Plasmonic Film with Diluted Nanostructures for Light Energy Harvesting and Sensing

Abstract

Harvesting the electromagnetic light field in spatially dispersed nanostructures and focusing the sensing events at those locations enables a gain of several orders of magnitude in sensitivity. It significantly reduces the amount of target material needed to produce a measurable signal. This paper establishes that, contrary to common belief, at very low target concentrations, increasing the periodicity of a nanoparticle array instead of diminishing it significantly lowers the limit of detection (LOD) of such structured plasmonic sensors. We demonstrate this numerically on a thin gold film covered by an array of 50 nm diameter nanocylinders with periodicity ranging from 400 to 3000 nm. We found a minimal capture target volume per surface unit of a few tens of nm³/μm², which is an improvement of orders of magnitude from about 10⁴ nm³/μm² necessary for obtaining the same minimal signal using a conventional propagative-based plasmon sensor, or about 10³ nm³/μm² for a similar plasmonic biochip structure but with a typical 200–400 nm periodicity array range. Two key mechanisms are involved in achieving such a significant breakthrough. First, energy harvesting is enhanced by incorporating the underlying thin film, which enables the coupling of electromagnetic field energy into the localized plasmon mode of the nanoparticles. This harvesting coupling effect is shown to be limited by the film’s plasmon propagation attenuation length and, consequently, its appropriate thickness. Second, target binding events must be precisely positioned in areas of enhanced optical field intensity.

Introduction

Surface plasmon resonance (SPR) biosensors are commonly employed for detecting the binding of biological molecules to a surface. This technique enables label-free, real-time monitoring of analytes attached to the sensor surface by measuring the shift in plasmonic resonance. This resonance occurs at a metal-dielectric interface, and depending on its geometry, the enhancement of the electromagnetic field is confined within 10 to 100 nm of the interface. This evanescent wave is highly sensitive to even small changes in the optical index within this minute volume near the interface. However, a relatively large number of molecules still needs to interact with the sensor surface to cause a detectable change in the refractive index. Many laboratory and industrial systems have been developed and utilized within these limits over the past several decades.

Direct measurements by plasmonic sensors using solely propagative plasmons reached their limits over a decade ago. As expressed by the “easy to quantify” sensitivity to a global optical index change, a value (wavelength-dependent) of around 10^–7 to 10^–6 refractive index units (RIU) can be achieved. More interestingly, as measured by sensitivity to binding of small biochemical molecules, it allows subnanometric average adlayer quantification over μm² areas.

Nevertheless, the relatively high sensitivities of SPR sensors are still insufficient in many important fields of application, such as early cancer diagnosis, where the biomarker concentration is extremely low (in pg/mL). Two main families of approaches have emerged to overcome this limitation. One approach aims at increasing the analyte’s refractive index by attaching large molecules or nanoparticles. Significant orders of magnitude gains in the measured signals have been reported in the literature. − However, some of the advantages of the label-free and real-time approach are lost, and more detection steps are involved. The second strategy involves nanostructuring the gold film’s surface to locally enhance light amplification, as recently reviewed and discussed.

The work and results reported in this article aim to further push the limits of nanostructured plasmonic-based sensing instrumentation, following on previously established milestones, − initially investigating the indirect effect of 1D grating periodicity, then in 2D arrays of nanodisk cylinders, stretching numerically and experimentally the importance of the underlayer metal film, ,, and finally experimentally demonstrating the importance of probe localization.

In the Kretschmann configuration, nanostructured gold films support a propagative surface plasmon (PSP) through the underlying continuous film and localized surface plasmon (LSP) resonance through the nanostructures. The interaction between the PSP and the LSP creates a coupled hybrid mode with both propagative and localized plasmon properties. When fully covered with targets, biosensors based on the excitation of the hybrid mode can exhibit improved sensing properties (sensitivity improvement by a factor of ∼9.5) due to the greater total active surface size per μm² and a slightly enhanced light amplification.

