The Effect of MoS₂ and Si₃N₄ in Surface Plasmon Resonance Biosensors for HIV DNA Hybridization Detection: A Numerical Study

Abstract

This study presents a numerical investigation of surface plasmon resonance (SPR) biosensors incorporating silicon nitride (Si₃N₄) and molybdenum disulfide (MoS₂) for HIV DNA hybridization detection. By optimizing the thickness of Ag and Si₃N₄ and the number of MoS₂ layers, two configurations, Sys₂ (Ag-Si₃N₄) and Sys₃ (Ag-Si₃N₄-MoS₂), were selected for comparative analysis. Performance metrics, including the resonance angle shift, sensitivity, detection accuracy, and quality factor, demonstrated that Sys₂ achieved the highest sensitivity of 210.9°/RIU and an enhanced figure of merit (86.98 RIU⁻¹), surpassing state-of-the-art SPR sensors. Although Sys₃ exhibited a lower sensitivity of 158.1°/RIU due to MoS₂-induced optical losses, it provided a lower limit of detection, suggesting a trade-off between sensitivity and spectral broadening. Compared to previous SPR biosensors, the proposed configurations achieve superior sensitivity while maintaining stability and selectivity, positioning them as promising candidates for next-generation nucleic acid detection platforms.

1. Introduction

Detecting HIV DNA hybridization is fundamental for diagnosing and monitoring human immunodeficiency virus (HIV) infections, particularly in early detection and antiretroviral therapy (ART) management [1]. As a retrovirus, HIV primarily targets the immune system [2], and its detection through DNA hybridization refers to the identification of complementary single-stranded DNA (ssDNA) sequences that indicate the virus’s presence in biological samples [3]. During infection, viral RNA undergoes reverse transcription, producing complementary proviral DNA that integrates into the host genome, serving as a crucial genetic marker of both latent and active infections [4].

Conventional nucleic acid detection techniques such as polymerase chain reaction (PCR) [5], loop-mediated isothermal amplification (LAMP) [6], and enzyme-linked immunosorbent assay (ELISA) [7] provide high specificity for detecting HIV DNA hybridization. However, these methods typically require specialized laboratory infrastructure, costly reagents, and trained personnel, limiting their feasibility for point-of-care (POC) diagnostics.

Among the various biosensing strategies, optical detection techniques have gained prominence due to their ability to deliver direct, rapid, and quantitative results without requiring extensive sample preparation [8,9]. Surface plasmon resonance (SPR) biosensors have emerged as a particularly promising approach owing to their exceptional sensitivity to molecular interactions and their ability to function without the need for fluorescent or electrochemical labels [10,11]. Unlike electrochemical biosensors, which depend on electron transfer reactions, SPR exploits the interaction between incident light and collective electron oscillations at a metal-dielectric interface [12].

To further emphasize this, fluorescence and electrochemical biosensors have been widely used for HIV DNA hybridization detection [10,11,12], but both present limitations that SPR overcomes. For instance, fluorescence-based sensors require labeling, are prone to photobleaching, and involve complex optical setups, making them less practical for real-time, point-of-care applications. Electrochemical biosensors, while label-free, rely on redox reactions and electrode modifications, which can introduce chemical instability and signal variability. In contrast, SPR biosensors enable real-time, label-free detection by directly measuring refractive index changes upon DNA hybridization, eliminating the need for additional reagents.

A widely used configuration for SPR-based detection is the Kretschmann setup, which employs total internal reflection (TIR) within a high-refractive-index prism to efficiently excite surface plasmons [13,14]. At a specific incident angle, known as the resonance angle, the energy from the incident light is transferred to the surface plasmons, producing a characteristic dip in reflected light intensity. This angle is highly sensitive to changes in the refractive index at the sensor surface, making it particularly effective for detecting biomolecular interactions, including HIV DNA hybridization [15]. As complement to ssDNA strands hybridizing to form double-stranded DNA (dsDNA), the local refractive index increases, shifting the resonance angle, which serves as a quantifiable detection signal [8].

Traditional SPR sensors commonly use gold (Au) [16] and silver (Ag) [17] thin films as plasmonic materials due to their ability to sustain strong plasmonic excitations in the visible and near-infrared spectral ranges. However, these noble metals suffer from several inherent limitations, including broad resonance linewidths, high Ohmic losses, and chemical instability [18]. To mitigate these challenges, researchers have turned to alternative plasmonic and dielectric materials to enhance the sensitivity, stability, and spectral resolution of SPR-based biosensors.

