The full modeling details are given in Refs. [25, 28]. Briefly, the total reflection of the N^th-layer model can be described as follows:

By Equation 1, the reflectance as a function of the angle of incidence can be obtained, the so-called SPR curve, from which we calculate the peak position, full-width half maximum (FWHM), and attenuation percentage. Then, we analyse the following parameters:

Where, Δθ represents the angle shift variation in degrees and Δn represents the refractive index variation.

Where, R min represents the lowest normalized reflection value of the SPR curve.

R max represents the maximum reflectance before resonance deep. All numerical computations in this investigation are performed using a data sampling of 5 × 10³ points. To point out, the proposed modeling approach in the current study has been validated by using the experimental data reported in Ref. (20) and shown in Supplementary Figure S1.

Supplementary Table S1 outlines the five multilayer assemblies investigated through transfer-matrix simulations. The baseline configuration, Sys0, pairs a BK7 prism with a copper film in contact with phosphate-buffered saline (PBS). Substituting PBS with an average cancer-related biofluid (27) yields Sys1 and isolates the bulk refractive-index increment introduced by pathological serum. Sys2 adds a silicon nitride spacer between copper and the analyte; this high-index dielectric confines the evanescent field near the sensing interface (29), sharpens the resonance dip, and shields the metal surface. Sys3 incorporates an MXene sheet on top of the silicon nitride. The conductive two-dimensional layer intensifies surface charge oscillations and offers additional adsorption sites for future biochemical functionalization (30). Sys4 reverses the order of the dielectric and MXene films, permitting evaluation of interfacial symmetry effects and the individual contribution of each thin layer to plasmon confinement.

To remark, copper retains a lower cost than gold (31), and the protective dielectric–MXene coatings impede oxidation, keeping the stacks compatible with standard sputtering or spin-coating protocols.

On the other hand, Supplementary Table S2 compiles the optical constants and nominal thicknesses assigned to each element of the multilayer sensor. The BK-7 prism couples the incident beam through its refractive index of 1.5151 at 633 nm (15). A 45 nm copper film, characterised by n = 0.0369 + 4.5393i, supplies the plasmonic core while moderating ohmic loss (25). A 5 nm silicon nitride spacer with n = 2.0394 introduces a high-index, low-loss phase-matching layer that sharpens the resonance dip (21). The simulation treats a single-layer Mxene sheet as a 0.933 nm coating with n = 2.38 + 1.33i, matching ellipsometry data for Ti₃C₂T_x flakes (25). Two analyte indices bracket physiological conditions: 1.335 for phosphate-buffered saline, used as the non-pathological reference [16], and 1.349 for the averaged cancer serum employed in sensitivity calculations (27). These parameters set the boundary conditions for the transfer-matrix analysis that follows.

Figure 1a presents the reflectance traces for the four cancer-sensing stacks relative to the PBS baseline. Each additional functional layer shifts the resonance minimum toward larger incidence angles: 68.86° for Sys₁, 71.27° for Sys₂, and a narrow interval around 72.1° for Sys₃ and Sys₄ (Supplementary Table S3). The monotonic drift confirms that the evanescent field penetrates further into successively higher-index overlayers, raising the momentum requirement for plasmon coupling.

The bar chart in Figure 1b quantifies the percentage rise in sensitivity with respect to the copper-only reference. MXene-free Sys₁ delivers only 2.4% improvement, whereas insertion of a Si₃N₄ spacer nearly triples that value to 6%. Adding MXene lifts the gain above 7%, with Sys₄ edging slightly ahead of Sys₃ (7.22% versus 7.17%). The trend indicates that dielectric confinement and metallic two-dimensional screening act cooperatively to amplify the field response to refractive-index perturbations.

Figure 1c and the Δθ column in Supplementary Table S3 trace the absolute angular displacement produced by the cancer medium. The shift rises from 1.60° in Sys₁ to about 4.8° in the MXene-containing stacks, a threefold enhancement. Such large excursions reduce the need for angular interpolation during interrogation, easing hardware requirements for goniometric resolution.

Attenuation at resonance, plotted in Figure 1d, separates the dielectric-only design from the MXene hybrids. Both Sys₁ and Sys₂ lose just over 28% of the incident power at the dip, a consequence of ohmic absorption in copper. Once MXene enters the stack, the loss plunges to 1.38% for Sys₃ and 0.74% for Sys₄. The conductive sheet redistributes surface currents away from the bulk metal, leaving more energy available for re-radiation into the prism—a desirable feature for signal-to-noise optimisation.