Unlike the smooth film, the electric field intensity above the nanostructured film is not uniform but is mainly confined to the structure due to the PSP/LSP coupling. The real benefits of a nanostructured gold surface are unveiled when considering targets only immobilized in the most sensitive regions, i.e., where the electric field intensity is the highest. As sensitivity to an additional layer is directly proportional to electric field intensity, , performances can be evaluated by calculating the field around the structures. Experimentally, diverse methods can be used to achieve local functionalization. Most recently, methods based on the local modification of surface chemistry triggered by high electric fields or hot electron transfers have emerged. , Although these approaches are still to be developed, they are promising due to the intrinsic spatial overlap between the most sensitive regions and the functionalized area. Along those lines, a metal-dielectric substrate could also be used, where differential functionalization is achieved through so-called orthogonal chemistries. For instance, thiol-based probes attach to the gold areas, and silane-grafted passivating groups attach to the silica areas. This technique will certainly benefit from new advances in gold chemical-mechanical planarization (CMP) to allow the top of gold pillars to be accessible, while the rest of the metallic structure stays buried in silica.

Another possibility was demonstrated some time ago by Zijltra et al. using steric hindrance to functionalize the tip of gold nanorods and achieved single molecule detection using photothermal microscopy. , As for the orthogonal chemistry, material-selective surface functionalization combined with a heterogeneous deposition was used to control the area’s functionalization, as Browne et al. also put forward.

However, only very few studies have evaluated the sensitivity obtained by spatially localizing the target capture events only on the electromagnetic hot spots, and this was only estimated for 1D gratings. Byun et al. predicted a sensitivity gain of 21 compared to a smooth film by binding molecules on the sides of nanowires with a 100 nm period, 50 nm width, and 10 nm height. In a previous study, we evaluated the impact of the nanowire’s width (6 to 250 nm) and periodicity (12 to 560 nm) on the sensitivity enhancement. We then numerically predicted a continuously increasing sensitivity around the wires as the wire width decreased and, more surprisingly, when the periodicity of the grating increased. This counterintuitive behavior is related to the energy-harvesting effect of the hybrid mode. Fabrication and characterization of patterned immobilization of quantum dots on metallic nanogratings was also successfully demonstrated by Hoa et al.

Similar to the “extraordinary optical transmission” in nanohole arrays, PSPs on nanopatterned films transport energy within the film, which couples to the LSPR of the particles, increasing the local electric field around them. Therefore, we can expect that increasing the surface area of the underlying flat film (referred to as “bottom” later on (Figure )) relative to the total nanostructured surface area (referred to as ‘All’ afterward) used for sensingby either increasing the periodicity or decreasing the nanoparticle sizewill enhance the amount of light energy transferred to the individual nanostructures. Additionally, reducing the particle size and periodicity allows the concentration of light to be at smaller and fewer points. While fabrication methods limit the minimum size of the ridges or particles, they do not limit the maximum size of the periodic spacing. The upper limit is determined by the minimum measurable signal’s strength and the mode’s propagating length, which can be as high as a few to a few tens μm, depending on the geometry. Despite their great potential for low-concentration detection and lower fabrication costs, nanostructured 2D films with micrometers of periodicity have not been thoroughly investigated. Moreover, the parametric studies mentioned above were conducted with a unique excitation wavelength for all configurations, while the mode position shifts with changes in the particle geometry and film thickness.

1.

Component structure and areas: (a) Nanostructured film geometry. The nanostructured gold film surface is composed of an array of 50 nm diameter circular cylinders of thickness H _s on top of a thin film of thickness H _f. The angle between the top and side sections is rounded, with a curvature radius R _c = 5 nm. When evaluated as a sensor, this nanostructured surface is usually covered by a 1 nm thick biological layer of a higher optical index. We divided such a layer into four distinct domains: (b) “Top”, (c) “Side”, (d) “Curve”, and (e) “Bottom”.

This paper quantifies the maximum sensitivity achievable by locating the target molecules’ binding events on the most sensitive spots of a highly diluted nanostructured film, which is opposite to what is usually focused on. Indeed, we postulated that diluting the nanostructures would allow for a more substantial field enhancement, compensating for the dilution effect and surface concentration of binding events. An optimum should be reached, and further dilution is expected to decrease the sensing performance. The greater the propagation length, the larger the dilution limit. Attention must be paid to remaining within a range of experimentally detectable signals. We investigated the importance of precise target positioning on nanostructures for enhancing sensitivity. We chose a 2D grating of gold nanocylinders atop a thin gold film as a model case. Finally, we detail the sensing potential of a grating with a 3 μm periodicity, examining various combinations of film thickness and structure height to determine the optimal geometry for detecting low concentrations. Calculations were realized over a wide range of wavelengths and light incident angles to achieve the sensor’s optimal performance.

