2016), black phosphorus, and transition metal dichalcogenides (TMDCs). The basic recognition element (BRE) used in the proposed work is Black phosphorus (BP). Since 2014, with honeycomb lattice structure BP gaining popularity in SPR sensor designing. The optoelectronic and mechanical features such as high surface to volume ratio (SVR) , higher biomolecular adsorption energy than graphene, and molybdenum disulfide (MoS 2 ) (Cho et al. 2016), high mobility, low extinction constant (Mao et al. 2016), direct bandgap. Toward target, analytes are more sensitive. Its sensing capability is approximately twenty times of other 2D materials like MOS 2 (Su et al. 2020) due to its greater molar response factor. Although BP oxidizes quickly, adding other material results in low oxidation as molecular binding is effective inside the sensing layer.
The other material we are using in our work is zinc sulfide (ZnS). It is a compound semiconductor with exclusive optical properties like a broad energy band gap of 3.72 eV and 3.77 eV and excellent chemical, thermal stability. Its popular applications are in the sensing field, including lasers, gas, light sensors (Wang et al. 2012). With the entry of ZnS in photonics, optoelectronics significantly grew over the years and gained popularity (Heydarian et al. 2019). Another optimized layer in which we include our proposed design is silicon dioxide (SiO 2 ). Its inclusion in our design is due to its unique properties like higher surface area ( 700 and 500 m 2 /g ), good chemical and thermal stability, larger bio compatibility, and non-toxic makes it useful for adsorption, in bio sensing catalysis (Karki et al. 2021;Zhao et al. 2019a;Ud et al. 2018).
Section 2 explains the constructional part of our design and various mathematical expressions used to model the SPR sensor. Section 3 gives the results and discussions for the proposed sensor. Section 4 consists of the conclusion of the proposed work.

Prism and metal layer refractive indices
The proposed design based on modified Kretschmann configuration consists of a coupling prism (BK 7 type) with layers of Ag metal, ZnS, BP, and sensing medium (analyte) to produce required surface plasmons (SPs), as shown in Fig. 1. These SPs get generated when a P-polarized wave (TM mode) is incident on the coupling prism, generating an evanescent wave along the interface section of prism and metal and penetrates the structure. At resonance angle ( res ) the SPs generates at the next interface of metal (Ag) and ZnS. It is used as a fundamental recognition element with some exclusive optical properties of black phosphorus (2D material). The refractive index of the sensing medium changes as BP adsorbs biomolecules on its surface.
The refractive index μ BK7 expressed by the numerical formula (Zeng et al. 2015): ( Here λ is the wavelength of incident light. The He-Ne source is used, and the wavelength is 633 nm. The metallic layer's refractive index calculation is given by Drude-Lorentz model (Gupta and Sharma 2004): where c and p is the collision and plasma wavelengths, having values 1.7614 × 10 −5 m and 1.4541 × 10 −7 m respectively for Ag (metal) layer. The other layers which we are using in our proposed SPR sensor design, ZnS, have a refractive index of 2.35521 + i * 0.00523 (Mei and Menon 2020), SiO 2 has 1.4570, and of BP layer is 3.531 − i * 0.04087 (Singh and Raghuwanshi 2019). The refractive index for sensing layer is computed numerically as: Here μ = change in sensing media refractive index.

Modeling theory
The performance analysis of the SPR biosensor is done by employing a reliable Transfer matrix method (TMM) and Fresnel equations. The TMM used here does not include any approximation. The multilayers used here have a thickness and dielectric dimension of d r and ϵ k , respectively.
The different thicknesses of layers mounted on prism are, for Ag, ZnS, SiO 2, and BP layer as 45 nm, 0.8 nm, 50 nm, and 0.34 nm, respectively. The matrix formation for tangent component for starting and ending boundary given by Lili et al. (2019):

Fig. 1 Constructional view of ZnS and SiO 2 based SPR sensor
Here, at the first boundary, P and Q are electric, and magnetic field components are P n−1 and Q n−1 are electric and magnetic field components at the last boundary. T indicates characteristics transfer matrix, its value given by Maharana and Jha (2012): Here, T r = rth layer matrix. Here β r , q r are the optical admittance and phase factor respectively given by, here, θ = incidence angle, and Υ 0 = free space wave number.
The mathematical expression for the reflection coefficient r p is given by Mueller et al. (2010): Here, R p = reflectivity of input polarized radiation. The tabulation chart characterizing different SPR parameters is summarized in Table 1. The characteristic parameters that define the SPR biosensor reliability are Sensitivity (S), which defines the ratio of SPR angle change with the RI change. The second is the Figure of merit (FOM)/ quality factor which gives information about the quality of the bio-sensor. The third one is detection accuracy, which gives information about the sensor's accuracy, and lastly, the Full width half maximum (FWHM) talks about resonance curve width at 50% reflectivity.

