1. Introduction

The drive to integrate complicated photonic functionalities into handheld devices requires alternatives for bulky free-space optical components. Planar arrays of subwavelength scatterers, called metasurfaces (MTSs), have been suggested as a miniaturization solution, and indeed, many designs have emerged to create comparable lenses, polarizers, and more [1–4].

MTSs are commonly designed to discretize an arbitrary field transformation across the surface, then reconstruct it using individual subwavelength unit cells, or to create hotspots of maximum electromagnetic field enhancement. Nanoplasmonic resonators are particularly well-suited to MTS integration as they can be significantly miniaturized at resonance and support strong electromagnetic field confinement. In particular, aperture-based plasmonic resonators can exhibit better performance than their complementary nanoantenna-based counterparts; for example, the increased metallic area can improve heat dissipation; apertures have been shown to better localize fields leading to increased field enhancement [5,6]; and strong magnetic fields can be localized by the excitation of enhanced conduction currents [7].

Unfortunately, current design methods have been insufficient to entirely replace conventional optical components due to limitations on efficiency and bandwidth. Emerging inverse design methods promise to improve plasmonic MTS performance through numerical optimization, but these optimized designs are often difficult to realize experimentally due to the fine patterning resolution required [8–12]. Moreover, as MTS technology is scaled to increasingly short wavelengths and applied to ultraviolet and x-ray nanophotonics, feature scales will necessarily need to be minimized to engineer the scattering spectra [13,14]. Methods to increase the patterning resolution of arbitrary MTS elements are therefore required to improve the efficiency of plasmonic MTSs.

For aperture-based MTSs, the metal film often has to be thick to render the film opaque away from resonance. This significantly increases the signal-to-noise ratio for transmissive MTSs [15], but implies that top-down approaches must be used to fabricate the structures. Few options exist for creating fine features for nanoaperture-based MTSs due to the high aspect ratios (feature width:feature depth) and anisotropic etching required, often relying on Ga $^{+}$ focused ion beams (FIBs), which have a maximum resolution of $\sim 20$ nm [16]. Using high-resolution electron-beam lithography resists, gaps as small as 10 nm have been shown with high aspect ratios, but this technique limits the metallic feature shape and produces rough sidewalls [17].

Recently, He $^{+}$ gas field ion sources (GFISs) have emerged for FIB-based imaging applications to produce a sub-nm probe size. Helium ion microscope (HIM) milling has proven to be the only fabrication technology that can achieve both high aspect ratios (over 1:10) and extremely fine features in noble metals (as small as 3 nm) [18–24]. Unfortunately, the HIM has been hampered by relatively slow speed and reproducibility, which is particularly important for the fabrication of MTSs as they must be larger than the illuminating beam size, which often requires hundreds of identical unit cells. We have previously shown that with a careful choice of patterning parameters, the HIM can be used to reliably fabricate complicated metamaterial (MTM)-lined aperture MTSs unit cell patterns with 10-nm nanogaps and 10-nm nanowires in gold, with a 1:5 aspect ratio and over a large area [25]. The design shown in Fig. 1(a) provides resonant transmission in the near-infrared (NIR), where $b=120$ nm, $w=10$ nm, and $p=300$ nm. Regretably, the MTS could not be characterized optically due to repeated fabrication defects suppressing the resonance. The fabrication defects were caused by the selective etching of polycrystalline film grains, the redeposition of gold in the nanogaps, and poor contrast in the HIM images as the gap depth was increased hiding these issues.

 

Fig. 1. (a) Eight-wire MTM-lined aperture design for operation in the NIR, (b) Optical two-wire MTM-lined aperture design for visible-frequency operation, and (c) the transmission, reflection and absorption spectra for a nominal design resonating at 425  THz/700 nm. Geometric parameters for this design are $w=g=10$ nm, $b=25$ nm, $p=150$ nm, and the film thickness is $t=50$ nm. (a) © 2019 IEEE. Reprinted, with permission, from [37]. (b), (c) reproduced from [36].