Structure Geometry, Numerical Model, and Calculated Parameters

Figure illustrates the model geometry considered in this study. We chose a 2D square grating over the 1D ridge studied previously to further lower the fill factor and increase the sought-after energy harvesting effect. The studied structure consists of a gold film of thickness “H _f” with a grating of periodicity “P” of gold circular nanocylinders (a particle morphology commonly studied in the literature due to its simplicity) of height “H _s”. We chose a particle diameter D of 50 nm, which can be fabricated with e-beam lithography. The edges of the particles are modeled as rounded with a 5 nm curvature radius to account for the experimentally obtained shape and avoid simulation artifacts resulting from sharp edges. The smooth gold film is atop a 2 nm titanium adhesive layer and a BK7 substrate. The plasmonic sensor surface is excited from the bottom with a plane wave polarized in TM mode with a variable incidence angle and wavelength. Adhesion of target molecules is modelled as a 1 nm thick layer of optical index n _Bio = 1.48, which is divided into four distinct domains: “top”, “curve”, “side”, and “bottom” (see Figure b–e). The grating is immersed in a semi-infinite aqueous solution with a refractive index of n _w = 1.33. The refractive indices of the metallic gold, the titanium layer, and the BK7 glass media are taken from Johnson and Christy and calculated at 20 °C from the Sellmeier equation.

We evaluated the plasmonic sensor properties using a lab-written numerical model that has been used and improved over the years with great success in numerous plasmonic substrate configurations. Indeed, using this modeling software, we can also consider geometrical defects versus simple shapes. ,,

Briefly, the electromagnetic model is a mixture of a finite element model (FEM) and the Fourier modal method (FMM). This enables the calculation of curvilinear geometry response faster than that of classic FEM by utilizing FMM to determine the far-field response. The geometry is meshed with tetrahedra of adaptive size; the mesh is thinner at the interface between metallic, gold, and dielectric media, particularly at the top of the grating, where the spatial variations in the electric field are the greatest. Quantitative details on the adaptive mesh used and the convergence test are given in Figure S1 of the Supporting Information section. A simplified version of the code, which can calculate the angular-spectral maps shown in this article using only the FMM, has been made available as a MATLAB toolbox at https://hal.science/hal-04093350. Calculations are made over a wavelength range in the visible and near IR from 500 to 900 nm, where classical detectors and cameras can be used, and over associated incident angles ranging from 63 to 85° with step values of 5 and 0.5°, respectively. This angulo-spectral range allows the excitation of hybrid modes over the studied period range.

The numerical model enables us to calculate both the grating specular reflectivity (R) and the electric field distribution. The sensitivity can also be calculated by adding an extra molecular layer, with an optical index of 1.48, against the gold material surface. The signal that would be measured from such a binding event is classically measured as a variation of reflectivity ΔR = R _bound – R _initial. For each studied configuration, the maximum of such a ΔR signal is determined within the angulo-spectral range. Choosing to optimize ΔR rather than Δλ or Δθ is, on one hand, more classical and easier to compare to the literature, and it also, on the other hand, allows us to stay within regimes of reasonable amplitude resonance.

The sensitivities per quantity of the target material are compared to a conventional SPR, and its gain is evaluated by the sensitivity enhancement factor SEF_V:

$${\mathrm{SEF}}_{\mathrm{V}}=\frac{\mathrm{\Delta }{R}_{\mathrm{HSPR}}}{\mathrm{\Delta }{R}_{\mathrm{SPR}}}\frac{V_{\mathrm{SPR}}}{V_{\mathrm{HSPR}}}$$

ΔR _SPR and ΔR _HSPR represent the reflectivity change caused by the binding of targets on a conventional SPR flat sensor surface, as well as the evaluated structure based on hybrid plasmonic mode, HSPR. This enhancement factor is also scaled according to the total bound material volume per unit area (calculated in /μm²). The corresponding normalized volume is V _SPR = S × e, where S represents the sensor surface (with e = 1 nm and S = P ²), and V _HSPR refers to the target volume on the corresponding structured surface (which depends on H _s, D, and P, as well as the biological layer domain being studied). In the following study, we assume that the binding event locations, depending on the functionalization strategy considered, are happening at the different areas defined in Figure , i.e., “top”, “side”, “curve”, or “bottom” or a combination of those, “all” being the sum of these four volumes, indicating total coverage, as in the standard case.

