PtSe2 and Black Phosphorus employed for sensitivity improvement of Surface Plasmon Resonance Sensor

doi:10.21203/rs.3.rs-1221524/v1

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PtSe2 and Black Phosphorus employed for sensitivity improvement of Surface Plasmon Resonance Sensor

https://doi.org/10.21203/rs.3.rs-1221524/v1

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The analysis aims to enhance the sensitivity of the surface plasmon resonance-based biosensor. The proposed sensor consists of a single layer of Ag metal, black phosphorus (BP), and PtSe2. The thickness of the Ag metal is considered as 45 nm. The study has been carried using attenuated total internal reflection (ATR). The refractive index of the sensor changes when analyte or biomolecules comes in contact with the sensing layer. The thickness of the BP layer has been taken as 0.34nm. The maximum sensitivity of the sensor is achieved for one layer of PtSe₂ and two layers of BP. The calculated performance parameters, sensitivity, figure of merit, and detection accuracy is 275.2$^\circ /\text{R}\text{I}\text{U}$, 43.1 RIU⁻¹, and 0.16 deg⁻¹, respectively. The sensitivity of the proposed sensor is 1.38 times the conventional sensor.

Surface plasmon resonance

PtSe2

Black phosphorus

sensitivity enhancement

Surface plasmons (SPs) are dense oscillating electrons cloud propagation at the metal and dielectric interface. They are useful for detecting molecular properties of the sensing medium such as size, concentration, and the analyte in biology and biochemistry [1]–[3]. When an analyte interacts with the bio recognize element (BRE) of the SPR sensor, the BRE elements’ biomolecular bonding enhances, the refractive index of the sensing medium changes significantly [4]. This phenomenon causes the change in the propagation constant of the surface plasmons, allowing the significant shift in the resonance curve [5], [6] The necessary condition for any good sensor must show high sensitivity, low full with half maximum (FWHM), high detection accuracy, repeatability and reproducibility, and high stability over the time in different chemical and physical condition [7], [8].

To design an SPR-based sensor, Kretschmann is the most widely used configuration [9]–[11]. The sensor's sensitivity is analyzed at the dip in the resonance curve, where the resonance angle is measured. In the dip, the absorbance of the light is maximum, and reflectivity is minimum. Here angle interrogation technique is used for the analysis of the sensor. The input signal of wavelength $\lambda =633 \text{n}\text{m}$ is used here. Conversional Kretschmann configuration is modify by stacking the layer of 2-Dimensional material or artificially developed heterostructure material such as graphene, black phosphorus, barium titanate, and tine selenide etc., shows the enhanced sensitivity and better performance than the conventional sensor [12]–[16].

In traditional biosensors, silver (Ag) metal layers are widely utilized [17], [18]. Near the infrared and near-infrared regions, the resonance curve of silver metal shows a significant dip, indicating that the sensor produces high sensitivity [19]. However, the Ag metal layer base sensor is more accurate than gold, has a narrower resonance curve with higher contrast, and has a lower FWHM than gold [20]. However, Ag has low stability since it is readily oxidized when exposed to air or water [21]. The sensor's sensitivity reduces due to the oxidation of the Ag layer. To reduce the oxidation problem and improve the sensor's performance, a bimolecular recognizing element (BRE) is used [22].

After experimental analysis, it is found that 2-D materials such as black phosphorus (BP) and graphene as BREs can improve the sensitivity and performance characteristic of the SPR sensors [23]–[27]. Some important points about BP are that its response time is very low compared to the other 2-D materials, which allows sensing the parts per billion quantities of the analyte. Adsorption energy is also very high compared to graphene, WS_2, and MoS₂. Furthermore, BP has a puckered lattice arrangement, giving it a substantially higher surface-to-volume ratio than other 2D materials [28]. As a result, BP may be ideal for biomolecule binding. The electrical and optical properties of the BP have been analyzed experimentally. Cai et al. observed that the effective carrier mass, energy bandgap, and work function depending on the BP material's thickness, decreasing with the thickness increase. But the only drawback is the stability issue, which is unstable in air and water [26]. Therefore, BP is the best suitable material for gas sensing. Rahman et al. theoretically investigated a biosensor using BK7 prism, PtSe₂, 2D materials, and maximum sensitivity 194°/RIU is achieved [28]. Fouad et al. proposed a biosensor based on the SPR mechanism using silver (Ag) and barium titanate (BaTiO₃) and achieve maximum sensitivity of 280°/RIU [31]. An SPR based gas sensor was proposed by Shrivastava and Jha using BP and MoS2 layers. They attained a maximum sensitivity for this was 110°/RIU [32]. PtSe₂ has extraordinary optical and electromechanical properties; its strong interlayer contact and quantum confinement effect have a large tunable energy bandgap [33]. Furthermore, while transitioning from bulk to a few layers form, it exhibits an outstanding transition characteristic from semimetal to semiconductor. It also provides toxicity resistance and chemical inertness, making it a potential material for sensing applications [29], [30].

