The Detection of Different Cancer Types Using an Optimized MoS₂-Based Surface Plasmon Resonance Multilayer System

Abstract

The early and accurate detection of cancer remains a critical challenge in biomedical diagnostics. In this work, we propose and investigate a novel surface plasmon resonance (SPR) biosensor platform based on a multilayer configuration incorporating copper (Cu), silicon nitride (Si₃N₄), and molybdenum disulfide (MoS₂) for the optical detection of various cancer types. Four distinct sensor architectures (Sys₁–Sys₄) were optimized through the systematic tuning of Cu thickness, Si₃N₄ dielectric layer thickness, and the number of MoS₂ monolayers to enhance sensitivity, angular shift, and spectral sharpness. The optimized systems were evaluated using refractive index data corresponding to six cancer types (skin, cervical, blood, adrenal, breast T1, and breast T2), with performance metrics including sensitivity, detection accuracy, quality factor, figure of merit, limit of detection, and comprehensive sensitivity factor. Among the configurations, Sys₃ (BK7–Cu–Si₃N₄–MoS₂) demonstrated the highest sensitivity, reaching 254.64 °/RIU for adrenal cancer, while maintaining a low detection limit and competitive figures of merit. Comparative analysis revealed that the MoS₂-based designs, particularly Sys₃, outperform conventional noble-metal architectures in terms of sensitivity while using earth-abundant, scalable materials. These results confirm the potential of Cu/Si₃N₄/MoS₂-based SPR biosensors as practical and effective tools for label-free cancer diagnosis across multiple malignancy types.

1. Introduction

Cancer remains a major contributor to global morbidity and mortality, with increasing prevalence observed across diverse demographic and geographic groups [1,2,3]. Malignant transformation originates from genetic and epigenetic disturbances that disrupt essential regulatory pathways involved in cell division [4], programmed cell death [5], and genomic repair [6]. These disruptions promote uncontrolled proliferation and metastatic progression. Among the various cancer types, breast [7], cervical [8], skin [9], adrenal [10], gland [11], and hematologic [12] malignancies frequently exhibit a high clinical burden due to their diagnostic complexity and variable biological behavior.

While early detection is a critical determinant of clinical outcome, current diagnostic protocols rely heavily on imaging [13], histopathology [14], and molecular assays [15], which are often limited by high cost, procedural invasiveness, and dependence on advanced instrumentation. These constraints hinder widespread adoption in population-level screening programs, particularly in resource-constrained environments. This has motivated the exploration of alternative diagnostic modalities that offer simplicity, real-time feedback, and sensitivity to cellular or molecular changes [16].

Surface plasmon resonance (SPR) biosensing is one such technique that allows for label-free and real-time detection of refractive index variations at the interface between a metallic film and a dielectric environment [17,18]. In the context of cancer diagnostics, changes in the refractive index are often linked to alterations in cellular morphology and protein content [19], both of which differ between healthy and malignant cells. These features render SPR sensors suitable for the optical sensing of cancer-related transformations without the need for biochemical amplification or labeling [20].

Recent advances in material science have led to the integration of two-dimensional nanomaterials into SPR platforms [21]. These atomically thin systems exhibit strong light–matter interactions, large surface-to-volume ratios, and highly tunable optoelectronic behavior, making them particularly suitable for biosensing applications [22]. Among them, molybdenum disulfide (MoS₂) has attracted attention for its semiconducting character, direct bandgap at the monolayer level, and capacity for exciton–plasmon coupling under optical excitation [23,24,25]. These properties can be exploited to enhance the local electromagnetic field and facilitate adsorption of biomolecular species, thereby improving sensor responsiveness.

Contrary to concerns that MoS₂ lacks visibility in high-impact biosensing applications, several recent studies have established its relevance across different contexts. For instance, MoS₂-based sensors have been reported for the detection of prostate-specific antigen through electrical measurements in oxide-free environments, yielding detection limits in the picogram per milliliter range [26]. Other configurations have demonstrated its application in food safety analysis, where MoS₂-based composite sensors enable the identification of chemical contaminants and pathogens with high selectivity and optical sensitivity [27]. Additional examples include the enzymatic detection of glucose using MoS₂/Ag nanocomposites [28] and the development of MoS₂-integrated SPR sensors for viral detection, including SARS-CoV-2 [29], with angular sensitivities exceeding 370 degrees per refractive index unit (°/RIU). Furthermore, transmission-based MoS₂-enhanced SPR fiber sensors operating in the terahertz regime have shown detection resolutions below 10⁻⁷ refractive index units [30].

The present study focuses on a theoretical design of an SPR sensor incorporating a Cu/Si₃N₄/MoS₂ multilayer configuration, optimized for the detection of multiple cancer cell types. The investigation employs the transfer matrix method (TMM) to simulate angular reflectance spectra under conditions mimicking the optical signatures of cancerous cells. Emphasis is placed on identifying material parameters and layer configurations that maximize resonance angle shift per refractive index unit. The model accounts solely for physical refractive index variations and does not involve experimental validation, biological interaction specificity, or fabrication procedures. Instead, the objective is to establish a high-fidelity computational framework for evaluating sensor feasibility, guiding subsequent experimental development, and expanding the landscape of MoS₂-based plasmonic biosensing.

2. Methodology

2.1. Numerical Framework

The numerical framework approach is given in Refs. [31,32]. To begin, the equation used to compute the total reflection of the N-layer model may be expressed as:

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

(1)

Then, the reflectance is noted as a function of the angle of incidence, the so-called SPR deep curve. Using (1), we can calculate the peak position, angle shift variation, full width at half maximum (FWHM), and attenuation percentage.

On the other hand, the performance metrics of the proposed SPR sensors are calculated as follows.

