1. Introduction

The production of plasmonic nano-antennae with reproducible and large field enhancements has remained a persistent challenge in the fields of tip-enhanced near-field optical microscopy (TENOM) and tip-enhanced Raman spectroscopy (TERS). The most common methods of probe fabrication, namely metal-coating of atomic force microcopy (AFM) tips [1] and electrochemical etching of metal wires [2], are known to produce structures with highly variable enhancements, largely caused by nanoscale structural differences [3,4]. One strategy that has partially mitigated issues with probe variability is the use of metallic or plasmonic substrates to operate instruments in a so-called “gap-mode” configuration [5–8], where intense (100x enhancement) and spatially localized fields are generated between the probe and substrate. Although gap-mode optical signal levels are high enough to meet the requirements of many near-field experiments, there are a wide range of dielectric, semiconductor, and organic surfaces of interest that cannot make use of this mechanism. For these substrates, maximizing probe enhancement is critical, especially for 2D near-field imaging where collection times per pixel must be small (<1 s).

In addition to increasing the magnitude of electromagnetic fields, there is a desire to control the spatial distribution, polarization, and resonant energy of near-field optical antennae. The polarization and near-field spatial distribution are known to strongly alter Raman scattering processes compared to far-field measurements [9,10]. Modeling and reproducibly controlling these effects is a prerequisite for quantitative analysis of near-field Raman spectra. Recent TERS experiments have even demonstrated that extremely high spatial field confinements (<1 nm) are possible, allowing chemical images of individual molecules to be obtained [11–13]. Although the full mechanism of this confinement is still an active area of research, it is clear that tuning the local plasmon resonance of the probe to match the energy of molecular transitions is a necessary component in the process.

The aforementioned applications would benefit from reproducible fabrication of near-field probes with precisely controlled nanostructures and several means of accomplishing this have been proposed, including focused ion-beam milling (FIB) to create arbitrary 3D antenna shapes [14] or attachment of a plasmonic nanoparticle to the probe apex [15,16]. The common trait between these structures is that they possess localized surface plasmon (LSP) resonances that can be tuned as a function of material and geometric parameters. Direct comparison of the achievable enhancements from these designs has not been possible experimentally due to variability in the design wavelengths, instrument geometries, probe dimensions, and reporter molecules.

In the present work, finite difference time domain (FDTD) simulations were used to quantitatively assess of the performance of four different resonant probe designs that have been proposed and fabricated by groups in the near-field research community. The probe designs were then geometrically optimized to have localized surface plasmon (LSP) resonances in the 633-647 nm spectral range using a set of physically relevant constraints. The lessons learned from our analysis are intended to assist experimentalists in choosing physical parameters that maximize enhancements achievable for a given probe design.

2. Numerical methods

FDTD calculations were performed using Lumerical software. For the majority of simulations, a scalar Gaussian beam source, with 11-point multi-frequency beam correction and 1 μm beam waist (1/e field points), was used in a 45° inverted illumination geometry. For the Au-coated Si cones in Fig. 2 and the trials using optimized structures from Fig. 7 with varying substrate materials, a 45° side-on illumination source (i.e., above the glass substrate) was used instead, with all other source and simulation settings held constant. The advantage of a Gaussian beam source over a standard plane wave is that for optical excitation at non-normal angles relative to the Cartesian simulation axes, the broadband frequency response can be accurately extracted from a single simulation. For probe-substrate simulations, a 1 nm gap was left between the lowest point of the probe apex and the substrate surface. Field values were recorded along a line at the center of the gap region (0.5 nm below the probe) that spanned the width of the entire probe apex. Plots that report E or E_gap values refer to the maximum field recorded along this line field monitor. This procedure was necessary to account for small changes in the maximum field position that occurs when using angled optical sources. The same procedure with a 0.5 nm probe offset was used for simulations without a substrate [Fig. 1]. In all cases, the field values were normalized by those produced at the same spatial location under identical simulation settings, but with the probe structure entirely removed (labelled E₀). An advantage of reporting results in this manner is that the influence of source type and excitation geometry are minimized, allowing one to focus directly on the physics of the near-field probes being studied. For a quantitative example of the details of this normalization procedure, please refer to the Appendix.

