Improved Transition Metal Dichalcogenides-Based Surface Plasmon Resonance Biosensors

: Surface plasmon resonance (SPR) biosensors based on transition metal dichalcogenides (TMDC) materials have shown improved performance in terms of sensitivity, detection accuracy (DA), and quality factor (QF) over conventional biosensors. In this paper, we propose a ﬁve-layers model containing black phosphorus (BP) and TMDC (Ag / BP / WS 2 ) in Kretschmann conﬁguration. Using TM-polarized light at 633 nm, we numerically demonstrate the highest sensitivity (375 ◦ / RIU), DA (0.9210), and QF (65.78 1 / RIU) reported so far over similar materials. Refractive index (RI) of the coupling prism has also played an essential role in enhancing the performance of these biosensors. The research on TMDC materials is still new, and these materials bring about opportunities to develop a new class of biosensor.


Introduction
Transition metal dichalcogenides (TMDC) materials such as MX 2 (where M stands for Mo or W and X for S or Se) exhibit unique optical and optoelectronic properties. The y are formed by a hexagonal network of transition metal atoms (Mo, W) hosted between two hexagonal lattices of chalcogenide atoms (S, Se). As a result, MX 2 materials have been considered excellent candidates for the semiconductor industry such as in high-speed electronics, flexible devices, next-generation solar cells, touch screen display panels, DNA sequencing, and personalized medicine, to name a few [1]. MX 2 materials behave like a two-dimensional semiconductor material with direct bandgaps lying in the visible and near-IR range, which is different from other TMDC material such as graphene and hBN whose bandgaps occur at much longer wavelengths. Because of these, recently MX 2 has gained considerable interest in biosensing based on surface plasmon polaritons (SPPs) [2][3][4][5].
SPPs are collective oscillations of the free-electron gas density at the boundary of the metal sensors (negative permittivity) and dielectric probing media (positive permittivity). The wavevector of these waves depends on the optical property of both the metal layers and surrounding dielectric media involved, the excitation wavelength of the incident light, and excitation conditions [6].
SPR phenomena based on SPP holds the maximum label-free, rapid and real-time sensing capability in the field of biochemical interactions on a surface. Recently, it has been shown that the reproducibility and longevity of the SPR biosensors can be dramatically improved with the help of suitable protective layers such as thin layers of carbohydrate as described in Ref. [7] and a Graphene-covered layer in Ref. [8]. Figure 1 shows a schematic of the proposed five-layer model used for simulation. The first layer is the prism (CaF 2 , BK7, SF10, 2S2G). The Ag or Au are coupled with the prism and constitute the second layer. In the third layer, black phosphorous (BP) is used for enhancing sensitivity. The fourth layer consists of TMDCs, and the fifth layer is the probing medium as shown by the solid circles in the fluidic channel.

Numerical and Mathematical Model
Out of three configurations (Otto, Kretschmann, and Grating) of exciting surface plasmons, in this work, Kretschmann configuration is used, as it is more compatible for coupling the prism with the metal film layers. For numerical analysis, we used the transfer matrix method and Fresnel equations performing on the N layer model. Since these methods do not involve approximation, the methods give the most accurate result.
For the calculation, the thicknesses of the layers, dk, are considered in the z-axis, and the The proposed SPR technology uses right-angled prism and metal layers for detecting the change in the refractive indices. MATLAB simulation and graphical analysis have been used to study the optical behaviour of the proposed sensor. The angular detection method has been employed for detection using a TM-polarized light having a wavelength of 632 nm. Reflected light intensity does not only vary with the angle of incidence but also with the thickness of TMDC layers. For developing optical nonlinearity for a specific frequency, p-polarized (TM-polarized) optical laser at the wavelength, λ = 633 nm is used [16] and a detector is used for recording the reflected light from the biosensor.
As shown in Figure 1, the thickness of the metal and MX 2 layers are defined by d 2 , d 3 , and d 4 , and the fluidic channel by d 5 . The thicknesses of metal, BP, and TMDC layers are taken as d 2 , d 3 , and d 4 with d 3 = L × 0.53 nm and d 4 = L × 0.65 nm (MoS 2 ), L × 0.7 nm (MoSe 2 ), L × 0.8 nm (WS 2 ) and L × 0.7 nm (WSe 2 ), where L is the number of BP and TMDC layers. The refractive index (n) of the probing medium is 1.33, and the variation of n is considered in the range of 1.33 to 1.35, i.e., ∆n in the range of 0.01 to 0.02. The se refractive indices correspond closely to the refractive index of urine (a bio-sample) with various concentrations concerning the specific gravity depending on whether the disease is normal, moderate, acute, or above average [17,18]. Due to the weak van der Waals bonding which exists between successive layers in the multilayers and despite having significant lattice mismatch between the layers, TMDC materials can form complex heterostructures with other layered materials with no misfit dislocations. We plan to grow these layers using molecular beam epitaxy as it has shown to enable high purity heterostructures [19].