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In this work, we report the design, fabrication, and characterization of a modified MTM-lined aperture MTS using 10-nm features to achieve minimum unit-cell miniaturization factor, $m = p/\lambda _0$, where $p$ is the MTS pitch and $\lambda _0$ is the free-space wavelength. Improved miniaturization of plasmonic MTS elements is desirable for sampling quickly varying phase profiles more accurately for phase-gradient based MTSs [26], and for increasing resolution for holograms with improved viewing angles [27], super-resolution imaging [28], plasmonic lithography [29], and magnetic memory [30]. Single-layer MTSs have been proposed with $m$ as small as $1/7$ [31], and other designs with multiple layers have not significantly improved on this metric [26,32–35].

We begin by summarizing the previously presented design of a class of two-wire MTM-lined aperture MTSs making use of 10-nm nanowire and 10-nm nanogap features [36]. Their performance is compared to conventional bowtie nanoapertures making use of only fine nanogaps, showing the importance of both finely featured nanogaps and nanowires for miniaturization and field enhancement. We then fabricate the MTS design using the HIM. To address the challenges posed by grain defects, redeposition, and substrate contrast, we grow an epitaxial gold film and transfer it to a free-standing transmission electron microscope (TEM) grid for patterning. Finally, we characterize the fabricated MTS and create a comparable simulation that accurately models the experimental and fabrication defects. This work establishes that such MTM-lined apertures are candidates for high-resolution surface-enhanced spectroscopy, near-field imaging, and enhancing nonlinear light-matter interactions. We show the widest-area fabrication to date of an MTS with extreme 10-nm nanowire and nanogap features, and with 1:5 aspect ratios. The MTS is successfully optically characterized using a reflection-mode microscope. Our methods may be applied to the fabrication of any number of emerging nanoplasmonic devices with extreme features.

2. Results

2.1 Design

In this section, we aim to establish that consistent 10-nm features can improve the miniaturization and field enhancement performance of miniaturized plasmonic resonator-based MTSs. To this end, we modify the NIR MTM-lined aperture shown in Fig. 1(a) for maximum miniaturization, which could be used to improve the spatial resolution of field transformations and near-field imaging probes, and increase the near-field enhancement for particle trapping, surface-enhanced spectroscopy, and strong nonlinearities. Moreover, we can shift the resonance frequency to the visible domain, where sensors can be made simpler through qualitative evaluation of the results.

To minimize the miniaturization factor ($m = p/\lambda _0$), either the resonant frequency of the MTM-lined aperture must be minimized, or the pitch of the array must be reduced without a commensurate increase in the resonance frequency [36]. In the parametric studies of the NIR MTM-lined aperture, two major features improved the miniaturization factor: reducing the number of wires and scaling down the size of the unit cell (both the aperture radius and the array period simultaneously) [37].

Decreasing the number of nanowires to decrease the miniaturization factor is intuitive with a basic equivalent-circuit analogy, where the resonance is due to the nanowires modelled as inductors, in series with the gap capacitance at the centre of the aperture. The nanowire inductance is dominated by the kinetic inductance of the gold. Reducing the number of wires inside the aperture decreases the number of inductors in parallel, increasing the overall inductance loading the aperture. Similarly, the number of capacitors in series at the tips of the nanowires is reduced, increasing the effective capacitance of the aperture.

The same equivalent-circuit analogy can be applied to the change in aperture size. Consider the aperture loaded with two nanowires shown in Fig. 1(b). When the aperture is shrunk, the overall capacitance decreases slowly and eventually saturates at the gap capacitance, while the inductance falls linearly. As a result, the resonance frequency $\omega =1/\sqrt {LC}$ only increases at a rate of $\sim \sqrt {b}$, while the size decreases linearly with $b$, and the miniaturization factor can be reduced with a proportionate decrease of the array period $p$.