This work has comprehensively designed a hybrid multilayer sensor based on Ag metal, PtSe2, and black phosphorus to analyze the conventional structure. Here angular interrogation method based on attenuated total reflection (ATR) is used to analyze the sensor. The performance parameters are based on sensitivity, detection accuracy, the figure of merit, and quality factor, etc. The manuscript is structured in the following manner: Section 2 consists of design consideration and theoretical cum mathematical modeling of the proposed sensor. Section 3 explains results and discussion, while the conclusion of the work is provided in section 4.

2.1 Design analysis and theoretical modeling

Figure 1 consists of the schematic of the proposed sensor, which is a modified Kretschmann configuration. The thickness of the Ag layer 45 nm is taken and deposited over the prism. The dispersion profile of the metal is computed using the Drude-Lorentz model and given as [9]:

$${n}_{Ag}={\left(1-\frac{{\lambda }^{2}*{\lambda }_{c}}{{\lambda }_{p}^{2}({\lambda }_{c}+\lambda *i)}\right)}^{1/2}$$

where, ${\lambda }_{c}$ and ${\lambda }_{p}$ are the collision and plasma wavelength of the material, and its values are $1.4541\times {10}^{-7}$ and $17.614\times {10}^{-6}$ respectively. The proposed configuration utilizes the BK7 coupling prism. The refractive index of the BK7 is low, so it provides better sensitivity. Here monochromatic plane polarizes TM optical signal is used for the operation of the proposed sensor. The refractive index of the prism is calculated using this formula [11]:

$${\text{n}}_{\text{B}\text{k}7}={\left(\frac{{1.03961212{\lambda }}^{2}}{{{\lambda }}^{2}-0.00600069867}+\frac{{0.231792344{\lambda }}^{2}}{{{\lambda }}^{2}-0.0200179144}+\frac{{1.0104694{\lambda }}^{2}}{{{\lambda }}^{2}-103.560653}+1\right)}^{\frac{1}{2}}$$

The metal layer of the sensor is attached with the thin layer of PtSe₂, and after that, a thin layer of black phosphorus is spread over it. The heterostructure of transition metal diselenide/2-D materials is taken as an affinity layer to interact with the sensing layer or analyte while preventing metal oxidation. Design parameters and their respective refractive index (RI) are given in Table 1. The refractive index of the sensing medium is taken as 1.33, and $\delta n$is the variation in the RI of the sensing medium when the analyte comes in contact with it.

Table 1: Dimension and refractive index of the material used in the sensor

2.2 Mathematical Modelling

To analyze the sensitivity/performance of the sensor, first, investigate the reflection intensity of the TM polarized light at the detector of the sensor. The mathematically modeling of the multilayer configuration of the sensor can be fulfilled by analyzing the Drude-Lorentz model/Fresnel equation and transfer matrix method (TMM). This study uses no approximation because the TMM technique provides the best results. MATLAB is used to estimate the SPR modulation analogy. To proceed with the mathematical modeling, some parameters need to specify. The individual thickness of each layer is described as ${d}_{k}$They are stacked in the Z-direction. The sufficient condition for surface plasmon resonance is when the propagation constant of the evanescent wave matches with the surface plasmon by taking the specific value of the angle. This condition is known as wavevector matching because incident light wavevector matches with the surface plasmon wavevector.

$$\frac{2\pi }{\lambda }{n}_{pr}sin\theta =Re\left({\beta }_{SP}\right)$$

where $\theta$ is the angle of incidence, ${n}_{pr}$ is the RI of the prism, ${\beta }_{SP}$ is the propagation constant of surface plasmon, and numerically it can be written as $\left(\frac{2\pi }{\lambda }\sqrt{\frac{{\epsilon }_{m}{\epsilon }_{s}}{{\epsilon }_{m}+{ϵ}_{s}}}\right)$. It is necessary to generate surface plasmon momentum, and energy must be conserved. The relation between angular frequency and wavevector in the X-direction can be written as:

$${k}_{x}=\frac{\omega }{c}\sqrt{\frac{{\epsilon }_{1}{\epsilon }_{2}}{{\epsilon }_{1}+{ϵ}_{2}}}$$