 

Fig. 1 Example of how LSP modes of Au cones are very sensitive to cone length, optical excitation source, and simulation boundary conditions. (a) When using a focused beam source of finite width (1 μm), the apex fields converge to the infinite cone limit when the cone length >6 μm. (b) Field convergence is much slower when using a planewave source spanning the entire simulation cross-section, due to the launching of surface plasmon-polaritons (SPPs) along the cone lateral surface. (c) Combining a Gaussian beam source and perfectly matched layer boundary conditions along the cone’s upper surface allows a 2 μm structure to accurately mimic the infinite cone limit.

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To minimize computation times while maintaining accuracy, adaptive meshing was utilized. A 1 nm mesh was applied over the first 100-200 nm of the probe apex, with a finer 0.25 nm mesh present only along the center of the probe-substrate gap. Perfectly matched layer boundary conditions were used in all simulations to minimize reflected light. Rigorous convergence testing was performed for all simulation parameters, including the size of custom mesh regions, minimum mesh sizes, and optical source settings. Parameters were deemed converged when subsequent refinements produced relative changes in local field values of <5%. Experimental permittivity data for Au, Si, W, and Pt were taken from The Handbook of Optical Constants of Solids [17] and Si₃N₄ refractive index values from the work of Luke et al. [18]

3. General model for optical characterization of near-field probes

Extensive simulation work has been carried out using finite difference time domain (FDTD), finite element (FEM), and boundary element (BEM) methods to investigate the optical response of near-field probes as a function of their physical properties (apex radius, cone angle, probe/substrate materials) and illumination geometry [19–23]. A fundamental question when performing such work is how to accurately represent the probe, which in reality, is a spatially extended structure such as a metallized AFM tip or electrochemically etched metal wire, within a computationally feasible, microscopic simulation volume. Most studies use a metal cone to represent the general shape of a near-field probe, and investigate its optical behavior as a function of cone length, excitation source (beam or plane wave), and simulation boundary conditions [24–26]. A similar procedure was followed in the present work, with a generalized summary of the results presented in Fig. 1.

Gold cones of varying length (L) were optically pumped using either a Gaussian beam source [Fig. 1(a); spatial FWHM = 833 nm at λ_center = 576 nm] or a planewave spanning the entire simulation cross-section [Fig. 1(b)]. The enhancement spectra of shorter cones (L = 500-2000 nm) contain peaks and oscillations that correspond to LSP resonances supported by the finite metal surface between the apex and upper cone boundary. The intensity of these oscillations decreases for longer cones, and by L = 6 μm, they are completely absent for the beam source, resulting in a smooth enhancement spectrum that does not change with further increases in cone length. This transition occurs as the cone length exceeds the attenuation length of surface plasmon-polaritons (SPPs) confined to the Au-air interface, which is <5 μm for optical wavelengths [27]. SPPs launched at the apex will be almost fully attenuated before reflecting off the upper cone boundary and returning to the apex, thus making the 6 + μm cones respond equivalently to those of infinite length. In contrast, convergence to the infinite cone limit is slower for a planewave source filling the entire simulation space because SPPs are also launched from the upper cone boundary. As shown in Fig. 1(c), the simulation volume can be significantly reduced (i.e., 2 μm cone, converging to the 6 μm and infinite cone limit with < 1% error across all λ) using a beam source and perfectly-matched layer (PML) placed along the upper cone surface. The PML acts as a nearly perfect absorber, eliminating reflection of SPPs from the upper boundary for the Gaussian case, but only partially for planewave excitation.