• The sensitivity enhancement regarding the baseline sensors after/before analyte adsorption:

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

  (2)
• The sensitivity to the refractive index after analyte adsorption:

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

  (3)

  where $∆\theta$ is the angle shift variation and $∆n$ is the refractive index variation (dimensionless).
• The detection accuracy (DA) is expressed in terms of $∆\theta$ and FWHM (in degrees) as:

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

  (4)
• The quality factor (QF) is denoted in terms of $S_{RI}$ and FWHM:

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

  (5)
• The figure of merit (FoM) is expressed as:

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

  (6)

  where $R_{min}$ shows the lowest normalized reflection value from the SPR curve.
• The limit of detection (LoD) is calculated as:

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

  (7)
• The comprehensive sensitivity factor (CSF) ratio is computed based on Ref. [33] (and reference inside):

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

  (8)

  $R_{max}$ represents the maximum reflectance before deep resonance. The investigation is conducted with a data sampling of $5\times {10}^4$ points. Notably, all simulations assume TM-polarized light, as required for surface plasmon excitation at the metal–dielectric interface.

It is important to clarify that the current study is grounded in a theoretical framework that models cancer detection solely through physical variations in the refractive index (RI) at the metal–dielectric interface. This approach assumes that malignant transformations induce measurable RI shifts due to changes in cell morphology, density, and intracellular composition. However, the modeling approach does not incorporate biochemical specificity or molecular recognition mechanisms, such as antibody–antigen interactions, which would be required for the selective identification of specific cancer types or biomarkers in complex biological samples. Therefore, the proposed SPR sensor configurations should be interpreted as early-stage, label-free platforms designed to assess the feasibility and sensitivity of detecting bulk RI contrasts associated with malignant cell populations.

2.2. Systems and Initial Parameters

To assess the optical and sensing performance of the proposed biosensor, five distinct configurations were analyzed, as outlined in

Table 1. Configurations considered in the current work.

Sys No.	Code	Full Name	Nick Name
0	Sys0	Prism/Copper/PBS	P/Cu/PBS
1	Sys1	Prism/Copper/Cancer Sample	P/Cu/MCancer
2	Sys2	Prism/Copper/Si3N4	P/Cu/SN/MCancer
3	Sys3	Prism/Copper/Si3N4/Molybdenum disulfide/Cancer Sample	P/Cu/SN/MoS2/MCancer
4	Sys4	Prism/Copper/Molybdenum disulfide/Si3N4/Cancer Sample	P/Cu/MoS2/SN/MCancer

. The baseline system (Sys₀, P/Cu/PBS) comprises a BK-7 glass prism and a copper thin film interfaced with phosphate-buffered saline (PBS), serving as a reference without any biological perturbation. In Sys₁ (P/Cu/M_Cancer), a biological and generic cancer sample [34] replaces the PBS medium to model the initial interaction between copper and a representative cancerous analyte, enabling the characterization of surface plasmon resonance (SPR) shifts due to biological refractive index changes alone. Building upon this system, Sys₂ (P/Cu/SN/M_Cancer) introduces a 5.00 nm thick silicon nitride (Si₃N₄) layer between the copper and the sensing medium. Si₃N₄ is a robust dielectric known for its high transparency, thermal stability, and low optical loss in the visible spectrum and has previously demonstrated significant field-confining capabilities in SPR structures [35]. This layer also provides protection against copper oxidation and supports stable field propagation.

In Sys₃ (P/Cu/SN/MoS₂/M_Cancer), a monolayer of molybdenum disulfide (MoS₂) is added on top of the Si₃N₄ layer, followed by the cancer sample. MoS₂, a two-dimensional transition metal dichalcogenide, has shown exceptional light–matter interaction characteristics and supports increased surface adsorption of biomolecules due to its large surface-to-volume ratio [36]. In Sys₄ (P/Cu/MoS₂/SN/M_Cancer), the positions of Si₃N₄ and MoS₂ are reversed to evaluate the influence of layering sequence on plasmonic coupling and resonance efficiency. This comparative framework enables an in-depth exploration of how nanomaterial integration affects SPR sensitivity and specificity.

The corresponding material parameters for each layer are summarized in

Table 2. Initial parameters.

Material	Refractive Index	Thickness (nm)	Refs.
BK-7 (P)	1.5151	---	[37]
Copper (Cu)	0.0369 + 4.5393i	45.0	[38]
Si3N4 (SN)	2.0394	5.00	[35]
Molybdenum disulfide (MoS2)	5.0805 + 1.1723i	0.65	[39,40,41]
PBS (M)	1.335	---	[34]
Cancer Sample ($∆n$)	1.349	---	[34]

. The BK-7 prism (n = 1.5151), selected for its favorable dispersion characteristics and cost-effectiveness, serves as the input medium for the excitation of surface plasmons [37]. Copper is employed as the plasmonic metal due to its high electrical conductivity and strong plasmonic response. Although less chemically stable than gold or silver, the use of copper is justified by its cost efficiency and ability to support intense field confinement when properly encapsulated. Copper presents a complex refractive index n = 0.0369 + 4.5393i at the excitation wavelength of 633 nm and a thickness of 45 nm; these values were chosen based on previous reports [38].

Si₃N₄ is modeled with a real refractive index of 2.0394 and thickness of 5.00 nm, a configuration supported by prior biosensing literature [39]. The MoS₂ layer is modeled with a refractive index of n = 5.0805 + 1.1723i and a monolayer thickness of 0.65 nm, in alignment with experimental data for optoelectronic applications [40]. For the biological layers, PBS is represented by a refractive index of 1.335 [41], and the cancer sample layer is modeled with an average refractive index of 1.349, which reflects the optical response of a malignant cell environment due to increased protein and nuclear content [34]. The combination of copper, Si₃N₄, and MoS₂ in Sys₄ is expected to yield a synergistic enhancement in field localization, analyte interaction, and sensing precision.