Results and discussions
The prism coupler having greater RI gives sharp resonance curves compared to lower values coupler prism. But the BK7 prism with lower RI for SPR sensor gives better sensitivity (Yue et al. 2019). The coming Fig. 4 gives an idea about the outcomes of inserting Zinc sulfide and Black phosphorus films over the conventional biosensor with RI at 1.33 and 1.335 . A silicon dioxide (SiO 2 ) layer is also taken with a constant (1.7) and phase factor, q r =   Figure 2a shows the plot for reflectivity with different incidence angles from (55° to 90°) for conventional SPR sensor ( Z = 0, B = 0 ) with basic Kretschmann configuration in figure giving sensitivity, S = 103.6 • /RIU, and change in incidence angle, Δθ = 0.518 . The sensitivity and reflectivity are the basic sensors analysis parameters which can be varied by placing layers (2D materials) between prism and sensing layer. So, after adding the ZnS layer ( Z = 1, B = 0 ) over the Ag metal layer, and SiO 2 layer also added in the sensor configuration, get sensitivity as S = 102.6°/RIU and Δ = 0.513 , reducing reflectivity (shown in Fig. 2b). The third case, with a single BP layer ( Z = 0, B = 1 ) along with SiO 2 layer and no ZnS layer between metal and sensing layer, is shown with Fig. 2c, the parameter, sensitivity, comes out to be S = 103 • /RIU with Δθ = 0.515. At last, Fig. 2d gives the impact of single ZnS and single BP layer (Z = 1, B = 0) on the conventional sensor, increasing sensitivity values up to 107°/RIU and lowering the reflectivity value of reflectivity. This happens due to the absorption of the incident light at the BP and sensing layer because surface plasmons are generated. With the continuation to this, the next set of figures shown by Fig. 3 gives an idea about the layer's  Figure 3 shows sensitivity alteration with sensing media RI (varies from 1.33 to 1.36). For different zinc sulfide (Z) and black phosphorus (B) layers, the minimum sensitivity and maximum sensitivity are given in Table 2.
The analysis made here clearly concludes that with modifications on the conventional sensor ( Z = B = 0 ), the sensitivity increases by inserting zinc sulfide and black phosphorus layers. The sensitivity value is maximum for the case of Z = 1 and B = 1, i.e., S = 129.2 • /RIU at RI = 1.36.
The sensitivity and reflectivity values are being calculated with Z = 0, B = 0 as 118 • /RIU (maximum), and 0.05676 (minimum) for RI = 1.36, shown in Fig. 4a. Further, by adding a single layer of black phosphorus ( BP = 1 ) without any zinc sulfide ( Z = 0 ) layer (Fig. 4b), the sensitivity and reflectivity come out to be 121.2°/RIU (maximum) and 0.05558 (minimum) respectively at RI = 1.36 . The following case is shown by Fig. 4c, giving maximum sensitivity as 126 • /RIU and minimum reflectivity as 0.04745 at RI = 1.36 for single zinc sulfide and no black phosphorus layer (i.e., Z = 1, B = 0 ). Figure 3d gives the best values at RI = 1.36 , maximum sensitivity as 129.2 • /RIU, and minimum reflectivity as 0.04501 for one zinc sulfide and one black phosphorus layer (i.e.,Z = B = 1). Figure 5a shows the variation in sensitivity (S) and detection accuracy (DA) for combination layers for different zinc sulfide (Z) and black phosphorus (B). The interchange of both parameters is visible from the multilayer plot in Fig. 5a. The sensitivity and DA of the sensor should be high for the better performance of the sensor. The DA is low here, and it needs to be improved. The other two performance parameters, Full width half maximum (FWHM) and quality factor (QF) alteration with the same combination of layers (Z/B), as   shown in Fig. 5b. The parameter FWHM should be low so that the resonance angle can be computed precisely. The high value of the quality factor is desirable. The subsequent results for which Fig. 6 is drawn show the sensitivity range for different refractive indices varying from 1.33 to 1.36. The sensitivity varies from 277.8 • /RIU to 664.6 • RIU . For RI 1.36, the SPR sensor shows maximum sensitivity. Figure 7 shows a plot for reflectivity alteration with incidence angle variation in zinc sulfide and black phosphorus layers, respectively. The optimum thickness value taken for our SPR design is 45 nm for the silver (Ag) layer; for Silicon dioxide (SiO 2 ), it is 50 nm. In Fig. 7a gives the analysis for performing parameters after changing the zinc sulfide layer ( Z = variable ) with constant black phosphorus layer set as B = 1 . The sensitivity comes to about 664.6 • /RIU.
The significance of the statements also boosts up by seeing the increase in reflectivity and SPR curve broadness. With the following Fig. 7b, using single-layer zinc sulfide and variable black phosphorus layer (i.e., Z = 1, B = variable ), we got the maximum sensitivity for our proposed SPR sensor design as high as 266 • /RIU . The resonance  . 7 a, b Graphs showing the impact of layer variation on sensor's performance curve's shift and reflectivity's decrement are seen as we increase the black phosphorus layer.
The distribution of the electric field enhancement with respect to the distance, which is orthogonal to the prism interface for different numbers of black phosphorus layers, is shown in Fig. 8. Figure 8a, b shows the X-component of the electric field and Y-component of the electric field at the RI = 1.33 of the sensing layer. The electric field distribution inside the sensor is shown in Fig. 9. The electric field intensity is high at the metal and zinc sulfide interface, and intercity decreases at zinc sulfide and SiO 2 . It indicated that field intercity is more when light absorption is more significant. Further electric field intercity increases at the black phosphorus and sensing layer interface. It shows that greater absorption of light to have significant SPW excitation. A proposed electric field plot has been designed for a single layer of ZnS and BP.
A tabular comparative analysis of this work with earlier literature is being compared here with the help of fundamental parameters with operating wavelength and design configuration of Table 3.