Hence, this study proposes an advanced SPR biosensor that incorporates silicon nitride (Si₃N₄) and molybdenum disulfide (MoS₂) to improve the detection of HIV DNA hybridization. Si₃N₄ is a high-refractive-index dielectric material that exhibits low optical loss, excellent chemical stability, and broad spectral transparency, making it highly suitable for optical biosensing applications [19]. Furthermore, Si₃N₄ is fully compatible with complementary metal-oxide-semiconductor (CMOS) technology, the dominant fabrication platform for modern microelectronics and photonics, allowing for the potential integration of SPR sensors into miniaturized, cost-effective photonic circuits [20,21]. This compatibility offers a pathway toward scalable manufacturing for lab-on-a-chip biosensing applications [22].

In addition to Si₃N₄, MoS₂, a two-dimensional (2D) transition metal dichalcogenide (TMD), has gained attention for its unique optical and electronic properties that can further enhance SPR sensor performance [23,24]. Unlike conventional plasmonic metals, MoS₂ exhibits a layer-dependent bandgap, which ranges from approximately 0.3 eV (bulk) to 2.0 eV (monolayer), making it highly adaptable for optimizing sensor response across various wavelengths [25]. Additionally, MoS₂ demonstrates strong anisotropic optical behavior, meaning that its response varies based on crystal orientation, enabling highly confined surface plasmon polaritons (SPPs) with lower propagation losses, ultimately improving detection sensitivity [26].

Several key parameters are considered to evaluate the sensor’s performance in detecting HIV DNA hybridization, including sensitivity, the full width at half maximum (FWHM), the quality factor (QF), the figure of merit (FoM), the limit of detection (LoD), and the detection accuracy (DA). To systematically assess the performance of the proposed Si₃N₄–MoS₂-based SPR sensor, this study employs the Transfer Matrix Method (TMM) as a computational framework for modeling multilayer optical systems [27]. Our findings provide a robust theoretical foundation for future experimental validation and demonstrate the potential for practical applications in HIV diagnostics, biosensing, and nucleic-acid-based disease detection.

2. Materials and Methods

2.1. Theoretical Framework

The reflective intensity of the proposed Nth-layer sensor model is calculated using the TMM approach [28,29,30] (Scheme 1). The analysis of the sensor considers boundary conditions for the tangential component, with the initial limit of Z = Z₁ = 0, and the final limit of Z_n−1, giving the following expression:

$$\left[\begin{array}{c}{E}_1\\ H_1\end{array}\right]=M_{ij}\left[\begin{array}{c}{E}_{N-1}\\ H_{N-1}\end{array}\right]$$

(1)

In Equation (1), E₁, E_N−1, V₁, and V_N−1 represent the tangential components of the electric and magnetic fields for the initial and Nth layers, respectively. M_ij indicates the transfer matrix characteristics of the Nth-layer model, computed as:

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

(2)

With

$$M_k=\left[\begin{array}{cc}\cos {\beta }_k& (-\mathrm{i\; sin}{\beta }_k)/q_k\\ -\mathrm{i}{q}_k\sin {\beta }_k& \cos {\beta }_k\end{array}\right]$$

(3)

Denoting

$${\beta }_k={\displaystyle \frac{2\pi d_k}{{\lambda }_0}}\sqrt{{\epsilon }_k-n_1^2{\sin }^2\theta }$$

(4)

And

$$q_k={\displaystyle \frac{\sqrt{{\epsilon }_k-n_1^2{\sin }^2\theta }}{{\epsilon }_k}}$$

(5)

In Equations (3)–(5):

• ${\lambda }_0$ represents the wavelength of the incident light,
• $n_1$ is the refractive index,
• ${\epsilon }_k$ represents the dielectric constant,
• ${\beta }_k$ represents the phase constant,
• $\theta$ represents the entrance angle,
• $d_k$ represents the depth of the $k^{th}$ layer.

For comparison with experiments, we adopt the use of an He-Ne laser with ${\lambda }_0=633$ nm. After straightforward computations, the total reflection of the Nth-layer model can be expressed as:

$$R={\left|{\displaystyle \frac{\left(M_{11}+M_{12} q_N\right)q_1-\left(M_{21}+M_{22} q_N\right)}{\left(M_{11}+M_{12} q_N\right)q_1+\left(M_{21}+M_{22} q_N\right)}}\right|}^2$$

(6)

By using Equation (6), the reflectance as a function of the angle of incidence (SPR curve) can be calculated.

Scheme 1. Illustration of numerical modeling approach using the TMM in SPR sensors.

