Numerical Investigation on High-Performance Cu-Based Surface Plasmon Resonance Sensor for Biosensing Application

This numerical research presents a simple hybrid structure comprised of TiO2-Cu-BaTiO3 for a modified Kretschmann configuration that exhibits high sensitivity and high resolution for biosensing applications through an angular interrogation method. Recently, copper (Cu) emerged as an exceptional choice as a plasmonic metal for developing surface plasmon sensors (SPR) with high resolution as it yields finer, thinner SPR curves than Ag and Au. As copper is prone to oxidation, especially in ambient conditions, the proposed structure involves the utilization of barium titanate (BaTiO3) film as a protection layer that not only preserves Cu film from oxidizing but enhances the performance of the sensor to a great extent. Numerical results also show that the utilization of a thin adhesive layer of titanium dioxide (TiO2) between the prism base and Cu film not only induces strong interaction between them but also enhances the performance of the sensor. Such a configuration, upon suitable optimization of the thickness of each layer, is found to enhance sensitivity as high as 552°/RIU with a figure of merit (FOM) of 136.97 RIU−1. This suggested biosensor design with enhanced sensitivity is expected to enable long-term detection with greater accuracy and sensitivity even when using Cu as a plasmonic metal.


Introduction
The SPR sensor is found to be prominent among the various current sensing approaches owing to its reliability, rapid analysis, high sensitivity, accurate detection, and label-free detection method for chemical and biological analytes [1][2][3].This makes it possible to use the SPR sensor for various purposes, including environmental monitoring, pressure sensing [4], temperature sensing [5], medical diagnosis [6], DNA hybridization detection, discovering drugs [7], spotting molecules, glucose monitoring [8], formalin detected in the food preservatives [9], etc.The SPR method has the virtue of being able to identify even minute variations in the refractive index (RI) of the sensing medium [10].The attenuated total reflection (ATR) phenomenon is supported by the angular interrogation method, and SPR sensors frequently prefer the angular method because of its simplicity and high resolution [11].In general, plasmonic materials, including silver (Ag) and gold (Au), have been utilized in SPR sensors.As gold is invulnerable to degradation and corrosion, it is recommended as a superior plasmonic material for the SPR sensor.The drawbacks of Au are that it has low biomolecule adhesion capabilities and provides wider reflectance curves [12,13].Ag is considered a potential substitute metal since it is less expensive and application is shown in Figure 1.The RI of the first layer (BK7 prism) is 1.5151 [52].The RI of the second layer (TiO 2 ) is 2.5837 [48].The third layer (Cu) is coated on the TiO 2 layer.

Structure Description
A schematic representation of the modified Kretschmann configuration utilizing a five-layer configuration (BK7 prism, TiO2, Cu, oxide layer, and sensing layer) for biosensing application is shown in Figure 1.The RI of the first layer (BK7 prism) is 1.5151 [52].The RI of the second layer (TiO2) is 2.5837 [48].The third layer (Cu) is coated on the TiO2 layer.The dielectric constant of metal (Cu) is obtained using the Drude model and is given by Equation ( 1) where εmr and εmi represent the metal layer dielectric constant real part and imaginary part, respectively.For Cu: plasma wavelength (λp) = 0.13617 × 10 −6 m and collision wavelength (λc) = 40.852× 10 −6 m [16].The fourth layer (oxide layer) used to inhibit the oxidation of Cu metal and its RI is given in Table 1.The fifth layer is the sensing zone, whose RI is assumed to change in the range of ns = 1.33 to ns = 1.33 + δn, where δn denotes the change in RI of the sensing medium due to the adsorption of biomolecules.The range of change in refractive index (δn) for biomolecular adsorption is typically on the order of 0.005.This means that even tiny amounts of biomolecules binding to the sensor's surface can lead to detectable shifts in the SPR signal.The specific range of change in RI depends on factors like the size and mass of the The dielectric constant of metal (Cu) is obtained using the Drude model and is given by Equation ( 1) where ε mr and ε mi represent the metal layer dielectric constant real part and imaginary part, respectively.For Cu: plasma wavelength (λ p ) = 0.13617 × 10 −6 m and collision wavelength (λ c ) = 40.852× 10 −6 m [16].The fourth layer (oxide layer) used to inhibit the oxidation of Cu metal and its RI is given in Table 1.1.8233 + 0.00204i [31] The fifth layer is the sensing zone, whose RI is assumed to change in the range of n s = 1.33 to n s = 1.33 + δn, where δn denotes the change in RI of the sensing medium due to the adsorption of biomolecules.The range of change in refractive index (δn) for biomolecular adsorption is typically on the order of 0.005.This means that even tiny amounts of biomolecules binding to the sensor's surface can lead to detectable shifts in the SPR signal.The specific range of change in RI depends on factors like the size and mass of the biomolecules, the density of the immobilized ligands, and the interactions between the molecules themselves.Here, we assumed the adsorption of biomolecules occurred on the surface of the metal oxide layer, and the refractive index of the sensing medium changed from 1.33 to 1.335 [54].