Numerical and Mathematical Model
Out of three configurations (Otto, Kretschmann, and Grating) of exciting surface plasmons, in this work, Kretschmann configuration is used, as it is more compatible for coupling the prism with the metal film layers. For numerical analysis, we used the transfer matrix method and Fresnel equations performing on the N layer model. Since these methods do not involve approximation, the methods give the most accurate result.
For the calculation, the thicknesses of the layers, d k , are considered in the z-axis, and the refractive index (n) of kth layers and the dielectric constant are considered as e k and n k , respectively. The tangential fields at first boundary z = z 1 = 0 are associated with the final boundary tangential field at z = z N−1 [20] as: (1) Here, P 1 and Q 1 are the tangential elements of electric and magnetic fields of the first layer boundary, and P N−1 and Q N−1 are the boundary fields of the Nth layer where M is represented by the characteristic matrix with M ij [20] and is given as: The coefficient of reflection and the reflectivity of the reflected light from the sensor are expressed as: and, where M 11 , M 22 , M 12 , and M 21 represent elements of the transfer matrix, respectively.

Sensitivity and Other Parameters
The sensitivity (S) of an SPR-based biosensor is the most important parameter for evaluating the performance. It is ascertained by the ratio of change in the resonance angle, δθ, and change in refractive index, ∆n s of probing media [27] as: The resonance condition is evolved as [28]: where sinθ SPR defines the resonance angle, n x is the prism RI, ε m is the real part of the metal permittivity, and n d is the RI of dielectrics or probing medium. The ratio of ω o and C measures the propagation constant of an incident light beam (ω o = light frequency and C is the speed of the light). The detection accuracy (DA) is calculated by the ratio of change in resonance angle (δθ) and the full width at half maximum (FWHM) of the reflectance curve. A relatively low FWHM is preferred when it comes to designing a biosensor that will show the best performance. The sharper the FWHW, the accuracy in determining the angular modulation with high accuracy detection. The magnitude of FWHM is mainly dependent on the excitation configuration, the layers, and the optical properties of the prism used. The detection accuracy can be given as [29]: The quality factor (QF) is the ratio of the sensitivity of a biosensor and FWHM, and is given as [29]:

Results and Analysis
The optical properties of prism materials and their refractive indices have direct effects on the sensitivity of the biosensor. Figure 2 shows the sensitivity of the sensor plotted as a function of the refractive indices of the four types of prism materials at λ = 633 nm for a p-polarized (TM polarized) incident light: CaF 2 , BK7, SF10, and 2S2G. As shown in Figure 2, the sensitivity decreases with the increasing RI of the prism. The highest sensitivity is achieved for a prism with a smaller refractive index, in this case, CaF 2 , and it is considered for the final design of the biosensor.  Next, we optimize the Ag and Au layers. Figure 3 describes the calculated performance of Agand Au-based sensor configurations with the CaF2 prism. As shown, the sensitivity of the Ag-based configuration shows better coupling with the CaF2 prism over the Au-based configuration. The sensitivity is also increasing with the increase of the refractive index of Ag as well as the overall sensitivity of the model is higher than the sensitivity of the Au-based configuration, and therefore Ag is chosen for the final design. Next, we optimize the Ag and Au layers. Figure 3 describes the calculated performance of Ag-and Au-based sensor configurations with the CaF 2 prism. As shown, the sensitivity of the Ag-based configuration shows better coupling with the CaF 2 prism over the Au-based configuration. The sensitivity is also increasing with the increase of the refractive index of Ag as well as the overall sensitivity of the model is higher than the sensitivity of the Au-based configuration, and therefore Ag is chosen for the final design.

