2D-layers coupled with metal nitrides as efficient plasmonic materials in surface plasmon resonance sensor: Gold-level performance and urine glucose detection

2.1 Device structure

The SPR sensor structures considered are based on the Kretschmann prism-coupling configuration shown in Fig. 1(a). The sensor consists of a prism of refractive index n_P coated with a plasmonic thin layer of thickness d_m and complex dielectric constant $\epsilon ={\epsilon }_m^{\text{'}}+i{\epsilon }_m^{"}$. In this work, we consider Au, TiN, and ZrN as plasmonic materials. The dielectric SM of dielectric constant is ${\epsilon }_S=n_S^2$ (n_S is the refractive index), then comes above the plasmonic layer. The sensor is illuminated by a TM-polarized laser source with a wavelength of 633 nm from one side of the prism. The sensor mechanism is based on angular interrogation, where the incident angle of light (q) is varied and the reflected light is detected from the opposite side of the prism at each incident angle. When the incident angle (q) exceeds the critical angle at the boundary between the prism and plasmonic layer, an evanescent wave is generated at the top side of the prism, which penetrates the thin plasmonic layer and generates a surface plasmon wave at the boundary between the plasmonic medium and the SM. In this case, the reflection of light is controlled by the difference between the refractive indices of the prism and SM. At a specific incident angle called “resonance angle q_RES”, SPR occurs at which the incident light is coupled and most absorbed and the field is most enhanced at the plasmonic layer-SM interface. This resonance is recorded as a dip in the reflection profile, noted as a minimum reflection level R_min (Kumar et al., 2020; Brahim et al., 2021). At this angle θ_RES, the propagation constant of light in the prism matches the transverse component of the surface plasmonic wave, which is mathematically formulated as(Sharma et al., 2018):

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Fig. 1.

A scheme of the Kretschmann sensor-coupling sensor under investigation: (a) using a plasmonic material of TiN, ZrN, or Au, and (b) adding a 2D-layer.

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Therefore, the SPR angle is determined from the optical constants of the prism, plasmonic layer, and SM as:

Seeking improvement of the sensor performance, other sensor configurations are tried using 2D materials, as seen in Fig. 1(b). A 2D-layer of dielectric constant ε_2D and thickness d_2D is inserted between the plasmonic layer and SM. The 2D materials used include G, BP, MXene, h-BN, and MoSe₂.

2.2 Transfer-matrix model of light reflection

The value of the power reflection is calculated using the matrix method of a multilayer structure. Considered as an N-layered multilayer system, the tangential components of the transverse-magnetic (TM) at the first boundary are related to those at the final boundary along the propagation axis (Hasib, et al., 2018). The Fresnel coefficients of reflection r_p, and transmission, t_p, for the p-wave of the incident light are given as functions of the incident angle q as:

and the power reflectivity and field enhancement of the prism configuration are given by (Rok et al., 2010):

where Mnm are the elements of the following 2×2 matrix

$M_{ij}={\prod }_{k=2}^{N-1}{M}_k=\left(\begin{array}{cc}{M}_{11}& M_{12}\\ M_{21}& M_{22}\end{array}\right)$

The M_k-matrix of the k^th layer is determined by its optical properties as (Nguyen et al., 2010):

with

2.3 Performance parameters of the SPR-Sensor

The profile of reflection R versus incident angle q is used to evaluate the sensor performance. The performance metrics include sensitivity (S), DA (DA), and QF. The variation in the resonance angle, $\Delta {\theta }_{res}$, that corresponds to a certain variation in the refractive index, $\Delta$n, of the SM decides the sensitivity S as (Gumaih et al., 2024; El Barghouti., 2022):

The full width at half-maximum (FWHM) of the reflection profile around the dip that occurs at the resonance angle q _RES decides the DA of the sensor as

The QF of the sensor is defined as the sensitivity per unit FWHM,

This QF is commonly used as the FOM of SPR sensors (Gumaih et al., 2024;Hiramatsu N et al., 2017).

3.1 Material parameters

In this study, seven types of prisms are used to design the prism configurations under investigations: namely, BK7, BAK1, BAF10, SF5, SF10, SF11, and LASF9. Table 1 lists the refractive index n_P of the prism used at the sensor wavelength of 633 nm, arranged in an ascending manner (Didar et al., 2024).