The angular linewidth, displayed in Figure 1e, broadens as the stack complexity grows. Sys₁ records the narrowest dip (1.08°), Sys₂ widens moderately (1.46°), and the MXene architectures approach 2.6–2.7°. Broader dips soften the slope at half depth, which can limit detection accuracy, yet the simultaneous rise in Δθ partially compensates. In practice, the balance between linewidth and angular excursion defines the optimum operating point; Sys₄ achieves the widest shift while keeping the linewidth slightly below that of Sys₃.

Collectively, the data indicate that silicon nitride alone yields noteworthy gains in both sensitivity and angular displacement, yet the greatest benefits emerge when MXene is incorporated. The MXene-above-dielectric arrangement (Sys₄) offers the best compromise among large angular shift, minimal attenuation, and acceptable linewidth, marking it as the leading candidate for further optimisation in subsequent sections. However, all these systems are analysed in the current work for a proper comparison.

Figure 2 and Supplementary Table S4 show the evolution of the resonance angle as the copper film is varied from 30 to 55 nm in all four stacks. In the simplest layout, Sys₁ (prism / Cu / cancer medium) (Figure 2a), the minimum shifts from 69.25° at 30 nm to 68.83° once the metal reaches 55 nm. The downward drift observed between 30 and 45 nm points to reduced field penetration once the copper thickness exceeds its optical skin depth; after that threshold, additional metal adds little phase delay, and the curve levels off. Adding a 5 nm silicon-nitride spacer (Sys₂, Figure 2b) largely insulates the surface mode from variations in the underlying metal. The resonance holds in a narrow corridor—71.40° at 30 nm and 71.28° at 55 nm—yielding a total excursion below 0.15°. Such angular stability relaxes deposition tolerances during fabrication.

Introducing MXene on the spacer (Sys₃, Figure 2c) pins the resonance near 72°. The angle edges upward by only 0.15° across the full thickness sweep, settling at 72.10° once copper reaches 45 nm. The two-dimensional conductor concentrates the plasmonic field at the dielectric interface, so minor changes in bulk metal thickness have little influence on phase-matching conditions. In Sys4 (Figure 2d), where MXene lies directly on copper and silicon nitride sits above, the minimum rises from 72.00 to 72.15° as the metal grows. The gentle positive gradient likely reflects a small impedance mismatch introduced by the MXene-metal junction; thicker copper compensates by increasing confinement.

Figure 3 traces how angular shift (Figure 3a), sensitivity enhancement (Figure 3b), attenuation (Figure 3c), and spectral width (Figure 3d) evolve as the copper film is thickened, revealing that attenuation—the percentage of power dissipated at resonance—acts as the most decisive indicator of overall performance. In Sys₁, attenuation falls monotonically from almost 75% at 30 nm to just 1.38% at 55 nm, while Δθ and the sensitivity enhancement diminish only modestly (1.83 → 1.57° and 2.72 → 2.34%). Because every additional nanometre of copper removes loss without a commensurate penalty in angular response, the minimum-loss point at 55 nm is adopted as the optimum thickness for this architecture.

Sys₂ behaves in much the same way: the silicon-nitride buffer does not alter the trend but shifts the absolute figures. At 55 nm the dip absorbs a mere 1.30% of the incident light, the resonance narrows to 0.77°, and Δθ stabilises near 1.80°. No thinner film achieves a comparable suppression of loss; hence the attenuation minimum again dictates a 55 nm choice.

The MXene-containing stacks present a subtler picture. In Sys3, the attenuation reaches its lowest value, 1.40%, at 40 nm. Thickening the metal further trims the linewidth, yet the gain is small and comes at the cost of a slight rise in loss and no significant change in Δθ or sensitivity. Selecting the 40 nm minimum therefore balances reduced dissipation with satisfactory angular performance.

For Sys₄, the attenuation curve bottoms out at 45 nm (0.74%), after which the dip deepens again and the linewidth ceases to improve. At this thickness, the sensor still delivers a high angular shift of 1.88° and one of the best sensitivity enhancements in the series (2.68%). Moving away from the attenuation minimum in either direction would either waste optical power or broaden the plasmon feature. Consequently, 45 nm is retained as the optimal copper thickness for Sys4. Thus, the study ensures that every subsequent analysis builds on a metal thickness that maximises usable signal while keeping angular responsivity and spectral sharpness within desirable limits.