Reducing the number of nanowires in the NIR MTM-lined aperture from 8 to 2 redshifts the resonance frequency from $\sim 200$ THz to $\sim 150$ THz. Although this frequency shift is only 25% and hence does not greatly improve the miniaturization factor, the effects of this shift on the aperture geometry are important. First, the symmetry of the aperture is reduced and the MTM-liner resonance becomes polarization-sensitive, allowing the design of different aperture responses for different polarizations, or polarization selectivity for applications such as ellipsometry and near-field sensing. Second, the central region of the liner can be made more compact. Enforcing the minimum feature size of $10$ nm requires that the tip of each wire be $g=10$ nm from its nearest neighbour, and under the constraint that the wire width $w=g$, the radius $a$ of a circle enclosing the central region, including the tapered nanowire tips and capacitive gaps, can be calculated from the law of cosines:

2.2 Simulation

2.2.1 Two-wire metamaterial-lined apertures

The nominal design of the polarization-sensitive MTM-lined aperture, which we call the two-wire aperture, is shown in Fig. 1(b). The structure was simulated in Ansys Lumerical FDTD, where the $w=10$ nm is the nanowire width and $g=10$ nm is the minimum gap width based on fabrication constraints, and $b=25$ nm is the aperture radius chosen to shift the resonance into the visible regime. The array pitch $p=150$ nm is chosen for a small fill factor to potentially multiplex many apertures into one cell, and $t=50$ nm is the film thickness chosen for opacity. This corresponds to a maximum aspect ratio of 1:5, which cannot be reliably achieved for 10-nm features with any fabrication process other than HIM milling.

The film is made of gold due to its chemical stability, as it will not passivate in air and fill the nm-scale patterned features. The model for gold is a numerical fit to experimental data and the film is suspended in air, while the nanowire tips are filleted to model the rounding that occurs in fabrication [39].

The results of the simulation are shown in Fig. 1(c). The designed resonance is seen at 425  THz/700 nm when excited with a $y$-polarized incident plane wave, where there is a sharp decrease in reflection and a significant fraction of the incident power is absorbed by the MTS. For an $x$-polarized excitation, the plasmonic nanowire liner is not excited and the spectrum is that of an array of empty apertures, where the fundamental resonance frequency is well outside of the range of interest.

2.2.2 Bowtie nanoapertures

From another perspective, one could visualize the MTM-lined aperture as the limiting case of a bowtie-shaped aperture, where the bowtie has been flared to full half-sectors. This concept is shown in Fig. 2(a) by overlaying the MTM-lined aperture with a conventional quarter-sector bowtie aperture. Due to symmetry, it is most convenient to describe the structure by the sector half-angle $\theta$, as labelled in the figure, i.e., $\theta =90^\circ$ for the two-wire MTM-lined aperture, and $\theta =45^\circ$ for the conventional bowtie aperture. Bowtie-shaped nanoapertures are commonly used as subwavelength elements to focus electric fields into a small volume at the centre of the aperture with large field enhancements. This technique finds use in applications such as subwavelength near-field microscopy [40], surface-enhanced Raman scattering [41], and fluorescence imaging [42]. The most important factor for these applications is the local field enhancement at the centre of the aperture as the signal strength is a function of powers of the local electric field strength, $|E|^x$ [43]. For subwavelength near-field microscopy, the miniaturization of the aperture is important as it ultimately sets the limit on the achievable resolution of the near-field probe.

 

Fig. 2. (a) A schematic of the relation between a bowtie aperture ($\theta =45^\circ$) and a two-wire MTM-lined aperture ($\theta =90^\circ$). (b) Reflection spectra of the aperture shown in part (a), for various angles $\theta$. The input is a $y$-polarized plane wave at normal incidence, $b=40$ nm, $g=10$ nm, and $w=10$ nm is the minimum wire width.

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To compare the performance of the MTM-lined aperture MTS to that of a bowtie nanoaperture antenna, we implemented the bowtie nanoaperture array shown in Fig. 2(a) in Ansys Lumerical FDTD and performed a sweep of the sector half-angle $\theta$, with radius $b=40$ nm, gap width $g=10$ nm, minimum nanowire width $w=10$ nm, and array pitch $p=100$ nm. The 10-nm nanogap is present in all cases and the conductive tips are circularly rounded, hence all the studied structures would require fabrication by HIM. Nevertheless, the gap width is critical to the field enhancement, therefore, it should be held constant for a meaningful comparison.

