Multidimensional Hybridization of Dark Surface Plasmons - ACS Nano

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Multidimensional Hybridization of Dark Surface Plasmons Andrew B. Yankovich,* Ruggero Verre, Erik Olsén, Anton E. O. Persson, Viet Trinh, Gudrun Dovner, Mikael Kal̈ l,* and Eva Olsson* Department of Physics, Chalmers University of Technology, 41296 Gothenburg, Sweden S Supporting Information *

ABSTRACT: Synthetic three-dimensional (3D) nanoarchitectures are providing more control over light−matter interactions and rapidly progressing photonic-based technology. These applications often utilize the strong synergy between electromagnetic fields and surface plasmons (SPs) in metallic nanostructures. However, many of the SP interactions hosted by complex 3D nanostructures are poorly understood because they involve dark hybridized states that are typically undetectable with far-field optical spectroscopy. Here, we use experimental and theoretical electron energy loss spectroscopy to elucidate dark SPs and their interactions in layered metal-insulator-metal disc nanostructures. We go beyond the established dipole SP hybridization analysis by measuring breathing and multipolar SP hybridization. In addition, we reveal multidimensional SP hybridization that simultaneously utilizes in-plane and out-of-plane SP coupling. Near-field classic electrodynamics calculations provide excellent agreement with all experiments. These results advance the fundamental understanding of SP hybridization in 3D nanostructures and provide avenues to further tune the interaction between electromagnetic fields and matter. KEYWORDS: plasmon hybridization, electron energy loss spectroscopy (EELS), nanoplasmonics, dark surface plasmons, layered nanoparticles produce massive near-field electromagnetic field enhancements within a NP gap, which are utilized in applications such as single molecule detection.18−20 The full set of SPs supported by recent 3D nanostructures has not yet been observed because many SPs are invisible using common light excitation techniques. Bright SPs (radiative SPs that have a large net dipole), which include bright hybridized dipole SPs,21 are easy to excite and measure with far-field planewave optical techniques,22 making them extensively studied. Dark SPs (nonradiative SPs that have near-zero net dipole) are difficult to excite and measure with light, making them more elusive. Some dark SP signatures have been optically measured through Fano interference with bright modes,23 however they are much more efficiently analyzed using near-field excitation techniques such as electron energy loss spectroscopy (EELS) in a scanning transmission electron microscope (STEM).24−28 Dark SPs, including breathing SPs,29−32 multipolar SPs,24,33−38 and some hybridized SPs,39−46 have generally required EELS to experimentally observe. Breathing SPs have radially symmetric surface charge density oscillations, while multipolar SPs have surface charge density oscillations with different angular

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ontrol over the interaction between electromagnetic fields and nanomaterials is rapidly advancing because of our ability to synthesize complicated three-dimensional (3D) nanoarchitectures using a variety of fabrication techniques.1,2 This progression is fueling the nanophotonics and plasmonics research fields and contributes to technological applications such as solar energy harvesting,3 catalysis,4 computing and communications,5 light manipulation,6 cancer therapy,7 and biological sensing.8 Many of these applications utilize the strong and tunable interactions between light and noble metal nanoparticles (NPs) that are facilitated by the excitations of localized surface plasmons (SPs), which are the collective oscillation modes of the free electron gas at the metal NP surface. Tuning SP resonances is easily achieved by controlling NP size and morphology or the dielectric properties of the NP and the surrounding environment.9,10 However, SP properties can also be strongly modified through interactions between SPs on neighboring NPs if they have sufficient overlap in SP resonance energy and induced near-fields. The individual NP SPs hybridize into distinct coupled SPs that have modified resonance energies and field patterns. For NP separations greater than ∼3 nm where SP quantum tunneling charge transfer is negligible,11−14 hybridization has been shown to be mathematically and conceptually analogous to the eigenvalue problem that describes the bonding and antibonding atomic orbitals in molecular orbit theory.15−17 Hybridized SPs can © 2017 American Chemical Society

Received: February 24, 2017 Accepted: March 28, 2017 Published: March 28, 2017 4265

DOI: 10.1021/acsnano.7b01318 ACS Nano 2017, 11, 4265−4274

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Figure 1. SP naming definition and multidimensional hybridization schematics. (a) Definition of the SP naming scheme and the considered SP modes (Z). (b) X denotes the in-plane hybridization state, shown schematically for the SL dimer dipole case. (c) Y denotes the out-ofplane hybridization state, shown schematically for the MIM monomer dipole case. 0 and 1 signify out-of-phase and in-phase charge oscillations, respectively. (d) Side-view TEM image of a MIM structure on a SiN membrane. Scale bar is 25 nm. (e) Schematic showing the possible longitudinal hybridized dipole SPs in a MIM dimer. For all surface charge density figures, red signifies positive charge, white signifies no charge, and blue signifies negative charge. More color represents larger charge density.