We applied the Drude-Lorentz model to describe the dielectric function of the plasmonic materials Au, TiN, and ZrN, including many N oscillators as follows (Cheng et al., 2024; Vertchenko et al., 2019):

where ${\epsilon }_b$ is the background dielectric constant from the core electrons’ contribution, ${\epsilon }_{Drude}\left(\omega \right)$ and ${\epsilon }_{Lorentz}\left(\omega \right)$ are the intraband and interband transition parts. The plasma frequency (${\omega }_p)$ and the scattering rate (γ_p) are associated with the intraband transitions. The plasma frequency is proportional to free electron density and inversely proportional to the electron effective mass (Cheng et al., 2024). $A_k$ is the amplitude of the contributing k^th-oscillator and is equal to $A_k=\sqrt{f_k}{\omega }_k$, where $f_k$ is the oscillator strength and ${\omega }_k$ is the oscillator frequency. g_p is the damping rate of the k^th- interband transition (Gharbi et al., 2020). The parameters of the TiN films deposited at 800°C are ${\epsilon }_{\infty }$ =4.855, ${\omega }_p$=7.9308eV, ${{\rm Y}}_p$=0.1795eV, $f_1$=3.2907, ${\omega }_1$= 4.2196eV, ${{\rm Y}}_1$=2.0341. The parameters of the ZrN are taken as ${\epsilon }_{\infty }$=3.4656$, {\omega }_p$=8.018eV, ${{\rm Y}}_p$=0.5197eV, $f_1$=2.4509, ${\omega }_1$= 5.48eV, ${{\rm Y}}_1$=1.7369eV (Naik et al., 2012). The Values of the parameters characterizing the dielectric constants of gold are ${\epsilon }_{\infty }$ =1, ${\omega }_p$ =9.03eV, $f_0=0.760,$ ${{\rm Y}}_0$ =0.053eV, ${\omega }_1$ = 0.415eV, ${{\rm Y}}_1$ =0.241eV, ${ƒ}_1=$0.024, ${\omega }_2=0.830$eV, ${{\rm Y}}_2=0.345eV$, $f_2=$0.010, $f_3=0.071,{\omega }_3=$2.969eV, ${{\rm Y}}_3=$0.870eV, $f_4$=0.601, ${\omega }_4=4.304eV, {{\rm Y}}_4=2.494,eV, {ƒ}_4=$0.601, $f_5=$4.384, ${\omega }_5=$13.32eV, ${{\rm Y}}_5=$2.214eV (Rakic et al., 1998).

On the other hand, the 2D-materials used in this study to improve the sensor performance include BP, graphene, h-BN Mxene, MoSe₂. For the graphene layer, the relative dielectric function takes the form of (Matthaiakakis et al., 2016):

${\epsilon }_G=5.5+\frac{i}{2\pi c{\epsilon }_0}\frac{\lambda {\sigma }_{tot}}{d_G}6.913i$

where s_tot is the total optical conductivity taking into account the intraband and interband transitions, c and ${\epsilon }_0$ are the speed of light and permittivity in free space, respectively, and d_G = 0.34nm is the thickness of the graphene layer. s_tot is given using the Kubo formula in (Matthaiakakis et al., 20216; KravetsVG et al., 2010). By using Fermi energy (chemical potential) of 0.3eV, temperature 300K, and hopping parameter equal to 2.7eV, the dielectric constant at wavelength of 633nm is equal to ${\epsilon }_G=5.124+6.913i$.

BP exhibits strong in-plane optical anisotropy and polarization/orientation-dependent absorption. The refractive index of the BP layer of thickness d_BP = 0.53 nm at λ = 633 nm is obtained from the experimental measurement in (Mao N et al., 2015) as 3.5 + 0.01i. This value is an average of the (ZZ) and (AC) orientations for use in this metric's calculation (Wu L, et al., 2017). Thus, the dielectric constant of the BP layer is ${\epsilon }_{BP}=3.5+0.07i$. For MoSe2, h-BN, and MXene, the values of the dielectric constant and thickness of a single layer have been listed in Table 2 at the wavelength of λ = 633 nm.