3. Results and Discussion

3.1. Systems Under Consideration

To evaluate the sensing performance of the proposed SPR biosensor architecture for detecting cancer, four multilayer systems (Sys₁ to Sys₄) were analyzed relative to the baseline configuration (Sys₀). Each system includes a representative cancer sample to assess its ability to detect refractive index variations associated with malignant cells [34]. The comparative analysis was based on simulated reflectance behavior, with quantitative metrics shown in Figure 1 and summarized in Table S1.

As shown in Figure 1a, the baseline structure Sys₀, consisting of Cu interfaced with PBS (black curve), produces an SPR dip at 66.90°, which serves as a reference. Replacing PBS with a cancer sample in Sys₁ (violet curve) causes a resonance shift to 68.86°, indicating the sensor’s ability to detect changes in the surrounding refractive index. With the inclusion of a Si₃N₄ layer in Sys₂ (cyan), the SPR dip further shifts to 71.28°, suggesting improved field confinement and light–matter interaction. The addition of a MoS₂ monolayer in Sys₃ (green) results in a peak at 72.62°, and rearranging the stack to form Sys₄ (red) slightly moves the peak position to 72.50°.

Sensitivity enhancement relative to the reference system is shown in Figure 1b. Sys₁ achieves a 2.38% increase, while Sys₂ performs notably better with 5.97%. Sys₃ and Sys₄ offer the highest enhancements at 7.96% and 7.79%, respectively. These results indicate a stronger electromagnetic response when MoS₂ is integrated, either directly at the sensing interface or sandwiched between the metal and dielectric layers.

The angular shift Δθ, shown in Figure 1c, follows a consistent trend. Sys₁ exhibits a minor shift of 1.60°, while Sys₂ responds with 4.02°. Both MoS₂-based configurations record larger angular deviations: 5.36° for Sys₃ and 5.24° for Sys₄. This behavior is beneficial for distinguishing subtle changes in the refractive index, which is particularly important for early-stage cancer detection.

The attenuation percentage, as shown in Figure 1d, differs considerably between the systems. Sys₁ and Sys₂ show pronounced resonance dips (28.19% and 28.21%), while Sys₃ and Sys₄ maintain reflectance levels near baseline with minimal attenuation (0.32% and 0.01%, respectively). This characteristic may contribute to improved signal clarity in systems with lower attenuation.

The full width at half maximum (FWHM), plotted in Figure 1e, is a key factor in assessing spectral sharpness and resolution. Sys₁ offers the narrowest dip at 1.09°, followed by Sys₂ at 1.48°. While Sys₃ exhibits a broader dip at 2.81°, it also achieves the highest angular shift. Sys₄ presents a slightly narrower FWHM at 2.60°, suggesting a more compact resonance while retaining strong sensing performance. Rather than prioritizing a single design, this study considers all four configurations as viable candidates for refractive-index-based cancer detection. Their respective trade-offs in angular resolution, sensitivity, attenuation, and FWHM could guide subsequent application-specific evaluations.

3.2. Cooper Optimization

Copper thickness directly influences the strength and shape of plasmonic resonance in SPR biosensors. To identify the optimal conditions for each system (Sys₁ through Sys₄), simulations were carried out over a Cu thickness range from 30 nm to 55 nm. Results are presented in Figures S1 and S2 and Table S2, with key parameters including angular shift (Δθ) (Figure S2a), sensitivity enhancement (Figure S2b), attenuation (Figure S2c), and FWHM (Figure S2d).

The reflectance curves in Figure S1a–d reveal a common trend: thinner Cu layers (30–35 nm) lead to broader and weaker resonance dips across all systems, indicating inefficient field confinement. As the thickness increases to 45 nm, the dips become sharper and deeper, suggesting improved coupling and reduced loss. In some cases, thicker layers beyond 45 nm begin to degrade resonance sharpness slightly, indicating diminishing returns.

The angular shift behavior shown in Figure S2a reflects distinct patterns for each system. Sys₁ and Sys₂ show a mild decline in Δθ as thickness increases, with Sys₁ dropping from 1.83° at 30 nm to 1.58° at 55 nm and Sys₂ decreasing from 1.93° to 1.81°. Despite this reduction, the simultaneous improvements in attenuation and FWHM justify the choice of 55 nm for these two systems. As shown in Figure S2c, attenuation drops dramatically—from above 70% at 30 nm to just 1.38% and 1.38% for Sys₁ and Sys₂ at 55 nm. This improvement is critical for enhancing the signal-to-noise ratio. Additionally, Figure S2d shows that FWHM narrows significantly, reaching 0.56° for Sys₁ and 1.04° for Sys₂. These results support the use of 55 nm as the most balanced thickness for stable and precise resonance in these simpler Cu-based structures.

Sys₃ and Sys₄ follow a different trajectory. In both systems, Δθ increases steadily with thickness, reaching 1.99° and 1.98° at 55 nm. Sensitivity enhancement also improves with thickness, peaking at 2.82% for Sys₃ and 2.81% for Sys₄. However, attenuation and FWHM show an inflection point. As seen in Figure S2c, attenuation reaches its lowest values at 45 nm—0.32% for Sys₃ and 0.006% for Sys₄—but starts to rise again beyond this point. Similarly, Figure S2d indicates that FWHM is minimized at 45 nm. For example, FWHM in Sys₄ decreases from 2.60° at 45 nm to 1.88° at 55 nm, reducing the spectral sharpness that is crucial for high-resolution detection.

Based on these combined observations, 55 nm is selected for Sys₁ and Sys₂, where the marginal loss in Δθ is compensated by significant gains in spectral clarity and signal stability. For Sys₃ and Sys₄, the 45 nm condition provides the best balance between sensitivity, angular shift, attenuation, and FWHM. These optimized thickness values—55 nm for Sys₁ and Sys₂ and 45 nm for Sys₃ and Sys₄—are used in all subsequent analyses.

