Article www.acsnano.org Imaging of Antiferroelectric Dark Modes in an Inverted Plasmonic Lattice Javier Rodríguez-Á lvarez,* Amílcar Labarta, Juan Carlos Idrobo, Rossana Dell’Anna, Alessandro Cian, Damiano Giubertoni, Xavier Borrisé, Albert Guerrero, Francesc Perez-Murano, Arantxa Fraile Rodríguez, and Xavier Batlle Cite This: ACS Nano 2023, 17, 8123−8132 Read Online ACCESS Metrics & More Article Recommendations * sı Supporting Information ABSTRACT: Plasmonic lattice nanostructures are of techno- logical interest because of their capacity to manipulate light below the diffraction limit. Here, we present a detailed study of dark and bright modes in the visible and near-infrared energy regime of an inverted plasmonic honeycomb lattice by a combination of Au+ focused ion beam lithography with nanometric resolution, optical and electron spectroscopy, and finite-difference time-domain simulations. The lattice consists of slits carved in a gold thin film, exhibiting hotspots and a set of bright and dark modes. We proposed that some of the dark modes detected by electron energy-loss spectroscopy are caused by antiferroelectric arrangements of the slit polarizations with two times the size of the hexagonal unit cell. The plasmonic resonances take place within the 0.5−2 eV energy range, indicating that they could be suitable for a synergistic coupling with excitons in two-dimensional transition metal dichalcogenides materials or for designing nanoscale sensing platforms based on near-field enhancement over a metallic surface. KEYWORDS: plasmonic, honeycomb lattice, inverted lattice, dark modes, EELS, antiferroelectric, SLR L ocalized surface plasmons (LSP) can be excited at the interface between a metallic nanostructure and a dielectric medium by coupling with an external electromagnetic wave under the appropriate conditions.1 LSP excitations create subwavelength confinement of the light in realizations of lattices of plasmonic nanostructures vary considerably, both in design and functionality.16−18 Although the LSP of neighboring nanoparticles can also be coupled, the corresponding excitations are severely affected by radiative damping. SLR, in contrast, often exhibit highly tunable, intense the vicinity of the nanostructures, as well as an enhanced and narrow resonances.19 intensity of such a near-field distribution.2−4 Consequently, In this work, we focus on geometrically frustrated honey- they have extensively been used in a wide variety of comb lattices, which have previously been studied for its applications involving electromagnetic radiation in the infra- unique plasmonic band structure and its similarities with the red-visible-ultraviolet range, such as nanoantennas,5 high behavior of graphene and other 2D materials.20−22 We sensitivity spectroscopies,6,7 biomedical applications,8−10 non- investigate the plasmonic properties of an inverted honeycomb linear harmonic generation,11 ultrafast phase modulation,12 lattice (inverted as the nanostructure is carved in a continuous and sensors13 among others. layer). The interest for inverted structures arises, among other An additional level of complexity arises when metallic applications, from further increasing the sensitivity of surface nanostructures are organized in a periodic array. In this case, enhanced Raman spectroscopy (SERS) to ultrasmall amounts the radiative coupling between the LSP and the diffracted waves in the plane of the array enables the appearance of coherent excitations of the scatterers in the lattice, known as Received: November 4, 2022 surface lattice resonances (SLR). Introduced by Carron and Accepted: April 11, 2023 co-workers14 and found experimentally by Hicks and co- Published: April 24, 2023 workers,15 the excitation of these resonances occurs near the frequency at which the diffracted wave is radiating in the plane of the array, that is, at the Rayleigh anomaly. Experimental © 2023 The Authors. Published by American Chemical Society https://doi.org/10.1021/acsnano.2c11016 8123 ACS Nano 2023, 17, 8123−8132 ACS Nano www.acsnano.org Article of a given analyte,20,23 which is relevant for the detection of and LSP modes in the optical range, which was achieved diseases in early stages24 and traces of contaminants in through the combination of state-of-the-art manufacturing of wastewater.25 According to Babinet’s principle21,22, the optical the samples and the outstanding spectral and spatial resolution response of a plasmonic nanostructure must be equivalent to of the STEM. A comprehensive spectral analysis of both the that of its inverted counterpart. Besides, the excitation of SLR far-field and near-field measurements from Fourier-transform is perfectly possible in these type of inverted systems.20 This infrared spectroscopy (FTIR) and EELS, respectively, and the enables designing inverted structures with a very similar good agreement with the numerical electromagnetic simu- spectral behavior to their counterparts, in terms of the lations have enabled the identification of a variety of both excitation energy and spectral features of the resonances - bright and dark modes, the latter unable to be detected using while corresponding to a very different near-field distribution light. Furthermore, dark modes that are be caused by around the structure.22,26,27 arrangements of the slit polarizations that divide the system Here we show that the manufacture of a honeycomb array of into two antiferroelectric sublattices have been found. These