There are numerous literature examples of cones with L ~100-1000 nm being used as models of scanning near-field probes [28–33], whose plasmonic response consists of LSP or SPP reflection modes that depend on the cone size. In our work, we are specifically interested in characterizing the optical physics of probes with resonant apex nanostructures, and the presence of any plasmon resonances supported by the larger probe structure will tend to obscure those effects. For this reason, all subsequent results presented herein use the 2 μm cone + PML model. This ensures the baseline probe optical response is relatively flat and smooth, making it straightforward to identify the appearance of new LSPs created by the apex nanostructures.

The results presented in Fig. 1 are exclusively for solid Au cones, but near-field probes are also commonly made by metallizing AFM tips. Simulations of Si probes with apex radii between 5 and 50 nm and uniform Au coatings of varying thickness were performed to determine if significant differences existed in the physics of solid vs. coated probe models. The metal coating thickness and underlying support radius were varied while keeping the total radius (support + coating) constant. Enhancement spectra were examined to determine the coating thickness necessary to completely mask the presence of the Si support. Figure 2(a) gives an example of results for a fixed probe radius of 25 nm, where a 20 nm Au coating on a 5 nm Si probe is required to produce field enhancement within 10% of the solid Au probe. It is also seen that thinner Au coatings have large enhancement variations across the visible spectrum, likely due to interference effects from reflections within the Si tip itself, created by the cavity formed by the Au-coating on the Si probe. This interference phenomenon may be constructive (λ = 500 nm) or destructive (λ = 650 nm), and depends on the coating thickness, excitation wavelength, and optical pumping configuration. In practice, such interference is challenging to rationally incorporate into a probe design, as it is highly dependent on the local morphology of the probe and the excitation geometry of the optical source. No experimental demonstration in the literature could be found where metal coating thickness was used to tune interference resonances of this type.

 

Fig. 2 Plasmonic response of Au-coated Si probes of varying size in comparison to solid Au probes. (a) Enhancement spectra of Au-coated Si probes with a constant total radius (Si base + Au coating) of 25 nm and a cone angle of 15°. The 5 nm Si + 20 nm Au probe (red) produces an optical response nearly identical to that of the 25 nm solid Au cone (black). (b) The minimum Au coating thickness required to optically mask the presence of the Si substrate as a function of apex radius. The excitation source was a 45° Gaussian beam with side-on illumination geometry with the probe placed 1 nm above a glass substrate.

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The same process of varying Au/Si thickness was repeated systematically for probes with different total radius values until the minimum required Au coating thickness across a range of common near-field probe sizes could be determined [Fig. 2(b)]. A 60 nm Au coating was found to fully mask the presence of the Si support, regardless of the size of the Si structure. This is caused by the Au coating becoming essentially opaque, due to strong absorption at optical frequencies, which prevents light from reaching the Si core, e.g., transmission through a 60 nm Au film at normal incidence is <10% in the visible. For smaller Si probes, the amount of Au deposited can be reduced significantly, e.g., a 5 nm Si probe requires only 15 nm of Au. The minimum amount of metal possible should be deposited to minimize the size of the probe apex, as sharper probes yield larger enhancements due to geometric field concentration (i.e., the lightning rod effect [34]), while also avoiding interference effects present for thin coatings. The general conclusion of our simulation benchmarking work is that a single model, namely the solid metal probe, can capture the important plasmon physics involved, even for metal-coated probes that would be used in practice. Moreover, the general framework of local field normalization and the use of an (effectively) infinite cone, i.e., 2 μm cone + PML model [Fig. 1] to remove resonance contributions from the larger probe structure, allows the apex optical physics of near-field probes to be studied in a very general manner

4. Results and discussion

4.1 Engineering resonant near-field probes

A quantitative comparison of several probes with specifically designed plasmonic resonances was made using the general FDTD framework developed in the previous section. The purpose in doing so is to provide a quantitative comparison of the achievable enhancements from these structures, which is experimentally difficult due to differences in instrumentation, design wavelengths, and reporter molecules used to generate near-field scattering signals. A secondary goal is to understand how different material and geometric parameters influence the plasmonic behavior of probes, and to provide guidance on how to optimize the performance of these structures.