momentum (l). Until now, EELS studies have primarily focused on the SPs hosted by single NPs with different geometries, dipole SP hybridization between two NPs, and in-plane NP oligomers. However, there has been a lack of attention given to dark SP hybridization and multidimensional hybridization. The accepted hybridization picture for dipolar resonances can therefore be extended to dark SPs, including breathing, multipolar, and already hybridized SPs. Many of these hybridized modes cannot be observed in single isolated structures, but become available by nanostructuring in three dimensions because constituent NPs need to support degenerate SP modes and near-field distributions. In particular, here we realize and investigate a plethora of hybridized SP modes using single layer (SL) and metal-insulator-metal (MIM) nanodisc oligomers. Figure 1d shows a side-view TEM image revealing the multilayered geometry, which was chosen because it allows for independent control of out-ofplane and in-plane SP hybridization.47−50 Previously, the outof-phase hybridized dipole SPs in MIM monomers were shown to produce optically driven magnetism, a proposed ingredient for next-generation metamaterial applications.51 In order to describe various hybridized SPs, we define in Figure 1a the naming scheme ZYX. Z defines the SP angular momentum, where Z = B represents the l = 0 breathing SP, Z = D represents the l = 1 dipole SP, Z = Q represents the l = 2 quadrupole SP, and Z = H represents the l = 3 hexapole SP. The subscript X and superscript Y can either be a 0 or 1 and represent the coupled SP phase relationship in the in-plane and out-of-plane directions, respectively. X = 1 if the in-plane SP coupling is inphase, and X = 0 if the in-plane SP coupling is out-of-phase (Figure 1b). Y = 1 if the out-of-plane SP coupling is in-phase, and Y = 0 if the out-of-plane SP coupling is out-of-phase (Figure 1c). For the coupled dipole SP case, 0 denotes no net

dipole, and 1 denotes a net dipole. The four possible longitudinal (x-polarized along the dimer direction) hybridized dipole SPs for a MIM dimer structure are shown schematically in Figure 1e, and their relative energies may be altered depending on the specific MIM dimer arrangement. The transverse and out-of-plane polarized SPs are not considered. Here, we report EELS experiments and simulations on NP monomers, dimers, and dumbbells composed of SL and MIM Au nanodiscs. Despite using state-of-the-art instruments, the spectra acquired using conventional EELS methods often display a low signal-to-noise ratio (SNR) in the low-energy region, which can inhibit the detection of weak SPs (further discussion in the Supporting Information, Supplementary Note B (SN-B)). We used hyperspectral imaging to map the SP excitations with nm spatial resolution and identify key electron beam impact parameters. Then the experimental SP SNR is enhanced at the selected electron beam impact parameters by combining EELS point spectrum series acquisition and postacquisition data processing tools. We confirm the presence of breathing, dipole, and multipole SPs in SL monomers and the well-established in-plane dipole SP hybridization in SL dimers. We then show that dark breathing SPs and dark multipole SPs can hybridize to create in-phase and out-of-phase coupled SPs in MIM monomers. These previously unreported dark SP hybridizations are studied as a function of disc diameter and compared against classical electrodynamics theory, showing excellent agreement. We then show the hybridized SPs hosted by MIM monomers can further be hybridized in multiple dimensions in MIM dimer and dumbbell structures. The dependence of the multidimensional SP hybridization on MIM dimer gap distance is studied experimentally and compared to numerical simulations, again showing excellent agreement. These results demonstrate that EELS analysis is able to 4266

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Figure 2. Experimental and simulated STEM EELS spectra of SL and MIM monomers at various disc diameters and at two STEM probe impact parameters: (a) center impact (green circle) and (b) aloof edge impact (green cross). The HAADF STEM images on the left are of the measured MIM monomers with diameters between 45 and 190 nm (bottom disc). The markers on the 190 nm MIM HAADF STEM image show the locations of the two probe impact parameters. The solid and dashed line spectra are from the MIM and SL monomers, respectively. Blue, pink, green, black, red, and purple curves are from the 190, 130, 110, 88, 65, and 45 nm diameter monomers, respectively.