3.2 Numerical procedures

The above material parameters were computed and used to calculate the M-polarized reflectance using the N-layer transfer-matrix method at oblique incidence, as given in subsection 2.2. For the three sensor structures using Au, TiN, and ZrN layers, the incident angle was scanned from 40° to 90° in 0.01° steps, and the reflection dip R_min, SPR angle q_SPR, and FWHM were calculated. The calculations were done over a range of the refractive index of the SM of n_S = 1.330 ∼ 1.335, and the corresponding variation Dq_SPR of SPR-angle was determined. The thickness of the plasmonic layer, d_m, was optimized to achieve the maximum sensitivity. The corresponding DA and QF were then calculated using equations (11) and (12), respectively. These steps were executed for the proposed sensor configurations by adding a 2D-layer above the plasmonic layer, and the obtained results of the performance metrics were compared. A Mathcad (ver. 15) code was developed to execute the present calculations.

4.1 Surface plasmonic performance of Au, TiN, and ZrN

It is worth gaining insight into the performance of surface plasmonics of the metal nitrides (TiN and ZrN) and comparing with gold as a benchmark of noble plasmonic material. The performance of the plasmonic layer is evaluated in terms of QF (Q_SPP), propagation length along the interface between the layer and SM (L_SPP), and the penetration depth (d_d) into the SM. Q_SPP is given by the real and imaginary parts of the dielectric constant e_m (Rakib AKM et al., 2023):

The propagation length L_SPP of the SP wave is determined by the imaginary part of the wavevector b_SPP as (Hiramatsu et al., 2016):

The penetration depth (d_d) into the SM depends on the wavelength of the incident laser beam l and is given as (Barnes et al., 2006):

Table 3 lists the values of Q_SPP, ${\delta }_d$, and $L_{SPP}$ of the three materials at the sensor wavelength of l = 633nm. The table indicates that the highest value of QF is for gold, Q_SPP = 48.27, while the smallest value corresponds to TiN, Q_SPP = 21.479. On the other hand, the value of Q_SPP of gold is twice as large as the value of ZrN. The field penetration depth in the metal remains virtually constant, while the field penetration depth in the SM is markedly enhanced, facilitating a considerably greater probe depth. The values of the penetration depth ${\delta }_d$ ​​are comparable for Au and ZrN, and both are larger than the value for TiN. In a similar manner, the value of the propagation length $L_{SPP}$ is highest in gold (1616nm), smaller in ZrN (983.63nm), and smallest in TiN (725.56nm). It is worth noting that these calculated values of the plasmonic properties of TiN and ZrN are large enough to qualify them for use in SPR applications.

4.2 Performance of Au, TiN, and ZrN-based sensors

This subsection elaborates on the performance of the Kretschmann configuration, deploying a single plasmonic layer among Au, ZrN, and Au in addition to a BK7 prism and water (n_S = 1.330) as the SM. Figs. 2(a-c) depict the (reflection R versus incident angle q) profile for three values of the refractive index of the SM of n_S = 1.330, 1.335, and 1.340. The plasmonic layer thickness is optimized to yield the highest sensitivity, resulting in values of d_m = 50, 39, and 39nm for Au, TiN, and ZrN, respectively. Figs. 2(d-f) plot the corresponding variation of the field enhancement.

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Fig. 2.

(a,b,c) Reflection and (e,d,f) field enhancement of BK7-prism/(Au, TiN, or ZrN)/SM sensors vs. refractive index n_S of SM.