3.3. Silicon Nitride Optimization

The integration of a dielectric spacer such as Si₃N₄ between the metal layer and sensing medium in SPR biosensors offers both chemical stability and enhanced field confinement. To determine the optimal thickness of the Si₃N₄ layer, the sensor response was investigated in Sys₂, Sys₃, and Sys₄ across a range from 5 nm to 15 nm. The reflectance behavior and corresponding metrics are summarized in Figures S3 and S4 and Table S3.

As shown in the reflectance profiles (Figure S3a–c), increasing Si₃N₄ thickness consistently shifts the SPR dips toward higher incidence angles in all systems, indicating stronger light–matter interaction with the cancer sample. This trend is quantitatively confirmed in Figure S4a, where Δθ increases with Si₃N₄ thickness. For instance, in Sys₂, Δθ rises from 1.8° at 5 nm to 14.5° at 13 nm before declining slightly to 9.5° at 15 nm. A similar but more linear behavior is observed in Sys₃ and Sys₄, where Δθ reaches 15.0° and 15.9° at 15 nm, respectively.

Sensitivity enhancement, as shown in Figure S4b, mirrors the angular shift trend. Sys₂ displays a substantial increase from 2.6% at 5 nm to a peak of 20.9% at 13 nm, followed by a reduction to 13.6% at 15 nm. Sys₃ and Sys₄ maintain a consistent rise, peaking at 21.3% and 22.5%, respectively, at 15 nm. These results confirm the ability of a thicker dielectric layer to extend the evanescent field into the sensing region, thus increasing sensitivity to refractive index changes.

However, the improved sensitivity and angle response must be evaluated alongside attenuation and FWHM to ensure overall sensor effectiveness. Figure S4c reveals that Sys₂ maintains very low attenuation from 5 nm to 11 nm (e.g., 1.1% at 7 nm) but exhibits a sharp increase to 97.1% at 15 nm, significantly compromising resonance quality. Sys₃ and Sys₄ show less extreme but still notable increases, with attenuation rising to 67.9% and 67.4%, respectively, at 15 nm. Such high values reflect strong reflectance suppression at resonance and can limit detection contrast.

The FWHM data in Figure S4d further clarify this trade-off. At 7 nm, Sys₂ presents a narrow dip width of 0.96°, which broadens to 7.64° at 15 nm. Sys₃ and Sys₄ follow the same upward trajectory. For instance, FWHM in Sys₄ increases from 5.06° at 7 nm to 8.44° at 15 nm. This broadening reduces angular resolution and could impair the distinction of closely spaced resonance features in practical applications.

Given these observations, 7 nm emerges as the most balanced Si₃N₄ thickness across all systems. At this thickness, the following occurs:

• Sys₂ achieves Δθ = 3.7°, sensitivity = 5.4%, attenuation = 1.1%, and FWHM = 0.96°.
• Sys₃ records Δθ = 4.0°, sensitivity = 5.6%, attenuation = 12.9%, and FWHM = 5.36°.
• Sys₄ offers Δθ = 3.9°, sensitivity = 5.5%, attenuation = 19.8%, and FWHM = 5.06°.

These values show meaningful improvements in sensing performance relative to the baseline while preserving dip sharpness and minimizing reflectance loss. Thus, 7 nm provides the most reliable configuration for maintaining a stable and detectable SPR signal in all three systems. This thickness is adopted in the remaining simulations for consistency and optimal performance.

3.4. Molybdenum Disulfide Optimization

To further emphasize, MoS₂ has emerged as a promising 2D material in SPR biosensing due to its strong light–matter interaction, high surface adsorption capability, and refractive index sensitivity [42,43]. To determine the optimal number of MoS₂ monolayers in the proposed sensor architectures, Sys₃ and Sys₄ were evaluated for layer counts ranging from 1 to 6 (denoted as L1–L6). The impact on reflectance behavior and performance metrics was assessed using the results in Figures S5 and S6 and Table S4.

As shown in the reflectance curves (Figure S5a,b), increasing the number of MoS₂ layers leads to a systematic redshift of the SPR dip in both systems, accompanied by a broadening of the resonance curve. These shifts reflect deeper field penetration and increased interaction with the analyte, especially in multilayered MoS₂ configurations [42].

Quantitative analysis in Figure S6a shows that Δθ increases steadily with the number of MoS₂ layers. In Sys₃, Δθ grows from 2.0° at L1 to 10.7° at L6. In Sys₄, the same trend is observed, rising from 2.0° at L1 to 11.1° at L6. Similar behavior is reported for sensitivity enhancement in Figure S6b, where Sys₃ reaches 14.9% at L6 and Sys₄ peaks at 15.5%. These results indicate that additional MoS₂ layers effectively enhance sensor response by amplifying the evanescent field’s interaction with the biological analyte [43].

However, improvements in Δθ and sensitivity must be weighed against attenuation and FWHM. As shown in Figure S6c, attenuation in Sys₃ initially decreases to a minimum of 0.87% at L2 before rising again to 45.9% at L6. Similarly, in Sys₄, attenuation drops to just 0.004% at L3 but increases beyond that, reaching 33.2% at L6. This rise in attenuation at higher layer counts suggests a growing energy loss at resonance, which can degrade detection contrast and the signal-to-noise ratio. Indeed, FWHM, as presented in Figure S6d, also shows a consistent increase with additional MoS₂ layers. In Sys₃, FWHM widens from 5.1° at L1 to 12.3° at L6, while Sys₄ grows from 4.8° to 11.5° over the same range. Broader FWHM indicates reduced angular resolution, which can compromise the ability to differentiate subtle changes in analyte concentration.