A straightforward means of producing a resonant near-field probe is the addition of a plasmonic nanostructure to the apex of a larger probe ‘support’. Attaching particles with diameters less than several hundred nanometers is challenging, but can be done by functionalizing the probe and/or nanoparticle with an organic linker (e.g., epoxy, polymers, complementary DNA) [15,16] and then picking up a single particle by scanning the probe over a surface. Alternatively, plasmonic nanoparticles can be selectively grown at the probe apex via electrochemical reduction of metal ions in solution [35,36]. Regardless of the specific fabrication process used, the presence of the probe support material will modify the plasmon resonance of the attached nanoparticle. To characterize this effect, simulations were performed on a 50 nm dia. Au sphere with a 10 nm wide connecting junction of varying material [Fig. 3]. Six different junction materials were tested, three with very low extinction (SiO₂, Si₃N₄, Si) and three that strongly absorb at visible energies (Au, W, Pt). All of the high absorption materials were found to decrease local field enhancements relative to those of the isolated Au nanoparticle, due to the dipolar LSP of the sphere losing energy via absorption in the connection junction. This contribution adds to the damping inherent to the nanoparticle and decreases the amplitude of charge oscillations when an optical field is applied.

 

Fig. 3 Perturbations to the dipolar LSP mode of an Au nanoparticle (dia. = 50 nm) caused by the addition of a 10 nm wide connecting junction. Materials that strongly absorb at optical energies (Au, W, Pt) cause damping of the plasmon resonance and lead to lower field enhancements, while those with small extinction coefficients (Si, Si₃N₄, SiO₂) increase the coupling of far-field radiation into the dipolar plasmon mode of the nanoparticle. Maximum fields (E_max = E_gap/E₀), as well as the real and imaginary parts of the refractive index of each support material at λ_max (i.e., where E_max occurs), are also noted.

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The observation that low extinction coefficient materials actually increase enhancements above those of the isolated sphere was initially unexpected. Justification for this effect can be found in the Mie solution for the extinction cross-section of a metal sphere in the quasistatic limit (size << λ) [37]. In this case, extinction is proportional to the polarizability of the sphere. The support material, with a refractive index greater than unity, increases the polarizability of the combined sphere-support structure, leading to a larger cross-section for coupling far-field radiation into the dipolar plasmon mode. This explanation is supported by the observation that absorption cross-sections for the apex increased by ~100% for the Si junction compared to the isolated nanoparticle. Higher refractive index supports (Si) are more polarizable than low refractive index materials (SiO₂), which increases the magnitude of this effect and produces larger relative field enhancements.

The conclusion from Fig. 3 would appear to be that a high refractive index support material with low absorption, such as Si, is the ideal support for a nanoparticle-based near-field probe. Surprisingly, simulation and experimental data on Ag-coated conical supports show different behavior, with low index materials yielding the largest optical fields [38,39]. This apparent contradiction was resolved when two additional resonant probe geometries were studied, namely a cone with an Au-coated apex and an Au-hemisphere on a post [Fig. 4]. The support materials that maximized enhancement were found to vary for both of these structures, as well as the nanoparticle functionalized probe discussed earlier, with refractive index values ranging from 2 to 4. From these data, it is clear that the idea of a universally superior support material is not correct. Instead, the support refractive index should be viewed as a parameter that must be optimized for a particular apex geometry. In general, higher index materials work well for solid plasmonic structures, where the support is connected at the surface, while low index supports are superior when the plasmonic metal takes the form of a thin film coating.

 

Fig. 4 Enhancement spectra (E_gap/E₀) of near-field probes with resonant Au-apex nanostructures can be maximized by varying the refractive index of the support material. Probes were placed 1 nm above a glass surface with a 45° inverted beam source, and the support structures were extended to the simulation boundary, placed 2 μm above the surface. The approximate refractive indices of the low absorption materials studied are: n = 1.5 (glass), 2 (Si₃N₄), 3 (a generic dielectric), and 4 (Si). Au and Pt were included as examples of lossy support materials and produced lower field enhancements for all three geometries simulated.