slits fosters the formation of out-of-plane hotspots related to modes present a primitive unit cell twice that of the fabricated the SLR that present large enhancement factors of the electric honeycomb lattice. field, even hundreds of nanometers away from the 2D array into the surrounding medium. Such an out-of-plane electric RESULTS AND DISCUSSION field enhancement is crucial for their integration in sensing and The studied sample consists in a 20 nm thick continuous layer advanced spectroscopic architectures such as refractive index of Au deposited on a thin (50 nm) Si3N4 membrane. The Au sensors.28 layer is patterned by carving slits through the entire thickness The implementation of any design pathway for enhanced of the Au layer. The slits are approximately 400 nm long and plasmonic nanoarchitectures requires of an understanding of 45 nm wide. They follow the arrangement of a honeycomb the plasmonic near-field response. A possible route to obtain a lattice with a pitch of p = 906 nm. This structure can be clear picture of the plasmonic resonances supported by a considered as a dielectric (air) planar honeycomb lattice particular structure is to use electron energy loss spectroscopy embedded in a metallic (Au) layer (see Figure 1). (EELS). This technique, probing the local photonic density of states,29 allows the excitation and mapping of the local distribution of electromagnetic modes by measuring a spectrum of the energy loss resulting from local interactions with the sample, thereby becoming an important tool for near- field imaging of plasmonic optical excitations.30 When performed in a monochromated aberration-corrected scanning transmission electron microscope (STEM), the achieved energy resolution of EELS can be of the order of 10 meV while preserving sub-Å spatial resolution.31−34 A crucial advantage of this technique is the combination of the spectral features with their 2D projected intensity maps, allowing high sensitivity to subtle spatial modifications.35 In the case of studying plasmonic responses with a STEM, an acquired EELS signal is closely related to the optical extinction spectra, and has proven to be a useful tool for studying localized and surface plasmon resonances of a variety of structures, including films, pillars, and holes of varying diameters, as well as slots and Figure 1. (a, b) Scanning electron microscopy images of the coaxial resonators,36 metallic nanostructures,37−39 nanocav- manufactured sample. (c) Schematic cross-sectional view of the ities,40,41 nanowires,42 surface-plasmon modes in nano- studied sample. particles,43,44 coupled nanoparticles,45 molecular excitations,46 or excitation of modes in 3D.47 In addition to the experimental The response of the structure presents a plethora of contributions, advances in EELS simulations and theoretical resonances in the visible and near-infrared (NIR) ranges. modeling have also been crucial for interpretation of the This is clear from the finite-difference time-domain (FDTD) results.35,48−50 simulations, FTIR measurements, and the data acquired during A key aspect regarding our work is the fact that, in addition the EELS experiments. The corresponding spectral results are to bright modes, EELS can also reveal optically dark presented in Figure 2. Prior to an in-depth discussion, it is modes,35,36,51−54 that is, modes with a vanishing net dipole important to stress the differences between the three data sets moment, thereby providing a full modal spectral map of a shown in Figure 2. plasmonic system. Dark modes can store electromagnetic FDTD simulations and FTIR measurements show the energy more efficiently than bright modes due to suppression response of the system under the excitation of unpolarized of radiative losses. This results in narrower line widths and light with normal incidence onto the array. However, EELS longer lifetimes than their radiative counterpart, making them data rely on the energy-loss of a highly monochromatic beam ideal candidates for lossless nanoscale waveguides and of electrons that are inelastically scattered by the system. subwavelength high-Q optical cavities,55 as well as enhanced Therefore, FDTD simulation and FTIR data show only peaks biological and chemical sensors or nanolasing applica- associated with bright modes since electromagnetic radiation tions.56−59 can only couple with modes exhibiting a net dipole moment.55 In this work, we focus on the excitation and mapping of the In contrast, the scattering of electrons in an EELS experiment bright and dark plasmonic resonances associated with the SLR will excite all the available resonances in the structure,50,60 8124 https://doi.org/10.1021/acsnano.2c11016 ACS Nano 2023, 17, 8123−8132 ACS Nano www.acsnano.org Article Figure 2. Absorption spectra obtained through (a) FDTD simulations (blue line) and FTIR measurements (red line). (b) EEL spectrum computed as the integral of the counts across the whole hexagon (black line). Peaks and anomalies only present in the EELS spectrum are associated with the excitation of dark modes by electron scattering. EELS and FTIR measurements were performed on the same sample. Vertical dashed lines indicate the energy of the bright modes that are discussed in the text. including not only bright modes but also dark ones (those showing zero net dipole moment). This constitutes a key point in understanding the differences and similarities among the Figure 3. Left hand-side panels (a, d, g, and j) show colormaps