Sensitivity Improvement of a Surface Plasmon Resonance Sensor Based on Two-Dimensional Materials Hybrid Structure in Visible Region: A Theoretical Study

In this paper, we propose a surface plasmon resonance (SPR) sensor based on two-dimensional (2D) materials (graphene, MoS2, WS2 and WSe2) hybrid structure, and theoretically investigate its sensitivity improvement in the visible region. The thickness of metal (Au, Ag or Cu) and the layer number of each 2D material are optimized using genetic algorithms to obtain the highest sensitivity for a specific wavelength of incident light. Then, the sensitivities of proposed SPR sensors with different metal films at various wavelengths are compared. An Ag-based SPR sensor exhibits a higher sensitivity than an Au- or Cu-based one at most wavelengths in the visible region. In addition, the sensitivity of the proposed SPR sensor varies obviously with the wavelength of incident light, and shows a maximum value of 159, 194 or 155°/RIU for Au, Ag or Cu, respectively. It is demonstrated that the sensitivity of the SPR sensor based on 2D materials’ hybrid structure can be further improved by optimizing the wavelength of incident light.


Introduction
Surface plasmon resonance (SPR) is an optical phenomenon that occurs at the interface between the metal and dielectric. The surface plasma wave (SPW), excited by a specific incident condition, is very sensitive to the change in the refractive index (RI). SPR sensing technology, owing to the merits of no labeling, fast analysist speed and real time [1], is widely applied in various fields, such as biomolecular detection [2], food safety [3], and chemical sensing [4]. A traditional SPR sensor generally employs a Kretschmann configuration, based on attenuated total reflection (ATR) for exciting the SPW, due to its convenience and efficiency. A typical Kretschmann configuration consists of a thin film of metal coated on a high index prism, and a sensing medium touching the metal film [5]. When the propagation constant of the incident light matches with that of the SPW the energy is absorbed, and will form a narrow dip in the reflectance curve that can be used for sensing.
Sensitivity, defined as the resonance angle or wavelength shift per analyte refractive index unit (RIU), is a significant parameter for an SPR sensor. A few of the schemes based on sensor structure optimization were put forward to enhance the sensitivity. For example, Alleyne at al. created a six-fold enhancement in sensitivity using periodic metallic structures [6]. Kapoor et al. found a SPR sensor with and the sensitivity of three different metal-based sensors with a monolayer graphene all displayed a maximum value with varying wavelengths of the incident light [29].
In this paper, we study the sensitivity improvement of an SPR sensor based on a graphene/ MoS 2 /WS 2 /WSe 2 hybrid structure in the visible region. To explore the maximum sensitivity of the proposed sensor at a specific wavelength and figure out which 2D materials are helpful for improving its sensitivity, the thickness of the metal film and the layer number of each 2D material in the sensor are optimized using GA. Then, the sensitivity of the proposed sensor that utilizes different metals (Au, Ag, Cu) at the different wavelengths in the visible region has been compared. Furthermore, the performances of proposed SPR sensors are investigated, and the origin of sensitivity improvement is determined.

Structure of Proposed SPR Sensor
The proposed SPR sensor with a prism/metal/graphene/MoS 2 /WS 2 /WSe 2 structure is shown in Figure 1. In the sensor, we choose SF11 glass as the coupling prism, then use a metal (Au, Ag or Cu) layer covering the prism to excite the SPR. Then, the 2D materials' hybrid structure (graphene, MoS 2 , WS 2 , WSe 2 ) is coated on the metal film. In the present study, the proposed sensor uses a Kretschmann configuration based on angular interrogation, and the sensitivity of the proposed SPR sensor is investigated in the visible region (400-800 nm).
Sensors 2020, 20, x 3 of 11 In this paper, we study the sensitivity improvement of an SPR sensor based on a graphene/MoS2/WS2/WSe2 hybrid structure in the visible region. To explore the maximum sensitivity of the proposed sensor at a specific wavelength and figure out which 2D materials are helpful for improving its sensitivity, the thickness of the metal film and the layer number of each 2D material in the sensor are optimized using GA. Then, the sensitivity of the proposed sensor that utilizes different metals (Au, Ag, Cu) at the different wavelengths in the visible region has been compared. Furthermore, the performances of proposed SPR sensors are investigated, and the origin of sensitivity improvement is determined.