Figure 4 and Supplementary Table S5 capture the systematic drift of the resonance minimum produced by increasing the silicon-nitride spacer from 5 to 15 nm in the three stacks that contain this dielectric material. In Figure 4a, Sys₂ shifts from 71.28° at 5 nm to 80.17° at 15 nm, a cumulative change close to nine degrees. Each additional two-nanometre increment adds roughly 1.5–2.0° to the required coupling angle. The high-index layer increases the effective optical path and forces the plasmon to satisfy momentum matching at steeper incidence.

Figure 4b displays a similar progression for Sys3, which also carries a MXene sheet above the spacer. The resonance begins at 72.05° for 5 nm and arrives at 81.06° for 15 nm. The presence of MXene raises the starting angle by about one degree relative to Sys₂. Yet, the slope with thickness remains comparable, indicating that the dielectric dominates the phase shift while MXene chiefly offsets the baseline.

Figure 4c shows Sys₄, where MXene lies below the dielectric. The initial angle is 72.11° and reaches 81.90° when the spacer reaches 15 nm, yielding the largest overall excursion in the series. Reordering the two thin films slightly magnifies the phase accumulation, consistent with the MXene–Si₃N₄ interface altering the impedance profile in a way that lengthens the optical trajectory.

Across all three architectures the resonance moves almost linearly with spacer thickness and approaches or exceeds 80° once the layer exceeds 13 nm. Such high angles reduce the dynamic margin available in standard Kretschmann benches and can challenge goniometer precision. Practical implementation is therefore likely to favour intermediate spacers, for example 7–9 nm, which position the dip within a more accessible angular window while still gaining a sizeable shift relative to the 5 nm reference.

Figure 5 gathers the four performance indicators that vary with the Si₃N₄ spacer while Supplementary Table S5 lists their numerical values. As the dielectric grows from 5 to 15 nm, all three stacks show a nearly linear rise in angular shift and sensitivity (Figures 5a,b). At the same time, the attenuation (Figure 5c) and spectral width (Figure 5d) do not follow a single trend: Sys₂ benefits from a gradual fall in loss, Sys₃ reaches a minimum near 11 nm, then rises, and Sys₄ climbs almost monotonically. The linewidth increases in every case. A decision point is therefore needed where the gain in responsivity still outweighs the penalties in loss, linewidth, and operating angle.

The 7 nm spacer meets that balance for every architecture. Compared with the 5 nm reference, it roughly doubles Δθ and the relative sensitivity (for example, Sys₂ moves from 1.82 to 3.05° and from 2.62 to 4.39%), yet keeps attenuation at or below 1% in Sys₂ and Sys₃ and just under 1% in Sys₄. At 9 nm, the incremental improvement in Δθ is matched by a similar percentage rise in linewidth, and above 11 nm, the resonance angle exceeds 75–78°, pushing the dip close to the mechanical limits of standard SPR goniometers while continuing to broaden the spectrum. The 7 nm choice therefore preserves an accessible coupling range (≈ 72–74°), maintains a sharp enough dip for reliable tracking, and avoids the steep loss variations seen in thicker spacers.

On this basis, the spacer is fixed at 7 nm for Sys₂-Sys₄, providing a practical compromise that secures a clear two-fold enhancement in angular responsivity without introducing excessive optical loss, resonance broadening, or unwieldy operating angles.

Figure 6a reveals a nearly linear migration of the resonance minimum in Sys₃ as MXene is stacked. A single sheet places the dip at 73.33°. Adding a second layer advances it to 74.31°, still within the angular window that standard goniometers accommodate with good precision. Each additional sheet pushes the peak farther, reaching 75.38° with three layers and approaching 79° when six layers are present. Once the angle exceeds roughly 75°, the available dynamic range narrows, and mechanical alignment becomes more demanding. The two-layer configuration, therefore, captures a clear shift while preserving a practical coupling geometry, and it is adopted as the optimised design for Sys₃.

In Figure 6b, the starting point for Sys₄ is 73.45°, with a single MXene layer deposited directly on copper. The next sheet lifts the minimum to 74.53°, then successive additions draw it steadily toward and beyond 77°. Because the single-layer case already secures an ample angular displacement and keeps the resonance well inside the manageable 70–75° interval, the attraction of further layers is outweighed by the loss of angular headroom. The sensor is thus configured with one MXene sheet in Sys₄.

To further emphasise the previous statements, Figure 7a records a steady rise in angular displacement as additional MXene sheets are introduced. In Sys₃, the shift grows from 1.96° with a single layer to 7.23° when six layers are present. Sys₄ follows a similar path, reaching 7.90° at the highest count. Figure 7b shows that the relative sensitivity increases in near-lockstep with Δθ, passing 10% when six layers are used in Sys₄.