of three curves shown in Figure 2. We also point out that the the EELS signal across the sample for the four bright modes peaks shown by the FDTD simulated absorption do not indicated in Figure 2. The color scale bar represents the intensity exactly match the location of those on the FTIR and EELS of the EELS signal. Middle panels (b, e, h, and k) depict the curves because of the imperfections of the experimental sample calculated charge distribution on the surface of the array for the due to manufacturing defects, such as slight variations in size same bright modes from the FDTD simulations under the or vertical profile of the slits. illumination of linearly polarized light along the vertical axis. The lowest energy mode of the honeycomb array of slits Blue and red colors represent negative and positive net charge appears around 0.54 eV and corresponds to a relatively intense densities, respectively. The charge intensity has been multiplied by a factor, indicated by the number on the top-right side of the broad peak that is clearly visible in the three spectra shown in panels, for an easier comparison between resonances. Right hand- Figure 2. It is a dipolar mode caused by the distribution of side panels (c, f, i, and l) show simulations of the corresponding opposite charges round the longitudinal facing edges of each electric field intensity under the illumination of unpolarized light. slit, as it is disclosed by the FTDT simulations of charge These colormaps were obtained 10 nm above the structure. distributions shown in Figure 3b. Moreover, it is a bright mode since the net dipole moment corresponding to the three slits emanating from every vertex (primitive unit element of the some anomalies in the curves for region I in Figure 4a. Based lattice) in Figure 3b is nonzero along the vertical direction on the results of the EELS mapping and the FDTD simulations parallel to the polarization axis of the exciting radiation in the for unpolarized light, the near-field distribution of this FDTD simulations. Note that the charge distributions shown resonance presents a diffuse hotspot around the center of in Figure 3 were obtained from an FDTD simulation with each hexagon accompanied by a multipolar excitation of the linearly polarized light in the vertical direction. EELS slits (Figure 3d and f). measurements and the distribution of the intensity of the The charge distribution shown in Figure 3e, which was electric field for unpolarized light obtained from FDTD obtained from an FDTD simulation with linearly polarized simulations support the occurrence of significant values of the light in the vertical direction, also indicates a multipolar electric field only in the hollow space inside the slits (Figure 3a excitation of the slits. Each slit contains three parallel dipoles of and c) in accordance with the major dipolar nature of the alternating sign. So, as in the case of the previous excitation at mode in the directions perpendicular to the slits. 0.54 eV, every three converging slits at each vertex has a net To get a deeper insight into the energy of the rest of the dipole moment in the vertical direction. At the same time, the bright modes, the values of the integral of the EELS signal inferior and superior halves of the hexagons exhibit diffuse computed in several specific regions of the hexagon are shown charges of opposite sign that contribute to the total dipole in Figure 4 as a function of the energy loss within 1.2 and 1.8 moment of the structure in the vertical direction (Figure 3e) eV, the energy range where most of the bright modes appear. and cause the central diffuse hotspot found under unpolarized The next bright mode can be found at about 1.41 eV in the radiation (see Figure 3d and f). EELS and FTIR curves, and at 1.38 eV in the simulated The mode at 1.57 eV corresponds to the coherent excitation absorption (see Figure 2). At 1.41 eV, there is also a clear peak of the whole lattice in a SLR. The small peak in the absorption in the light brown curve in Figure 4a (region III), as well as spectrum obtained by FDTD simulations around this energy 8125 https://doi.org/10.1021/acsnano.2c11016 ACS Nano 2023, 17, 8123−8132 ACS Nano www.acsnano.org Article plane crosscut for the z-component of the electric field shown in Figure S1 in the Supporting Information is also character- istic of a breathing mode. Besides, for this mode, the intensity of the electric field for unpolarized light shows a central hotspot with a ring shape, revolving around a minimum of intensity at the center of the hexagon (see Figure 3i). It is worth noting that a central structure like that of Figure 3i is clearly distinguishable in the EELS colormap (Figure 3g). This qualitative interpretation of the EELS colormap is also quantitatively confirmed by the local maximum of the green curve in Figure 4b corresponding to the integral of the EELS signal in region V (central ring). It should also be noted that, in relation to this mode, a small shoulder is shown in the red curve in Figure 4a (region I corresponding to the vertex). Finally, at an energy of 1.74 eV we find an excitation in the EELS experiment (Figure 3j) with a maximum in the center of the hexagons surrounded by an approximately hexagonal hotspot. This central structure may appear due to an averaging along the directions perpendicular to the edges of the hexagon of charge distributions such that in Figure 3k for linearly polarized light in the vertical direction. The