Structure of Proposed SPR Sensor
The proposed SPR sensor with a prism/metal/graphene/MoS2/WS2/WSe2 structure is shown in Figure 1. In the sensor, we choose SF11 glass as the coupling prism, then use a metal (Au, Ag or Cu) layer covering the prism to excite the SPR. Then, the 2D materials' hybrid structure (graphene, MoS2, WS2, WSe2) is coated on the metal film. In the present study, the proposed sensor uses a Kretschmann configuration based on angular interrogation, and the sensitivity of the proposed SPR sensor is investigated in the visible region (400-800 nm). , (1)Due to the dispersion of metals in the visible region, the refractive index and extinction coefficient of metals are distinctive at different wavelengths. The refractive index and extinction coefficients of used metals in this paper are taken from [30], shown in Figure 2. It seems that the refractive index of Ag is lower, but its extinction coefficient is higher than that of Au and Cu. The refractive index of SF11 glass can be calculated by the following formula, Due to the dispersion of metals in the visible region, the refractive index and extinction coefficient of metals are distinctive at different wavelengths. The refractive index and extinction coefficients of used metals in this paper are taken from [30], shown in Figure 2. It seems that the refractive index of Ag is lower, but its extinction coefficient is higher than that of Au and Cu.
In addition, 2D materials also show obvious dispersion in the visible region, which is shown in Figure 3. All data of refractive index and extinction coefficient originate from [31,32]. In addition, the thickness of the monolayer of each 2D material is exhibited in Table 1 [33]. Sensors 2020, 20, x 4 of 11 In addition, 2D materials also show obvious dispersion in the visible region, which is shown in Figure 3. All data of refractive index and extinction coefficient originate from [31,32]. In addition, the thickness of the monolayer of each 2D material is exhibited in Table 1 [33].

Thickness of Monolayer
The sensing medium, which is assumed to be water with ss-DNA biomolecules for our simulations, keeps in contact with the 2D materials. These 2D materials, which work as the biomolecular recognition element, can adsorb the biomolecules on its surface to form an additional ss-DNA layer whose thickness is around 100 nm, and produce a local increase in the refractive index (Δn = 0.005) at the surface of SPR sensor [34]. In addition, 2D materials also show obvious dispersion in the visible region, which is shown in Figure 3. All data of refractive index and extinction coefficient originate from [31,32]. In addition, the thickness of the monolayer of each 2D material is exhibited in Table 1 [33].  The sensing medium, which is assumed to be water with ss-DNA biomolecules for our simulations, keeps in contact with the 2D materials. These 2D materials, which work as the biomolecular recognition element, can adsorb the biomolecules on its surface to form an additional ss-DNA layer whose thickness is around 100 nm, and produce a local increase in the refractive index (Δn = 0.005) at the surface of SPR sensor [34].  The sensing medium, which is assumed to be water with ss-DNA biomolecules for our simulations, keeps in contact with the 2D materials. These 2D materials, which work as the biomolecular recognition element, can adsorb the biomolecules on its surface to form an additional ss-DNA layer whose thickness is around 100 nm, and produce a local increase in the refractive index (∆n = 0.005) at the surface of SPR sensor [34].

Transfer Matrix Method
The proposed SPR sensor can be regarded as a multilayer structure, and its reflectivity could be calculated by the well-known transfer matrix method as follows Sensors 2020, 20, 2445 M is the characteristic matrix of the multilayer. δ j = 2πn j d j cosθ j , in which n j and d j are the refractive index and the thickness of each layer in the SPR sensor, and θ j is the angle of light travelling in each layer. η j = n j /cosθ j denotes the optical admittance of each layer for the p-polarized light. η 0 and η N+1 are representative of the optical admittance for incident media (SF11 prism) and emergent media (water).
The sensitivity (S) defines as the ratio of the change in value of the resonance angle to the change in value of refractive index of the analyte, and can be expressed by where ∆θ res is the offset of resonance angle, and ∆n stands for the change in the refractive index of the analyte.

Genetic Algorithm
In order to achieve high sensitivity by optimizing the thickness of metal film and the layer number of each of the 2D materials, a merit function (MF) with a constraint condition is used in GA, θ 0 and θ 1 are resonance angles before and after ss-DNA addition. The constraint condition of θ 1 > θ 0 in MF is used to avoid a negative shift, which may lead to fake high-sensitivity.
In order to ensure the GA finds the optimal parameters that realize high sensitivity, the population number and the genetic generation in GA are set to 300 and 500, respectively. Besides this, the values of crossover proportion and mutation proportion are both 0.7 to achieve a fast convergence speed. In GA, the optimization range of metal thickness is set to be from 0 to 60 nm, while the range in numbers of layers of 2D materials is set to be from 0 to 15. One thing that should be stressed here is that the optimal 2D materials' hybrid structure for sensitivity improvement is not always the same for different wavelengths, because the optimized layer number of a certain 2D material may be zero, which means the present type of 2D material is of no use for sensitivity improvement in the proposed SPR sensor, which should be discarded.