For total coverage, the chosen reference signal value is ΔR _SPR = 10.15%. Such a value can indeed be achieved using solely propagative plasmons with an optimal gold film thickness of 56 nm, without nanostructures, under coupling conditions of λ = 886 nm and θ = 65°.

To help understand the origin of the local SEF_V evolution, we also calculate the local mean electric field intensity. This quantity is defined as

$$\stackrel{-}{E_{\mathrm{loc}}^2}=\frac{1}{V}\sum E_{\mathrm{loc},i}^2{V}_i$$

with E _loc,i being the electric field intensity inside the elements i of the elementary cell considered, and V _i the corresponding volume (sum of V_i = V), and this calculation can be applied to the different binding locations.

Effect of Localization of Target Binding Events

Figure a shows the angulo-spectral reflectivity map of the studied nanocylinder grating with the following parameters: period P = 400 nm, film thickness H _f = 55 nm, and nanostructure height H _s = 45 nm. Three reflectivity dips (bluish) are present on the map. The first one, around 500 nm, is the gold interband transition, which has no use for detection purposes (as can be seen in Figure b). The two other dips correspond to the hybrid mode resulting from coupling the particle’s plasmonic localized mode, LSP, and film’s plasmonic propagative mode, PSP. , This hybrid mode manifests as an anticrossing with an upper and lower branch. In this region, the plasmon mode has both propagative and localized properties. To assess sensor sensitivity, we simulate target adsorption by varying the refractive index from 1.33 to 1.48 within a 1 nm layer above the metal. The corresponding reflectivity variation map is shown in Figure b. The maximum ΔR is reached close to the hybrid mode, particularly where the distance between the upper and lower branches is the smallest, i.e., when the coupling is the strongest. A maximum absolute reflectivity variation of 7.98% is obtained for λ = 695 nm and Θ = 65° (white cross in Figure b). With a total target volume per period (166,765 nm³) slightly larger than the one corresponding to a perfectly flat surface (160,000 nm³), the sensitivity enhancement factor is equal to

$${\mathrm{SEF}}_{\mathrm{v}}=\frac{0.07978}{0.1015}\frac{1\times {400}^2}{\mathrm{166,765}}=0.75<1$$

2.

Numerical angulo-spectral maps of plasmonic coupling and sensitivity; (a) Reflectivity map (R _1.33) of a 2D grating of 50 nm diameter discs with H _F = 55 nm, H _s = 45 nm, P = 400 nm, immersed in water and excited from the bottom (BK7 substrate with 2 nm TiO₂ adhesive layer). (b) Reflectivity variation (ΔR = R _1.33 – R _{+1 nm @1.48}) map was calculated by adding a 1 nm layer with an index of 1.48 above the structured film. The white cross point is located where the maximum of |ΔR| is reached.

Despite the nanostructuring of the film, the sensitivity per captured target unit volume is lower than that of an optimized conventional SPR sensor. In some strongly corrugated cases, the overall signal at saturation may be increased, primarily due to a larger surface area binding more target material. In the current case, the SEF is significantly below 1, as the structure resonance occurred at a far shorter wavelength, 685 vs 886 nm. Indeed, at such a wavelength of 685 nm, the solely propagative plasmon on a flat film is indeed already significantly lower than the one at 886 nm (8.45% vs 10.15%).

Such a difference can also be attributed to the mean electric field intensity at the metal’s surface. Figure a,b shows the local mean electric field intensity amplification ( $\stackrel{-}{E_{\mathrm{loc}}^2}$ ) in the biological layer for an optimal smooth film of 56 nm and the previous grating as a function of the light incidence angle and wavelength. A maximum value of 38 V² m^–2 is reached for the flat underlying film, while the value drops to 22 V² m^–2 for the structured one. However, the mean electric field intensity values in the “bottom”, “curve”, “side”, and “top” of the biological layer in the same conditions (λ = 705 nm and Θ = 65.5°) are 12, 293, 143, and 45 V² m^–2, respectively. Thus, the electric field amplification is reduced at the bottom of the grating in favor of the layer above the particle. Binding targets on the latter would trigger a signal enhanced by a very significant factor compared to a smooth film, depending on the location considered (“side”, “top”, or “curve”). Hence, even though the grating’s macroscopic sensitivity is lower than that of the conventional SPR sensor, the local sensitivity is significantly improved.