existence of this central structure can also be confirmed by the maxima in the green and blue curves in Figure 4b for the EELS signal integrated in regions V (central ring) and IV (central hotspot), respectively. In addition, the EELS map also suggests a multipolar excitation of the slits in agreement with the FDTD simulation for the electric field distribution in Figure 3l. The four modes discussed so far are bright, since they display a net dipole moment per primitive unit cell of the hexagonal lattice. In this respect, they can be considered Figure 4. EEL spectra computed as the integral of the counts ferroelectric modes of the system, since the dipole moment per across the regions of the hexagon colored in orange in the inset of primitive cell forms a ferroelectric lattice with the same panel (a). (a) Red, purple, and light brown solid curves correspond symmetry as that of the hexagonal array of slits. to the integrals of the EELS signal over regions I, II, and III, In addition, dark modes are also excited in the structure. In respectively. (b) Blue and green solid curves correspond to the this work, we present the detection of two types of dark modes. integrals of the EELS signal over regions IV and V, respectively. Depending on whether the unit cell of the charge distribution The total signal across the whole hexagon is also shown as the fits into a single primitive cell of the honeycomb lattice, or it black solid line in panel (b) for the sake of comparison. The extends outside of it, we will denote these modes as local or vertical dashed lines indicate the energy of the bright (gray lines) extended, respectively. A first approach to understanding the and dark (black lines) modes discussed in the text. local charge distributions excited in a dark mode is to consider the behavior of three slits converging on the same vertex (blue curve in Figure 2a) is associated with the diffraction (Figure S2 in the Supporting Information) that will act as the condition of the lattice at the interface between the metal and unit element of the lattice. Bearing in mind that we are dealing the air. In fact, a photon of 1.57 eV in air has a wavelength of with an inverted lattice, most of the excitation of this unit 790 nm, which is very close to p cos30 = 785 nm, the first element will take place through currents flowing around the diffraction condition of the lattice for normal incidence, being central vertex, giving rise to a central out-of-plane magnetic p the pitch of the lattice. Interestingly, the imperfections of the moment.61 Therefore, by placing a perpendicular magnetic experimental sample do not affect its pitch (see Figure 1a and dipole source above the vertex shared by these three slits, b). This means that the SLR of the lattice takes place at the several dark modes of increasing multipolar order can be same energy as the FDTD simulations and experimental simulated as the energy increases. The lowest energy dark results. In this case, most of the excited charge is found to mode (Figure S2a in the Supporting Information) shows a spread inside the hexagons, relatively far from the slits forming dipolar excitation across the slits, akin to the bright mode at the array (see Figure 3h for FDTD results with linearly 0.54 eV but, in this case, all the slits are equivalent due to the polarized light). The two opposite sign charge distributions in 3-fold symmetry of the element, and the net dipole moment the upper and lower halves of each hexagon cause a large vanishes. The other local dark modes shown by the simulations electric field with an out-of-plane component that extends as the energy increases follow the same overall behavior but hundreds of nanometers from the structure28 (see Figure S1 in with multipolar excitation of the slits (see Figure S2b,c in the the Supporting Information). For unpolarized radiation with Supporting Information). normal incidence, the charge distribution will oscillate from the Homologous dark modes can be found in the inverted center of the hexagon to the outer part following a kind of honeycomb lattice by exciting the system with an array of in- breathing mode and giving rise to the EELS signal and electric- phase magnetic dipoles situated on those vertices of the field distribution depicted in Figure 3g and i. Moreover, the xy- hexagons that coincide with the Bravais lattice (see Methods 8126 https://doi.org/10.1021/acsnano.2c11016 ACS Nano 2023, 17, 8123−8132 ACS Nano www.acsnano.org Article Figure 5. Left hand-side panels (a, e, and i) show colormaps of the EELS signal across the sample for the three dark modes indicated in Figure 4a. The color scale bar represents the intensity of the EELS signal. Panels (b, f, and j) depict the average of the profile of the EELS signal along the slits computed integrating the counts across the slits. Panels (c, g, and k) show the simulated charge distributions of these three dark modes. Right hand-side panels (d, h, and l) show the near field distribution for each energy computed 10 nm above the structure. Note that for the modes arising at 1.28 and 1.52 eV an array of magnetic dipoles has been used to excite the system, whereas for the mode at 1.69 eV the system has been excited using a combination of an array of magnetic dipoles and a plane wave with normal incidence. Panel (k) shows the charge distribution for the vertical polarization of the plane wave while panel l is the average between two orthogonal polarizations. These colormaps