Conclusion
We proposed a new SPR optical biosensor in this study with high sensitivity. The suggested biosensor's configuration includes a ZnS layer to improve sensitivity and protect the nanocomposite layer from oxidation. Furthermore, our findings demonstrate that using black phosphorus as a biological diagnosis component can be helpful for sensing. We examined Fig. 8 The field component of P-polarized optical signal at resonance condition with (N S = 1.33): a x-components of an electric field; b y-components of electric field Fig. 9 Electric field distribution at resonance angle of SP wave in the proposed sensor how different prisms affected the sensitivity of this proposed SPR optical biosensor. The results reveal that when the refractive index of the prism increases, the sensitivity of the suggested SPR biosensor diminishes. As a result, we chose BK7 as the coupling prism in our biosensor design. Our calculations also suggest that the proposed biosensor with the maximum sensitivity requires a SiO 2 layer with a thickness of 50 nm that contains a silver metal layer with a thickness of 45 nm. Finally, we demonstrated that the best-proposed biosensor has six layers of ZnS on both surfaces of the nanocomposite layer, with a maximum sensitivity of 664.6 • /RIU. Author contributions BK formulated the problem statement, giving the theoretical background and mathematical modeling for the SPR biosensor. He also helped in drafting and finalizing the manuscript. YT provided the theoretical background to biosensing and the importance of Optical Biosensing. He also helped in finalizing the design of the proposed sensor. AU worked towards the complete manuscript, formatting, and finalizing the manuscript. AP provided statistical analysis for the results. He provided the theoretical background to SPR biosensors. He also helped in formatting the manuscript.

Conflict of interest The author declares no conflict of interest.
Consent to participate I am willing to participate in the work presented in this manuscript.

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The author has given their consent to publish this work.
Ethical approval Not applicable. The work presented in this manuscript is mathematical modeling only for the proposed biosensor. No experiment was performed on the human body and living organism/animal. So, ethical approval from an ethical committee is not required.