Drude - Lorentz model shows the dependency of the wavelength of an incident optical signal to the dielectric constant of the metal. The refractive index of the BK7 prism is estimated using the Sellemeier equation. The transfer matrix method is used to compute the reflectivity of the TM polarized light. The tangential component of the light at the metal surface is given as:

$$\left[\begin{array}{c}{A}_{1}\\ {B}_{1}\end{array}\right]={M}_{2}{M}_{3}{M}_{4}\dots \dots \dots ..{M}_{-1}\left[\begin{array}{c}{A}_{N-1}\\ {B}_{N-1}\end{array}\right]=M\left[\begin{array}{c}{A}_{N-1}\\ {B}_{N-1}\end{array}\right]$$

Here, ${A}_{1}$ and ${B}_{1}$ are tangential components of electric field and magnetic field respectively at the surface of the first layer. Similarly, electric and magnetic field components at the N^th layer’s boundary is given as ${A}_{N-1}$ and ${B}_{N-1}$ respectively. M shows the characteristic transfer matrix of the N – layered configuration is as follows:

$$M=\prod _{K=2}^{N-1}{M}_{K}=\left[\begin{array}{cc}{M}_{11}& {M}_{12}\\ {M}_{21}& {M}_{22}\end{array}\right]$$

where,

Where ${q}_{k}$ and ${\beta }_{k}$ can be written as ${q}_{k}=\sqrt{\left(\frac{{\mu }_{k}}{{\epsilon }_{k}}\right)}cos{\theta }_{k}$ and ${\beta }_{k}=\frac{2\pi }{\lambda }{n}_{k}cos{\theta }_{k}\left({d}_{k}\right)$ respectively.

After simplifying the equations as mentioned above, the reflection coefficient is written as:

$$R={\left|r\right|}^{2}=\left(\frac{\left({M}_{11}+{M}_{12}{q}_{N}\right){q}_{1}-({M}_{21}+{M}_{22}{q}_{N})}{\left({M}_{11}+{M}_{12}{q}_{N}\right){q}_{1}+({M}_{21}+{M}_{22}{q}_{N})}\right)$$

The sensitivity is the necessary parameter of the sensor, showing how resonance angle varies to change in the refractive index of the sensing medium; more precisely, it is said to be the limit of detection. The sensitivity should be high for the sensor, and it is defined as:

$S=\frac{{\delta \theta }_{res}}{\delta n}$ ($^\circ$/RIU) (9)

where, ${\delta \theta }_{res}$ is the shift in the resonance angle of the incidence, and $\delta n$ is the variation in the refractive index of the medium. The Figure of merit (FoM) is another important parameter for the sensor, and it shows the sensor's resolution, high value is desirable. FoM is defined as:

$FoM=\frac{S}{FWHM}$ $1/\text{R}\text{I}\text{U}$ (10)

For the best performance of the biosensor, FWHM should be low. So, the resonance curve should be narrow and sharp. Detection accuracy is computed as reciprocal of the FWHM ($1/FWHM$). The FoM is a useful parameter to show the sensor's performance. It combines the result of sensitivity and FWHM.

To demonstrate the enhancement in sensitivity performance, the plots between the reflectance of the structure and incidence angle at distinct refractive indexes (1.33 and 1.335) of the sensing medium are shown in Fig. 2. For the first Fig. 2 (a), it indicates the traditional SPR sensor setup, with the absence of both layers of PtSe₂ and BP ($P=0, B=0$). Our study demonstrated that the reflectance exhibits a sharp dip at a specific angle range due to the stimulation of SPR. This event shows that the stimulating SPR absorbs the incident light in our biosensor setup. Further, with molecules' cooperation, the refractive index of the sensing medium changes with this setup, the change in resonance angle ($\varDelta \theta =0.576ᵒ$ and sensitivity is calculated ($S=115.2 ^\circ /\text{R}\text{I}\text{U})$ as in equation 9. Figure 2(b) indicates a single BP layer ($B=1$) and no PtSe₂ ($P=0$); the other parameters were kept constant as in the previous condition. The values for $\varDelta \theta =0.59ᵒ$ and $\text{S}= 118 ^\circ /\text{R}\text{I}\text{U}$ are calculated. It is clearly shown that with a single BP layer, the sensitivity increases when compared with Figure 2(a) without BP. The next case is shown by Figure 2 (c) gives the sensitivity and change in resonance angle ($\varDelta \theta =0.632ᵒ and S=126.4 ^\circ /\text{R}\text{I}\text{U})$ with the presence of PtSe₂ layer and absence of BP layer.