were obtained 10 nm above the structure. section). The lowest energy dark mode found by simulation is Finally, at about 1.69 eV there are maxima in the red (EELS shown in Figure S3 in the Supporting Information. However, signal at the vertices of the hexagonal lattice) and light brown due to the similarity between the near-field distributions of this (EELS signal from regions of the slits that exclude their ends mode and that of the broad bright one at 0.54 eV and the and center) curves in Figure 4a that coincide with a broad spectral proximity of both, this excitation cannot be maximum in the curve for the total signal (black solid line in distinguished in the EELS spectrum in Figure 2. The rest of Figure 4b). In accordance with the results of the simulations the local dark modes are presented in Figure 5, in order of with magnetic dipoles, this should be a dark mode with increasing energy. Figure 5b shows the average of the profile of octupole polarization of the slits and relatively low intensity. the EELS signal at 1.28 eV computed as the integral across the However, only two poles close to the center of the slits are slits, where the purple curve in Figure 4a (EELS signal from shown by both the EELS color map in Figure 5i and the profile the ends and center of the slits) exhibits a local maximum. This of the EELS signal along the slits in Figure 5j. In addition, profile supports the fact that most of the excitation occurs at EELS color map in Figure 5i shows a distinctive ring around both ends of the slits following a quadrupolar polarization, and the center of the hexagon. Such an electric field pattern does is in good agreement with the simulated charge and near-field not arise from the sole excitation of charge across the slits, but distributions in Figure 5c,d. We point out that any quadrupolar from a charge arrangement in the continuous gold layer found arrangement of the charge distribution around the slits in the hexagons formed by the honeycomb lattice of slits. nonhaving 3-fold symmetry gives rise also to dark modes of Therefore, this mode may result from the hybridization of the similar energies. octupole dark mode and a bright mode like that at 1.74 eV. To At 1.52 eV there are local maxima in the red (EELS signal at simulate this mode, we have used the simultaneous excitation the vertices of the hexagonal lattice) and purple (EELS signal of the system by an array of in-phase magnetic dipoles like in from the ends and center of the slits) curves in Figure 4a that the previous cases and a plane wave with normal incidence, are associated with a dark mode with the sextupole polarization aiming at exciting both dark and bright modes. The charge of the slits. Accordingly, the respective EELS profile along the distribution depicted in Figure 5k, which was obtained for the slits (see Figure 5f) shows three approximately equidistant polarization axis of the plane wave along the vertical direction, poles. The results of the simulations using magnetic dipole shows a kind of quadrupolar excitation close to the center of sources shown in Figure 5g,h support this interpretation. the horizontal slits (those perpendicular to the polarization axis 8127 https://doi.org/10.1021/acsnano.2c11016 ACS Nano 2023, 17, 8123−8132 ACS Nano www.acsnano.org Article of the plane wave) that is compatible with the EELS profile charge across the slits alternates along the zigzag chains, and shown in Figure 5j. Moreover, the near-field distribution the remaining slits, rotated 60 degrees from the horizontal, are computed for an unpolarized plane wave in Figure 5l shows less charged and show a kind of quadrupolar excitation. This overall features in qualitative agreement with EELS color map results in two antiferroelectric sublattices whose net dipole in Figure 5i, including the ring around the center of the moments (indicated by arrows in Figure 6b) per primitive cell hexagon and the two central poles in the slits. of the honeycomb lattice point in the direction of the zigzag In addition to the local dark modes discussed so far, there chains and are arranged antiparallel to each other, so they are several other ways to get an extended dark mode in an cancel out in pairs of primitive cells. Note that the unit cell of ordered lattice. For instance, the system can be divided into the antiferroelectric mode is indicated by the dashed black line two sublattices of opposite net dipole moment per primitive in Figure 6b and is two times bigger than that of the unit cell, so that the net dipole moment cancels out in pairs of honeycomb lattice. It is worth noting that for this kind of two primitive cells. This implies that there is a net dipole extended dark modes, one of the slits of each threesome shows moment associated with each threesome of slits converging in a different excitation (different multipolarity and/or intensity) a vertex coincident with the Bravais lattice (unit element of the than the other two, as expected. This is a distinctive feature of lattice) that cancels out with the opposite net dipole moment these extended dark modes that can be checked in the results of a neighboring threesome of slits. Therefore, the excitation of of the simulations for the near-field distribution at other the slits in each of these threesomes must be nonequivalent energies that are shown in Figure S4 in the Supporting under the 3-fold symmetry to have a net dipole moment, like Information. Consequently, there exists an almost