Scheme 1. Illustration of numerical modeling approach using the TMM in SPR sensors.

2.2. Performance Metrics

We now move on to the main performance metric of the proposed sensors [19,31,32]. The first parameter is the sensitivity enhancement regarding the baseline sensors after/before pathogen adsorption, denoted as:

$$∆S_{RI}^{after}={\displaystyle \frac{(S_{RI}^{after}-S_{RI}^{before})}{S_{RI}^{before}}}$$

(7)

Then, the sensitivity to the refractive index change can be expressed as:

$$S_{RI}={\displaystyle \frac{∆\theta }{∆n}}$$

(8)

Here, $∆\theta$ represents the angle shift variation and $∆n$ represents the refractive index variation. The detection accuracy (DA) can be expressed as in terms of $∆\theta$ and the full width at half maximum (FWHM) of the SPR curve, as:

$$DA={\displaystyle \frac{∆\theta }{FWHM}}$$

(9)

The quality factor (QF) can be expressed in terms of $S_{RI}$ and FWHM, as follows:

$$QF={\displaystyle \frac{S_{RI}}{FWHM}}$$

(10)

The figure of merit (FoM) can be expressed as:

$$FoM={\displaystyle \frac{S_{RI}(1-R_{min})}{FWHM}}$$

(11)

Here, $R_{min}$ represents the lowest normalized reflection value of the SPR curve.

The limit of detection (LoD) can be calculated as:

$$LoD={\displaystyle \frac{∆n}{∆\theta }}\times 0.005°$$

(12)

The Comprehensive Sensitivity Factor (CSF) ratio can be calculated:

$$CSF={\displaystyle \frac{S_{RI}\times (R_{max}-R_{min})}{FWHM}}$$

(13)

$R_{max}$ represents the maximum reflectance before resonance, typically at non-resonant wavelengths or angles. To ensure high accuracy and numerical reliability, our simulations were performed using a data sampling of 1.0 × 10⁵ points for each reflectance curve, allowing for a smooth and well-defined response.

2.3. Biosensor Architecture

Table 1. Summary of the different SPR sensor configurations considered in this study.

Sys No.	Code	Full Name	Nickname
0	Sys0	Prism/Silver/PBS Medium	P/Ag/MPBS
1	Sys1	Prism/Silver/PBS + HIV Medium	P/Ag/MPBS+HIV
2	Sys2	Prism/Silver/Si3N4/PBS + HIV Medium	P/Ag/SN/MPBS+HIV
3	Sys3	Prism/Silver/Si3N4/Molybdenum Disulfide/PBS + HIV Medium	P/Ag/SN/MoS2/MPBS+HIV

summarizes the SPR sensor configurations analyzed in this study, each incorporating different material layers (Figure 1). The reference system, Sys₀ (P/Ag/M_PBS), consists of a prism and a silver (Ag) thin film immersed in a phosphate-buffered saline (PBS) medium, serving as the baseline structure. Sys₁ (P/Ag/M_PBS+HIV) replaces the PBS medium with an HIV DNA-containing PBS solution, enabling the study of resonance shifts induced by DNA hybridization. Sys₂ (P/Ag/SN/M_PBS+HIV) introduces a silicon nitride (Si₃N₄) dielectric layer. Sys₃ (P/Ag/SN/MoS₂/M_PBS + HIV) further incorporates a molybdenum disulfide (MoS₂) monolayer, which is expected to optimize resonance shift, sensitivity, and spectral resolution.

Our SPR sensor differs from the dual-channel design [8] by operating under a thermally controlled environment, eliminating the need for Polydimethylsiloxane (PDMS) for temperature compensation. PDMS was used to track and correct temperature-induced refractive index variations, but in our approach, stable conditions are assumed to ensure that resonance angle shifts result solely from HIV DNA hybridization, making an independent temperature-sensitive layer unnecessary.

Additionally, we adopt the same approach as in [8], where the refractive index (RI = 1.340) corresponds to a modified PBS solution containing biomolecules that are essential for HIV DNA hybridization. This approach ensures consistency in modeling the resonance angle shifts, allowing us to evaluate sensor performance under well-defined conditions. The baseline refractive index (1.335) represents pure PBS (

Table 2. Initial parameters used in the SPR sensor model, including the refractive index and thickness of each material.