Reflectance
The reflectance of incident light (p-polarized) is calculated for this multi-layer structure using the transfer matrix method [55].The tangential fields at the first boundary Z = Z 1 = 0 and the tangential fields at the last boundary Z = Z N−1 are related by where U 1 and V 1 are the tangential components of electric and magnetic fields, respectively, at the first layer boundary.U N−1 and V N−1 are the corresponding fields at the Nth layer boundary.M refers to the characteristic matrix of the N-layer model and is given by with The phase factor (q k ) and optical admittance (β k ) of the kth layer are expressed by Here, θ 1 , n 1 , and λ denote the incident angle, RI of the prism, and wavelength of the incident light (633 nm), whereas µ k , ε k , and d k represent the permeability, dielectric constant, and thickness of the kth layer, respectively.
Reflectance (R p ) and reflection coefficient (r p ) of incident light are given as Sensitivity is defined as the ratio between the resonance angle switching (δθ) and the sensing layer's RI variation (δn s ).It is given as below [13]: Even if the RI of the sensing layer is just slightly changed, the best SPR sensor will offer the largest changes in resonance angle.

Detection Accuracy (DA) or Signal-to-Noise Ratio (SNR)
The detection accuracy is inversely related to the FWHM (curve width at 50% reflectance) of the reflectance curve [13].
The exact spot of the resonance angle can be identified if the reflectance spectrum is narrow (i.e., smaller FWHM), which leads to improved detection accuracy.A figure of merit is an important criterion used to demonstrate sensitivity and FWHM impact on the sensor's performance [43].
The extent to which the field has been efficiently focused along the BaTiO 3 -analyte interface is shown by the electric field intensity enhancement factor [56,57].For p-polarized light, the EFIEF is the ratio of the square of the electric field (E) or magnetic field (H) at the oxide layer/analyte interface to the square of the field E or H at the prism/TiO 2 interface.EFIEF is expressed by the where t is indicated as the transmission coefficient and ε 1 and ε N are denoted as the dielectric constants of the first layer and the Nth layer, respectively.