3.

Structural field intensity enhancementMean local electric field intensity $\stackrel{-}{E_{\mathrm{loc}}^2}$ calculated in the 1 nm layer above (a) a flat film of 56 nm thickness. $\stackrel{-}{E_{\mathrm{loc}}^2}$ calculated in a thin layer atop (b) all, (c) the bottom, (d) the side, (e) the top, (f) the curve of a grating with H _f = 55 nm, H _s = 45 nm, and P = 400 nm. To better visualize and compare the resonant field enhancements, all graphs use the same logarithmic color scale. The white cross point is located where the maximum of $\stackrel{-}{E_{\mathrm{loc}}^2}$ is reached.

Local sensitivity can be further increased by using excitation conditions that optimize the local electric field. Figure c–f shows the $\stackrel{-}{E_{\mathrm{loc}}^2}$ value in the “bottom”, “curve”, “side”, and “top” versus the wavelength and the incident angle. Interestingly, the electric field intensity in the upper branch of the hybrid mode is significantly stronger than that in the lower branch for “curve” and “top”. In contrast, it is the opposite of the “bottom”. This illustrates the distinct nature of the mode: the lower branch is more closely aligned with a PSP, while the upper one is more closely aligned with an LSP. At optimal conditions, the mean electric field values rise to 15, 844, 175, and 236 V² m^–2, respectively, increasing the sensitivity on the nanostructure by a factor of 22.2 for the “curve”, 4.6 for the “side”, and 6.2 for the “top”. This demonstrates the significance of adjusting excitation parameters to the area functionalized when considering local functionalization.

Numerically, with our choice of 5 nm radius of curvature, the surface of each of these accessible areas is S _Top = 1.3 × 10^–3 μm², S _Side = 6.3 × 10^–3 μm², and S _Curve = 1.1 × 10^–3 μm², and represents, respectively, 14.5, 72.4, and 13.1% of the accessible nanostructure interface with the dielectric medium. In the case of a 400 nm periodicity, and therefore 0.16 μm² per nanostructure, the total nanostructure accessible surface of 8.7 × 10^–3 μm² represents approximately 5.43% of the component surface. In the case of a 3 μm period, this relative quantity drops to 0.01%. The “All” angulo-spectral map is a weighted average of the four components (bottom, side, curve, and top) based on their respective surface areas (158, 6.3, 1.1, and 1.3 in 10^–3 μm²), and it therefore closely resembles the bottom one.

The core idea of target localization is to induce local optical index variation only in areas where it causes significant changes in reflectivity. This is essential for our “harvesting and localization” approach, especially when the periodicity is increased, as the structure will increasingly resemble a flat film yet is orders of magnitude more sensitive to minute changes if adequately localized.

Furthermore, the distribution of the plasmonic localized mode energy across the nanostructure areas at resonance can be numerically estimated at approximately 12, 46, and 42% for the “Top”, “Side”, and “Curve” sections, respectively. Note that these fractions are largely independent of the periodicity. This can also be observed in the SEF distribution of those three areas relative to the SEF of the entire nanostructure (see Figure S2 of Supplementary Information).

We will next focus on the increase in SEF_V by orders of magnitude that can be achieved through nanostructure dilution and energy harvesting. We verified that changing structural parameters, such as the curvature radius, does not significantly impact our findings and subsequent conclusions regarding the interest in such a type of structure. Explicitly, simulations were run with a structure curvature radius of 2.5 and 10 nm. We also checked the SEF_V values when thickening the target layer, and those were in agreement with what could be expected for this type of sensor with evanescent hybrid modes (typically a little less than twice the signal for a 2 nm thick layer instead of 1 nm and with an additional decrease for a 5 nm one). We also, for the sake of responsible use of computer time, did not attempt to quantify the actual optimized maximum values but kept the ones that intersected our angulo-spectral mesh grid. Again, our interest here is to direct attention to the orders of magnitude that can be gained through this “harvesting and locating” approach.