Material	Refractive Index	Thickness (nm)	Ref.
BK-7 (P)	1.5151	---	[34]
Silver (Ag)	0.056253 + 4.2760 i	55.0	[35]
Si3N4 (SiN)	2.0394	5.00	[19]
Molybdenum disulfide (MoS2)	5.0805 + 1.1723 i	0.65	[31]
PBS (M)	1.335	---	[8]
PBS + HIV DNA hybridization (BSA + Strep. + dsDNA)	1.340	---	[8]

), a widely used biosensing medium due to its stable pH, ionic strength, and ability to maintain biomolecular interactions [33]. PBS minimizes non-specific adsorption and preserves DNA structure, making it an ideal control medium. The transition from 1.335 to 1.340 occurs due to the addition of biomolecular components, including biotinylated bovine serum albumin (b-BSA), streptavidin, biotinylated probe DNA, and HIV target DNA, all of which contribute to the refractive index shift upon hybridization. The other initial parameters (i.e., refractive indices and thicknesses) used in the current study are reported in Table 2.

3. Results and Discussions

3.1. Selecting the Best Configurations

The results presented in Figure 2 and Table S1 provide insight into the impact of Si₃N₄ and MoS₂ on the SPR sensor’s performance for HIV DNA hybridization detection. The SPR peak position (Figure 2a), representing the resonance angle, shows a progressive shift with the addition of layers. Sys₀, the baseline system, exhibits a resonance angle of 68.06°, while the introduction of HIV DNA in Sys₁ leads to a slight shift to 68.65°. A more pronounced shift occurs in Sys₂ (71.29°) with the inclusion of Si₃N₄, and the largest shift is observed in Sys₃ (72.85°) due to MoS₂ integration. This trend confirms that Si₃N₄ and MoS₂ effectively alter the local refractive index, thereby enhancing plasmonic interactions and improving biosensing performance.

The attenuation percentage (Figure 2b), indicative of plasmonic losses, varies across configurations. Sys₀ and Sys₁ show minimal losses at 0.02% and 0.02%, respectively, while a significant reduction is observed in Sys₂ (0.004%), highlighting the role of Si₃N₄ in minimizing optical losses. In contrast, Sys₃ exhibits a notably higher attenuation of 20.705%, which can be attributed to MoS₂-induced absorption, affecting the overall efficiency of the sensor. Although MoS₂ enhances resonance effects, its increased plasmonic losses must be carefully considered when optimizing SPR performance.

Spectral broadening (Figure 3c), measured through FWHM, provides information about resonance dip sharpness. Sys₀ has the narrowest FWHM at 0.90°, and a slight increase is seen in Sys₁ (0.93°) due to HIV DNA hybridization effects. The introduction of Si₃N₄ in Sys₂ results in a broader FWHM of 1.27°, which remains within an acceptable range for spectral resolution. However, Sys₃ exhibits broadening with an FWHM of 2.63°, suggesting that MoS₂, while improving sensitivity, contributes to a loss in resonance sharpness. This balance between sensitivity and spectral resolution is critical in sensor optimization.

Sensitivity enhancement is measured relative to Sys₀ (Figure 3d). Sys₁ shows a marginal improvement of 0.87%, reflecting the impact of HIV DNA presence alone. A substantial increase is seen in Sys₂ (4.75%), reinforcing the effectiveness of Si₃N₄ in boosting plasmonic response. The highest enhancement is observed in Sys₃ (7.04%), demonstrating the additional advantage provided by MoS₂. Thus, the selection of Sys₂ and Sys₃ for further comparison is justified by their superior resonance shift and sensitivity improvement. In particular, Sys₂ achieves a balanced trade-off with reduced attenuation and moderate spectral broadening, making it suitable for high-precision biosensing. As well, Sys₃ exhibits the highest sensitivity but with increased optical losses, which could affect long-term stability.

3.2. Optimization: Metal Thin Film

The optimization of silver (Ag) thickness for Sys₂ and Sys₃ reveals the importance of balancing plasmonic losses, spectral resolution, and sensitivity enhancement to achieve the best sensing performance (Figure 3 and Table S2). The SPR peak position shows only slight variations across different Ag thicknesses, confirming that adjusting the silver layer primarily fine-tunes the plasmonic response rather than drastically altering resonance conditions (Figure 3a,b). However, the impact on attenuation and spectral broadening is far more pronounced (Figure 3c). In Sys₂, attenuation decreases sharply with increasing thickness, reaching its lowest value at 55 nm (0.004%), before increasing again at 60 nm (4.60%) and 65 nm (17.14%). This confirms that 55 nm minimizes plasmonic losses, ensuring a well-defined resonance dip with minimal energy dissipation. In Sys₃, attenuation follows a different trend due to the presence of MoS₂, remaining low at 45 nm (0.18%) but increasing significantly at 55 nm (20.71%), 60 nm (37.41%), and 65 nm (53.28%). The steep rise in losses beyond 45 nm suggests that thicker silver layers, combined with MoS₂, lead to excessive energy absorption, reducing sensor efficiency.