The gain in responsivity is tempered by optical loss. Figure 7c, plotted on a logarithmic scale, reveals that attenuation climbs modestly for the first two sheets—remaining below 4% in Sys₃ and below 14% in Sys₄—before accelerating. At four layers, the loss already exceeds 25% in Sys₃ and 40% in Sys₄, eventually surpassing 50% at five and six layers in the latter.

Figure 7d demonstrates that the resonance linewidth broadens concurrently. For Sys₃, the width doubles between one and three layers, rising from 3.79 to 7.21°, and exceeds 10 degrees at six layers. Sys₄ starts with a narrower line (2.99°), yet the broadening trend is steeper, reaching 10.66° at the upper limit. A wider dip reduces the local slope and erodes detection accuracy even when the angular shift is large.

Then, Supplementary Table S6 quantifies these trends. Two MXene sheets in Sys₃ deliver a 2.95° shift and a 4.14% sensitivity enhancement while keeping attenuation at 3.84% and the linewidth at 5.47°. Further layers raise sensitivity but also bring a rapid escalation in loss and spectral broadening. In Sys₄, the single-layer case already secures a 2.02° shift with sub-one-per-cent attenuation and a sharp 2.99° width; the second sheet adds roughly one degree of shift but multiplies loss by 15 and stretches the dip to 4.66°. Hence, balancing these competing tendencies confirms the earlier optimisation: two MXene layers in Sys₃ and a single layer in Sys₄ provide substantial gains in angular responsivity while preserving low optical loss and maintaining a narrow resonance conducive to precise angle tracking.

Supplementary Table S7 condenses the material sequences and thicknesses that yield the most balanced performance for each architecture. The BK7 prism remains unchanged throughout, providing a refractive index of 1.5151 at the operating wavelength. Sys₁ retains a single functional layer: a 55 nm copper film with a complex refractive index of 0.056253 + 4.2760i. This thickness lies just beyond the optical skin depth, so joule heating is strongly suppressed while field penetration remains adequate for sensing refractive-index perturbations in the adjoining medium (32).

Sys₂ keeps the 55 nm copper layer and introduces a 7 nm silicon-nitride spacer (n = 2.0394). The dielectric elevates the evanescent field intensity at the sensing boundary, almost doubling both the angular shift and the relative sensitivity without expanding the resonance width or inflating optical loss (33). Sys₃ relies on the combined action of metal, dielectric, and MXene. Copper is reduced to 40 nm, limiting attenuation that would otherwise arise when additional lossy components are present. A 7 nm silicon-nitride spacer again sets the plasmon phase, and two MXene sheets add a conductive layer of 1.99 nm total thickness (0.993 nm per sheet, n = 2.38 + 1.33i). This stack secures strong field confinement while keeping the resonance angle near 74°, well within the mechanical range of standard Kretschmann benches (34).

Sys₄ adopts an alternate ordering in which a single MXene sheet (0.993 nm) rests directly on a 45 nm copper film, followed by the same 7 nm silicon-nitride spacer. The slightly thicker metal offsets the extra damping introduced by MXene–metal interactions, preserving sub-one-per-cent attenuation and a narrow spectral line. Reversing the MXene/Si₃N₄ sequence shifts the resonance baseline upward by about one degree relative to Sys₃ but avoids the broader linewidth encountered with additional MXene layers.

On the other hand, Supplementary Table S8 lists the bulk refractive indices (RI) adopted for the simulation of six cancer models and their healthy counterparts. The increments Δn fall within a relatively narrow span—0.014 to 0.024—which matches values reported experimentally for cell-rich media and conditioned buffers in earlier surface-plasmon studies (35–40). Four malignancies (blood, adrenal, and the two breast subtypes) share an RI rise of 0.014, moving from 1.376–1.387 in normal media to 1.390–1.401 when tumour cells are present (37–40). These modest shifts originate from elevated protein and lipid content released during cellular proliferation and do not require specific biochemical binding to disturb the optical field, as noted for Jurkat acute-leukaemia cells and PC-12 adrenal models.

Cervical HeLa cultures exhibit a larger increment, 0.024, increasing from 1.368 to 1.392 (36). The higher value reflects pronounced cytoskeletal reorganisation that raises the effective dielectric constant of the medium, an effect already exploited in silicon-nitride-based SPR assays. Basal skin-cancer simulants present the greatest RI jump, 0.020 (35). Although basal cells originate from epidermal layers with a lower baseline index than serum, their dense keratin network amplifies scattering and drives the observed optical contrast once malignant transformation begins.