The reflection spectra are shown in Fig. 2(b) for four $\theta$ angles, where it is clear that as the sector angle increases toward the MTM-lined aperture case, the resonance becomes redshifted. This implies an improved miniaturization factor from $m=1/7.5$ to $m=1/10$ as the aperture radius and unit cell period are constant. From the equivalent-circuit perspective, a redshift is expected due to the kinetic inductance of $Z_w$ scaling inversely with the cross-sectional area of the nanowires, which increases as $\theta$ decreases. $Z_c$ decreases linearly with decreasing $\theta$, which is slower than the change in $Z_w$. The resistance of the nanowires is also inversely proportional to the nanowire cross-sectional area, and a commensurate decrease in the transmission amplitude is observed (though not shown).

The electric-field profiles at resonance are shown in Fig. 3 for four sector angles $\theta$. The permittivity of the gold layer is dispersive, and hence each resonator sees a slightly different material at resonance. Naturally, as the frequency is reduced, the effective permittivity of the gold layer trends toward that of a perfect electric conductor, and the miniaturization factor for the fundamental resonance decreases to $m=\sim 1/2$. Increasing the sector angle works against this trend to enhance the overall miniaturization factor at lower frequencies.

 

Fig. 3. Electric-field profiles of the bowtie-shaped aperture arrays at resonance for a $y$-polarized, normally incident plane wave and various sector angles $\theta$.

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As the sector angle grows, the induced surface charge is pulled to the tips of the nanowires due to the lightning rod effect, causing an increase in the resonant local electric field magnitude at the centre of the aperture [44]. If we approximate the aperture nanowires as oblate spheroids with tip width $w$ and length $b\sin \theta$, the MTM-lined aperture is expected to increase the field enhancement by a factor of 2 over the $45^\circ$ bowtie case. Instead, an enhancement of only 20% is observed despite the reduced loss of gold at lower frequencies. The increased dissipation from the nanowire resistance caused by the reduction in the nanowire cross-section is intuitively consistent with a damped field enhancement. Thus the improved field enhancement and miniaturization in the MTM-lined apertures are balanced by increased loss. Nevertheless, a 20% difference in field enhancement implies at least 44% more signal in surface-enhanced infrared absorption spectroscopy (SEIRA) applications, and twice the signal in surface-enhanced Raman spectroscopy (SERS) [43]. The enhanced miniaturization can be used to pack apertures closer together for higher spatial resolution in near-field sensing and higher hotspot density in surface-enhanced sensing. The additional loss is undesirable in surface-enhanced fluorescence applications, where the active signal will be suppressed; however, in applications involving nonlinear processes, such as SERS, suppressing the scattering of the excitation is acceptable.

It is clear that both 10-nm nanogaps and nanowires can be combined to achieve improved performance, particularly as MTSs created through inverse-design methods continue to push the boundaries of nanoplasmonic MTS performance. Nevertheless, their nanofabrication remains a significant challenge.

2.3 Nanofabrication

Our previously published analysis of the reliable patterning of 10-nm features using the HIM showed that the main challenges were the use of polycrystalline films that introduced grain defects, low substrate contrast leading to an underestimation of the milling depth, and redeposition modifying the patterned structures [25]. Below, we address these challenges by growing an epitaxial film on LiF and subsequently removing the substrate by dissolution in HF.

2.3.1 Epitaxial growth of gold

For the present study, we have mitigated grain defects by growing gold films by physical vapour deposition on a lattice-matched substrate. Using the process of Fedotov et al., high-quality films were grown on LiF that exhibited no grain defects during patterning by the HIM [45]. Full process details and film structure analysis are included in the Supplementary Materials. The grown film was 65-nm thick, and Fig. 4(a) shows a HIM micrograph of the film, where it is clear the film is largely flat and no grain contrast can be seen. Some pitting is highlighted, and gaps exist along crystal cleavage boundaries in other parts of the film. Otherwise, the film is largely continuous.

 

Fig. 4. HIM micrographs of the films grown on LiF, showing (a) the epitaxial film grown on LiF, where no grain contrast is seen and some pitting is highlighted, and (b) a bubble created by patterning a small array of apertures, the image was collected at a 45$^\circ$ angle to accentuate the topography.