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It is also important to note that for all of the geometries studied in Fig. 4, the Au and Pt supports perform significantly worse than any of the low-absorption materials. This trend can be rationalized in terms of dipole and monopole antenna resonances. Dipolar antennae are those with two field nodes located at each end of a finite structure, such as a nanorod, with the geometry and length of the antenna determining the specific resonant wavelength [40,41]. Monopole antennae are those with a finite resonant structure attached to a much larger conductive or plasmonic support, such that only a single field node is spatially localized around the finite structural component. Examples of monopole antennae in the context of near-field probes are metallized probes with FIB-milling to produce a sharp spike at their apex [41,42]. The use of a conductive support causes the structures in Fig. 4 to act as monopole antennae, while insulating supports create a finite resonant structure and enable dipolar LSPR modes. Thus, these results suggest that probes with dipolar plasmonic antennae will enable significantly larger enhancements than monopole antennae designs.

A resonant probe design with large potential enhancement that makes use of the aforementioned results can be constructed by FIB-milling a circular groove into a metallized commercial AFM probe a short distance above the probe apex [39,43], forming a nano-cone on the end of a dielectric post [see Fig. 5]. A possible issue when applying the metal coating prior to FIB processing is that ion implantation from the FIB beam may degrade the plasmonic properties of the metal. This can be avoided by first making FIB cuts on the bare probe, and then evaporating metal normal to the probe axis so that the apex cone acts as a shadow mask [39]. Achieving a strong optical response from these structures requires the conical metal apex coating to act as a continuous plasmonic cavity. To promote formation of a smooth and continuous film, a thin adhesion layer (~1 nm) of Ge, Cr, or Ti [44,45] can be applied to the substrate probe prior to evaporation of the plasmonic metal. Even with efforts made to maximize film smoothness, it has been shown that nanoscale spatial variations on the apex surface of near-field probes, potentially down to atomic length scales, can strongly influence the optical response of a probe [46]. Understanding how nano-structural variations affect the plasmonic resonances and near-field spatial localization of enhancing structures, as well as how these mechanisms can be controlled, is an active area of research [47,48].

 

Fig. 5 Effects of different geometric parameters on the field enhancement (E_gap/E₀) produced by a metal-coated SiO₂ probe with FIB structuring near the apex. (a) The LSP wavelength can be tuned by the apex length, with longer apices producing larger enhancements. (b) A cut length of roughly 100 nm is necessary to optically decouple the metal apex from the coating on the rest of the probe surface. (c) The cone angle of the underlying support shows a weak positive correlation with enhancement. The default values of parameters not being varied in each series were: apex length = 75 nm, cut length = 100 nm, and cone angle = 15°. In all cases, the SiO₂ apex radius was 5 nm with a 20 nm thick Au coating.

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Simulations were used to estimate the enhancements produced by this structure as a function of the apex length, cut length, and cone angle, as determined by FIB processing. The apex length is the parameter used to primarily control the LSP wavelength, with longer lengths leading to red-shifting of the resonance [Fig. 5(a)]. The additional length of the dielectric support post also increases the total polarizability of the apex, providing stronger coupling with far-field excitation and hence larger enhancements. The cut length controls the optical coupling between the apex and support Au coatings [Fig. 5(b)]. Enhancement was found to increase with longer posts, with distances ≥100 nm being sufficient to optically isolate the apex metal layer from the rest of the probe tip. The cone angle is determined by the shape of the original probe being coated, with larger angles showing a weak positive correlation with enhancement [Fig. 5(c)]. A variation on the Fig. 5 structure, where FIB milling was performed parallel to the probe central axis instead of perpendicular to it, was proposed by Zou et al. [49]. In this design, the apex metal layer is tapered, and our simulations show that dipolar LSP modes are relatively weak; as such, this probe design was not considered in subsequent simulation studies.