Spectral resolution also follows a predictable trend (Figure 3d), with FWHM narrowing as Ag thickness increases, improving resonance sharpness. However, Sys₃ consistently exhibits broader resonance dips than Sys₂, reinforcing that MoS₂ contributes to spectral broadening, which must be carefully controlled. The sensitivity results further justify the choice of 55 nm for Sys₂ and 45 nm for Sys₃. While sensitivity increases with thickness (Figure 3e), the improvement beyond 55 nm in Sys₂ (0.97%) and 45 nm in Sys₃ (0.90%) is marginal, whereas plasmonic losses rise significantly. This trade-off confirms that these thicknesses provide the best balance between high sensitivity, minimal attenuation, and optimal spectral resolution.

Hence, 55 nm for Sys₂ ensures minimal plasmonic losses, well-defined resonance characteristics, and strong sensitivity, making it the most stable configuration. A thickness of 45 nm for Sys₃, on the other hand, prevents excessive attenuation while maintaining a high sensing response, ensuring optimal performance despite the strong light–matter interactions introduced by MoS₂.

3.3. Optimization: Si₃N₄

The optimization of silicon nitride (Si₃N₄) thickness for Sys₂ and Sys₃ highlights the importance of selecting a suitable thickness to balance plasmonic performance, energy dissipation, and sensing sensitivity (Figure 4 and Table S3). The SPR peak position shifts significantly with increasing Si₃N₄ thickness, confirming its strong influence on resonance conditions (Figure 4a,b). For Sys₂, the peak moves from 71.29° at 5 nm to 84.45° at 20 nm, while for Sys₃, it increases from 72.75° at 5 nm to 83.65° at 20 nm. This shift indicates that thicker Si₃N₄ layers lead to stronger plasmonic interactions.

Attenuation results confirm that excessive Si₃N₄ thickness leads to a rise in plasmonic losses (Figure 4c). In Sys₂, attenuation remains minimal up to 7 nm (about 0.0%), increases moderately at 13 nm (0.59%), and rises significantly at 16 nm (7.01%) before becoming excessive at 20 nm (96.36%). A similar trend is observed in Sys₃, where attenuation is 0.18% at 5 nm, remains manageable at 7 nm (0.54%), but increases rapidly beyond 10 nm (1.95%), reaching 49.28% at 16 nm and an overwhelming 90.24% at 20 nm. These results confirm that thinner Si₃N₄ layers are necessary to prevent energy dissipation.

Spectral broadening follows a consistent pattern (Figure 4d), with FWHM increasing as Si₃N₄ thickness grows. In Sys₂, it starts at 1.30° at 5 nm, increases gradually to 2.40° at 13 nm, and reaches an extreme 39.50° at 20 nm, making detection unreliable at high thicknesses. Similarly, Sys₃ shows a progressive FWHM increase, from 3.85° at 5 nm to 6.72° at 13 nm, reaching 14.52° at 20 nm. As noted, the broadening effect is particularly pronounced in Sys₃.

Sensitivity enhancement is reported in Figure 4e. In Sys₂, sensitivity steadily increases with thickness, peaking at 13 nm (10.85%), after which it continues rising but at a much lower rate relative to the increase in attenuation. For Sys₃, sensitivity increases consistently, but the optimal trade-off is observed at 7 nm (3.22%), where performance is maximized without introducing excessive spectral broadening or attenuation. Hence, all these findings show that 13 nm of Si₃N₄ in Sys₂ provides the best combination of high sensitivity, moderate spectral broadening, and controlled attenuation, making it the most effective thickness for this configuration. In contrast, Sys₃ benefits from a thinner 7 nm layer, maintaining low losses, a well-defined resonance peak, and strong sensitivity enhancement without excessive spectral distortion.

3.4. Optimization: MoS₂ Layers

The optimization of molybdenum disulfide (MoS₂) layers in Sys₃ is shown in Table S4 and Figure 5. The SPR peak position shifts progressively from 73.40° with one layer (L1) to 81.45° with six layers (L6), reflecting the increased refractive index (Figure 5a). However, the shift slows beyond three layers (L3), indicating diminishing benefits. Attenuation remains low at 0.44% with one layer but rises drastically to 10.78% with two layers, 25.74% with three layers, and reaches an impractical 74.03% with six layers, demonstrating the severe plasmonic losses caused by excessive MoS₂ thickness (Figure 5b).