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Unfortunately, with the introduction of a crystalline substrate, the implantation of helium can cause the substrate to swell as the helium diffuses and coalesces into bubbles within the crystal [46]. When patterning films that were grown on LiF, this problem becomes increasingly obvious as more gold is milled away. The bright area in Fig. 4(b), taken at a 45$^\circ$ angle, shows a bubble formed under a small array of apertures. Thus to reliably pattern subwavelength features into this nearly epitaxial film over a wide area, the crystalline substrate must be removed and the film must either be transferred to a polycrystalline substrate or simply left free-standing.

2.3.2 Substrate removal

To remove the substrate, the LiF crystal was dissolved in HF. The gold-on-LiF sample was submerged entirely in HF for 5 minutes then carefully removed, and without drying, transferred to a beaker of water. A few sections of the film separated and were retrieved with TEM grids. The samples prepared this way were reliable to pattern, showing no problems with contamination, grain defects, or charging/swelling. These films were used for the patterning presented below.

In the present study, we left the film free-standing on copper TEM grids. Since our example uses a continuous film of gold, we do not need the structural support of a substrate (as would be required for a nanoantenna array), though transferring the film to a polycrystalline substrate is a common procedure [47–49]. This also allows us to avoid the complications of substrate charge accumulation and sputtered material can be redeposited on both sides of the film. The drawbacks of this approach are that the film may be structurally unstable where there is no support and films of contaminants may be grown on both sides of the metal.

2.3.3 Two-wire MTS nanopatterning

The free-standing, epitaxial gold films may now be patterned to create our MTS; however, the reliable nanopatterning of features as small as 10 nm in gold films with an aspect ratio as high as 1:5 is an extreme challenge with the HIM. While single patterns can be patterned without significant difficulty, stabilizing the HIM for several continuous hours of patterning without loss of resolution required extensive development time. To gauge the reliability of array patterning, we define a figure-of-merit, $F_{AF}$, as the ratio of one side of the patterned area to the minimum feature size, and propose a ratio $F_{AF}>320$ as a wide area. Practically, the lateral extent of the MTS should be at least $3\lambda _0$, such that it can be excited by a poorly focused beam and over a wide bandwidth. We have identified a number of intuitive best practices to reduce the drift of the beam while patterning and increase the fabrication fidelity [25]. These practices include: (1) structures exhibiting symmetry are more robust to grain defects, but these defects can be eliminated with single-crystal films, (2) crystalline substrates must be avoided, and careful choice of the ion dosage is required when using insulating amorphous substrates, (3) contamination is difficult to address at later stages in the fabrication process, requiring destructive plasma cleaning, and should thus be eliminated as early as possible, (4) time permitting, the microscope should be allowed to stabilize as long as possible between loading, moving the stage, and patterning to reduce drift, and (5) as the patterning area increases, the mounting procedure of the sample on the microscope stub becomes increasingly important and methods to eliminate tilt must be applied.

For the patterning parameters: (1) the ion dosage required to fully mill through the film must be established first to minimize overmilling, (2) the current and spot size should then be tuned simultaneously to achieve the desired feature size over a cell in the minimum patterning time to avoid drift, and (3) the dwell time should be tuned to minimize the redeposition on nearby features.

Combining these recommendations, we patterned the $\sim$65-nm thick epitaxial film that was grown on LiF and transferred to a TEM grid. A mechanical clamp was used to secure the grid in place on the scanning electron microscope (SEM) stub, reduce tilt, and maintain conductivity. No contamination growth was observed, hence the plasma-cleaning step was omitted. The nominal array feature sizes were an aperture radius of $b=40$ nm, a gap and wire size of $g=w=10$ nm, and an array pitch of $p=120$ nm. The relatively large pitch was chosen to reduce the effect of redeposition on the nanowires, and the MTS now resonates at a wavelength of 850 nm.