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In all figures of reflection, the reflection is almost flat at the regime of small angles and then exhibits an edge before dropping to a dip R_min at the resonance angle ${\theta }_{SPR}$ at which the SPR is excited. This edge corresponds to the total internal reflection and corresponds to the critical angle (θ_c), i.e., the angle at which total reflection depends solely on the difference of the dielectric constants of the two infinite media: prism and SM. Because these values are the same for the three sensors, θ_c is fixed at 63^o. Both the resonance angle ${\theta }_{SPR}$ and the corresponding value of minimum reflection R_min are the quantities to be determined. This angular position ${\theta }_{SPR}$ is determined by the optical constants of the prism, SM, and the type of metal, as given in equation (2). The values of the SPR angle are θ_SPR = 74.901^o, 80.203^o, and 72.243^o for the Au, TiN, and ZrN-based sensors, and the corresponding values of the reflectance dip are R_min = 0.099, 0.049, and 0.032, respectively. These dips must not be zero, i.e., the plasmon must not always touch the zero line. This depends quite critically on the thickness of the metal layer. The FWHM corresponds to the half-value of the flat (edge) reflectance and is to be determined to evaluate the performance metrics DA and QF, as given in equations (11) and (12), respectively. This FWHM depends on the imaginary part ${\epsilon }_m^{\text{'}\text{'}}$ of the dielectric constant of the metal e_m. As indicated in Table 3, the values of the imaginary parts are ${\epsilon }_m^{\text{'}\text{'}}$ = 1.967, 2.592, and 3.912 for Au, TiN, and ZrN, respectively, which then explain the reason why the gold sensor appears sharper (FWHM = 9.4^o) and narrower than the TiN sensor (FWHM = 14 deg) and the ZrN sensor (FWHM = 13 deg). Although Figs. 2(d-f) indicates that the field enhancement at the resonance angle θ_SPR is largest for the Au sensor (4.8), and comparable for the TiN (3.38) and ZrN sensors (3.68), the difference is not big. That is, the metal nitride-based sensors yield field enhancement at the interface with the SM comparable to that of the noble metal Au.

The sensitivity of the sensor to the variation of the refractive index n_S of the SM is seen in Figs. 3(a) and (b) as not only a shift of the reflection dip to higher values of θ_SPR but also a decrease in the value of the minimum reflection R_min. The angle shift is Dθ_SPR = 0.63^o, 0.63^o, and 0.49^o, and the rise-up of the reflection dip is DR_min = 0.003, 0.017, and 0.002 for the Au, TiN, and ZrN sensors, respectively. That is, the three sensors are sensitive to the variation in the optical properties of the SM.

In Figs. 3(a,b), we plot the variation of the resonance angle θ_SPR and the frequency dip R_min with the refractive index n_S of the SM in the range between 1.330 and 1.340, which is appropriate for applications in biological sensors (Uwais et al., 2023) and gas sensors (Elsayed HA et al., 2024; Xu Y et al., 2019). The figures show that the dynamic ranges of the sensors, i.e., the range of the angle variation that corresponds to the range of the refractive index Dn_S, are Dθ_SPR =1.86, 1.54, and 1.33 deg for the Au, TiN, and ZrN-based sensors, respectively. Interestingly, both θ_SPR and R_min vary linearly with n_S for the three sensors. The proposed SPR sensors demonstrate high linear characteristics for sensing the refractive index variation. The slope of variation of θ_SPR in Fig. 3(a) decides the optical sensitivity, as given in equation (10). The values of the sensitivity for the Au, TiN, and ZrN sensors are 167.4, 155.3, and 131 deg/RIU, respectively. That is, the sensitivity of the metal-nitride (TiN and ZrN) sensors is 12 ∼ 36 deg/RIU lower than that of the Au sensor. The sensitivity of the TiN-based sensor is about 24deg/RIU higher than that of the ZrN-based sensor. Also, we can determine the sensitivity based on the variation of R_min (in reflection units RIU) in Fig. 4. The slope of this relationship is 1.96, 1,13, and 0.62 reflection units/RIU. These values of sensitivity are much smaller than the angle-based optical sensitivity.

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Fig. 3.

Variation of (a) the SPR angle θ_SPR, and (b) minimum reflection, of BK7-prism/(Au, TiN, or ZrN)/SM vs. refractive index of SM.

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Fig. 4.

(a) Sensitivity, (b) DA, and (c) QF of the BK7-prism/Au/SM, BK7-prism/TiN/SM, and BK7-prism/ZrN/SM.