Results
First of all, we use the GA to optimize the thickness of the metal and the layer number of each 2D material in the proposed SPR sensors in the visible region. The curve of optimal sensitivity of the proposed SPR sensor with Au, Ag or Cu film, varying with the wavelength changing from 400 to 800 nm, is shown in Figure 4a.
In Figure 4a, the sensitivity is distinct for the optimized SPR sensor with different metal films, originating from the different refractive index and extinction coefficient of various metals, which also causes different optimal thicknesses of metal, as shown in Figure 4b. The sensitivity of Ag-based sensors decreases first and then increases, while the sensitivities of Au-and Cu-based SPR sensors both show an upward trend with increasing wavelength. The sensitivity of the Ag-based sensor is higher than the other metal-based ones at most wavelengths in the considered region, which can be attributed to its lower refractive index and higher extinction coefficient. The maximum sensitivity of an Au-, Ag-or Cu-based SPR sensor is 159, 194 or 155 • /RIU.  In Figure 4a, the sensitivity is distinct for the optimized SPR sensor with different metal films, originating from the different refractive index and extinction coefficient of various metals, which also causes different optimal thicknesses of metal, as shown in Figure 4b. The sensitivity of Ag-based sensors decreases first and then increases, while the sensitivities of Au-and Cu-based SPR sensors both show an upward trend with increasing wavelength. The sensitivity of the Ag-based sensor is higher than the other metal-based ones at most wavelengths in the considered region, which can be attributed to its lower refractive index and higher extinction coefficient. The maximum sensitivity of an Au-, Ag-or Cu-based SPR sensor is 159, 194 or 155 °/RIU. The optimal number of layers of each of the 2D materials in a graphene/MoS2/WS2/WSe2 hybrid structure also exhibits a different value for the sensors with different metals, or at different wavelengths, as shown in Figure 5. In addition, it seems that not all 2D materials are needed for sensitivity improvement under a specific wavelength, because many values of the layer number are zero for the proposed sensor. This can be easily understood because each 2D material has its fixed refractive index and extinction coefficient at a specific wavelength, and could affect the sensitivity independently. During the optimization, GA only picks up the 2D materials that increase the merit function (sensitivity). In that case, the materials that have an adverse effect on sensitivity optimization will be discarded. Using this method, we can realize the intelligent selection of 2D materials in the hybrid structure for sensitivity improvement, instead of the tedious manual screening of materials one by one. The optimal number of layers of each of the 2D materials in a graphene/MoS 2 /WS 2 /WSe 2 hybrid structure also exhibits a different value for the sensors with different metals, or at different wavelengths, as shown in Figure 5. In addition, it seems that not all 2D materials are needed for sensitivity improvement under a specific wavelength, because many values of the layer number are zero for the proposed sensor. This can be easily understood because each 2D material has its fixed refractive index and extinction coefficient at a specific wavelength, and could affect the sensitivity independently. During the optimization, GA only picks up the 2D materials that increase the merit function (sensitivity). In that case, the materials that have an adverse effect on sensitivity optimization will be discarded. Using this method, we can realize the intelligent selection of 2D materials in the hybrid structure for sensitivity improvement, instead of the tedious manual screening of materials one by one.  In Figure 4a, the sensitivity is distinct for the optimized SPR sensor with different metal films, originating from the different refractive index and extinction coefficient of various metals, which also causes different optimal thicknesses of metal, as shown in Figure 4b. The sensitivity of Ag-based sensors decreases first and then increases, while the sensitivities of Au-and Cu-based SPR sensors both show an upward trend with increasing wavelength. The sensitivity of the Ag-based sensor is higher than the other metal-based ones at most wavelengths in the considered region, which can be attributed to its lower refractive index and higher extinction coefficient. The maximum sensitivity of an Au-, Ag-or Cu-based SPR sensor is 159, 194 or 155 °/RIU.
The optimal number of layers of each of the 2D materials in a graphene/MoS2/WS2/WSe2 hybrid structure also exhibits a different value for the sensors with different metals, or at different wavelengths, as shown in Figure 5. In addition, it seems that not all 2D materials are needed for sensitivity improvement under a specific wavelength, because many values of the layer number are zero for the proposed sensor. This can be easily understood because each 2D material has its fixed refractive index and extinction coefficient at a specific wavelength, and could affect the sensitivity independently. During the optimization, GA only picks up the 2D materials that increase the merit function (sensitivity). In that case, the materials that have an adverse effect on sensitivity optimization will be discarded. Using this method, we can realize the intelligent selection of 2D materials in the hybrid structure for sensitivity improvement, instead of the tedious manual screening of materials one by one. In order to further study the performances of the SPR sensors with optimized structures, we plot the reflectance curves of the sensors at the wavelengths of 400, 600 and 800 nm, as shown in Figure  6. The parameters of those optimized sensors are listed in Table 2. The letters K, L, M and N in Table  2 are representative of the layer number of graphene, MoS2, WS2 and WSe2, respectively. In order to further study the performances of the SPR sensors with optimized structures, we plot the reflectance curves of the sensors at the wavelengths of 400, 600 and 800 nm, as shown in Figure 6. The parameters of those optimized sensors are listed in Table 2. The letters K, L, M and N in Table 2 are representative of the layer number of graphene, MoS 2 , WS 2 and WSe 2 , respectively. In order to further study the performances of the SPR sensors with optimized structures, we plot the reflectance curves of the sensors at the wavelengths of 400, 600 and 800 nm, as shown in Figure  6. The parameters of those optimized sensors are listed in Table 2. The letters K, L, M and N in Table  2 are representative of the layer number of graphene, MoS2, WS2 and WSe2, respectively.   As shown in Figure 6, both the resonance angle θ res and the sensitivity S increase with the wavelength for Au-and Cu-based sensors. Besides this, we find that the SPR sensor exhibiting the higher sensitivity does not necessarily show smaller reflectivity at resonance angle R res . However, R res at 600 nm is always higher than at other wavelengths. At the same time, in conjunction with Table 2, we discovered that the optimized hybrid structure of the sensor with different metals, or at different wavelengths, exhibits a distinct combination of 2D materials. This indicates that the optimal 2D materials' hybrid structure of the sensor is related to not only the wavelength, but also the metal used in the SPR sensor. It is interesting to see that when the wavelength is lower than 600 nm, all sensor structures do not need MoS 2 , which may be to blame for the high extinction coefficient of MoS 2 at 400 and 600 nm, as shown in Figure 3b.
To study the origin of the sensitivity improvement in 2D material-based SPR sensors, we calculate the electric field intensity enhancement factor (EFIEF) of the proposed sensors using the method described by Shalabney and Abdulhalim [35], as shown in Figure 7. By comparing the sensitivity and the EFIEF of these sensors at various wavelengths, we found that the case which exhibits a larger value of maximum EFIEF always shows higher sensitivity. For example, for an Au-based SPR sensor, the maximum EFIEF is 2.22, 2.63 and 5.27 while the sensitivity is 45, 88 and 142 • /RIU at wavelengths 400, 600 and 800 nm. Meanwhile, the SPR sensor with different metals also fulfills this rule. The results indicate that the sensitivity improvement in the proposed sensor is attributed to the electric field intensity enhancement. As shown in Figure 6, both the resonance angle θres and the sensitivity S increase with the wavelength for Au-and Cu-based sensors. Besides this, we find that the SPR sensor exhibiting the higher sensitivity does not necessarily show smaller reflectivity at resonance angle Rres. However, Rres at 600 nm is always higher than at other wavelengths. At the same time, in conjunction with Table 2, we discovered that the optimized hybrid structure of the sensor with different metals, or at different wavelengths, exhibits a distinct combination of 2D materials. This indicates that the optimal 2D materials' hybrid structure of the sensor is related to not only the wavelength, but also the metal used in the SPR sensor. It is interesting to see that when the wavelength is lower than 600 nm, all sensor structures do not need MoS2, which may be to blame for the high extinction coefficient of MoS2 at 400 and 600 nm, as shown in Figure 3b. Further, a comparison of sensitivity is made based on the other, similar works on 2D material-based SPR sensors, and tabulated in Table 3. From Table 3, it is clear that the proposed SPR sensor can provide a significantly higher sensitivity compared with previously published SPR sensor schemes.

