Interaction of Localized Surface Plasmons of a Silver Nanosphere

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C: Plasmonics; Optical, Magnetic, and Hybrid Materials

Interaction of Localized Surface Plasmons of a Silver Nanosphere Dimer Embedded in a Uniform Medium: STEM-EELS and DDA Simulation Norihito Sakaguchi, Shuji Matsumoto, Yuji Kunisada, and Mikito Ueda J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.8b11434 • Publication Date (Web): 27 Feb 2019 Downloaded from http://pubs.acs.org on March 5, 2019

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The Journal of Physical Chemistry

Interaction of Localized Surface Plasmons of a Silver Nanosphere Dimer Embedded in a Uniform Medium: STEM-EELS and DDA Simulation Norihito Sakaguchi1,*, Shuji Matsumoto1, Yuji Kunisada1, and Mikito Ueda2 1Center

for Advanced Research of Energy and Materials, Faculty of Engineering, Hokkaido University, Sapporo, Hokkaido 060-8628, Japan

2Division

of Materials Science and Engineering, Faculty of Engineering, Hokkaido University, Sapporo, Hokkaido 060-8628, Japan

ABSTRACT. Localized surface plasmon resonance (LSPR) in a silver (Ag) nanosphere dimer embedded in silicate glass was investigated using scanning transmission electron microscopy electron energy loss spectroscopy (STEM-EELS). Passing the electron probe near the Ag nanospheres excited LSPR in the multipole as well as the dipole. STEMEELS analysis of the Ag dimer indicated that some LSPR coupling modes appeared because of energy loss from the coupling of two dipoles or multipoles. When the

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electron beam was incident on the outside of the Ag dimer, a longitudinal bonding mode of two dipoles appeared and its resonance energy was lower than that of the dipole of a single Ag nanosphere. Conversely, when the electron beam was incident between the Ag nanospheres of the dimer, two more modes appeared at higher energies than the resonance energy of a single Ag nanosphere. Analysis of the electric field distribution around the Ag dimer suggested that these modes had the nature of the classical longitudinal antibonding LSPR mode of two dipoles. Furthermore, the DDA simulation suggested the possibility that the mode on the highest energy may include a negligible contribution of an antibonding-type quadrupolar interaction.

1. INTRODUCTION Electromagnetic radiation interacts strongly with metallic nanoparticles and can excite a collective oscillation of conduction electrons known as localized surface plasmon resonance (LSPR). The unique optical properties of metallic nanoparticles are dominated by the excitation of LSPR. The LSPR of metallic nanoparticles has facilitated their use as waveguides,1–3 resonators and concentrators,4–6 chemical and biological sensors,7–9 photocatalysts,10,11 and in surface-enhanced Raman spectroscopy,12–15 which relies on a local enhancement of the electromagnetic field by LSPR. The spatial distribution and energy of LSPR modes strongly depend on the nanoparticle structure, composition, and environment. Therefore, understanding the interaction between LSPR


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modes occurring in assemblies of nanoparticles as well as the LSPR in single metallic nanoparticles is important. In scanning transmission electron microscopy (STEM), electron energy-loss spectroscopy (EELS) is attractive to characterize the plasmonic properties of individual nanoparticles and aggregate systems because of its spatial resolution of a few nanometres. STEM-EELS spectrum imaging (SI) is an important technique for interpreting the LSPR mode of metallic nanoparticles nanocubes, nanorods, etc., and a lot of detailed spectral analysis and mapping of the resonance modes based on this technique have been carried out.16–22 Furthermore, for the assemblies of nanoparticles, arrays of the nanostructures and bimetallic structures, a great deal of research on the interaction between these LSPs has been made.23–34 For example, Quillin et al.30 analysed the LSPR modes in a silver (Ag) nanoparticle dimer in detail and showed that four different vibration modes appeared in the energy slice maps obtained from STEM-EELS SI data. These modes arise from the interaction between the dipoles excited by each Ag particle. In addition, Scholl and colleagues clarified that the LSPR coupling is based on the interaction between the quadrupole modes and tunnel effect in an Ag nanosphere dimer by STEM-EELS measurements.26 However, some problems have arisen when analysing the LSPR of metallic nanoparticles with EELS. One is the plasmonic interaction between metallic nanoparticles and the supporting dielectric membrane. Due to the symmetry-breaking presence of the substrate, it is reported that some resonance modes further splits.35–39 This makes