Considering these trade-offs, two MoS₂ layers (L2) are selected as the optimal condition for Sys₃. At this point, Sys₃ achieves a substantial angular shift (3.8°), sensitivity enhancement (5.3%), and a remarkably low attenuation of 0.87%, with FWHM maintained at 6.98°. For Sys₄, three MoS₂ layers (L3) provide the most balanced performance. At L3, the system records Δθ = 5.5°, sensitivity enhancement = 7.6%, and an exceptionally low attenuation of 0.004%, while keeping FWHM at 8.05°. Although higher layers improve Δθ further, they introduce more significant losses and reduce spectral definition, making L3 the most efficient and stable configuration. These configurations are adopted in all subsequent analyses.

3.5. Optimized Parameters and Cancer Samples Tested

Table 3. Optimized parameters of the different systems.

Material	Refractive Index (RI)	Thickness (nm)
Sys1
BK7 (P)	1.5151	---
Cu	0.0369 + 4.5393	55.0
Sys2
BK7 (P)	1.5151	---
Cu	0.0369 + 4.5393	55.0
Si3N4 (SN)	2.0394	7.0
Sys3
BK7 (P)	1.5151	---
Cu	0.056253 + 4.2760	45.0
Si3N4 (SN)	2.0394	7.0
Molybdenum disulfide (MoS2)	5.0805 + 1.1723 i	0.65 * L (L = 2)
Sys4
BK7 (P)	1.5151	---
Cu	0.0369 + 4.5393	45.0
Molybdenum disulfide (MoS2)	5.0805 + 1.1723 i	0.65 * L (L = 3)
Si3N4 (SN)	2.0394	7.0

presents the optimized material configurations and corresponding structural parameters for the four multilayer systems evaluated in this study. These values result from sequential parametric optimization aimed at maximizing resonance angle sensitivity while minimizing reflectance broadening. In Sys₁ and Sys₂, the copper layer thickness was fixed at 55.0 nm, whereas in Sys₃ and Sys₄, a thinner copper layer of 45.0 nm was selected to enhance coupling efficiency in the presence of additional functional layers. The dielectric silicon nitride (Si₃N₄) layer, where included, was maintained at a uniform thickness of 7.0 nm, based on its role in improving field confinement and reducing damping losses. The molybdenum disulfide (MoS₂) layer was introduced in Sys₃ and Sys₄, with a thickness corresponding to two monolayers (1.30 nm) and three monolayers (1.95 nm), respectively. These layer counts were chosen to balance the trade-off between increased light–matter interaction and signal attenuation, ensuring favorable spectral resolution across the operational range.

Regarding the origin and consistency of the refractive index values used in this theoretical investigation,

Table 4. Refractive index values for the different cancer types [44,45,46,47,48,49]. The values of RI are reported before (normal) and after the presence of cancer, and other important aspects are reported.

Cancer Type	Cell Line	Refractive Index (Normal)	Refractive Index (Cancerous)	Reported Concentration/Ratio	Specificity/Detection Method Description
Breast Cancer (Type 1)	MDA-MB-231	1.368	1.397	80% cancer cells	SPR detection based on refractive index modulation induced by MDA-MB-231 morphology; label-free physical interaction
Breast Cancer (Type 2)	MCF-7	1.368	1.401	80% cancer cells	SPR response enhanced by multilayer design; detects RI shift induced by MCF-7 cell optical profile
Cervical Cancer	HeLa	1.368	1.392	80% cancer cells	SPR configuration using Si3N4; monitors HeLa cell-induced RI variations without surface binding agents
Skin Cancer	Basal cells	1.368	1.382	80% cancer cells	SPR reflectance profile adjusted to identify basal-cell-induced RI changes in a non-functionalized setting
Adrenal Cancer	PC-12	1.368	1.385	80% cancer cells	SPR simulation of RI shift due to PC-12 cell morphology; detection through physical adsorption effects only
Blood Cancer	Jurkat/JM	1.368	1.389	80% cancer cells	Detection via RI perturbation from Jurkat/JM cells; no biochemical tags or functionalization involved

provides a comparative summary of the normal and cancerous refractive indices (RIs) for six representative cancer types, together with relevant experimental details reported in prior studies. These values were not derived from the direct experimentation in the present work but were selected from previously validated literature sources [44,45,46,47,48,49], where consistent cancer-induced RI shifts were quantified under controlled conditions. In each referenced case, simulations were based on a cancer cell concentration of approximately 80%, as adopted in Ref. [34], which represents a biologically plausible scenario for evaluating optical contrast between malignant and non-malignant cell populations. This concentration enables the modeling of maximum expected optical perturbation, thereby providing a rigorous framework for assessing the theoretical sensitivity limits of SPR-based detection systems.

Regarding specificity, the current sensor model does not incorporate chemical functionalization or molecular recognition layers. Instead, the detection relies on the intrinsic optical contrast introduced by physical changes in cancer cell morphology and density, which affect the local refractive index at the metal–dielectric interface. While this approach does not distinguish between cancer types through biochemical affinity, it enables label-free and rapid identification based on optically resolvable parameters. The SPR systems evaluated here use angular interrogation to capture small RI variations, which are amplified by the multilayer design, particularly in configurations integrating MoS₂ and Si₃N₄ layers. As noted, these materials enhance local electromagnetic field confinement and resonance sharpness, improving the ability to resolve subtle RI differences associated with specific cell lines.

Each cancer type modeled corresponds to a well-characterized cell line with distinct biophysical properties. For instance, the MDA-MB-231 and MCF-7 breast cancer lines exhibit differing nuclear densities and membrane compositions, contributing to measurable RI disparities. Similarly, Jurkat (blood), HeLa (cervical), and PC-12 (adrenal) cells have been reported to induce RI changes in the range of 0.014 to 0.033 units compared to their normal analogues. These differences, while moderate, fall within the angular resolution capacity of SPR systems operating with optimized multilayer stacks.