Near-field probes that do not require a separate support, but instead involve direct structuring of a plasmonic material, have also been proposed. One design is very similar to Fig. 5, except that FIB cuts are now made in an etched, solid metal probe [50] [Fig. 6(a)]. Simulations of an Au probe of this type were run, and the trends for apex length, cut length, and cone angle were found to be similar to those given in Fig. 5. A new observation was the dependence of LSP strength on the FIB cut depth. The magnitude of peak enhancement increased with cut depths up to 20-30 nm, beyond which, deeper cuts only altered the LSP peak energy. Making the cuts too deep raises concerns about the mechanical stability of the probe. For this reason, it is recommended that a probe with a wide cone angle be used, and the cut depth not exceed 20-30 nm. The original study by Vasconcelos et al. reported a TERS signal increase of 5x, before and after the FIB process, for a probe with a relatively narrow cut length (L_c ~25 nm) [50]. Our simulations suggest that if the cut length were increased to 100 nm, while maintaining the same 20-30 nm cut depth, the apex electric field strength could be further doubled, with the TERS signal increasing by an order of magnitude.

 

Fig. 6 Important geometric parameters to control field enhancement of FIB-milled, solid Au near-field probes. (a) Maximum field enhancement at the resonance peak (E_max/E₀) for a 35° Au cone as a function of the FIB cut depth. A minimum cut depth of approximately 20 nm is required to maximize the LSP resonance supported by the apex. (b) The apex radius of curvature is the primary LSP tuning parameter for probes with a sphere and cone geometry. This type of structure can be produced by metal coating a commercial AFM tip with an electron-beam deposited apex structure [36].

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Another fully metallized probe design that has been proposed involves growth of a spherical structure at the end of a conical support, typically done using electron-beam deposition of carbonaceous material on and AFM tip [36,51], followed by application of a plasmonic metal coating [see Fig. 6(b) inset]. In this case, the LSP energy is primarily controlled by the radius of the apex sphere, with the connection width between the sphere and cone acting as a secondary tuning parameter. Enhancements were maximized using a sphere radius of R = 75 nm, with radii >100 nm showing a rapid decrease in field strength, corresponding to a loss of geometric field concentration (i.e., the probe is no longer sharp enough for a strong lightning rod effect). Even for spheres of moderate size, there will be some reduction in the lateral spatial localization of the enhanced fields. For example, the FWHM of the |E|⁴ profile along the probe-substrate gap nearly doubles from 12 nm to 22 nm for radii of 35 nm and 75 nm, respectively.

4.2 Optimization of resonant probe geometries

The important physical parameters of several probe designs have now been described, and at this point, it is useful to ask which of these structures can produce the largest enhancement. To help answer this question, an effort was made to optimize the enhancements of each probe over a commonly used wavelength range (633-647 nm, for HeNe and Kr⁺ laser lines) and subject to a similar set of design constraints [Fig. 7(a) and Table 1]. The designs included were conical apex structures with FIB cuts in a metallized SiO₂ support (Probe 1) and solid Au etched wire (Probe 2), an Si support functionalized with an Au nanoparticle (Probe 3), a metallized sphere-cone structure (Probe 4), and a smooth semi-infinite cone (Probe 5) as a point of reference. Final values of the geometric parameters for each optimized probe are provided in Table 1, along with the constraints enforced on these parameters to maintain physically realistic structures. To eliminate the influence of probe sharpness on enhancement, the apex radius of curvature of all probes was intentionally fixed at 25 nm, except in the case of Probe 4, where increasing this value was necessary to tune the LSP energy.