Determination of TMDC Performances
The proposed biosensors were optimized (layer thicknesses, minimum Rp, and δθ) using numerical calculation. The performance results of the biosensors are listed in Table 2. As shown, among all the types, sensors with the WS 2 layer exhibit the highest sensitivity, QF, and DA for n = 1.3440. Likewise, TMDCs, MoS 2 shows the highest sensitivity for n = 1.3450, and MoSe 2 and WSe 2 showed the highest sensitivity for n = 1.3460. Between all the four types of TMDCs-based sensors studied here, the sensors with a WS 2 layer have much lower energy loss and higher performance (sensitivity of 375 • /RIU, QF of 65.78 1/RIU and DA of 0.921).
Next, we optimize the Ag and Au layers. Figure 3 describes the calculated performance of Agand Au-based sensor configurations with the CaF2 prism. As shown, the sensitivity of the Ag-based configuration shows better coupling with the CaF2 prism over the Au-based configuration. The sensitivity is also increasing with the increase of the refractive index of Ag as well as the overall sensitivity of the model is higher than the sensitivity of the Au-based configuration, and therefore Ag is chosen for the final design.

Determination of TMDC Performances
The proposed biosensors were optimized (layer thicknesses, minimum Rp, and dq) using numerical calculation. The performance results of the biosensors are listed in Table 2. As shown, among all the types, sensors with the WS2 layer exhibit the highest sensitivity, QF, and DA for n = 1.3440. Likewise, TMDCs, MoS2 shows the highest sensitivity for n = 1.3450, and MoSe2 and WSe2 showed the highest sensitivity for n = 1.3460. Between all the four types of TMDCs-based sensors studied here, the sensors with a WS2 layer have much lower energy loss and higher performance (sensitivity of 375 o /RIU, QF of 65.78 1/RIU and DA of 0.921).

Determination of Proposed Performance Parameter
Taking out the final model with the optimized layers, we must satisfy three steps: combination parameter, sensitivity, and optimization of layer thickness, which we describe below.

Combination Parameter
The most fundamental aspect of understanding the performance of an SPR biosensor is the study of spectral and angular studies at variable refractive indices. Figure 4 shows the reflectance versus incident angle, θ. In modelling, we considered four types of structures. Firstly, we took Ag

Effect of Refractive Indices on Resonance Angle and Sensitivity
The refractive index plays a vital role in the minimum change for the resonance angle. For obtaining better sensitivity, a high resonance angle is targeted as it shows a better response in the shortest change of n. Figure 5a shows the relation between the resonance angle and variable n, and Figure 5b shows the relation between sensitivity versus n with different layer compositions.

Effect of Refractive Indices on Resonance Angle and Sensitivity
The refractive index plays a vital role in the minimum change for the resonance angle. For obtaining better sensitivity, a high resonance angle is targeted as it shows a better response in the shortest change of n. Figure 5a shows the relation between the resonance angle and variable n, and Figure 5b shows the relation between sensitivity versus n with different layer compositions.

Optimization of Layer Thicknesses
The individual layers and their thicknesses in the Kretschmann configuration have a large effect on sensor performance such as sensitivity, minimum reflectance, and change in resonance angle (dq). In Figure 6a,b, Ag layers are optimized. As shown in Figure 6a, the maximum sensitivity is obtained for the Ag layer thickness, tAg = 35 nm. The maximum dq and minimum reflectance shown by these sensors at tAg = 35 nm are shown in Figure 6b.

Optimization of Layer Thicknesses
The individual layers and their thicknesses in the Kretschmann configuration have a large effect on sensor performance such as sensitivity, minimum reflectance, and change in resonance angle (δθ). In Figure 6a,b, Ag layers are optimized. As shown in Figure 6a, the maximum sensitivity is obtained for the Ag layer thickness, t Ag = 35 nm. The maximum δθ and minimum reflectance shown by these sensors at t Ag = 35 nm are shown in Figure 6b.
We also optimized the BP layers for the best sensor performance. Figure 7a shows the sensitivity versus number of BP layers. Figure 7b shows δθ and Rp plotted against the number of BP layers. The maximum sensitivity, minimum reflectance, and maximum change in resonance angle are observed for L = 3 layers of BP in the configuration. Figure 8a,b shows the sensitivity, δθ, and Rp of the biosensor with optimized WS 2 layer thicknesses. By analyzing these figures, the value of maximum sensitivity, δθ, and minimum reflectance are obtained for L = 3, 1, 1, respectively.