These Δn values set an exacting but realistic detection target for the optimised sensors. The smallest increment (0.014) demands angular shifts on the order of two degrees in the present designs, whereas the largest (0.024) produces shifts of at least five degrees, comfortably above the instrument noise floor assumed in earlier sections. The RI values, therefore, define both the lower bound of refractive-index sensitivity required for blood-borne markers and the upper bound encountered when probing epithelial tumours, providing the context for the performance comparisons that follow.

The angular reflectance profiles illustrated in Figure 8 offer an insightful comparison of the spectral behavior of the optimized SPR systems (Sys₁–Sys₄) in response to six different cancer types: skin, cervical, blood, adrenal, and breast (T1 and T2) (35–40). The continuous curves represent the baseline performance of each system prior to cancer-cell detection, while the dashed lines reflect the angular shifts induced by the refractive index perturbations associated with the cancerous states, as reported in Supplementary Table S8. The corresponding SPR peak positions, extracted from Supplementary Table S9, enable a precise quantification of these spectral displacements.

In Figure 8a, Sys₁, which comprises a BK7/Cu/Ag structure, exhibits relatively small angular separations between the baseline and post-cancer profiles. This is reflected in the modest peak shifts reported in Supplementary Table S9, ranging from 2.11° (blood) to 3.55° (cervical). These limited shifts stem from the simpler two-layer configuration, which lacks the optical field enhancement mechanisms provided by additional dielectric or 2D materials. Figure 8b shows the response of Sys₂, where the addition of a Si₃N₄ layer considerably enhances the angular dispersion. Notably, the SPR peak positions shift more significantly upon cancer-cell detection, with values ranging from 3.44° (adrenal) to 5.10° (cervical). The broader dynamic range observed in this configuration reflects improved field confinement and increased interaction with the external analyte, enabled by the high refractive index and dielectric nature of Si₃N₄.

In Sys₃ (Figure 8c), the combination of Si₃N₄ and a bilayer MXene further amplifies the angular displacement of the reflectance minima. SPR peak positions span from 3.30° (blood) to 5.43° (cervical), as recorded in Supplementary Table S9. The incorporation of MXene introduces additional light–matter interactions through its high index and plasmonic contribution, yielding more pronounced shifts. However, the angular broadening and reflectance distortion at higher RI values are also apparent, suggesting increased propagation loss and damping effects that must be considered in practical implementations. Lastly, Figure 8d reveals the performance of Sys₄, which employs a reversed MXene–Si₃N₄ architecture. Here, the angular separation remains comparable to Sys₃, but the reflectance minima are sharper and more distinct, especially for higher-index cancer cases such as cervical and breast T2. The recorded peak shifts reach up to 5.44° (cervical), affirming the system’s capacity to resolve small RI variations while maintaining a favorable spectral profile.

Figure 9 contrasts the key diagnostic metrics extracted from the optimised stacks for each cancer model. In particular, Figure 9a shows that angular displacement grows in the order Sys₁ < Sys₄ ≈ Sys₃ < Sys₂ for every tumour type. Cervical media yield the largest shifts, reaching 5.10° in Sys₂, 5.44° in Sys₄, and 5.43° in Sys₃, while blood produces the smallest values. The two-degree window spanned by Sys₁ narrows the margin for reliable peak tracking; the three remaining architectures all exceed 3°, securing a clearer signal above instrument noise. The same hierarchy appears in Figure 9b for the index-normalised gain. Sys₂ delivers between 4.41% (adrenal) and 6.75% (cervical). Sys₃ and Sys₄ track closely, both surpassing 7% for cervical cells but trailing Sys₂ for the other cancers. Sys₁ lags, never exceeding 4.99%.

Attenuation profiles in Figure 9c reveal the chief trade-off. Sys₂ maintains sub-1% loss for five of the six media; only the breast-T2 test approaches 2%. Sys₁ stays below 1.2% across the board but at the cost of modest responsivity. Sys₃ and Sys₄ experience markedly higher losses once MXene enters the stack. In Sys₃, attenuation climbs above 8% for skin and reaches 36% for breast-T2, while Sys₄ ranges from 3.25% (skin) to 22% (breast-T2). The logarithmic scale underscores how rapidly joule heating grows with stronger field confinement in the MXene layers. Figure 9d plots the spectral width. Sys₁ presents the sharpest dips, all below one degree. Sys₂ remains acceptably narrow, spanning 1.21–1.78°. MXene again introduces broadening: Sys₃ widens to 6–7°, and Sys₄ settles near 4–5°. These broader profiles reduce the slope at half depth, lowering angle-tracking accuracy unless compensated by a higher signal-to-noise ratio.