continuous family of extended dark modes with increasing energy, where in the bright modes. the differences among them come from the multipolarities of Examples of this kind of dark modes can be simulated by the slits in each threesome, and/or their relative intensities of FDTD using a tailored source of radiation that excites excitation. neighboring primitive unit cells in opposition of phase, in This kind of extended dark mode can be excited by EELS in such a way that they form two antiparallel ferroelectric the experimental sample as discussed below. Previous sublattices. An array of magnetic dipoles in phase opposition observations of local dark modes by EELS, among other and placed above the vertices coincident with the Bravais techniques, have been reported.36,45,62 Nevertheless, the lattice was the excitation source used for this purpose (see finding of extended (antiferroelectric) dark modes is also more details in the Methods section). Thus, Figure 6a,b shows reported in this work. an example of these extended dark modes at 0.68 eV where the Between 0.6 and 1.4 eV, there are no bright modes in the spectral response of the system, so all the peaks and anomalies shown by the EELS signal in this range in Figure 2b could be assigned to dark modes. To find out the nature of these dark modes, we represent in Figure 6c the average integral of the EELS signal as a function of energy computed separately over two subsets of slits (those forming zigzag chains and the remaining ones, colored in green and orange in the inset of Figure 6c, respectively). Interestingly, the EELS signals for the green and orange slits coincide for the bright mode at 0.54 eV, as expected. But as the energy increases and becomes larger than 0.6 eV, the two curves in Figure 6c start to separate and stay that way until around 1.2 eV, from where they coincide again within the experimental error. In this energy range (light brown region in Figure 6c) the slits forming the zigzag chains (shown in green in the inset of Figure 6c) are excited more strongly than the remaining isolated slits (shown in orange in the inset of Figure 6c), indicating that the system cannot be excited through local dark modes, since, if that were the case, the intensity of excitation of the slits in each threesome would be equal. Consequently, there should be a net dipole moment associated with each threesome of slits converging in a vertex since the excitations of them are not equivalent under the 3- fold symmetry, and the system may be excited through a kind Figure 6. (a, b) Simulated electric field and charge distribution, of extended dark mode, as described above. However, it is respectively, corresponding to the antiferroelectric mode at 0.68 worth noting that, in an EELS experiment with an ideal sample, eV. The arrows in panel (b) indicate the total electrical dipole all the mode variants equivalent by symmetry (three in a moments for threesomes of slits converging at points of the honeycomb lattice) are simultaneously excited with the same Bravais lattice. The dashed lines show a primitive unit cell of the probability, in such a way that the resulting state exhibits antiferroelectric mode. (c) Average integral of the EELS signal always the same average intensity and multipolarity for all the computed separately over the two subsets of slits (the green and orange curves correspond to the green and orange subsets of slits slits, even for an extended dark mode. In our case, the in the inset showing a unit cell of the lattice, respectively). EELS imperfections in the fabrication of the sample (especially in the color maps labeled with Roman numerals show some representa- oblique slits) enable a distinct excitation of the three variants tive examples of the extended dark modes taking place in the of the extended mode, yielding an average state where the energy range within 0.6 and 1.22 eV. signature of an extended dark mode can be inferred by the 8128 https://doi.org/10.1021/acsnano.2c11016 ACS Nano 2023, 17, 8123−8132 ACS Nano www.acsnano.org Article different excitation intensity of the three slits of each Au substrate, 1.75 and 1.9 eV, respectively,63 could be targeted threesome. by easily tuning manufacturing parameters such as the pitch of The EELS color maps labeled with Roman numerals i, ii, iii, the lattice, thus changing the spectral position of the plasmonic and iv in Figure 6c show some representative examples of the resonances. excitation of the system corresponding to three local maxima Other applications include transport measurements in 2D of the EELS signal in this energy range and the limit of the materials in which a local gating could be done by means of the energy range where extended dark modes can be excited, hotspot in the nanostructure and the introduction of localized respectively. The EELS color maps i and ii in Figure 6c and the defects in the lattice. EELS profiles along the slits in Figure S4,a,b in the Supporting Information indicate a dipolar excitation of the slits but with METHODS stronger intensity for the slits forming zigzag chains. The results of the simulations for the electric field and the average Manufacture Process. A thin Au film was deposited on a 50 nm thick Si3N4 membrane using an ultrahigh vacuum (UHV) electron profile along the slits obtained with the array of magnetic beam evaporator. The Si3N4 membrane is 500 × 500 μm2 wide. These dipoles in phase opposition (Figure S4e,f,i,j in the Supporting types of structures