Spectral broadening follows the same trend (Figure 5c), with FWHM increasing from 4.28° (L1) to 13.67° (L6), reducing the sharpness of the resonance dip and impairing detection accuracy. Sensitivity improves initially (Figure 5d), reaching 12.17% with five layers (L5), but this gain is outweighed by the excessive attenuation and loss of spectral resolution. Beyond four layers (L4), additional MoS₂ does not significantly enhance sensitivity, confirming that thicker films introduce more drawbacks than benefits. These findings support the selection of monolayer MoS₂ as the optimal configuration for Sys₃, ensuring high sensitivity while maintaining low plasmonic losses and sharp resonance characteristics, making it ideal for HIV DNA hybridization detection.

3.5. Sensing HIV DNA Hybridization

Table S5 presents the final optimized structural parameters for Sys₂ and Sys₃, including refractive index (RI) and thickness values for each material layer. For Sys₂, the configuration consists of a BK7 prism (RI = 1.5151), a 55 nm silver layer, and a 13 nm silicon nitride layer. In Sys₃, the silver layer is thinner (45 nm), the Si₃N₄ layer is 7 nm, and a monolayer of molybdenum disulfide (MoS₂, 0.65 nm) is added. These parameters define the final sensor designs for assessing HIV DNA hybridization detection, determining their effectiveness as SPR biosensors.

The results in Figure 6 and Table S6 provide a direct comparison of the SPR response of the optimized Sys₂ and Sys₃ configurations before (PBS only) and after (PBS + HIV DNA hybridization). The observed resonance shifts confirm the effectiveness of both sensor designs, with Sys₂ demonstrating a larger shift (Figure 6a), while Sys₃ exhibits increased spectral broadening due to MoS₂ integration (Figure 6b). For Sys₂, the SPR peak shifts from 77.21° to 78.27° after hybridization, indicating a resonance shift of 1.06°. The attenuation increases moderately from 0.30% to 0.59% (Figure 6c), while FWHM remains relatively stable between 2.28° and 2.41° (Figure 6d), ensuring a well-defined resonance dip. The sensitivity enhancement reaches 1.37% (Figure 6e), highlighting the role of Si₃N₄ in improving plasmonic confinement without excessive optical losses.

To further remark, in Sys₃, the resonance shift is slightly lower, moving from 73.55° to 74.34° (0.79° shift), reflecting a reduced sensitivity compared to Sys₂. The attenuation increases from 0.45% to 0.55%, and FWHM broadens from 4.30° to 4.43°, confirming that while MoS₂ enhances sensitivity, it also introduces higher plasmonic losses and wider resonance dips. Sensitivity enhancement reaches 1.08%, which is slightly lower than that of Sys₂.

These findings evidence the unique contributions of Si₃N₄ and MoS₂ in improving SPR-based biosensing. Sys₂ exhibits superior spectral sharpness and a higher resonance shift, making it the most effective configuration for detecting HIV DNA hybridization. Meanwhile, Sys₃ benefits from MoS₂-enhanced sensitivity but at the cost of increased spectral broadening and higher losses, reinforcing that material selection must balance sensitivity and optical performance to optimize biosensor efficiency.

3.6. Performance Metrics of SPR Biosensor

The results in Figure 7 and

Table 3. Numerical results corresponding to the performance metrics shown in Figure 7 for optimized Sys₂ and Sys₃ after HIV DNA hybridization detection.

Configuration	$∆\mathit{\theta }$	$\mathit{S} (°/\mathit{R}\mathit{I}\mathit{U})$	DA	QF (RIU−1)
Sys2-PBS+HIV	1.054	210.9	0.437	87.493
Sys3-PBS+HIV	0.791	158.1	0.178	35.674

provide a comprehensive assessment of key biosensing performance metrics for optimized Sys₂ and Sys₃ after detecting HIV DNA hybridization. The comparison is based on four essential parameters: resonance angle shift (Δθ) (Figure 7a), sensitivity (S) (Figure 7b), detection accuracy (DA) (Figure 7c), and quality factor (QF) (Figure 7d). Then, Sys₂ outperforms Sys₃ on all critical metrics, confirming its superior performance for HIV DNA hybridization detection. The resonance angle shift for Sys₂ is 1.05°, which is significantly larger than the 0.79° shift in Sys₃, indicating a more pronounced response to biomolecular binding events. This larger shift translates directly into higher sensitivity, where Sys₂ achieves 210.9°/RIU, compared to 158.1°/RIU in Sys₃, demonstrating its enhanced ability to detect small refractive index changes.