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The calculated values of the sensitivity (S), DA, and QF of the three sensors deploying Au, TiN, and ZrN layers have also been listed in Table 4, and plotted in Figs. 4(a-c), respectively. While the QF of the gold sensor is QF = 17.8 RIU^-1, and it is almost twice the value of the TiN and ZrN sensors, the values of DA are comparable, DA(Au) = 0.107 deg^-1, whereas those of the TiN and ZrN sensors are DA = 0.071 and 0.077 deg^-1, respectively. Although the values of the performance metrics of the noble metal (Au) based sensors are larger than those of the metrics of the metal nitride (TiN and ZrN) based sensors, the estimated values of the latter sensors are appropriate for applications. It is worth mentioning that the previous research on the performance metrics of Kretschmann SPR sensors based on metal nitrides as the main plasmonic material was minor either in experiment or theory. The estimated values of the QF agree with the values of 12.17 and 17.93 RIU^-1 estimated (Surre et al., 2019) for TiN and ZrN sensors using a sapphire prism when the excitation wavelength is 1300 nm. They also reported that the dielectric-constant sensitivity of TiN sensors is better than that of ZrN sensors. The performance of metal nitrides in SPR sensors could be improved by integration with noble metals. Mukhtar and Nuraddin assessed the performance of the Kretschmann sensor using hybrid layers of Ag/TiN and Ag/ZrN for glucose and sucrose detection, pointing out that adding well-controlled layers of TiN and/or ZrN to the Ag surface results in increasing the sensitivity and QF (Mukhtar&Nuraddin.,2021).

The TiN Drude-Lorentz parameter set used in the above calculations corresponds to sputtered TiN films parameterized near the visible with one Drude and interband Lorentz terms (Naik et al., 2013). Such parameterizations are standard and comparable to datasets compiled for plasmonic TiN in the 1.5-2.2 eV range where interband loss onsets appear around 2.1-2.4 eV and 3.5-3.8 eV (Jude K et al., 2021) and are consistent with ellipsometric extractions across multiple stoichiometries and growth conditions (Patsalas et al., 2015). Comparable reviews report the same interband structure and showed ${\epsilon }_m^{\text{'}}$ and ${\epsilon }_m^{\text{'}\text{'}}$ at 633 nm span ranges depending on the degree of stoichiometry and scattering rate, which then underscores the need to bound ε_m in uncertainty analysis. From the literature spread, we adopt ε_r ∈ [−6, −10] and ε₂ ∈ (Patsalas et al., 2015; Naik et al., 2012) at 633 nm as measured variability across deposition methods/stoichiometry near 633 nm in literature (Jude K et al., 2021; Patsalas et al., 2015; Chris-Okoro et al., 2025; Naik et al., 2012; Chang et al., 2019; Patsalas et al., 2015; Polyanskiy et al., 2024). Within these bounds, θ_SPR shifts by roughly 0.5-1.1 deg for the BK7-prism/TiN/water stack, and FWHM broadens with higher ${\epsilon }_m^{\text{'}\text{'}}$ by ≈1-2 deg. These variations map to S changes of about ±6 – 10 deg/RIU, DA changes of about −0.008 to −0.012 deg⁻¹, and QF changes of about −1.0 to −2.0 RIU⁻¹ relative to the nominal TiN results reported. Using compiled datasets of ZrN, we adopt ε_r ∈ [−9, −12] and ε_i ∈ [2.7, 4.2] for ZrN near 633 nm (magnetron sputtered and reactive conditions) (Shabani et al., 2021; Vallejo et al., 2023). For BK7-prism/ZrN/water, the corresponding θ_SPR varies by ≈ 0.4-0.9 deg, FWHM by ≈ 0.8-1.6 deg, translating to S variations of about ±5-8 deg/RIU, DA variations of −0.006 to −0.010 deg⁻¹, and QF variations of −0.8 to −1.6 RIU⁻¹ around the nominal ZrN values. Even under the pessimistic ends of ε_m ranges for TiN and ZrN, the rank ordering Au > TiN ≳ ZrN for QF at 633 nm holds, because the increase of ${\epsilon }_m^{\text{'}\text{'}}$ broadens the resonance more for nitrides than for Au, in line with nitrides’ lower plasmonic QF at 633 nm in Table 1. Thus, the qualitative comparison trends remain intact within the stated ε_m variability.