Results and Discussion
The Fresnel formula and the transfer matrix method are implemented to properly assess all functional parameters.A proper covering layer strategy is required to avoid a Cu-based SPR sensor showing degraded performance due to the oxidation effect of Cu.Here, we suggested to use three different oxide coatings, namely BaTiO 3 , Fe 2 O 3 , and MoO 3 , over Cu to inhibit its oxidation effect [30,38,40], and the proposed model also includes a thin layer of TiO 2 as an adhesive that strongly binds Cu on the prism base [45,[47][48][49][50].The thickness of every layer is well optimized, which leads to achieve high sensitivity, the lowest minimum reflectance (R min ), and the thinnest FWHM of the resonance curve [58].Here, we meticulously examined the role that each layer plays in the proposed configuration.
Initially, we investigated the effect of BaTiO 3 on copper and found out its optimized thickness to achieve the best sensing performance.Figure 2a shows the change in sensing parameters (sensitivity, R min , and FWHM) corresponding to the change in the Cu layer thickness in the range of 20 nm to 60 nm for 5 nm BaTiO 3 protection coating on the copper layer.It is observed that the FWHM and R min values of the SPR dip decrease as the Cu layer thickness increases, whereas the sensitivity is observed to increase from 120 • /RIU to 132 • /RIU.It is also noted that the sensor performance is better for the 55 nm thickness of the copper layer as the resonance curve R min value is closer to zero (0.013), with sensitivity around 132 • /RIU, and the FWHM as small as 0.72 • .Further examining the same configuration using a 10 nm thickness of BaTiO 3 cover over the Cu layer, 55 nm thickness of Cu again shows maximum sensitivity (178 • /RIU) with R min as 0.009 at 1.33RI and 0.0081 at 1.335RI, and the FWHM value as 1.23 • .It is also observed that further increasing the thickness of BaTiO 3 to 15 nm, the 45 nm Cu layer shows an R min value close to zero and exhibits high sensitivity of about 486 • /RIU with the FWHM of the resonance curve increased to 4.27 • .From the above three cases, it is observed that 15 nm BaTiO 3 coated on a 45 nm Cu layer provides excellent sensing capability and hence it is considered for further optimization.
In the next phase of optimization, the impact of utilizing TiO 2 adhesive film between the BK7 prism and the Cu layer is analyzed.Figure 3 shows the same as Figure 2 but for sandwiching a 5 nm thickness of TiO 2 as an adhesive layer between the prism and Cu film.Here, it is observed that the maximum sensitivity achieved for 5 nm and 10 nm of BatiO 3 cover layers are 132 • /RIU and 180 • /RIU, corresponding to the thickness of the Cu layer as 55 nm for both cases.Though the sensitivity remains almost the same as in the previous cases without the TiO 2 adhesive layer (Figure 2a,b), the FOM for these cases are improved  2. Figure 3c shows that upon utilizing a 15 nm thickness of BaTiO 3 , the maximum sensitivity around 552 • /RIU with FOM around 136.97 RIU −1 is achieved for a 45 nm thickness of Cu.This is because the TiO 2 layer induces a significant SPR effect when joined with metal as it assists in enhancing surface plasmons (SPs) at the metal/prism interface and hence improves sensitivity and reduces SP damping (FWHM) [59].In the next phase of optimization, the impact of utilizing TiO2 adhesive film between the BK7 prism and the Cu layer is analyzed.Figure 3 shows the same as Figure 2 but for sandwiching a 5 nm thickness of TiO2 as an adhesive layer between the prism and Cu film.Here, it is observed that the maximum sensitivity achieved for 5 nm and 10 nm of BatiO3 cover layers are 132°/RIU and 180°/RIU, corresponding to the thickness of the Cu layer as 55 nm for both cases.Though the sensitivity remains almost the same as in the thickness of BaTiO3, the maximum sensitivity around 552°/RIU with FOM around 136.97 RIU −1 is achieved for a 45 nm thickness of Cu.This is because the TiO2 layer induces a significant SPR effect when joined with metal as it assists in enhancing surface plasmons (SPs) at the metal/prism interface and hence improves sensitivity and reduces SP damping (FWHM) [59].In the following phase, we examined the sensor performance for Fe 2 O 3 protection layer situated over Cu layer.From Figure 4, we found that R min close to zero are obtained at 55 nm, 50 nm, and 45 nm thickness of Cu corresponding to 5 nm, 10 nm, and 11 nm Fe 2 O 3 layer.The calculated sensitivities are 142°/RIU, 282°/RIU, 406°/RIU with FOM as 1 RIU −1 , 85.97 RIU −1 , and 78.07 RIU −1 , respectively.Moreover, we also analyzed the effe the MoO3 cover layer on Cu film.
Figure 5 shows that for the MoO3 layer with thicknesses 5 nm, 10 nm, and 27 nm Rmin values reach values close to zero corresponding to thicknesses of Cu film as 55 50 nm, and 45 nm, respectively.For these cases, the sensitivity obtained is 118°/ 130°/RIU, and 386°/RIU with the corresponding FOM calculated as 203.4 RIU −1 , 1 RIU −1 , and 104.89RIU −1 , respectively.In the above three cases, the BaTiO3 layer ach maximum sensitivity as it possesses a large real part of the dielectric constant wit imagery part.So, it is the most suitable covering layer when compared to other o layers for the proposed sensor.Thus, we optimize that the 45 nm Cu sandwi between 5 nm TiO2 and 15 nm BaTiO3 outer cover is a better configuration that achi sensitivity and FOM as high as 552°/RIU and 136.97 RIU −1 , respectively, and the effec each oxide layer (BaTiO3, Fe2O3, and MoO3) is also compared in Table 2.The calculated sensitivities are 142 • /RIU, 282 • /RIU, 406 • /RIU with FOM as 147.9 RIU −1 , 85.97 RIU −1 , and 78.07 RIU −1 , respectively.Moreover, we also analyzed the effect of the MoO 3 cover layer on Cu film.
Figure 5 shows that for the MoO 3 layer with thicknesses 5 nm, 10 nm, and 27 nm, the R min values reach values close to zero corresponding to thicknesses of Cu film as 55 nm, 50 nm, and 45 nm, respectively.For these cases, the sensitivity obtained is 118 • /RIU, 130 • /RIU, and 386 • /RIU with the corresponding FOM calculated as 203.4 RIU −1 , 173.3 RIU −1 , and 104.89RIU −1 , respectively.In the above three cases, the BaTiO 3 layer achieves maximum sensitivity as it possesses a large real part of the dielectric constant with no imagery part.So, it is the most suitable covering layer when compared to other oxide layers for the proposed sensor.Thus, we optimize that the 45 nm Cu sandwiched between 5 nm TiO 2 and 15 nm BaTiO 3 outer cover is a better configuration that achieves sensitivity and FOM as high as 552 • /RIU and 136.97 RIU −1 , respectively, and the effects of each oxide layer (BaTiO 3 , Fe 2 O 3 , and MoO 3 ) is also compared in Table 2.The thickness of the oxide layer plays a critical role in the suggested sensor; thus, we carried out an extensive study to ensure the best possible value, as illustrated in Figure 6.It is noticed that the reflectance spectrum moves to a greater incidence angle as the thickness of the outer layer (BaTiO3, MoO3, and Fe2O3) increases.It is also noted that for 15 nm of BaTiO3, 27 nm of MoO3, and 11 nm of Fe2O3, the Rmin obtained is almost zero, and such condition is much favored for maximum conversion of incident light energy into surface plasmons.Further increasing of thickness above the previously prescribed values for all three cover layers Rmin values increases because the rate of light utilization reduces as the oxide layer thickness increases.The thickness of the oxide layer plays a critical role in the suggested sensor; thus, we carried out an extensive study to ensure the best possible value, as illustrated in Figure 6.It is noticed that the reflectance spectrum moves to a greater incidence angle as the thickness of the outer layer (BaTiO 3 , MoO 3 , and Fe 2 O 3 ) increases.It is also noted that for 15 nm of BaTiO 3 , 27 nm of MoO 3 , and 11 nm of Fe 2 O 3 , the R min obtained is almost zero, and such condition is much favored for maximum conversion of incident light energy into surface plasmons.Further increasing of thickness above the previously prescribed values for all three cover layers R min values increases because the rate of light utilization reduces as the oxide layer thickness increases.The performance of the SPR biosensor is also determined by field distribution at the interface of the metal/dielectric interface.The interaction between the evanescent field and the biomolecule in the sensing medium is crucial.There is more biomolecular interaction when the field dispersion is improved [56,57]. Figure 7 shows that the EFIEF decreases when the sensing medium RI changes from n s = 1.33 to n s = 1.335.This is because biomolecules strongly bind to the detection surface of the biosensor.The electric field distributions of the optimized configuration of the structure TiO 2 -Cu-BaTiO 3 is shown in Figure 8.It is noted that the electric field intensity at the interface of Cu-BaTiO 3 is increasing and reaches its peak at the interface of BaTiO 3 and the sensing medium.In this proposed structure, the numerical value of the probing field is much more intense in the sensing medium, which leads to a stronger excitation of SP waves, resulting in enhanced sensitivity.Comparing this proposed structure to prior published similar sensors structures, the sensing output is much higher and is compared with others in Table 3.