We point out that no experimental determination of the linear detection range was performed in the present study. However, based on previous experimental works [46,49], effective SPR detection in similar contexts has been demonstrated at concentrations as low as 1:10⁵ (e.g., MDA-231 in blood). This suggests that SPR sensors designed for physical refractive index interrogation, particularly those augmented with MoS₂ for enhanced field localization, are theoretically capable of detecting cancer cells at low abundance, provided that there is sufficient optical separation from background components.

3.6. Cancer Detection

The practical relevance of the proposed biosensor systems is evaluated by analyzing their performance in detecting six different cancer types: skin, cervical, blood, adrenal, breast T1, and breast T2. The sensor response before and after cancer onset is shown through reflectance curves in Figure 2, while detailed performance metrics are plotted in Figure 3 and quantified in Table S5.

The SPR reflectance curves in Figure 2a–d demonstrate resonance angle shifts upon exposure to malignant samples across all systems. In Sys₁ and Sys₂, these shifts are evident but modest, with well-defined dips and relatively narrow resonance profiles. In Sys₃ and Sys₄, the resonance shifts are larger and consistently differentiated across all cancer types, reflecting stronger plasmon–analyte interaction due to the presence of MoS₂ and optimized dielectric structuring. Quantitatively, Figure 3a shows that Δθ increases significantly in Sys₃, ranging from 2.67° (breast T2) to 5.76° (cervical). Sys₄ also performs well, but the shift reduces for high-RI samples such as breast T2 (0.37°) and breast T1 (0.79°), indicating decreasing sensitivity for later-stage malignancies. In contrast, Sys₁ and Sys₂ maintain moderate shifts, peaking at 3.56° and 5.10°, respectively, for cervical cancer.

The sensitivity enhancement trends in Figure 3b mirror those of Δθ. Sys₃ achieves the highest enhancement overall, with values up to 7.27% (cervical) and consistently above 4.30% across all cancer types. Sys₄ follows closely for skin and cervical cancers but drops significantly for breast and adrenal cancers, with a minimum of 0.43% (breast T2). Sys₂ maintains sensitivity levels between 4.01% (blood) and 6.75% (cervical), outperforming Sys₁, which remains mostly below 4.99% across all cases.

In terms of attenuation (Figure 3c), Sys₁ and Sys₂ demonstrate very low energy losses for all cancer types, ranging from 0.58% to 1.15% in Sys₁ and even reaching 0.001% for blood cancer in Sys₂. These low attenuation values produce sharp resonance dips, which are useful for accurate angle detection. However, Sys₃ also maintains manageable attenuation, with values mostly under 13.93%, and a minimum of 0.18% for skin cancer. Sys₄, by contrast, exhibits notably high attenuation in multiple cases, especially 61.46% (breast T2) and 55.89% (breast T1), which can obscure resonance detection.

The FWHM results in Figure 3d provide insight into the resolution quality of each system. Sys₁ and Sys₂ maintain narrow FWHM values under 1.79°, favoring high angular precision. However, these gains come at the expense of sensitivity. Sys₃ exhibits broader FWHM values between 7.47° (skin) and 7.93° (breast T2), which are acceptable given the strong angular shifts and sensitivity enhancements. Sys₄, although similar in architecture, displays slightly broader FWHM values up to 8.81°, combined with increased attenuation, which limits its practical advantage.

The comprehensive performance data in Table S5 highlight Sys₃ as the most effective biosensor design for detecting all six cancer types. Sys₃ delivers a high angular shift (e.g., 5.76° for cervical), strong sensitivity (e.g., 7.27%), and moderate attenuation (e.g., 0.87–12.33%) across the board. Its ability to maintain reliable detection across early- and mid-stage cancers, while balancing field confinement and signal clarity, supports its broader diagnostic applicability.

3.7. Performance Metrics of the Biosensor

To assess the diagnostic utility of the optimized SPR biosensors, an extended analysis was performed across six biologically relevant cancer types, using key performance indicators: sensitivity (S, Figure 4a), detection accuracy (DA, Figure 4b), quality factor (QF, Figure 4c), figure of merit (FoM, Figure 4e), limit of detection (LoD, Figure 4f), and comprehensive sensitivity factor (CSF, Figure 4g), with the results summarized in Figure 4 and

Table 5. Numerical values of sensor metrics for the optimized SPR biosensors for different cancer types.

Cancer Type	$\mathit{S} (°/\mathbf{R}\mathbf{I}\mathbf{U}$)	DA	QF (RIU−1)	FoM (RIU−1)	LoD (10−5)	CSF
Sys1
Skin	136.750	3.791	189.560	187.376	3.656	181.93
Cervical	148.125	4.399	183.328	181.712	3.375	175.48
Blood	151.429	2.676	191.165	189.373	3.301	182.98
Adrenal	158.750	2.667	190.569	189.062	3.149	182.44
Breast T1	165.357	2.663	190.250	189.004	3.023	182.25
Breast T2	169.107	2.664	190.316	189.211	2.956	182.39
Sys2
Skin	182.000	2.984	149.216	148.810	2.747	144.92
Cervical	212.500	3.510	146.277	146.214	2.352	141.72
Blood	221.071	2.203	157.428	157.425	2.261	152.68
Adrenal	245.893	2.238	159.916	159.483	2.033	154.46
Breast T1	273.750	2.272	162.305	160.324	1.826	155.09
Breast T2	291.964	2.287	163.384	159.653	1.712	154.33
Sys3
Skin	207.750	0.556	27.808	27.757	2.406	25.77
Cervical	239.792	0.747	31.163	29.149	2.085	26.06
Blood	252.321	0.461	32.954	31.611	1.981	28.45
Adrenal	254.643	0.459	32.851	28.799	1.963	25.39
Breast T1	221.964	0.395	28.283	21.035	2.252	17.96
Breast T2	190.714	0.336	24.060	15.862	2.621	13.19
Sys4
Skin	225.125	0.541	27.082	25.371	2.220	23.44
Cervical	196.667	0.562	23.439	15.782	2.542	13.45
Blood	195.179	0.326	23.340	17.244	2.561	15.00
Adrenal	123.929	0.204	14.630	8.338	4.034	6.81
Breast T1	56.964	0.092	6.571	2.898	8.777	2.18
Breast T2	26.607	0.042	3.019	1.163	18.791	0.82

.