Generalization of the present results of the TiN and ZrN-based sensors requires simulation of the sensor results at other wavelength regimes, especially the NIR range, for example, in vivo biosensing and medical applications in the biological window I (700–900nm) and II (1000–1700nm) (S. Moustafa et al., 2024). These calculations would be our next step of research.

4.3 Impact of prism material on sensor sensitivity

In this subsection, we have the interest to examine the amount of variation in the sensor sensitivity associated with varying the type of the prism as a principal component of the Kretschmann sensor. In Figs. 5(a-c) we plot the values of the sensitivity of the Au, TiN, and ZrN-based sensors, respectively, using seven types of prisms of BK7, BAK1, BAF10, SF5, SF10, SF11, and LASF9 with refractive indices listed in Table 1. The figures indicate that for the three sensors, the sensitivity decreases with the increase of the refractive index of the prism. That is, the BK7 prism records the highest sensitivity, while the LASF9 and SF11 prism reveals the smallest values of sensitivity. These results agree with the results obtained by Didar et al., who observed that for the BK7 prism with a lower RI, the sensitivity of this sensor is highest, and for the SF11 prism with a higher RI, the sensitivity of the sensor is lowest. The authors (Singh S et al., 2021) compared the sensor performance parameters among different prisms of CaF₂, BK7, FK51A, and SF10 coupled with a hybrid structure. The highest sensitivity was achieved for the CaF₂ prism with the smallest refractive index.

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Fig. 5.

Sensitivity of (a) Prism/Au/SM, (b) Prism/TiN/SM, and (c) Prism/ZrN/SM versus refractive indices for different types of prisms.

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4.4 Influence of adding 2D-layers on the performance of Au, TiN, and ZrN-based sensors

Adding a 2D layer has been found to improve the adhesion and combination of the sensor to biomolecules (Lin Z et al., 2016) or gases (Verma R et al., 2011). In this section, we quantify the impact of adding a 2-D atomic layer of different materials on the performance metrics of the three considered sensors of BK7-prism/Au, TiN, or ZrN)/SM configuration. The 2D-layer is supposed to cover the plasmonic layer and be attached to the SM. We consider graphene as the first 2D-layer developed, and four candidates from the 2D-families, such as h-BN, TMDs, MXene, and BP. The values of the real and imaginary parts of the dielectric constant e_2D and thickness d_2D of the used 2D layers have been listed in Table 2.

The calculated values of the performance metrics of the SPR-sensors: BK7-prism/Au/2D-layer/SM, BK7-prism/TiN/2D-layer/SM, and BK7-prism/ZrN/2D-layer/SM; namely, sensitivity, DA, and quality factor, are listed in Table 5. Figs. 6-8 are developed also for visual comparison of these performance metrics among the three configured sensors. As shown in Table 5 and Fig. 7(a), the sensitivity of the Au-based sensor is most increased (5 deg/RIU units, or 3.1%) with the addition of either the h-BN or BP layer. While the addition of graphene results in the increase of sensitivity by less than one unit, the sensitivity does not change when adding the MXene layer and even decreases to 166deg/RIU^-1 with adding the MoSe2 layer. On the other hand, while Fig. 7(b) shows that DA does not improve with the addition of the 2D-layers, Fig. 7(c) indicates an increase of QF = SxDA to 18.0RIU^-1 (1.2%) with the addition of the h-BN layer, and the next value of 17.9RIU^-1 corresponds to the BP layer.

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Fig. 6.

Dependence of (a) sensitivity, (b) DA, and (c) QF of the sensor configuration BK7-prism/TiN/2D-layer/SM on addition of 2D-layers.

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Fig. 7.

Dependence of (a) sensitivity, (b) DA, and (c) QF of the sensor configuration BK7-prism/Au/2D-layer/SM on addition of 2D-layers.

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Fig. 8.

Dependence of (a) sensitivity, (b) DA, and (c) QF of the sensor configuration BK7-prism/ZrN/2D-layer/SM on addition of 2D-layers.

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Figs. 6(a-c) of the sensor configuration of BK7-prism/TiN/2D-layer/SM and the corresponding data listed in Table 5 indicate that all metrics, including S, DA, and QF, do not improve with the addition of the 2D-layers. These metrics do not even maintain their value without the 2D layers. The value of S = 153deg/RIU closed to the original values (155.3deg/RIU) is predicted by the integration of the h-BN layer.