 

Fig. 7 Comparison of several near-field probe designs that have been optimized for operation in the 633-647 nm wavelength range. (a) The Au-coated dielectric and solid Au designs with FIB cuts made near the apex were predicted to produce the largest apex field enhancements (E_gap/E₀). (b) Example of tuning the LSP energy of a metal-coated SiO₂ probe (Probe 1) over the full visible spectrum by varying the coating metal (Ag vs. Au) and apex length. All other parameters are the same as the Probe 1 structure in panel (a). Points represent the wavelength of maximum field enhancement.

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Table 1. Geometric parameters of the optimized probe structures presented in Fig. 7. Cone angles in the range of 15-35° capture the apex profiles of commonly used commercial AFM tips and electrochemically etched wires. Constraints were placed on the allowed values of the cut length, cut depth, and connection width to maintain reasonable mechanical stability of the structures. Geometric constraints were imposed using conservative estimates from available experimental data on similar probes that have been fabricated and used in scanning probe instruments.

View Table

Of the designs considered, maximum field enhancements (~30x) were achieved using probes with FIB-milled apex grooves (Probes 1 and 2). This corresponds to a 300% increase when compared to the unstructured metal cone (Probe 5), which may yield an improvement in TERS signals of two orders of magnitude, based on the typical |E|⁴ estimation. Moreover, the resonance energy for maximum enhancement can be easily tuned by varying the plasmonic material and apex length [Fig. 7(b)]. Au coatings are effective above λ = 600 nm, where absorption from interband transitions is avoided; Ag coatings are expected to be effective over the entire visible spectrum. Experimental measurements using EELS, dark-field scattering, and TERS have verified the red-shifting of the LSP energy with increasing apex length [39,43,50]. Although not simulated here, experiments using Au probes have also shown that the LSP dipole mode can be extended into the near infrared range [50].

Nanoparticle functionalized structures (Probe 3) produced broadband enhancement of moderate intensity when a high refractive index support material (e.g., Si) was used. The use of metallic supports (Pt, W) led to much lower enhancements, while the use of another plasmonic material (Au) gave intermediate results, similar to the Probe 4 design. This suggests that dielectric probes with attached plasmonic nanoparticles are more effective than conductive probes with plasmonic structures selectively grown at the apex using electrochemistry. Enhancements were found to depend strongly on the nanoparticle attachment position (data not shown), with particles located on the side of probes yielding lower enhancements than attachments directly beneath the apex. This is because the nanoparticle dipolar LSP has two field nodes oriented nearly perpendicular to the sample surface, and the support more strongly influences the LSP when it is placed directly at the upper field node. It is expected that the enhancements of these probes could be further increased by 2-3x via attachment of more asymmetric nanoparticles (e.g., nanorods) with the long axis aligned perpendicular to the sample surface. The sphere and cone geometry (Probe 4) gave relatively low enhancements, as the LSP energy could not be adjusted without increasing the apex radius of curvature, thereby reducing the effect of geometric field concentration.

It should also be noted that the results presented in this work were obtained with probes positioned 1 nm above an SiO₂ substrate. A limited set of simulations were also performed using a 45° inclined, side-on excitation geometry in which the substrate material (500 nm thick, which was large enough to behave as semi-infinite) was varied (SiO₂, Si, Pt, Au). The purpose of this study was to determine how the enhancement ratio of the resonant groove designs (Probes 1 and 2) compared to the unstructured cone (Probe 5) as a function of the substrate optical properties. For SiO₂ and Si substrates, the on-resonance enhancement ratio was ~3, while for Au substrates, the ratio decreased to 1.5. The lower relative improvement for Au substrates is caused by the existence of a strong gap-mode plasmon that is supported even in the case of the unstructured cone. This situation lessens the importance of the additional apex LSP mode. A Pt substrate was also tested as an example of a metal without plasmonic behavior in the visible, and an intermediate enhancement ratio of 2 was obtained. Thus, resonant probes are not as critical for improving signal levels when metallic substrates are used, but they may still provide increases in electric fields of 50-100%.