are normally used as substrate for Transmission Information) are in qualitative agreement, since the average of Electron Microscopy (TEM). The square membrane windows are the excitation of the three slits in a threesome has major centered on 200 μm thickness silicon frames.64 dipolar character. On the contrary, the EELS color maps iii and The measured Au film thickness was 19.4 nm with a root-mean- iv in Figure 6 and the EELS profiles along the slits in Figures square roughness of 0.3 nm as measured by atomic force microscopy S4,c,d in the Supporting Information indicate a quadrupole (AFM). The Au film was then patterned using a Raith Velion focused excitation of the slits. The corresponding results of the ion beam (FIB) equipped with an Au−Ge−Si liquid metal alloy ion simulations for the electric field and the average profiles along source (LMAIS). A 35 keV Au+ beam, ∼5 pA ion current intensity the slits (Figure S4g,h,k,l in the Supporting Information) point and ∼15 nm diameter, was used for patterning the hexagonal array of slits. Au+ beam was chosen to avoid lateral contaminations along the toward the quadrupole character of the average excitation of milled lines that would occur with other commonly used ion species the slits. Therefore, as the energy increases from 0.6 eV, the in FIB like Ga+. The 350 × 350 μm2 wide array was milled using 200 average polarity of the extended dark modes progressively × 200 μm2 writing fields and applying a 3000 pC/cm linear dose of becomes of higher order, until the local dark mode Au+ (single loop passage, 10 nm step between ion spots, and dwell corresponding to quadrupole excitation with the same intensity time of 0.52 ms). This allowed for the patterning of the designed of all the slits in a threesome is reached at 1.28 eV. structures through the Au film while keeping the line width in plane of At energies higher than about 1.7 eV, the EELS signals for ∼45 nm. the green and orange slits in the inset of Figure 6c start to FTIR Measurements. The optical characterization was carried out significantly separate again, indicating the onset of a second using a Vertex 70 Fourier transform infrared (FTIR) spectropho- tometer attached to an optical microscope (Bruker Hyperion). range of energies where antiferroelectric dark modes may be Experiments were performed in the reflection and transmission excited, but with the intensity of the excitation of the two configuration with 2× and 4× objectives, respectively, under subsets of slits swapped with respect to those within 0.6 and unpolarized light illumination. A shutter was used to select the signal 1.2 eV. coming from the nanostructured area. The measured signal of the plain Au of a non-nanostructured area of the sample was used as a CONCLUSIONS background for the reflection measurements, whereas the trans- This work constitutes a comprehensive study of the plasmonic mission of the light in air was used for calibrating the transmission measurements. properties of an inverted honeycomb lattice of slits. The EELS Measurements. EEL spectra were collected using a Nion patterning quality of the samples, together with the spectral aberration-corrected high energy resolution monochromated EELS− and spatial resolution of the EELS measurements has led to the STEM (Nion HERMES) operating at a 60 kV accelerating voltage, direct observation and mapping of bright and dark plasmonic using a convergence semiangle of 30 mrad, a collection semiangle of modes. A detailed description of the charge and near-field 20 mrad, and a beam current of ∼10 pA.52−54 The resulting energy distributions in the structure has been given by virtue of the resolution of the spectra, measured by the full-width half-maximum good agreement between the EELS measurements, the optical (fwhm) of the zero-loss peak was 60 meV. measurements, and simulations. Some of the dark modes FDTD Simulations. The simulations were performed using the found are caused by antiferroelectric arrangements of the slit finite-difference time-domain (FDTD) method, implemented in the polarizations, giving rise to charge arrangements with a unit solver provided by Lumerical.65 The computation procedure starts by setting a 3D FDTD simulation with perfectly matched layers (PMLs) cell two times larger than that of the original honeycomb in the z-direction, perpendicular to the plane of the lattice and lattice. Additionally, plasmonic modes exhibiting hotspots far periodic boundary conditions in the other two directions, the x−y from the discontinuities of the metallic layer are found, ranging plane. Given the initial conditions, the software solves Maxwell’s from 1.3 to 1.8 eV approximately. equations to determine the Fourier components of the electric and The behavior of the inverted honeycomb plasmonic lattice is magnetic fields by using discrete time and spatial steps. The method relevant not only from a fundamental point of view. As shown allows for a direct observation of the physical phenomena taking place in a previous work,24 the appearance of hotspots far from the without imposing any further assumption on the behavior of the slits that form the lattice is highly correlated with a strong out- system. We obtained the transmission and reflection spectra by of-plane electric field ranging hundreds of nanometers away placing two monitors that compute the total power that flows through a surface. In addition, other monitors were placed on the surface of from the lattice. This electric field