To point out, these results position Sys₂ as the most balanced design. Sys₂ nearly matches the MXene stacks in angular shift and sensitivity while preserving the low attenuation and narrow width characteristic of the simpler metal film. Sys₁ offers the cleanest optical response but insufficient displacement for the smaller refractive-index increments. Sys₃ maximises responsivity at the expense of both loss and linewidth, whereas Sys₄ tempers those penalties yet still incurs higher damping than the dielectric-only arrangement.

Figure 10 underlines the decisive influence that MXene exerts on sensor responsivity. Figure 10a shows that introducing MXene sheets raises the angular sensitivity well beyond the levels reached with metal-dielectric stacks alone. Sys₃ delivers 196–254° RIU⁻¹ across the six cancer models, whereas Sys₄ extends this span to 192–312° RIU⁻¹ (Supplementary Table S10). The largest value, recorded for the breast-T2 surrogate, approaches twice the response of the copper-only reference. These gains confirm that even a single MXene layer, as in Sys₄, produces a substantial enhancement in the local field and the refractive-index leverage central to a high-performance SPR assay.

Figures 10b,c set those gains against resonance sharpness. Quality factors fall when MXene broadens the dip: Sys₃ ranges from 30 to 35 RIU⁻¹ and Sys₄ from 48 to 58 RIU⁻¹. Detection accuracy follows the same trend, settling just below one for Sys₃ and just above one for Sys₄. Although these figures are smaller than those for the dielectric-only design, they remain consistent across the cancer panel, indicating that the broader resonances do not fluctuate unpredictably with the analyte and can be tracked reproducibly.

For a MXene-centred sensor, the key point is that the sharp drop in loss—already demonstrated in earlier sections—offsets much of the penalty associated with a wider dip. In Sys₄, attenuation stays below 8% for four of the six cancers, leaving ample reflected intensity for precise angle interpolation. Sys₃ incurs higher loss, yet its two-layer MXene coating lifts sensitivity by a further 20–30% relative to Sys₄. This trade-off is attractive in applications where the lowest limit of detection outweighs constraints on light budget.

The data, therefore, position Sys₃ and Sys₄ as complementary MXene-enabled platforms. Sys₄ balances high sensitivity with moderate resonance width and low loss, yielding a versatile design for routine assays. Sys₃ prioritises maximal responsivity, suited to scenarios demanding the smallest possible refractive-index detection threshold. Both arrangements validate the premise of the study—that MXene, judiciously combined with silicon nitride and copper, can elevate SPR performance beyond that of purely dielectric-enhanced structures, while offering clear paths for tailoring the sensor to distinct clinical targets.

Figure 11 condenses the three aggregate indicators most often used to benchmark plasmonic biosensors across the six cancer models, with numerical values listed in Supplementary Table S10. FoM (Figure 11a) is governed by the interplay between angular sensitivity and resonance width. The narrow sub-degree dips in Sys₁ keep its FoM near 190 RIU⁻¹ for every analyte, the highest among the four designs. Introducing the Si₃N₄ spacer in Sys₂ broadens the dip but doubles the sensitivity, so FoM settles around 150–160 RIU⁻¹. MXene layers widen the resonance further and therefore suppress FoM: Sys₃ stays between 27 and 35 RIU⁻¹, and Sys₄ rises to 46–58 RIU⁻¹ owing to its single-layer configuration. Although these values sit below those of the dielectric-only stacks, they remain above the 20 RIU⁻¹ level often cited as the practical threshold for label-free biosensing, confirming that MXene-based architectures still occupy a performance regime suitable for analytical work.

LoD (Figure 11b) converts angular noise into a refractive-index threshold. Sys₂ attains the smallest LoD for all cancers, reaching 1.71 × 10⁻⁵ RIU for breast T2. Sys₄ follows closely, remaining below 2 × 10⁻⁵ RIU after cervical sensing. Sys₃ records values in the low-to-mid 10⁻⁵ RIU range (2.02–2.54 × 10⁻⁵ RIU), adequate for detecting the 0.014–0.024 RIU increments characteristic of the examined tumours. Sys₁ shows the least favourable LoD, exceeding 3 × 10⁻⁵ RIU for four of the media. The data indicate that MXene’s broader dips do not translate into prohibitive detection limits; the gain in sensitivity compensates for the increased linewidth.