Energy Harvesting EffectInfluence of Nanoparticle/Nanosensor Distancing Results

The main lever to amplify the local sensitivity of this type of sensor is to increase the light energy harvesting effect by spacing the structures. However, modifying the periodicity affects the reflectivity map, mainly through the excitation of Wood-Plasmon anomalies, propagative plasmons excited by the grazing diffracted light. For periods above 400 nm, this mode interacts with the hybrid modes, strongly modifying the reflectivity map. The corresponding spectra for periodicities varying from 400 nm to 3 μm are given in the Supporting Information–Figure S3 of Supporting Information. For this publication, we focus on the maximum SEF_V achieved in the angulo-spectral region of interest, independently of the nature of the corresponding plasmonic mode.

Figure a shows the result of this study as the sensitivity enhancement as a function of the squared of the period, i.e., the surface allotted per nanostructure, for different functionalization distributions: “Curve”, “CT” (“Curve” + “Top”), “CST” (“Curve” + “Side” + “Top”), “Top”, “Side”, “Bottom”, and “All”. For each period and functionalization distribution, the SEF is calculated by taking the optimum working point on the angulo-spectral maps. From S = 0.16 μm² (P = 400 nm) to S = 9 μm² (P = 3 μm), the SEF_V increases with the “free” surface allotted to the nanostructures.

4.

Distancing effects. (a) SEF, sensitivity enhancement factorsfilled symbols on the left axis, increasing as a function of surface domain per nanostructure (periodicity squared). On the right axis, with corresponding empty symbols, the averaged local field enhancements calculated for the same configurations are shown. (b) Maximum reflectivity signals that can be obtained with 100% coverage of the target adlayer onto the corresponding areas. Film thickness is 55 nm, and nanocylinders are 45 nm thick; the periodicity is varied from 400 nm to 3 μm. Together, Figure a and b illustrate the sensing potential of “harvesting” a larger incident light surface (a) and localizing the target interactions in precise locations (b).

For “bottom” and “all” functionalization, the SEF_V slowly rises from a value below 1, asymptotically approaching the performance of the conventional flat SPR sensor. The sensitivity is highest for the “curve” functionalization over the whole period range. At S = 9 μm² (P = 3 μm), the SEF_V reaches a considerable value of 317, outperforming the conventional SPR biosensor by more than 2 orders of magnitude. “CT”, “CST”, “side”, and “top” functionalization also perform well with a SEF_V of 196, 101, 68, and 86.

It appears that the SEF is also approximately linear with the square of the period, which corresponds to the variation of the available harvesting area around the nanoparticle.

As noted before, increasing the period has the drawback of diluting the spectral features of the nanostructures and, therefore, reducing the total reflectivity variation induced by target molecules binding to their functionalized areas. Figure b shows the reflectivity changes corresponding to the curves in Figure a. To be measurable, we chose that ΔR had to remain above 10^–3, a detection limit commonly reached with an SPR setup. For a 3 μm period, all the curves corresponding to the different areas are above this limit (see red line). Except for the “top”, which is close to the LOD, the curves could be extended to reach a higher SEF and still be measurable. Unfortunately, the calculation above P = 3 μm exceeds our computer resources’ reasonable available time and, we believe, without bringing new insights. Extrapolation to even slightly larger periodicities of 10 s of μm can be made.

In Figure S4 of the Supporting Information data, the minimal target volume required to produce such detectable reflectivity change for each functionalization is normalized by P ² and therefore in nm³/μm². For a “bottom” functionalization, which displays similar sensitivity to the conventional SPR sensor, the minimum volume is capped at around 10,740 nm³/μm². For a “curve functionalization”, this value decreases to 31 nm³/μm² at P = 3 μm. The minimum volume is only slightly larger, up to 97 nm³/μm² for “CST” functionalization, 50 nm³/μm² for “CT”, 114 nm³/μm² for “top”, and 144 nm³/μm² for “side”.

Such huge molecular sensitivity gain is directly related to the $\stackrel{-}{E_{\mathrm{loc}}^2}$ increase around the particle when increasing the periodicity as illustrated in Figure . The field intensity asymmetry around the nanostructure is due to the propagative component of the plasmonic hybrid mode, left to right in the figure.

5.

Normalized field intensity enhancement for three periodicities, 0.4, 1, and 3 μm, along the propagation direction of the propagative component of the hybrid mode. Structures are 50 nm in diameter and 45 nm thick on a 55 nm thick film.