Regrettably, we were unable to achieve ideal fabrication conditions and were forced to use an older, degraded source, which produced lower current and hence reduced our pattern quality. The He $^{+}$ gas pressure was set to 4e-6 Torr, resulting in a nominal current of 9 pA. Although the current varied during patterning, the nominal patterning time for a single aperture was $\sim$10 s. Otherwise, the beam parameters were chosen based on the recommendations published previously [25].

The drift-correction feature of the patterning software, Fibics Nanopatterning and Visualization Engine (NPVE), was used to correct the ion beam drift every 60 s. Due to the high current used while milling, the continuous scanning of the reference area changed the shape of the reference pattern by parasitic milling and redeposition, and the reference image had to be recollected when the image processing algorithm failed. This led to some dislocations of the array. Nevertheless, the drift-correction feature removed a significant amount of the drift normally observed while patterning large arrays. The additional imaging and drift correction, along with the slowly decaying current from the source, slowed the patterning speed to an average of about 15 s per aperture.

We fabricated a $3.6{\times }3.6\;\mathrm {\mu }\textrm {m}^{2}$ array of $30\times 30$ MTS cells in approximately four continuous hours of patterning, with the result shown in Fig. 5(a). This corresponds to an $F_{AF}$ of 360 and $\sim 4\lambda _0$ at the operating wavelength of 850 nm. The full array is composed of smaller $5\times 5$ arrays to minimize the effect of drift and redeposition on nearest neighbour apertures. From these images, the patterned features measure approximately $b=\sim 35$ nm, $w=\sim 12$ nm, $g=\sim 11$ nm, and $p=120$ nm, with variations of these dimensions on the order of $1$ nm. We attribute the difference between the nominal and patterned feature sizes to the redeposition of gold as later apertures are milled, which may be partially corrected by overmilling the apertures, or, if the array drift is sufficiently well-controlled, can be corrected in a second pass. This is significantly more practical over small arrays [50]. Additionally, NPVE offers very little control over the ion beam milling path. The recently-developed FIB-o-mat software provides full control over the raster pattern and has been shown to increase feature resolution to as small as 3 nm, though reliability continues to be a challenge [23]. Adding an optimized milling path to our methods may further improve feature fidelity.

 

Fig. 5. (a) Patterned two-wire MTS array, fabricated under suboptimal current and stability conditions. Profile view of the fabricated MTS array at $45^\circ$ oblique incidence, (b) parallel to the patterned nanowires, and (c) rotated with respect to the nanowires, (d) simulation model layout incorporating fabrication variation. The array is divided into four $2\times 2$ cells, and (e) shows a cutaway highlighting the reduced nanowire thickness.

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2.4 Characterization

We characterized the two-wire MTS shown in Fig. 5(a) using a home-made microspectrophotometer in reflection mode. The microspectrophotometer is fed by a supercontinuum laser coupled to a collimator. The collimated beam is reflected towards the sample using a non-polarizing 50/50 beamsplitter, and the beam is then focused onto the sample using a $100\times$ objective, achieving a spot size of approximately $3.5\mathrm {\mu }\textrm {m}$. After reflecting off the sample, the beam returns to the 50/50 beamsplitter, transmitting the reflected spectrum through a linear polarizer, and the beam is focused using a collimator to a large-core fibre coupled to the spectrometer. Full details of the microspectrophotometer layout and components are available in the Supplementary Materials. Perfect alignment between the MTS and the laser was difficult to achieve due to low-precision stage controls and the similar size of the focused beam and the MTS.

Since the MTS is polarization-sensitive, the goal of the measurement was to observe a contrast between oppositely polarized spectra to see the full effect of the resonant nanowire loading. The polarizer was placed at the output to ensure that any misalignment would not affect the position of the beam on the sample as the polarizer was rotated. This way, the MTS spectrum can always be collected, though some small differences in power levels may occur due to the movement of the beam on the output fibre face. We used a large-core collection fibre in combination with a suitable collection collimator to maximize the spatial and angular field-of-view.