zero loss peak (ZLP) subtraction. Experimental EELS data are compared against theory using numerical simulations within the MNPBEM toolbox56,57 that are based on the boundary element method.58 The simulated MIM models utilized an effective dielectric value for the surrounding material to account for the aluminum oxide spacer layer. This value was determined by minimizing spectral differences between simulations and experiments. Experimentally and theoretically observed SPs are interpreted using simulated surface charge density distributions. More details about sample fabrication and geometry, EELS experiments, simulations, and data processing can be found in the Methods section and in SN-A−C. Figure 2 shows experimental and simulated EELS spectra from SL and MIM monomers for disc diameters ranging from 45 to 190 nm and for two different electron beam impact parameters: (a) center impact and (b) aloof edge impact. For MIM monomers, the indicated disc diameter is for the larger bottom disc. The EELS spectra from the 45 nm monomers are not included for the center impact parameter (Figure 2a) due to spontaneous MIM monomer sample damage that prohibited data acquisition, but are present for the edge impact parameter (Figure 2b) because the aloof excitation caused no sample damage. The EELS spectra from the center impact SL monomer (dotted curves in Figure 2a) show a single peak at all diameters with a slight decrease in peak energy from ∼2.4 to ∼2.3 eV and an increase in peak amplitude with diameter. The center impact MIM monomer spectra (solid curves in Figure 2a) show a single peak at small diameters and two peaks at larger diameters separated by ∼0.4 eV for the 190 nm diameter case. The experimental spectra in Figure 2a are noisier than others in this manuscript because fewer spectra were used in the average for the center impact parameter to prevent electron beam induced damage. The EELS spectra from the edge impact

completely map out strongly hybridized dark SPs even in complicated 3D NP systems.

RESULTS AND DISCUSSION Experimental and Theoretical EELS. SL and MIM nanodiscs were fabricated by electron beam lithography on a ∼19 nm-thick SiN substrate membrane. The SL nanodiscs are composed of 35 nm-thick polycrystalline Au, while the MIM structures consist of 20 nm-thick polycrystalline Au discs separated in the out-of-plane direction by a ∼12.5 nm-thick insulating aluminum oxide disc (Figure 1d). The upper Au disc in the MIM monomers are ∼27 nm smaller than the bottom Au disc across all studied MIM diameters. The MIM nanostructure aspect ratios have been chosen to ensure the modes in the top and bottom discs resonate at very similar energies, validating the simplified hybridization picture shown in Figure 1. During EELS measurements, samples were in the STEM vacuum environment. Experiments were performed using 300 keV monochromated STEM EELS with ∼1 nm spatial resolution and ∼0.15 eV energy resolution. EELS data were collected using two methods: SPIM and point spectral series averaging. SPIM provides SP spatial excitation maps, while point spectral series averaging was used at specific electron beam impact parameters to enhance the SP SNR compared to what is possible with the conventional methods (discussed further in SN-B). Aloof EELS is used for all point spectral series experiments (except those measuring breathing SPs) to provide inelastic SP signals due to near-field coupling to the SPs while guaranteeing no metallic nanostructure damage during data collection.52−54 After acquisition, the SPIMs and spectral series are processed using various techniques, including dark spectrum subtraction, energy instability correction, Richardson−Lucy deconvolution,55 and 4267

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Figure 3. MIM breathing SP hybridization. Simulated STEM EELS spectra of the (a) SL and (b) MIM monomers for the center electron probe impact parameter (shown in the inset schematics) at disc diameters ranging from 40 to 200 nm. The EELS intensity color scale is included in the lower left corner and has arbitrary units. For MIM monomers, the indicated disc diameter is for the larger bottom disc. The black circle markers indicate the experimental peak positions. The white-black lines link the experimentally measured data points in order to show the mode evolution. (c) Simulated surface charge density distributions for the 190 nm diameter SL B SP, MIM B0 SP, and MIM B1 SP that are labeled in (a) and (b). For all surface charge density figures, SL monomers are displayed with a 45° top view, while MIM structures are displayed with a 45° top and 45° bottom view. The MIM 45° figures have been artificially separated after calculations to make the inside surfaces more visible.