Further, the presence of both layers of PtSe2 and BP ($\text{P}, \text{B}=1$) is shown in Figure 2(d). With the modification in the reflectance dip, the sensitivity increases to $0.65ᵒ$ and the change in resonance angle comes out to be 130$^\circ /\text{R}\text{I}\text{U}$.We can see that the alteration in the resonance angle of the biosensor in our construction is higher than the typical SPR structure due to the addition of the PtSe₂ layer and the BP layer. Only a coupling prism and a metal (Ag) layer make up the typical SPR structure. As a result, we may conclude that combining PtSe₂ and a BP layer to our SPR sensor improves its sensitivity significantly compared to a standard construction [Figure 2(a)]. The above analysis easily concludes that the sensing layer's refractive index can regulate the biosensor's sensitivity.

With Fig. 3. we also plot the dependence of the biosensor's sensitivity on the sensing layer’s refractive index to understand better the augmentation of the biosensor's sensitivity by PtSe₂ and BP layers. The refractive index of the sensing range is taken from 1.33 to 1.38, with 0.005 variations in between. With the increase in refractive index, the sensitivity enhances significantly, for $P=0,G=0$ the sensitivity varies from $115.2^\circ /RIU$ to $153.8^\circ /RIU$ then for $P=0,B=1$ it varies to $156.2 ^\circ /RIU$ from $117.4^\circ /RIU$. In the next case, when $P=0,B=1$the sensitivity, further reaches $180.2 ^\circ /RIU$maximum. Lastly, for $P=B=1$ the highest value of sensitivity as achieved as $187.4^\circ /RIU$. This analysis signifies that after introducing PtSe₂ and BP layer to the structure, the sensitivity increases from $153.8^\circ /RIU$ to $187.4^\circ /RIU$.

Further, we expand this study to a greater extent by seeing the impact of further addition of PtSe₂ and BP layer on the sensitivity of the proposed biosensor. Firstly, after adding the BP layer with constant PtSe₂ layer(P=1), its impact is observed on the sensitivity, as Fig. 4(a). Increasing the number of BP layers can improve reflectance. Furthermore, when the number of BP layers increases, a shift in reflectance dip is observed for a larger incidence angle, implying that the biosensor's sensitivity increases. From Fig. 4 (b), the impact of adding PtSe₂ layer on biosensor sensitivity is observed keeping one BP layer. It can be seen from the above plots [Fig. 4 (a) and (b)] that the SPR curve dip gets wider with increasing the number of BP and PtSe₂ layers. It signifies that the measurement is complicated at a near resonance angle, influencing biosensors' exactness. The prior discussion gives us the concept that the sensitivity increases to a greater extent by increasing the number of layers of BP and PtSe2. The absorption of biomolecules is higher for BP as compared to PtSe₂.With the increase of BP layers, its effect on the reflectance is observed, which is greater than the other layer’s case. The upcoming Fig. 5 (a) gives the sensitivity as a function of a number of BP layers. With the increase in the number of BP layers (1 to 9), the maximum sensitivity is found to be $275.2^\circ /RIU$ with eight BP layers ($B=8$). After eight-layer the sensitivity decreases. This decrement in value is because the utilization rate of the light wave decreases with enhancing the number of BP layers.