Background reflection spectra were collected for the gold film and polarizer angles between $0^\circ$–$180^\circ$ in steps of $10^\circ$. If no alignment issues are present, the second half of the polarization angles are identical to the first half, and are therefore redundant. We note that a number of the optical elements in the beam path (particularly the beamsplitter) were not uniform over all polarization angles, and hence the background spectra varied substantially for orthogonal polarizations. The stage was then moved to center the beam on the MTS, and spectra were collected for the same polarizer angles. The relative reflection measurement is the ratio between the MTS reflectance and the background reflectance taken at an unpatterned region of the gold film, which removes the effect of all the optical elements common to both measurements and leaves just the MTS spectrum.

To find the array axes with respect to the polarizer angle, we compared each normalized measurement to its orthogonal polarization angle. The polarizer proved to be well-aligned to the array axes, and the maximum difference occurred between the $0^\circ$ and $90^\circ$ cases. These cases are plotted in Fig. 6, where the data were smoothed through a 31-sample Savitzky-Golay filter. For comparison, the simulation data for the nominal MTS design and a film thickness of $t=65$ nm are also overlaid, normalized to a simulated solid 65-nm thick gold layer background spectrum. In the vicinity of the designed resonance, the experimental reflection of the surface is significantly lower when excited with a vertically-polarized beam than with a horizontally-polarized beam. It is clear that the MTS is operating as designed, though fabrication tolerances and experimental inaccuracies have shifted the resonance and reduced its strength.

 

Fig. 6. Experimental data normalized to the raw gold film background compared to nominal simulation data. The experimental data were smoothed using a 31-sample Savitzky-Golay filter, and the nominal geometric parameters were $b=40$ nm, $g=w=10$ nm, $p=120$ nm, and $t=65$ nm.

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3. Analysis

We now consider the differences between the experiment and the simulation. First, we address the nonresonant $x$-polarized spectrum since it is independent of the fine, 10-nm features and has fewer confounding factors. When comparing to the simulation, there are three main features to be matched: (i) the location of the material-based absorption peak of gold at $\sim 500$ nm, (ii) the level of the gold absorption peak at $\sim 500$ nm, and (iii) the overall reflectance.

The location of the gold absorption peak (or equivalently, the minimum reflectance) is controlled by the filling fraction of the array and the gold film thickness, where thicker films and smaller apertures marginally blueshift the observed minimum. Rough measurements made on Fig. 5(a) show that the designed aperture radius was well-patterned in experiment, and the radius varies from $\sim 39$–$41$ nm. Additional simulations with a 40-nm aperture radius match the reflectance minimum wavelength best for a film thickness of 65 nm.

With the film thickness and aperture radius set, no geometric variables remain to match the nonresonant absorption level. We expect that the difficulties in evaluating the alignment of the optical beam to the patterned MTS area caused a fraction of the collected signal to be collected from the solid surface near the MTS, rather than the MTS itself. To account for this difference, a scaling factor is added to the simulated spectrum:

Equation 2 is only able to increase the reflection amplitude and hence even with the above corrections, the spectra will never match from $650$–$1000$ nm. Curiously, the experimental scattered power is nearly constant over this range and never exceeds $85$%, even over all polarization angles. Due to gold’s high conductivity in the NIR, all variations of $b$ and $t$ in simulation show nearly 100% reflectance at 1000 nm. Moreover, a change in the surface conductivity (which would model the potential damage to the crystal structure of the film by the HIM) does not substantially improve the agreement. As a result, a shift in the alignment of the microscope between the background and the MTS measurement must have caused a uniform $\sim 15$% drop in the collected power. We introduce a power normalization factor $P_{Exp}$ to correct the expected power level. With the correction factors, $P_{Exp}$ and $BG_{ratio}$, the nonresonant spectrum experimental can be reliably matched to the $x$-polarized simulation spectrum.

For a deeply subwavelength MTS unit cell, the numerical aperture of the MTS is high as diffraction is avoided. We calculated the convergence angle of our lens geometrically to be $\sim 55^\circ$ and studied the effects off-normal excitations for all polarization conditions, both TE- and TM-polarized, and with the in-plane electric-field along both the $x-$ and $y-$ directions. The results are consistent with previous work on similar structures [51], where the background reflectance is decreased for TM-polarized incident waves, and the background reflectance is increased for TE-polarized incident waves. The resonance occurs at a constant frequency. When the contributions of each polarization are combined in equal proportions, the overall effect on the spectrum is minor and hence the match to experimental data is not improved.