magnitude compared to the rest of the structure, so it does not greatly affect or prohibit the in-phase breathing SP. There is no higher order breathing mode observed in the out-of-phase B0 SP. Multipole SP Hybridization. The theoretical EELS spectral dependence on disc diameters between 40 and 200 nm for the aloof edge impact parameter is shown in Figure 4a for the SL monomers and in Figure 4b for the MIM monomers. The experimental peak positions are marked by the black circles and show good agreement with the theory. For the SL monomer, there is a single peak at small disc diameters that transforms into two distinct peaks at larger disc diameters. For the largest discs, there is also a shoulder peak on the higher energy side of the higher energy peak. The simulated surface charge density distributions (Figures 4d−f) for the 190 nm SL monomer reveal that the first, second, and third peaks arise from a dipole SP (D), quadrupole SP (Q), and hexapole SP (H), respectively. Similar multipolar SPs have been previously reported in EELS studies.34 For MIM monomers, there is a single peak at small diameters that transforms into two and subsequently three distinct peaks as the disc diameter is increased (Figure 4b). In fact, for the 190 nm diameter MIM, the three peaks are composed of 6 overlapping SPs, as shown in the not-convolved simulated spectra (Figure 4c). The lowest energy peak arises from a single SP, D0. The middle energy peak is created by an overlap of two SPs, consisting of D1 and Q0 in increasing energy order. The peak with the highest energy is created by an overlap of three SPs, consisting of H0, Q1, and H1 in increasing energy order. The simulated surface charge density distributions of D0, D1, Q0, Q1, H0, and H1 (Figure 3d−f) reveal the hybridized multipolar nature of this MIM system. D0, Q0, and H0 are the bonding out-of-phase SPs, while D1, Q1, and H1 are the antibonding in-phase SPs. The surface charge density distributions of D1, Q1, and H1 reveal the same image charge phenomena on the top side of the bottom disc that was previously discussed for the B1 SP. These multipole image charges counteract the overall in-phase behavior of the antibonding SPs. However, the magnitude of the image charge is much smaller than the magnitude of the overall multipole surface charge, so the overall in-phase behavior is not lost.

SL monomers (dotted curves in Figure 2b) show one or two peaks depending on disc diameter. The EELS spectra from the edge impact MIM monomers (solid curves in Figure 2b) show one, two, or three peaks depending on disc diameter. In all experimental and simulated spectra, the nonzero EELS signal present at energies >2.5 eV is caused by the Au interband transitions. The number of peaks, the peak positions, and the peak splitting behavior in the experiments and the simulations are in excellent agreement for each structure and impact parameter. Breathing SP Hybridization. The theoretical EELS spectral dependence on disc diameters between 40 and 200 nm for the center impact parameter is shown in Figure 3a for the SL monomers and in Figure 3b for the MIM monomers. The experimental peak positions are marked by the black circles and show good agreement with theory. For SL monomers, a single SP, B, exists throughout the whole diameter range and slightly shifts to lower energy with larger diameters. The simulated surface charge density distribution of B, shown in Figure 3c for the 190 nm diameter SL monomer, reveals that it is a breathing SP, similar to those previously measured using EELS.29,30 For MIM monomers, there exists a single peak at small diameters that splits into two SPs, B0 and B1, at larger diameters, as shown in Figure 3b. For the 190 nm diameter MIM, the lower energy SP, B0, is separated by ∼0.4 eV from B1. The simulated surface charge density distributions of B0 and B1, shown in Figure 3c for the 190 nm diameter MIM monomer, reveal they are hybridized breathing SPs, which have not been reported until now. B0 is the bonding out-of-phase breathing SP, and B1 is the antibonding in-phase breathing SP. Breathing SP hybridization is only observed because of the out-of-plane stacking of the Au discs in the MIM monomer. This structure allows for overlap of the induced near-fields created by the inresonance individual breathing SPs. The simulated surface charge density distribution of B1 reveals that there is a weak higher order breathing mode present on the top side of the bottom Au disc that is likely induced by the image charge from the bottom side of the top disc. This higher order breathing mode is in-phase with the other breathing modes and has a small surface charge density 4268

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Figure 4. MIM multipole SP hybridization. Simulated STEM EELS spectra of the (a) SL and (b) MIM monomers for the edge aloof electron probe impact parameter (shown in the inset schematics) at disc diameters ranging from 40 to 200 nm. The black circle markers indicate the experimental peak positions. (c) Experimental and simulated (with and without convolution) EELS spectra from the 190 nm diameter MIM monomer with an edge aloof probe impact parameter. (d−f) Simulated surface charge density distributions for the D, D0, D1, Q, Q0, Q1, H, H0, and H1 SPs supported by the 190 nm SL and MIM monomers with an edge impact parameter, revealing the hybridization between multipole SPs.