CSF (Figure 11c) multiplies sensitivity by resonance contrast, providing an overall gauge of differential response. The high-contrast, narrow-width profile of Sys₁ again yields the largest CSF, clustering near 180 RU. Sys₂ follows at about 145–155 RU, reflecting its balance between sensitivity and moderate loss. Sys₄ achieves 43–50 RU, approximately double the values attained by the two-layer MXene stack, Sys₃ (18–27 RU). While CSF favours sharper resonances, the MXene configurations still maintain clear separation among the cancer-induced index shifts, especially when low reflected intensity is admissible.

In summary, the dielectric-only sensor (Sys₂) offers the highest FoM and the smallest LoD, making it attractive for applications where absolute precision outweighs other constraints. The MXene-enriched alternatives extend the sensitivity ceiling—Sys₃ maximising raw responsivity and Sys₄ striking a compromise between sensitivity and optical loss—while preserving detection limits within the 2 × 10⁻⁵ RIU bracket. These findings validate the central premise of the study: MXene layers, judiciously combined with silicon nitride and copper, expand the design space of SPR biosensors, enabling either peak sensitivity (Sys₃) or balanced, low-loss performance (Sys₄) depending on the demands of the diagnostic task.

Table 1 benchmarks the present MXene-assisted design against recent SPR configurations that target the same breast-T2 refractive-index increment (27, 41–43). The BK7–Cu–MXene–Si₃N₄ stack reported here attains a sensitivity of 312° RIU⁻¹, out-performing the PtSe₂–graphene composite (235° RIU⁻¹), and narrowly trailing the indium-nitride multilayer that currently sets the upper mark at 414° RIU⁻¹. It also surpasses the black-phosphorus (BP) variant of our own Si₃N₄ dielectric design (326.07° RIU⁻¹) once the higher reflected-power margin and lower attenuation of the present sensor are taken into account.

At the opposite end of the scale, the Cu–MoS₂–Si₃N₄ concept reported earlier by our group (43) yielded only 26.6° RIU⁻¹. The dramatic improvement observed here underscores the benefit of substituting MXene for MoS₂ in copper-based stacks: the metallic Drude response of Ti₃C₂T_x intensifies charge oscillations without the interband damping that limits transition-metal dichalcogenides, thereby boosting field confinement and angular leverage.

Although the Au–Ag–InN multilayer still holds the absolute sensitivity record, it relies on a three-metal system and a relatively complex deposition sequence. The present sensor achieves comparable performance with a single plasmonic metal (copper) and a seven-nanometre dielectric, supplemented by just one MXene sheet. This streamlined architecture reduces material cost, simplifies fabrication, and maintains reflected-intensity contrast below 10-per-cent loss—conditions favourable for clinical translation. In this context, the 312° RIU⁻¹ response establishes the MXene-enhanced design as a competitive alternative to more elaborate plasmonic stacks, combining high sensitivity with practical manufacturability.

The present work was designed as a proof-of-concept demonstration; consequently, several well-known technical constraints of SPR sensing in the Kretschmann geometry were not actively mitigated and may influence the absolute values of the kinetic parameters reported here.

First, the target protein was immobilised via standard amine coupling without orientation control. Partial unfolding or steric masking can accompany such chemistries, leading to a diminished active-ligand fraction and a shallow apparent association rate. Future iterations should employ site-directed capture—e.g., biotin-streptavidin or His-tag/NTA anchoring at solvent-exposed termini—combined with post-coupling activity checks against a reference ligand to verify that ≥ 95% of the theoretical R_max remains accessible. Low-density spotting and the inclusion of stabilising additives (2% glycerol, 1 mM DTT) in the running buffer would further preserve conformational integrity.

Second, the assay did not implement a dedicated strategy to suppress non-specific adsorption or to protect the ligand layer during regeneration. Baseline drift and minor signal inflation are therefore possible. Introducing a mixed surfactant/protein blocker (0.01% Tween-20 with 0.1 mg mL⁻¹ BSA), operating at moderate ionic strength (~0.3 M NaCl), and subtracting a reference-channel signal would curb matrix fouling. For multi-cycle formats, brief pulses of 10 mM glycine-HCl at pH 2.5—or adoption of single-cycle kinetics when sensitivity allows—would remove bound analyte while preserving ligand activity across repeated uses.