Finally, the resonant spectrum ($y$-polarized excitation, normal incidence) must be matched. When patterning fine features with the HIM, some overmilling of 10-nm wires is difficult to avoid [25]. This leads to a thickness gradient along the wire or a uniform decrease in the wire thickness. In the present experiment, the age of the ion source exacerbated this issue, significantly overmilling the nanowires. Figure 5 shows an inspection of the MTS after measurement with an incidence angle of $45^\circ$, such that the profile of the nanowires can be seen. A rough estimate of the film thickness in these images is $t=\sim 62$ nm, which is close to the thickness expected from the previous simulations, and the nanowire thickness is approximately $t_w=42$ nm. The nanogap widths were measured to vary between $g=11$–$14$ nm, and the nanowire widths were measured to vary between $w=11$–$13$ nm. Despite the high resolution of these images, no grain contrast is observed, confirming the sufficiently high crystal quality of the gold film. Additionally, the wires are significantly more rounded than those originally modelled in simulation.

The simulation model that incorporates all the geometrical variations of the fabricated MTS is shown in the bottom half of Fig. 5, with the geometrical parameters summarized in Table 1. The simulation model is divided into four $2\times 2$ sections that represent the extremes of the geometric variations observed. With $b$, $w$, and $g$ corrected, the resonant minimum reflection continues to maintain a very low value near 20%, and it is the incorporation of the overmilling of the nanowires (i.e. $t_w$) that can correct this discrepancy. To highlight this change, a cutaway is shown in Fig. 5(e), where the top, bottom and front surfaces of an aperture have been hidden.

Table 1. Geometric parameters used in the nonuniform simulation model

View Table

Figure 7 shows the spectra computed in COMSOL, matched to the scaled experimental data for both incident polarizations, where $BG_{ratio}=0.26$ and $P_{Exp}=1.17$ have been tuned numerically for the best possible agreement. The resonance frequency was shifted by the variation in $b$, $g$, and $w$, though the overall bandwidth below 80% reflection is not significantly increased. Shifting $t_f$ does not change the resonance frequency, but instead reduces the resonance amplitude by increasing the loss in the nanowires at resonance.

 

Fig. 7. Final simulation results, tuned to match the scaled experimentally acquired spectra. $BG_{ratio}=0.26$ and $P_{Exp}=1.17$.

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4. Discussion

We have presented the design, fabrication, and characterization of two-wire plasmonic MTM-lined aperture MTSs making use of fine 10-nm features. We have shown in simulation that maximum miniaturization and field enhancement can be achieved using both 10-nm nanogaps and nanowires. We have created a prototype displaying reliable fabrication of features as small as 11 nm using the HIM under imperfect fabrication conditions. Grain defects, redeposition, and undermilling were addressed by patterning a single-crystal film and removing the supporting substrate. Our characterized MTS shows evidence of thinning of the nanowires due to overmilling, which can be mitigated by operating with a fresh ion source or a redesign of the ion beam milling path using FIB-o-mat [23].

In experiment, our MTS resonates on a scale of $\lambda _0/7$, and the resonance is broadened due to fabrication inconsistencies. As a proof-of-concept, our MTS acts as a poor resonant polarization filter, but with minor modifications, could be used as a SERS substrate for a Raman microscope. Our methods show consistent fabrication of features as small as 11 nm and with geometric variations on the order of 1 nm. The fabrication fidelity could be improved by patterning under more ideal conditions, such as in a lower-noise environment and with a fresh ion source. Our results are a promising step toward full, high-resolution fabrication of plasmonic MTSs and other large-area nanoplasmonic devices, such as plasmonic gap waveguides and holograms, using just the HIM. Moreover, we have extended the minimum feature size achievable for inverse design methods to 11 nm. In the future, we intend to improve our results to the promised 10 nm resolution and with less variation by minimizing the noise in the fabrication environment during patterning.