In the case of the sensor configuration of BK7-prism/ZrN/2D-layer/SM, Fig. 8(a) and the data listed in Table 5 indicate that the sensitivity most increases from 131 to 140deg/RIU (an increase of 9deg/RIU, or ∼7%) by adding either MXene, BP, or h-BNlayer. While the graphene layer results in a sensitivity increase of 7deg/RIU (5%), adding the MoSe₂ layer causes keeps the sensitivity without changes. Fig. 6(b) shows that the DA does not improve by adding the considered 2D-layers, which indicates that the addition of the 2D-layers caused broadening of the reflection profile. The smallest drop of DA corresponds to the BP and h-BN layers while the largest drop corresponds to the MXene layer. Fig. 6(c) indicates that the QF (QF) increases most by adding the BP layer; it increases from 10.0 to 10.75RIU^-1 (7.5% increase), and the next increase to 10.7RIU^-1 (5% increase) corresponds to the h-BN layer. While there were no previous studies on the impact of 2D-layers on SPR sensors with TMNs as the main plasmonic layer, the obtained metrics of the Au-based sensor are in good agreement with some previous studies. Srivastava et al. reported on improvement of the sensitivity of an Au-based sensor from 164.4 to 178.76 by supporting the structure by a BP layer, which fits well with our prediction (Srivastava et al., 2019). The authors (Lin Z et al., 2016) optimized an Au-based sensor using layers of G and MoSe₂ and obtained sensitivity as high as 182^o/RIU. The authors (Ouyang et al., 2019) reported on the improvement of 12% in the sensitivity of 663nm-prism/Au/SM sensor structure by adding a layer of WS₂. Finally, experimental studies have demonstrated that graphene-enhanced SPR sensors can achieve sensitivities of 165°/RIU for Au-based systems and 162°/RIU for Ag-based configurations (Hamid et al., 2015).

4.5 Detection of glucose concentration in the urine samples

The World Health Organization research states that millions of people worldwide suffer from diabetes, and the disease claims the lives of approximately 1.5 million people annually. Glucose concentration in urine is typically expressed as a concentration, often measured in milligrams per deciliter (mg/dL). Normally, the kidneys filter and reabsorb glucose from the blood, so that very little or no glucose is excreted in the urine (Kumar et al., 2025; Srivastava et al., 2019). Because glucose imbalance has been linked to heart disease, stroke, kidney damage, and eye illness, it is vital to measure and control the glucose concentration (Ma Y et al., 2023). Fortunately, the refractive index of urine varies with the change in glucose content, and the SPR sensor can measure the concentration by measuring the change in the resonance angle (Kumar et al., 2025).

In this subsection, we investigate the potential of the proposed TiN and ZrN-based SPR sensors for use as biological sensors, specifically in the application to detect the glucose concentration in a urine sample. The sensor would detect a refractive index increase due to increased glucose concentration levels in urine samples by measuring the shift in the SPR angle. We use the data available in (Kumar et al., 2023; Karki B et al., 2022) of the variation of the refractive index of urine samples with a wide range of the glucose concentration, as listed in Table 6. We compare the performance of the proposed TiN and ZrN-based SPR sensors with those of the Au-based sensor for detecting these glucose levels. We apply the structures of these SPR sensors supported by 2D-layers that have best SPR performance as listed in Table 6; namely, Prism/Au/BP/SM, Prism/TiN/h-BN/SM, and Prism/ZrN/BP/SM.