Among all configurations, the MoS₂-integrated systems, Sys₃ and Sys₄, demonstrated the highest sensitivity to refractive index variations (Figure 4a). In Sys₃, S values ranged from 190.71 °/RIU (breast T2) to 254.64 °/RIU (adrenal), while Sys₄ achieved sensitivity up to 225.13 °/RIU (skin). These values confirm the enhanced light–matter interaction enabled by the MoS₂ layers. This behavior is especially advantageous for detecting early-stage cancers that manifest as subtle refractive index shifts, such as skin, cervical, or blood malignancies.

However, as expected from high-field enhancement systems, Sys₃ and Sys₄ exhibited trade-offs in terms of resonance sharpness. Detection accuracy values in Sys₃ fell below 0.75 across all cancer types, while Sys₄ registered even lower values, especially for blood and breast cancer, where DA dropped to 0.204 and 0.042, respectively (Figure 4b). These reduced values reflect the broader resonance profiles, which were previously linked to increased FWHM, and indicate a compromise in angular resolution. In cancers where precision localization of the resonance dip is essential, this trade-off becomes more critical.

Despite this, Sys₃ maintains balanced performance in early-to-mid index cancers. It demonstrates LoD values ranging from 1.96 × 10⁻⁵ (adrenal) to 2.62 × 10⁻⁵ (breast T2), which are comparable to or better than those of Sys₁, and still within the detection limits required for clinical applications (Figure 4f). Sys₄, while still sensitive in low-index cases, suffers performance loss in high-index malignancies—its LoD rises sharply to 18.79 × 10⁻⁵ for breast T2, and its CSF falls to 0.82 (Figure 4f), indicating instability in complex detection scenarios.

Sys₃ remains particularly strong for cancers with moderate refractive index change, such as cervical, skin, and blood cancers. For example, in cervical cancer, Sys₃ provides 239.79 °/RIU sensitivity, an FoM of 29.15 RIU⁻¹, and a reasonable LoD of 2.19 × 10⁻⁵, confirming its suitability in early detection with limited molecular mass (Figure 4e,f). For blood cancer, Sys₃ maintains high sensitivity (252.32 °/RIU), with a balanced FoM (31.61 RIU⁻¹) and competitive CSF (28.45). While its angular precision remains lower than that of Sys₁, the overall field interaction strength and low detection threshold justify its use when sensitivity is the driving factor.

Sys₄, while also MoS₂-based, shows a steeper decline in performance for cancers with high refractive index shifts, such as breast T1 and T2. Its sensitivity to breast T2 drops to 26.61 °/RIU, and its FoM reaches only 1.16 RIU⁻¹, with an extremely low DA and CSF. However, in low-RI cancers like skin and cervical cancer, Sys₄ provides solid metrics, e.g., 196.67 °/RIU sensitivity and 15.78 RIU⁻¹ FoM for cervical cancer—making it viable for detection in early-stage scenarios where the RI contrast is less dramatic.

By contrast, while Sys₂ offers a strong balance of metrics across all cancers, including sharp dips and a low LoD, its structure lacks the advanced nanomaterial interaction capability provided by MoS₂. Its performance remains robust but inherently limited in field enhancement compared to Sys₃. The current study, therefore, does not aim to downplay Sys₂ but rather positions it as a reference to highlight how MoS₂-enhanced architectures—especially Sys₃—can outperform conventional designs in high-sensitivity applications.

3.8. Literature Comparison

Table 6. Comparison with state-of-the-art biosensor records.

Configuration	$\mathit{S} (°/\mathbf{R}\mathbf{I}\mathbf{U})$	Refs.
BK7-Ag-PtSe2-Adrenal	212.85	[50]
BK7-Au-Ag-Si3N4-Cervical	341.00	[34]
BK7-Ag-Si3N4-BP-Adrenal	390.35	[51]
BK7-Ag-Si3N4-BP-Cervical	294.27	[51]
BK7-Cu-Si3N4-MoS2-Adrenal	254.64	This work
BK7-Cu-MoS2-Si3N4-Cervical	196.67	This work

presents a comparative summary of sensitivity values (S, in °/RIU) reported for surface plasmon resonance biosensors targeting adrenal and cervical cancer detection [34,50,51]. The benchmarked configurations incorporate various multilayer stacks based on noble metals (Ag, Au), 2D materials (PtSe₂, black phosphorus), and dielectric enhancements. In particular, Ref. [51] corresponds to a recent contribution from our research group, in which a dual BP–Si₃N₄ design demonstrated high angular sensitivity due to the synergistic interaction between anisotropic electronic behavior and dielectric confinement. In the present work, two novel configurations were evaluated: BK7–Cu–Si₃N₄–MoS₂ for adrenal cancer detection and BK7–Cu–MoS₂–Si₃N₄ for cervical cancer detection. These systems achieved theoretical sensitivities of 254.64 °/RIU and 196.67 °/RIU, respectively. While these values are modestly lower than those obtained using BP-based or dual-metal systems, they remain competitive and exhibit several advantages that merit emphasis.

First, copper offers a cost-effective and abundant alternative to gold and silver, making it suitable for scalable sensor production. The sensitivity observed here validates the plasmonic potential of copper when integrated within a multilayer stack that includes both a dielectric (Si₃N₄) and a two-dimensional semiconductor (MoS₂). This combination enhances field localization near the sensing interface while mitigating the oxidative instability of the metallic layer.