Third, artefacts intrinsic to the Kretschmann configuration were left uncorrected. Laminar flow through a rectangular channel can generate lateral concentration gradients, broadening the resonance minimum, while pixel-to-pixel gain variations in the line detector introduce subtle baseline distortions. A shallow staggered-herringbone mixer upstream of the sensing window and routine flat-field calibration (dark-frame subtraction followed by pixel-response normalisation) would homogenise mass transport and optical read-out, respectively. In addition, the 40 nm copper film employed here approaches the lower thickness limit at which island growth and damping become significant; depositing a slightly thicker (45–50 nm) Cu layer on a 2 nm Ti adhesion film, followed by low-temperature annealing, would sharpen the resonance and improve the refractive-index detection limit.

Addressing these factors in future studies will enhance both the biochemical fidelity of the immobilised target and the photonic resolution of the sensing platform, thereby narrowing confidence intervals on kinetic and affinity constants without materially increasing cost or complexity.

The three inorganic layers can be deposited sequentially in a standard sputter cluster. DC magnetron sputtering of copper at room temperature is routine and provides a continuous film at 40 nm (46). Without breaking vacuum, a 7 nm silicon-nitride cap is added by RF-reactive sputtering or low-temperature PECVD (Plasma-Enhanced Chemical Vapor Deposition, < 150°C) (47), creating a dense, oxidation-resistant barrier that also promotes adhesion for the subsequent MXene coating. Ti₃C₂Tx flakes dispersed in water or isopropanol are then transferred by spin-coating (45), spray-coating (48), or Langmuir–Blodgett assembly (49); each pass could deposit ≈ 0.99 nm, so two coats with mild vacuum baking (< 100°C) yield the required bilayer. Because no step exceeds 150°C, the process is compatible with BK7 glass and with photoresist patterning used later for microfluidic integration. The entire stack uses widely available targets and precursors, enabling wafer-scale or slide-scale production in conventional thin-film lines.

As well, Sys₄ follows the same copper deposition. A single MXene sheet is coated next; mild oxygen-plasma activation of the copper improves wettability (50), and a brief N₂ anneal (120°C) removes residual solvent. To over-coat this delicate layer, silicon nitride can be grown by plasma-enhanced ALD (atomic layer deposition) at 120–150°C or by very-low-power RF sputtering in N₂/Ar (51), conditions shown to preserve MXene conductivity and surface terminations. The conformal nitride film seals pinholes, stabilises the MXene against oxidation, and sets the optical phase. All steps remain below the glass-softening point and rely on the same tool set as Sys₃, ensuring process compatibility.

To remark, both stacks avoid noble metals and employ copper and Si₃N₄—materials ubiquitous in microelectronics—together with solution-processable MXene. Target utilisation is high, and deposition rates are fast (≈ 1 nm s⁻¹ for sputtered Cu). MXene inks can be delivered by roll-to-roll slot-die coating for large-area production, while pattern definition is achieved by lift-off or shadow masking. The resulting chips match the 1 × 2 inch format of many commercial SPR cartridges but can also be diced for disposable flow-cell inserts.

We point out that recent literature illustrates how the multilayer-engineering approach adopted here can be repurposed far beyond oncology. Rafi et al. (52) designed an N-FK51A/Ag/AlON/blue-phosphorus stack that detects six cancer cell lines and achieves angle sensitivities above 400°/RIU, confirming that 2D semiconductors can rival noble-metal composites for biomedical assays. In a subsequent study (53), the same group incorporated a WSe₂ sheet into a TiO₂/Ag/TiO₂ sandwich and, using transfer-matrix and finite-element modelling, projected sub-picomolar limits of detection for dengue virus antigens—evidence that layered-material SPR schemes can translate directly to infectious-disease diagnostics. Gumaih et al. (54) reported an Ag/BaTiO₃/black-phosphorus prism sensor whose hybrid plasmonic–ferroelectric interface boosts electric-field confinement, widening the application space to rapid histology-free tumour grading. Most recently, Rayhan et al. (55) demonstrated a CdS/Ag/CdS/black-phosphorus architecture tailored for non-invasive blood-glucose monitoring, achieving simulated sensitivities exceeding 300° RIU⁻¹ and underscoring the value of SPR platforms in chronic-disease management. Collectively, these works attest that the material-by-material optimisation strategy pursued in the present MXene–Si₃N₄ study is broadly transferable, enabling high-performance, label-free sensing across oncology, virology, and metabolic diagnostics.