peak would be necessary to fully separate the contribution of the D1, Q1, and H1 SPs. However, this is not necessary for this analysis, and the second peak will be defined D1/Q1/H1. By reducing the MIM dimer gap distance, the out-of-plane hybridized SPs are further hybridized in the in-plane direction, as evident by the change in the EELS spectra and SP spatial excitation maps shown in Figure 5a,b. With a 155 nm gap, the MIM monomers are virtually uncoupled, with spectra matching isolated MIM monomers. At reduced MIM dimer gap distances, simulations and experiments show similar impact parameter-dependent changes in SP energy and amplitude. The causes of the observed spectral changes are revealed by the simulated surface charge density distributions shown in Figure 5c and the more detailed EELS simulations shown in Figure S5. The variations of the first peak reveal the hybridization of the D0 SP into the D00 and D01 SPs. The in-plane in-phase coupled D01 SP is experimentally observed using an outside impact parameter, while the in-plane out-of-phase D 00 SP is experimentally resolved using a gap impact parameter. The D1/Q1/H1 peak shows virtually no spectral variation using an outside impact parameter. This is due to very little coupling between the MIM monomers with this impact parameter, as confirmed by the D1/Q1/H1 simulated surface charge density distributions shown in Figure 5c. However, using a gap impact parameter, the D1/Q1/H1 peak shows changes in resonance energy and excitation probability. Simulated surface charge density distributions reveal this is caused by the in-plane out-ofphase coupling of the D1/Q1/H1 SP. Experimentally observing the hybridization of the D1 SP into the D11 SP and the D10 SP is more difficult because of the spectral overlap of the D1, Q1 and H1 SPs. Despite not having the visibility of the D11 or D10 SPs in the spectra from the MIM

Hybridization of multipole SPs has not been reported until now and is present in these MIM structures because the inresonance multipole SPs have overlapped induced near-fields from the out-of-plane insulator gap between them. Not all six of the hybridized multipole SPs are resolved in the experimental EELS spectra because of experimental energy resolution limitations, SP mode splitting magnitudes, SP mode widths, and SP mode excitation amplitudes. The not-convolved EELS spectrum (Figure 4c) shows peaks and shoulders from each of the six multipolar hybridized SPs. However, when convolving the simulated spectra with a 0.08 fwhm Lorentzian function that is representative of the postprocessed experimental energy resolution (discussed more in the Methods section), some of the hybridized multipolar SP modes become unresolvable and consistent with the experimental observations. Multidimensional SP Hybridization. Multidimensional SP hybridization is experimentally and theoretically explored by reducing the dimer gap distance separating two 110 nm diameter MIM monomers, as shown in Figures 5 and S5, and discussed in greater detail in SN-F. SL dimer structures show clear hybridization of the dipole SP as a function of SL dimer gap distance, which closely matches our theoretical predictions and previous EELS results (discussed more in SN-D and Figures S2−S3).40,46 However, the MIM dimer case is not this straightforward because MIM monomers already host hybridized SPs. The EELS spectra from 110 nm MIM monomers using an edge impact parameter consists of two peaks, as seen in Figures 2b and 4b, and further discussed in SN-E and Figure S4. The first peak arises purely from the hybridized D0 SP that is responsible for the previously realized optically driven magnetism.47 The second peak arises from an overlap of the D1, Q1, and H1 SPs. A multipolar decomposition59,60 of the second 4269

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Figure 5. MIM dimer multidimensional hybridization. (a) Experimental and simulated STEM EELS spectra from 110 nm diameter MIM dimers with various dimer gap distances and two probe impact parameters. The inset images in (a) are HAADF STEM images of the 15, 28, and 155 nm gap MIM dimers. The green and purple spectra in (a) are from two aloof STEM probe impact parameters indicated by the colored circle markers in the HAADF STEM image and shown in the inset schematic. (b) Experimental and simulated STEM EELS maps from an 88 nm diameter MIM dimer with a 15 nm gap at 1.67, 1.88, 2.13, and 2.22 eV. All scale bars are 50 nm. (c) Simulated surface charge density distributions of the SPs hosted by the 110 nm diameter MIM dimer with a 15 nm gap. Distributions using the outside impact parameter are outlined in purple, and the gap impact parameter are outlined in green.

electron beam impact parameters, likely due to a weak excitation probability and spectral overlap with other SPs. These results illustrate the ability of STEM EELS to elucidate and map exotic dark SPs and their interactions in complicated 3D nanostructures. Future experiments could provide an even richer picture of hybridized SPs by using two approaches that would enhance the resolvability of the hybridized SPs. First, utilizing next-generation EELS spectrometers that can reach