Optimization of Layer Thicknesses
The individual layers and their thicknesses in the Kretschmann configuration have a large effect on sensor performance such as sensitivity, minimum reflectance, and change in resonance angle (δθ). In Figure 6a,b, Ag layers are optimized. As shown in Figure 6a, the maximum sensitivity is obtained for the Ag layer thickness, tAg = 35 nm. The maximum δθ and minimum reflectance shown by these sensors at tAg = 35 nm are shown in Figure 6b. We also optimized the BP layers for the best sensor performance. Figure 7a shows the sensitivity versus number of BP layers. Figure 7b shows δθ and Rp plotted against the number of BP layers. The maximum sensitivity, minimum reflectance, and maximum change in resonance angle are observed for L = 3 layers of BP in the configuration. Figure 8a,b shows the sensitivity, δθ, and Rp of the biosensor with optimized WS2 layer thicknesses. By analyzing these figures, the value of maximum sensitivity, δθ, and minimum reflectance are obtained for L = 3, 1, 1, respectively.      Ultimately, Table 3 renders all the performance parameters of the biosensors studied in this paper. These include the materials used, the sensitivity, QF, DA, resonance angle, θSPR and change in resonance angle, δθ where the proposed model substantiated the highest sensitivity, QF, and DA.  Ultimately, Table 3 renders all the performance parameters of the biosensors studied in this paper. The se include the materials used, the sensitivity, QF, DA, resonance angle, θ SPR and change in resonance angle, δθ where the proposed model substantiated the highest sensitivity, QF, and DA. A comparison of the sensitivity values shown by some of the prism-based SPR biosensors reported elsewhere and in this paper is shown in Table 4. As shown, the table corroborates that the proposed model ensured the highest sensitivity among all the reported results. The improvement of the sensitivity of our configuration is also due to the addition and optimization of a black phosphorus (BP) layer as it is found to significantly improve the electric field at the interface of the metal sensor and probing medium. For example, at room temperature, BP is thermodynamically stable, and it has a puckered lattice configuration that gives the benefit of a higher surface to volume ratio. Since. Van der Waals forces-the attraction of intermolecular forces between molecules is higher for BP; these forces tightly hold multiple layers of BP and consequently offer a higher molar response factor. The chosen WSe2 is also an excellent candidate for the SPR study as it offers a direct bandgap, higher absorption rate, and less energy loss of electrons. The refractive index difference between the metal sensor and probing medium (∆n) was kept constant at 0.014 to investigate the performance of the proposed biosensor. With the addition of a new magnetic layer in the proposed configuration and magnetic activity, our proposed structure is expected to exhibit an excellent magneto-optic effect and enhanced sensitivity, detection level and quality factors over the SPR biosensors as well. The refractive index values of the probing samples used in our calculation closely correspond to the refractive index of a bio-sample such as urine, as the biological properties are dependent on the variation of the refractive index of the dielectric medium. The proposed biosensor, if manufactured, is suitable for practical applications, for example, they can be used in public washrooms or private toilets in homes where people can test the samples. The measured results can act as a primary indicator for possible health issues in humans, thus preventing frequent visits to the doctor or hospital.

Conclusions
We numerically investigated biosensors based on transition metal dichalcogenides (TMDC) and black phosphorous layers and accomplished an excellent sensitivity, detection accuracy and quality factor. Among all the TMDCs, WS 2 ascertained the highest sensitivity of 375 • /RIU, a quality factor of 65.78 1/RIU, and a detection accuracy of 0.9210. We also explored the ability of Ag and Au layers to tune on the sensitivity, optimized prism material, and chose CaF 2 as the coupling prism. A long range of refractive indices is used for ensuring the maximum sensitivity of the proposed SPR biosensor. Although the research on TMDC-based biosensors is still very young, it offers many exciting promises and opportunities in biomedical industries.