Indeed, we expected the electromagnetic field enhancement to increase with the square of the periodicity as the SEF_V, at least up to a periodicity value close to the attenuation length of the plasmon (L _x = 1/(2k”), with k” the imaginary part of the surface plasmon wavevector). Propagative plasmons generated further than this distance are significantly attenuated when reaching the nanostructures due to the losses in the metallic film. In the case of Figure , with a 55 nm thick gold film and in those near-IR wavelength ranges, the attenuation length L _x is well above 10 μm. The induced losses can therefore be neglected in a first approximation for propagation along distances of the order of periodicity (3 μm in the case of Figure ).

In the Supporting Information section, Figure S5 provides a YZ and XY views of field enhancement, as seen from above, further illustrating the harvesting effect with an increased surface area for collection.

Interpretation and Discussion

It is well-known that the propagation length of a plasmonic wave at a metal-dielectric interface is wavelength-dependent, increasing with wavelength. It is essential to note that the metal film thickness is also a crucial factor, and this can be leveraged to enhance imaging resolution by using a thinner film than the standard. , One would expect the SEF to decrease with film thickness.

In this last section, we varied the nanostructure height H_S and film thickness H_F to confirm our interpretation and point toward the optimal geometry for this type of plasmonic sensor structure. For this set of calculations and figures, the sensing performance was evaluated for our largest calculated periodicity, P, of 3 μm and the “Curve” functionalization. Such SEF variation as a function of film thickness for different structure heights is shown in Figure . The optimal film thickness is between 45 and 65 nm, and the optimal structure height is between 35 and 55 nm. A thick metallic film limits the sensing performance due to poor coupling of the plasmon with the incident light. A too-thin film will also lead to diminished performance due to its shorter attenuation length and, consequently, lower harvesting efficiency of the plasmonic structure. An optimized architecture with a H _F = 55 nm and a H _s = 55 nm exhibits a sensitivity 500 times larger than that of a conventional propagative plasmonic biosensor. Indeed, this configuration would result in a measured signal of more than 0.1% reflectivity variation for as little as 22 nm³ of bound target material per μm² (coupling conditions of λ = 875 nm and Θ = 65°).

6.

Calculated sensitivity enhanced factor (SEF) as a function of film thickness H _F for different values of nanostructure height H _s and a periodicity P of 3 μm for the “Curve” area.

This behavior differs from previous studies, such as, , which have focused on the spectral sensitivity with respect to an overall change in the optical index of the surrounding dielectric media, expressed in nm/RIU. Especially, the underlying gold film, which is crucial to the harvesting effect, was not examined in these papers. The presence of this film also underscores the importance of structural features, as anticipated in the pioneering work of Miller & Lazarides. Thanks to the gold film, a coupling between propagative and LSPs can occur with appropriate excitation parameters. The hybrid plasmonic mode has been described analytically. In addition, we have found that the optimal thickness of the structure is considerably greater than in the case of Saison-Francioso et al., with the nanostructures immersed close to the interface of purely dielectric media.

To quantitatively check the agreement for the loss of enhancement with decreasing film thickness due to the harvesting effect, the maximum field that could be coupled into the nanostructure via film propagation from the point of incidence onto the structure was evaluated.

Figure a shows how attenuation length varies with gold film thickness for 700, 800, and 900 nm wavelengths. At 800 nm, when varying the film thickness from 15 to 65 nm, the attenuation length varies by more than an order of magnitude, from 1.3 to 14.3 μm; such a variation range is very significant, especially with respect to the periodicities used in this study.

7.

(a) Attenuation length of a classical propagative plasmon as a function of gold film thickness between 5 and 65 nm for 3 different wavelengths (700, 800, and 900 nm). Note the quantitative increase in attenuation length for the 800 nm curve and increasing thickness. (b) Potential harvested quantity from a disk area expressed as a function of attenuation length, L _prop (range selected according to values highlighted in Figure a); the chosen radius values of disk area parameters correspond to half the periodicities of 400 nm to 3 μm (the nanostructure is considered at the center of the harvested field). Such an integrated energy field value should be regarded as the grand maxima of relative enhancement values for our other simulations.