Figs. 9(a-c) plot the SPR (reflection R versus incident angle q) curves for detecting the glucose levels by the three SPR sensors. The figures show that for the three sensors, the resonance angle q _SPR shifts to higher value with the increase of the glucose level. This increase of the angle q_SPR is associated with an increase in the reflection dip R_min. The values of the SPR-angle q_SPR of the three sensors are listed also in Table 6. The table indicates that q _SPR increases from 76.42^o to 78.66^o for the Prism/Au/BP/SM sensor, from 78.31^o to 80.13^o for the Prism/TiN/h-BN/SM sensor, and from 74.67^o to 76.35^o for the Prism/ZrN/BP/SM sensor. The dynamic ranges of these sensors are displayed in Fig. 10(a), which shows that this range is widest of 2.42^o for the Au/BP-base sensor, narrowest of 1.68^o for the ZrN/BP-base sensor, while it is equal to 1.82^o for the TiN/BP-base sensor. Fig. 10(b) plots the corresponding variation of the SPR angle q _SPR of the three sensors with the glucose concentration. The figure indicates a linear behavior of q_SPR with the increase of the glucose concentration, which results in a measured sensitivity of 220, 180, and 165 deg/(g/dL) of the Au-BP, TiN/h-BN, and ZrN/BP-based sensors, respectively. These values are within the range of sensitivity reported by Kumar et al. for SPR sensors using layers of Ag and ZrN (Kumar et al., 2023).

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Fig. 9.

Reflectance curve at glucose concentration in the urine sample: (a) prism/Au/SM, (b) prism/TiN/SM and (c) prism/ZrN/SM.

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Fig. 10.

Performance of the prism/Au/BP/SM, prism/TiN/h-BN/SM, and prism/ZrN/BP/SM: (a) histogram plot of the dynamic range, and (b) plot of the SPR angle ${\theta }_{SPR}$ versus the glucose concentration.

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It is worth noting that selective glucose assays require integrating a glucose-specific affinity layer (boronic acid or UiO-66), rigorous antifouling, and differential referencing, which can result in high functional selectivity for glucose over common urinary interferents within the SPR angular readout (D. Lakayan, J et al., 2022). The present modeled TiN/ZrN devices are bulk RI sensors, and this glucose section uses literature RI–concentration correlations for surrogate calibration, and selectivity is not addressed in this work.

Although this study is entirely theoretical and simulation-based, we have carefully addressed issues of reproducibility, stability, and real-world testing. To ensure transparency, we relied on standard and widely accepted optical models and published material parameters, provided full definitions and metrics that allow others to reproduce the results, and benchmarked application-level sensitivity using published urine–glucose refractive index data. The modeling framework follows established practices in SPR: multilayer transfer-matrix optics, angle interrogation at 633 nm, and widely used definitions of sensitivity (S), DA (DA), and QF (QF/FoM). These formulae are explicitly stated, enabling other researchers to reproduce our curves directly from the parameters we report. All optical constants are taken from published Drude–Lorentz parameterizations for Au, TiN, and ZrN, as well as single-value dielectric constants for the 2D layers at 633 nm, with the numerical values clearly listed in the tables. This makes it possible to independently recalculate reflectance spectra and associated metrics. The chosen metrics (S, DA, QF/FoM) and their calculations are all standard within recent SPR simulation studies, allowing straightforward cross-comparison. Moreover, detection limits can be derived afterward by applying angular resolution assumptions, making benchmarking consistent across studies. An additional strength of this approach is the use of TiN and ZrN, which are refractory, mechanically durable plasmonic materials with excellent thermal and chemical resilience. These materials are well known for improving long-term sensor stability compared to noble metals. Finally, practicality is reinforced by benchmarking against experimental reports of how urine’s refractive index changes with glucose concentration. Translating simulated angles shifts into concentration sensitivity within clinically relevant ranges ensures that the study connects theoretical modeling with real-world diagnostic potential, which is a standard strategy before moving toward prototyping.

Finally, it is beneficial to highlight the novelty of the present work. The work adds four practical elements: (1) a head-to-head comparison of TiN and ZrN versus Au under identical conditions; (2) a systematic, single-layer survey of BP, MXene, h-BN, graphene, and MoSe2 specifically on TiN/ZrN, showing a distinct pattern (e.g., ZrN benefits from BP/MXene/h-BN while TiN shows little gain in the same conditions); (3) a fixed-wavelength prism sweep that distills a simple selection rule for nitrides at 633 nm; and (4) a direct mapping of the best stacks into urine-glucose calibration at 633 nm to demonstrate application relevance. Prior studies have explored many of these ingredients separately (often for Au/Ag, different wavelengths, or different readouts), but to our knowledge they have not been integrated into a single, reproducible baseline that a lab using a He–Ne line can apply immediately.