5. Summary

FDTD simulations were used to evaluate the efficacy of several near-field probe designs with engineered localized surface plasmon modes supported at their apices. For probes with a support material separate from the plasmonic metal used for primary optical field enhancement, such as plasmonic nanoparticle-functionalized AFM tips, the complex refractive index of the support was found to be critical in controlling the plasmonic properties. Support materials with strong absorption at optical energies (Pt, W) were found to damp plasmon resonances and lead to lower enhancements, while those with relatively low absorption (SiO₂, Si₃N₄, Si) could actually be used to increase enhancements by boosting the extinction cross-section of the nanostructure. These results imply that nanoparticle functionalized probes will yield greater enhancements than conductive structures created via electrodeposition of a plasmonic metal at the apex.

Probe designs predicted to give the largest local field enhancement (~30x) were those with grooves near the probe apex, made using focused ion-beam milling. Compared to an unstructured metal cone of similar size, FIB-milled probes provided a 300% improvement in field strength, and a potential boost in TERS signals of 1-2 orders of magnitude. Moreover, grooved probe resonances could be easily tuned over visible and near-infrared energies by varying the plasmonic metal (Ag or Au) and groove location. A barrier to more widespread use of these designs is the production cost associated with milling individual probes. However, they should be viewed as a useful option for experiments where signal levels are low, particularly for non-metallic substrates where gap-mode plasmons cannot be leveraged, or for resonant spectroscopy applications where the probe plasmon energy must be precisely tuned to match optical excitations of molecules and materials.

Appendix local electric field normalization procedure

All of the local electric field enhancements reported in this work, generated by near-field probes or other nanostructures, have been normalized by the field recorded at the same spatial location when the simulation is run with no enhancing structure present. This was done to minimize the influence of the optical source type and illumination geometry chosen for a specific simulation, and thus keep the analysis focused on the general optical physics of the near-field probes being studied. We refer to this procedure as ‘local electric field normalization’. Figure 8 provides a quantitative example of how this normalization is useful to study different illumination schemes and near-field probes. Three enhancing structures were considered: a smooth semi-infinite Au cone, a 50 nm dia. Au sphere, and a 50 nm dia. Au hemisphere attached to a semi-infinite Si cylinder. Each structure was excited using four different optical sources: a 45° Gaussian beam in a (i) side-on or (ii) inverted orientation, (iii) a radially polarized beam from below, and (iv) a 45° inverted plane wave. The structures were placed 1 nm above a glass substrate and electric field values were recorded at the mid-gap location.

 

Fig. 8 Quantitative example of the local electric field normalization procedure using four different illumination geometries and three different Au nanostructures: a semi-infinite Au cone, spherical Au nanoparticle, and hemispherical Au cap on a semi-infinite Si post.

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Panels (a) and (b) of Fig. 8 show that field enhancements for a semi-infinite cone and sphere do not have a strong dependence on illumination geometry, indicating that the coupling of radiation to these structures, and excitation of any plasmonic modes, remains essentially constant. However, using side-on excitation with the post-cap structure [Fig. 8(c)] causes the peak enhancement to more than double compared to the response of the other source types. This is a clear indication of a new physical response, and, upon closer examination, it becomes clear that the Si cylinder acts as a total-internal reflection waveguide that channels a larger cross-section of the excitation beam towards the Au apex. Note that none of the optimized probe designs considered in Fig. 7 displayed a strong dependence on excitation geometry like the post-cap probe discussed here. As such, the general design principles and physics of the near-field probe structures discussed in this work are believed to be applicable to a wide range of instrument configurations and experiments.

Funding

David and Lucille Packard Foundation (2010-35954); National Science Foundation Faculty Early Career Development Program (NSF-CAREER) (CHE-0953441); Institute for Collaborative Biotechnologies High Performance Computing cluster (U.S. Army Research Office, W911NF-09-0001); Dow Foundation Discovery Fellowship.

Acknowledgements

RJH thanks the Dow Foundation for support through a Discovery Fellowship.

Disclosures

The authors declare that there are no conflicts of interest related to this article.

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