Conclusions
In summary, we proposed an SPR sensor based on a 2D materials hybrid structure, and investigated the sensitivity improvement of the proposed SPR sensor in the visible region. We achieved the simultaneous optimizations of the thickness of metal (Au, Ag or Cu) and the layer number of 2D materials (graphene, MoS 2 , WS 2 and WSe 2 ) by genetic algorithm, and obtained high sensitivity in the visible region. The results indicate that the sensitivity of the proposed SPR sensor varies obviously with the wavelength of incident light, and shows a maximum value of 159, 194 or 155 • /RIU for Au, Ag or Cu respectively. In addition, an Ag-based SPR sensor exhibits a higher sensitivity than an Auor Cu-based sensor at most wavelengths in the visible region. Furthermore, the optimal number of layers of each 2D material in graphene/MoS 2 /WS 2 /WSe 2 hybrid structure also exhibits different values for the sensor with a different metal or at a different wavelength. By comparing the sensitivity and the electric field intensity of the optimized sensors at various wavelengths, we demonstrated that the sensitivity improvement in the proposed sensor is attributed to the electric field intensity enhancement. This research not only demonstrates the sensitivity enhancement of 2D material-based SPR sensors by optimizing the wavelength of incident light, but also provides a method that can realize the intelligent selection of 2D materials in a hybrid structure for sensitivity improvement.