Detection accuracy follows the same trend, with Sys₂ exhibiting a DA of 0.44, which is more than twice that of Sys₃ (0.18), reinforcing its higher precision in identifying HIV DNA hybridization events. Additionally, the quality factor (QF) of Sys₂ reaches 87.49 RIU⁻¹, which is more than double that of Sys₃ (35.67 RIU⁻¹), indicating a sharper and better-defined resonance dip, which is crucial for minimizing background noise and improving signal clarity.

Despite Sys₃ incorporating MoS₂ for additional plasmonic enhancement, the results suggest that the increased optical losses and spectral broadening introduced by MoS₂ compromise overall sensor performance. While Sys₃ remains a viable option, Sys₂ demonstrates superior sensitivity, precision, and resonance stability, making it the most effective configuration for HIV DNA hybridization detection.

The results in Figure 8 and

Table 4. Numerical results corresponding to the performance metrics presented in Figure 8 for optimized Sys₂ and Sys₃ after HIV DNA hybridization detection.

Configuration	FoM (RIU−1)	LoD (10−5)	CSF
Sys2-PBS+HIV	86.979	2.370	83.121
Sys3-PBS+HIV	35.480	3.163	32.862

further assess the biosensing performance of Sys₂ and Sys₃, focusing on additional key metrics: the figure of merit (FoM) (Figure 8a), the limit of detection (LoD) (Figure 8b), and the Comprehensive Sensitivity Factor (CSF) (Figure 8c). These indicators provide a more detailed understanding of the trade-offs between sensitivity, stability, and selectivity in both configurations. Particularly, Sys₂ demonstrates superior performance across all evaluated metrics, reinforcing its role as the optimal configuration for HIV DNA hybridization detection. The figure of merit (FoM), which quantifies the balance between sensitivity and spectral resolution, is significantly higher for Sys₂ (86.98 RIU⁻¹) compared to Sys₃ (35.48 RIU⁻¹). This suggests that Sys₂ maintains a sharper resonance dip while providing strong sensitivity, which is a crucial factor for minimizing detection errors.

The limit of detection (LoD), representing the lowest analyte concentration that can be reliably detected, is slightly better in Sys₃ (3.16 × 10⁻⁵) compared to Sys₂ (2.37 × 10⁻⁵). This indicates that Sys₃ benefits from MoS₂-enhanced sensitivity, enabling detection at slightly lower concentrations. However, this advantage comes at the cost of plasmonic losses and spectral broadening, as previously discussed.

The Comprehensive Sensitivity Factor (CSF), which evaluates overall sensor efficiency by considering sensitivity, stability, and selectivity, further supports Sys₂ as the superior configuration, with a value of 83.12, which is more than double that of Sys₃ (32.86). This highlights that despite MoS₂’s contribution to sensitivity, Sys₂ provides a more stable and selective sensing response, making it the most balanced and efficient biosensor design.

Figure 9 presents the limit of detection (LoD) as a function of the refractive index (RI), providing a standard curve to validate the LoD calculation. Since the refractive index of the sensing medium is directly influenced by the concentration, in this case, of HIV DNA hybridization, we followed the methodology reported in Ref. [36], where RI variations of up to ±0.4% were linked to changes in the analyte concentration of DNA hybridization. To extend the analysis, we considered a variation of up to ±0.6% to show a more comprehensive evaluation of LoD trends. The results demonstrate a linear relationship between the LoD (Equation (12)) and the refractive index, confirming the robustness of our detection model. Sys₂ consistently achieves a lower LoD compared to Sys₃, reinforcing its higher sensitivity and precision in detecting small analyte concentrations. The linear trend observed in both configurations further validates the reproducibility of our LoD estimations, supporting the feasibility of our numerical approach.

The comparison in

Table 5. Comparison of the maximum sensitivity of the optimized sensor (Sys₂ and Sys₃) with those available in the literature.