Figure b shows, as a crude approximation, the integral of the maximum harvested plasmonic field over a disk surface of half the periodicity when pondering each integrated subarea (rings) by the attenuation length (L _att) losses to propagate to the nanostructure, i.e., propagation losses over the required distance. As the attenuation length increases with film thickness (at 800 nm, as the film thickness is varied from 15 to 65 nm, it increases by more than an order of magnitude, from roughly 1 to 10 μm), there is a significant gain in the harvested field. This is consistent with the increase in sensitivity, as already shown in Figure . An optimum configuration is reached when the period is of the order of magnitude of the attenuation length, which is why we significantly increased the periodicity. Finally, one should be limited only by the experimental threshold at which the reflectivity variation will still be measurable at the macroscopic scale.

Also, the set of values of P/2 displayed can be used to visualize and correlate the data obtained for different periodicities, as displayed in Figure .

As additional discussion about the usage of such a sensor geometry type, one might also point out several issues, in particular related to the very low concentrations targeted. , In particular, it is well-known that the response time inherent in low concentrations will be the primary barrier constraining the development of these sensors. , This problem can be addressed using passive microfluidic structures , or even active microfluidics, such as thermal, acoustic, and electrophoresis. ,− We also anticipate this to be less of a problem in the gas phase due to the significantly shorter diffusion time constant of potential targets in air compared to water, and this applies to large application fields such as environmental air quality measurements. Additionally, in both phases, preconcentration modules are readily available and can be easily added to the system, thereby increasing the operational limit of detection (LOD). In all cases, the estimated target concentrations will be derived from the rate of binding of the targets rather than the quantity at equilibrium. Of course, such an equilibrium could be quickly reached in the case of higher concentrations, and the sensor would saturate with a relatively small quantity of material, but again, the concentration evaluation would be performed on the dynamics of the signal and not the equilibrium value, and such usage would be far from the case for which those systems would be deployed.

Conclusions

In this work, we numerically assessed the sensitivity of plasmonic sensors based on nanostructured surfaces of highly diluted 2D nanocylinder grating used in the Kretschmann configuration. We have demonstrated that, contrary to what is often emphasized, increasing the periodicity and spacing the nanostructures further apart significantly enhance the local field intensity focused on them. To some extent, the sensitivity to localized binding events within an experimentally measurable range (defined here as above 0.1% reflectivity variation) is subsequently increased. A 3 μm period, combined with local functionalization of the cylinders’ top curvature, significantly enhances sensitivity, resulting in a more than 2 orders of magnitude increase compared to a conventional SPR sensor based on propagating plasmons, while still maintaining a measurable ΔR. It represents a significant gain compared to the periodicity of a few hundred nanometers, which is typically used. Note that within the different parts of the nanostructure, as labeled “Top”, “Side”, functionalization, which are easier to obtain experimentally, display a sensitivity gain in the same order of magnitude as the “Curvature” one.

Within the range of parameters we have studied, we predict that for an optimal film thickness of about 50 to 60 nm, depending on the wavelength used and a structure height of around 50 nm, the SEF_V associated with the LSP component of the plasmonic hybrid mode reaches values in excess of 100 s for P = 3 μm. Such plasmonic sensors could experimentally detect the binding of only a few thousand to hundreds of small molecules per nanostructure, corresponding to a captured volume of the order of 10 to 100 nm³ only.

Considering the current numerical data and anticipated experimental limitations, it can be inferred from previous results that the nanostructures could be further spatially diluted and that a few-fold additional gain might be achievable. The primary experimental challenge lies in the quality of the local functionalization that can be achieved. Ongoing work is focused on this area. We believe that these types of structures could be very beneficial for applications involving trace concentration detection and measurement, especially in both linear and nonlinear processes (such as SERS). They could also significantly impact a broader community beyond sensing, leveraging localized light energy amplification through linear and nonlinear mechanisms to attain their objectives.

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acsaom.5c00307.

• Mesh used for calculating the angular spectral features–associated data convergence test; energy distribution within areas of the nanostructures as a function of the square of the periodicity; angulo-spectral reflectivity maps of the nanostructured (and flat) surfaces for various periodicities and their associated reflectivity variations upon binding of a 1 nm biological adlayer; normalized minimum volume per square micron that must bind to produce a measurable 0.1% reflectivity variation across different areas and varying periodicities; and YZ and XY (z = 0) views of the field enhancement for three periodicities (PDF)

The authors declare no competing financial interest.