Second, the integration of MoS₂ provides a valuable platform for future biochemical functionalization. Although the current model focuses exclusively on RI-based physical detection, MoS₂’s high surface activity, tunable bandgap, and strong light–matter interaction suggest that additional gains in sensitivity could be achieved upon biochemical interface engineering or hybrid functional layering.

Moreover, the simulated systems offer a balanced trade-off between sensitivity and design simplicity. Unlike more intricate BP-based configurations or dual-metal architectures, the proposed structures maintain low complexity and fabrication feasibility without compromising optical performance. Their ability to distinguish small refractive index changes associated with malignant transformation reinforces their applicability in practical diagnostic contexts.

3.9. Potential Fabrication of the Proposed Biosensors

The proposed SPR sensor structures (BK7–Cu–Si₃N₄–MoS₂ and BK7–Cu–MoS₂–Si₃N₄) can be fabricated using established thin-film deposition and 2D material transfer techniques, as outlined below [52,53]:

• BK7 glass substrates can be cleaned using piranha solution, rinsed with deionized water, and dried under nitrogen.
• A Cu film (45–55 nm) can be deposited via thermal evaporation or sputtering under high vacuum. Immediate processing is recommended to minimize oxidation.
• A 7 nm Si₃N₄ film can be deposited by low-temperature PECVD or ALD, depending on the configuration.
• Few-layer MoS₂ can be transferred using a PMMA-assisted wet transfer method from CVD-grown wafers, followed by PMMA removal and gentle annealing.
• Optional thermal annealing (~150 °C, inert atmosphere) may be applied to improve interfacial quality and reduce transfer residues.
• AFM, ellipsometry, and Raman spectroscopy may be used to validate layer thickness and material integrity prior to SPR interrogation.

To stress once more, from a physicochemical standpoint, MoS₂ possesses several characteristics that make it particularly favorable for enhancing surface plasmon resonance (SPR) sensing platforms as related 2D materials [54]. First, MoS₂ is a 2D transition metal dichalcogenide with a direct bandgap of ~1.8 eV at the monolayer level [55], which facilitates strong light–matter interaction near the visible spectrum, particularly at the commonly used SPR wavelength of 633 nm. Its high in-plane dielectric constant and moderate out-of-plane permittivity contribute to enhanced confinement of the evanescent electromagnetic field near the sensing surface [56]. This interaction not only amplifies the local field intensity but also promotes sharper resonance dips, thereby improving sensitivity and spectral resolution.

Furthermore, as stated, MoS₂ exhibits a high surface-to-volume ratio and favorable adsorption sites for biomolecules, which can be exploited in future work for biochemical functionalization [57]. Its optical absorption, although not as intense as that of metallic layers, is sufficient to support hybrid plasmon–exciton coupling in layered structures, especially when integrated with metals like copper that provide strong SPR excitation but suffer from oxidation. The addition of MoS₂ in a multilayer stack can improve sensor stability, sharpen resonance features, and allow for the tuning of the resonance angle response without compromising fabrication feasibility. These combined properties justify the selection of MoS₂ in the present model as a candidate material for enhancing next-generation SPR biosensor performance.

3.10. Limitations

While the proposed Cu/Si₃N₄/MoS₂-based SPR sensor shows strong theoretical potential, some experimental considerations merit discussion. The fabrication of few-layer MoS₂ via PMMA-assisted transfer can introduce challenges such as layer non-uniformity, polymer residues, and interfacial defects, which may affect reproducibility and sensor performance. Though thermal annealing mitigates some issues, achieving consistent optical quality across batches remains non-trivial.

Additionally, integrating MoS₂ with Cu and Si₃N₄ demands careful control of adhesion and layer interfaces to maintain plasmonic efficiency. From a translational perspective, although MoS₂ has demonstrated biocompatibility, its long-term behavior under physiological conditions and potential for non-specific adsorption require further study before in vivo application. These limitations, however, do not diminish the material’s promise, but rather outline key areas for future experimental refinement and validation.

4. Conclusions

This work introduced and evaluated a series of Cu/Si₃N₄/MoS₂-based SPR biosensors for the detection of various cancer types through refractive index variation. Four systems (Sys₁–Sys₄) were systematically optimized by adjusting copper thickness (45.00–55.00 nm), silicon nitride layer thickness (7.00 nm), and the number of MoS₂ monolayers (two or three layers) to improve plasmonic sensitivity, angular shift, and spectral performance.

The configuration Sys₃ (BK7–Cu–Si₃N₄–MoS₂) demonstrated the best overall sensitivity, reaching 254.64 °/RIU for adrenal cancer and 239.79 °/RIU for cervical cancer. It maintained low detection limits down to 1.96 × 10⁻⁵ RIU, with reasonable figures of merit (FoMs) up to 31.61 RIU⁻¹, despite broader resonance widths and reduced detection accuracy in high-RI cancers. For lower-index analytes such as skin and cervical samples, Sys₃ achieved CSF values of 25.77 and 26.06, respectively, confirming its suitability for early-stage diagnostic scenarios. While Sys₄ (BK7–Cu–MoS₂–Si₃N₄) showed promising sensitivity for select cases (e.g., 196.67 °/RIU for cervical cancer), it exhibited performance degradation in higher-index conditions, with the FoM dropping below 2.90 RIU⁻¹ and the CSF falling to 0.82 in breast T2 detection. In contrast, Sys₂ provided consistently narrow resonance dips and low attenuation, but did not match the high sensitivity achieved by the MoS₂-based systems.

The integration of MoS₂ into the sensor stack significantly enhanced field confinement and analyte interaction, confirming the potential of these 2D-material-enhanced designs as viable alternatives to noble-metal-based biosensors. Overall, the proposed configurations—particularly Sys₃—offer a compelling balance of sensitivity, stability, and material efficiency for the development of advanced label-free optical platforms for cancer diagnostics.