Configuration	$\mathit{S} (°/\mathit{R}\mathit{I}\mathit{U})$	Ref. #
Ag-ZnSe-based sensor	208.0	[8]
Au-MoS2-graphene-based sensor	89.29	[37]
Au-MoS2-graphene-based sensor	130.0	[38]
Au-WSe2-graphene-based sensor	178.87	[39]
Ag-Si2N4-based sensor (Sys2)	210.9	This work
Ag-Si2N4-MoS2-based sensor (Sys3)	158.1	This work

highlights how the optimized Sys₂ and Sys₃ perform against some of the most advanced SPR sensors reported in the literature. The exceptional sensitivity of Sys₂ (210.9°/RIU) not only surpasses that of all previously reported designs but also emphasizes the effectiveness of Si₃N₄ in enhancing plasmonic performance, making it a highly promising biosensor for HIV DNA hybridization detection. Among existing designs, the Ag-ZnSe-based sensor achieves a sensitivity of 208.0°/RIU, which is slightly lower than that of Sys₂, confirming that the Ag-Si₃N₄ combination provides better plasmonic field confinement and stronger light–matter interactions. Compared to Au-MoS₂-graphene-based sensors, which reach sensitivities of 89.29°/RIU and 130.0°/RIU, Sys₂ and Sys₃ show a clear advantage, demonstrating that the integration of Si₃N₄ and MoS₂ offers a more effective strategy for boosting SPR sensor response.

The Au-WSe₂-graphene-based sensor, with a sensitivity of 178.87°/RIU, also falls short of Sys₂, further reinforcing the significance of Si₃N₄ in improving detection sensitivity. While Sys₃ (158.1°/RIU) performs well, it does not surpass all previously reported values, likely due to the additional plasmonic losses introduced by MoS₂, which, while beneficial for sensitivity, also contribute to broader resonance dips and increased optical losses.

These results confirm that Sys₂ is one of the most sensitive SPR biosensors reported to date. The competitive performance of Sys₃ shows that MoS₂ can be a valuable addition for further sensitivity improvements, though careful optimization is needed to minimize trade-offs in optical losses. Overall, Sys₂ stands out as a next-generation biosensor, capable of achieving state-of-the-art sensitivity while maintaining spectral clarity and detection precision, making it a powerful tool for HIV DNA hybridization detection and broader biosensing applications.

4. Discussions

The numerical outcomes of Sys₂ and Sys₃ demonstrate significant enhancements in sensitivity, resonance stability, and detection accuracy. However, translating these computational results into realistic HIV detection scenarios requires careful consideration of practical implementation, sample preparation, and integration into clinical workflows. SPR biosensors have already proven their potential in POC diagnostics, but existing limitations, including cost, fragility, and operational complexity, have hindered their widespread adoption. The proposed Sys₂ and Sys₃ configurations introduce Si₃N₄ and MoS₂, materials that not only enhance sensitivity but also contribute to practical usability. Si₃N₄ offers excellent chemical stability, compatibility with CMOS technology, and low optical loss, making it a suitable choice for miniaturized, cost-effective biosensing platforms. The integration of MoS₂ in Sys₃ further enhances plasmonic interactions, though its trade-offs in spectral broadening must be addressed in experimental setups to avoid excessive signal degradation.

The resonance angle shifts of Sys₂ (1.05°) and Sys₃ (0.79°) correspond to highly detectable refractive index changes, suggesting that these sensors could reliably distinguish HIV DNA hybridization events even at low concentrations. Compared to traditional techniques like PCR or ELISA, which require trained personnel, time-consuming protocols, and expensive reagents, SPR-based detection offers a label-free, real-time alternative with the potential for rapid field deployment. The lower limit of detection (LoD) values of Sys₂ (2.37 × 10⁻⁵) and Sys₃ (3.16 × 10⁻⁵) confirm their feasibility for ultra-low-concentration biomolecular sensing, making them particularly relevant for early-stage HIV detection where conventional methods may struggle with sensitivity constraints.

Moreover, the practical integration of these optimized sensors into lab-on-a-chip devices could enable fully automated HIV screening in remote or resource-limited settings. The high stability of Si₃N₄ ensures that Sys₂ could be implemented in long-term clinical monitoring, while Sys₃’s MoS₂-enhanced sensitivity suggests potential applications in detecting minimal viral loads, which is crucial in monitoring antiretroviral therapy effectiveness.

5. Conclusions

This work explored the integration of Si₃N₄ and MoS₂ into SPR biosensors to enhance the detection of HIV DNA hybridization. Through systematic optimization, Sys₂ emerged as the most effective configuration, balancing high sensitivity, minimal optical losses, and sharp resonance characteristics. The introduction of MoS₂ in Sys₃ improved sensitivity at the cost of increased attenuation and spectral broadening, limiting its overall efficiency. Comparative analysis with existing SPR sensors confirmed the superior performance of Sys₂, which surpassed widely studied metal-dielectric configurations. These findings provide a theoretical foundation for future experimental validation and demonstrate the potential of hybrid dielectric-plasmonic structures in advancing biosensing technologies for disease diagnostics.