Conclusions
This numerical work demonstrates a highly sensitive SPR biosensor with a hybrid configuration made of layers of TiO2, Cu, and BaTiO3/Fe2O3/MoO3.The thickness of the suggested layers (TiO2, Cu, and BaTiO3/Fe2O3/MoO3) is carefully tuned to achieve distinctly higher sensitivity as well as FOM.Here, the utilization of the adhesion layer of TiO2 enhances light trapping capability, which, in turn, also enhances the sensitivity of

Conclusions
This numerical work demonstrates a highly sensitive SPR biosensor with a hybrid configuration made of layers of TiO 2 , Cu, and BaTiO 3 /Fe 2 O 3 /MoO 3 .The thickness of the suggested layers (TiO 2 , Cu, and BaTiO 3 /Fe 2 O 3 /MoO 3 ) is carefully tuned to achieve distinctly higher sensitivity as well as FOM.Here, the utilization of the adhesion layer of TiO 2 enhances light trapping capability, which, in turn, also enhances the sensitivity of the suggested sensor.This proposed structure, when using BaTiO 3 as a covering layer, attains high sensitivity (552 • /RIU) as well as high FOM (136.97RIU −1 ) when compared to Fe 2 O 3 (406 • /RIU and 78.07 RIU −1 ) and MoO 3 (386 • /RIU and 104.89RIU −1 ) for the optimized thickness of 45 nm Cu sandwiched between 5 nm TiO 2 and 15 nm BaTiO 3 outer cover.The proposed structure is expected to enable long-term detection with greater accuracy and sensitivity even when using Cu as a plasmonic metal.This study offers a novel possibility for the development of a more accurate and highly sensitive biosensor for biological sensing uses.

3 .
Figure of Merit (FOM) or Quality Factor (Q) 3 RIU −1 and 156.5 RIU −1 due to a reduction in the FWHM of the resonance spectrum, as shown in Table

Figure 7 . 17 Figure 8 .
Figure 7. Incidence angle vs. electric field intensity enhancement factor at n s = 1.33 and n s = 1.335 for the proposed TiO 2 -Cu-BaTiO 3 optimized configuration.Sensors 2023, 23, x FOR PEER REVIEW 14 of 17

Figure 8 .
Figure 8.The electric field intensity distributions of the optimized TiO 2 -Cu-BaTiO 3 -based structure for n s = 1.33.

Table 1 .
Refractive index of the oxide layers at λ = 633 nm.

Table 1 .
Refractive index of the oxide layers at λ = 633 nm.

Table 2 .
The oxide layers attain the best results (R min , FWHM, sensitivity, and FOM) at the optimized thickness of Cu layer.

Table 3 .
The comparison of the proposed structure to the similar type of former reported SPR sensor structure.