The next plot [Fig. 5 (b)] gives the impact of the number of PtSe2 layers on biosensor sensitivity. The plot is not following the same trend as in Fig. 5 (a); it decreases after the second layer. The peak value of sensitivity is found to be $215^\circ /RIU$ at $P=2$. So, with these discussions, we conclude that the optimization of the BP layer is done followed by the optimization of the PtSe₂ layer, and the maximum sensitivity we are getting is $275.2^\circ /RIU$ (for $P=1, B=8$). Using constant angular interrogation, various plots have been drawn for conclusive evidence. Multiple Y-axis parameters (FWHM and minimum reflectivity) with a single X-axis showing sensitivity is plotted for variable BP layers [$0 to 8$] with mono ($P=1$) layer of PtSe₂[Fig. 6 (a)] at RI of sensing layer 1.38. The maximum and minimum value of sensitivity attained was $180.2 ^\circ /RIU$ and $275.2^\circ /RIU$ with values of minimum reflectance and FWHM varying from 0.07129 to 0.23796 and 4.73$^\circ$ to 6.38$^\circ$ respectively. Fig. 6 (b) shows sensitivity's functional relationship between DA and FoM. The number of layers taken is the same as in the previous case. The highest values obtained with this plot for both parameters [DA and FoM] were 0.21 to 0.16 and 38.1 to 43.1, respectively. It depicts that the electric field distribution at the greatest sensitivity is accurate and sharper, while vice versa in the lowest sensitivity value. With next Fig. 6 (c), the plots for DA and FoM are plotted for biosensor sensitivity. These parameter calculations took constant BP layer ($B=1$) and varying PtSe2 layers (0 to 2).

The maximum sensitivity, FoM, and DA were calculated as $215^\circ /RIU$,36.1, and 0.17. Similarly, with Fig. 6 (d), the maximum values of FWHM and minimum reflectance (${R}_{min}$) values come out to be $5.95^\circ$ and 0.32291.

Figure 7 depicts the relation of electric field distribution inside the sensor with the distance of the prism interface. At the Ag-TiO₂ boundary, the electric field intensity increases, further increasing at the TiO₂-BP boundary. After the last boundary of BP-sensing media, its value decreases exponentially. It was observed that when light absorption is greater, field intensity enhances. It demonstrates that higher light absorption causes considerable SPW excitation. Figure 7 (a-c) shows the electric field distribution plots for the three thickness cases, D₂ of PtSe_2, 2 nm,3.3 nm, and 4 nm. With the upcoming Table 2, a comparison is made with the similar previous reported works, and an analysis is made with the help of performance parameters like sensitivity, DA, and FoM. This paper clearly shows that the achieved sensitivity and FoM are higher than earlier works.

With the upcoming Table 2, a comparison is made with the similar previous reported works, and an analysis is made with the help of performance parameters like sensitivity, DA, and FoM. This paper clearly shows that the achieved sensitivity and FoM are higher than earlier works.

Table 2

Comparative survey of present work with earlier reported works
Wavelength	Design Configuration	Sensitivity	DA	FoM	Reference
632.8 nm	BK7 + (ZnO, Ag, Au, Graphene)	76	-	13.79	[35]
632.8 nm	BK7+(Au & WSe₂)	179.32	0.17	-	[36]
633 nm	BK7 + (Ag + BlueP + MoS₂)	230.66	-	34.58	[37]
633 nm	BK7 + (Au, Al₂O₃, WS₂)	227.25	1.1123	28.26	[38]
633 nm	BK7 + (Au + MoS₂ + Au + graphene)	182	-	-	[39]
633 nm	BK7 + (Ag/Au, PtSe₂)	165	0.1412	14.12	[12]
633 nm	BK7 + (Ag, PtSe₂ & BP)	275.2	0.16	43.1	Present work

Finally, we theoretically studied a novel form of biosensor structure based on the Kretschmann configuration with the addition of a PtSe₂ and a BP layer. The inclusion of PtSe₂ and the BP layer has been beneficial as it increases the overall performance of the SPR biosensor. We have analyzed the results showing that the biosensor's sensitivity may be increased using the proposed design. By altering the number of BP layers in the design, the sensitivity can be improved to a maximum of 275.2$^\circ /RIU$. Our study gives a positive sign of more research exploration in bio sensing-based applications giving high-performance parameters.

Code Availability: Not applicable.

Funding Information: No funding available.

Conflicts of interest/Competing interests: The author declares no conflict of interest.

Availability of data and material: No data available.

Authors' 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.

GUA 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.

VK provided statistical analysis for the results. He provided the theoretical background to SPR biosensors. He also helped in formatting the manuscript.

Ethics 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/or living organism/ animal. So, ethical approval from an ethical committee is not required.

Consent to participate

I am willing to participate in the work presented in this manuscript.

Consent for publication

The author has given their consent to publish this work.

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PtSe2 and Black Phosphorus employed for sensitivity improvement of Surface Plasmon Resonance Sensor

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Figures

1. Introduction

2. Theoretical Analysis And Mathematical Modeling Of The Sensor

2.1 Design analysis and theoretical modeling

2.2 Mathematical Modelling

3. Results And Discussions

4. Conclusion

Declarations

References

Status:

Version 1