could foster a strong the sample and 10 nm above, from which we computed the charge coupling of the plasmonic lattice with other materials allocated and the electric field distributions, respectively. on top of the structure. Moreover, the inverted nature of this An override mesh region was defined along the structure to ensure lattice, thanks to its large mostly planar surface, presents this a correct level of detail in the description of the lattice. The cell size system as a platform for exploiting new synergies with 2D used was 3.816 × 3.824 × 1 nm3 in the x-, y- and z-directions, materials. The exciton energies for 2D WSe2 and MoS2 on an respectively. The dielectric functions for the materials used in these 8129 https://doi.org/10.1021/acsnano.2c11016 ACS Nano 2023, 17, 8123−8132 ACS Nano www.acsnano.org Article simulations were obtained by fitting analytical functions to the data Xavier Borrisé − Catalan Institute of Nanoscience and from refs 66 and 67 for Si3N4 and Au, respectively. Nanotechnology (ICN2), CSIC and BIST, Campus UAB, In these simulations, four different types of excitation sources were Bellaterra, Barcelona 08193, Spain used, depending on the targeted modes. Plane waves were the source Albert Guerrero − Institut de Microelectrònica de Barcelona of excitation for all the bright modes. The plane waves were injected at 500 nm from the structure following normal incidence and setting (IMB-CNM, CSIC), Bellaterra 08193, Spain periodic boundary conditions in the x−y plane for a unit cell of the Francesc Perez-Murano − Institut de Microelectrònica de system like that of the snapshots in Figure 3. For the simulations Barcelona (IMB-CNM, CSIC), Bellaterra 08193, Spain showing local dark modes, an array of in-phase magnetic dipoles, Arantxa Fraile Rodríguez − Departament de Física de la perpendicular to the system plane and placed 50 nm above the Matèria Condensada, Universitat de Barcelona, Barcelona vertices of the hexagons coincident with the Bravais lattice, was the 08028, Spain; Institut de Nanociència i Nanotecnologia excitation procedure. Bloch boundary conditions in the x-y directions (IN2UB), Universitat de Barcelona, Barcelona 08028, were set for the same unit cell than the one for the bright modes. The Spain; orcid.org/0000-0003-2722-0882 hybrid mode at 1.69 eV was simulated by the simultaneous excitation Xavier Batlle − Departament de Física de la Matèria of a plane wave with normal incidence and the array of in-phase magnetic dipoles. Finally, for the antiferroelectric dark modes, an Condensada, Universitat de Barcelona, Barcelona 08028, array of magnetic dipoles in phase opposition were placed 50 nm Spain; Institut de Nanociència i Nanotecnologia (IN2UB), above the vertices coincident with the Bravais lattice (see Figure S5 in Universitat de Barcelona, Barcelona 08028, Spain; the Supporting Information). The simulation unit cell, as shown in orcid.org/0000-0001-7897-2692 Figure S5 in the Supporting Information, was larger than in the Complete contact information is available at: previous cases to enable the excitation of extended modes. Bloch boundary condition were used in the x-y directions. https://pubs.acs.org/10.1021/acsnano.2c11016 Author Contributions ASSOCIATED CONTENT The manuscript was written through contributions of all * sı Supporting Information authors. All authors have given approval to the final version of The Supporting Information is available free of charge at the manuscript. https://pubs.acs.org/doi/10.1021/acsnano.2c11016. Notes Transversal electric field distribution for the SLR at 1.57 The authors declare no competing financial interest. eV; simulated electric field and charge distributions for a threesome of slits; simulated electric field and charge ACKNOWLEDGMENTS distributions for the simplest local dark mode of the inverted honeycomb lattice; profiles of the EELS signal The authors want to thank Pau Molet and Agustín Mihi, and the simulated electric field along the slits for the Institut de Ciència de Materials de Barcelona (ICMAB-CSIC), antiferroelectric dark modes; array of the magnetic for the FTIR measurements, and Paolo Mattevi of FBK for the dipoles over the structure used to simulate antiferro- UHV evaporation of Au on the Si3N4 membranes. This work electric dark modes (PDF) was supported by Spanish ICTS Network MICRONANO- FABS. The authors from Universitat de Barcelona thank the funding from Spanish MICIIN, grant numbers PGC2018- AUTHOR INFORMATION 097789−B-I00 and PID2021-127397NB-I00, and the Euro- pean Union FEDER funds. The EELS measurements were Corresponding Author supported by the Center for Nanophase Materials Sciences Javier Rodríguez-Á lvarez − Departament de Física de la (CNMS), which is a U.S. Department of Energy, Office of Matèria Condensada, Universitat de Barcelona, Barcelona Science User Facility, and using instrumentation within 08028, Spain; Institut de Nanociència i Nanotecnologia ORNL’s Materials Characterization Core provided by UT- (IN2UB), Universitat de Barcelona, Barcelona 08028, Batelle, LLC, under Contract No. DE-AC05-00OR22725 with Spain; orcid.org/0000-0001-5822-4013; the U.S. Department of Energy, and sponsored by the Email: javier.rodriguez@ub.edu Laboratory Directed Research and Development Program of Authors Oak Ridge National Laboratory, managed by UT-Battelle, Amílcar Labarta − Departament de Física de la Matèria LLC, for the U.S. Department of Energy. 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