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interpretation of the LSP interactions between nanostructures difficult. Sherry et al.35 clarified from the EELS experiments and the finite-difference time-domain (FDTD) simulation that the degree of peak splitting strongly depends on the permittivity of the substrate and the shape of nanoparticles. It has also been reported in which the resonance energy shifts even though the clear peak splitting is not visible.40,

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Furthermore, an EELS

measurement of localized surface plasmons (LSPs) is usually performed under vacuum inside a transmission electron microscopy column, but the interpretation of the measured resonance energy is not simple when the surface of the metallic nanoparticles is oxidized or sulfurized. For example, the LSPR energies measured for Ag nanospheres are in fact lower than the energy of dipole plasmon resonance (3.5 eV) in many experiments. Moreover, the contaminants deposited on the surface of the metallic nanoparticles during the STEM-EELS measurements markedly alter the resonance energy.23 Therefore, to understand LSPR, it is essential to perform EELS experiments under conditions where metallic nanoparticles are dispersed in a uniform medium so that the LSP interactions between the nanoparticles can be accurately measured. Here we report the analysis of LSP interactions between Ag nanospheres from STEMEELS measurements of Ag nanospheres embedded in silicate glass with a permittivity of 2.1 to avoid the above-mentioned problems. By embedding the Ag nanospheres in a uniform medium with a permittivity larger than that of a vacuum, we are able to clearly observe the higher-order LSPR mode reported by Raza et al..42 Therefore, we are able to


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investigate the LSP interactions in an Ag nanosphere dimer by STEM-EELS, and we discuss the possibility of observing the interaction between higher-order LSPR modes. To clarify the electric field distribution around the nanospheres, we also perform numerical simulations based on the discrete dipole approximation (DDA).

2. METHODS 2.1 Sample preparation.

The sample was prepared from a glass plate (Schott Desag AG:

Super White) containing SiO2 and Na2O as main components and K2O, CaO, and Sb2O3 as other components. Ag cations were introduced into the glass by an ion-exchange reaction in a molten salt mixture of KNO3 and AgNO3 (99.9:0.1 molar ratio) at 700 K for 24 h under continuous stirring. The glass was then reduced in a furnace at 800 K for 1 h under a hydrogen gas flow of 1.5 L/min. To obtain large Ag nanospheres, the glass was annealed again in the furnace at 940 K for 12 h in air. The glass was cut into small pieces. After mechanical polishing a piece of glass, it was mounted over a single hole with a 3-mm outer diameter, 1.5-mm inner diameter, and 20-µm thickness, and then subjected to ion milling (Gatan Inc., PIPS) with 3-keV Ar ions at an incident angle of 5°. To avoid the influence of thermal damage, the sample was cooled with liquid nitrogen during ion milling. After ion milling, a thin amorphous carbon film was deposited on the sample surface to provide paths for electrical and heat conduction and prevent surface sputtering of oxygen or silicon. 2.2 STEM-EELS measurement.

The STEM-EELS measurements were performed with an

FEI Titan3 G2 60-300 electron microscope with a monochromator and double spherical aberration correctors. An acceleration voltage of 60 kV was used to avoid retardation effects in


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the silicate glass. The full width at half maximum of a zero-loss peak measured with a probe of diameter 0.5 nm and probe current of 100 pA was less than 100 meV. The convergence semiangle of the electron probe was 16 mrad and the collection semi-angle of the EELS detector was 26 mrad. In STEM-EELS SI, an energy dispersion of 0.025 eV/ch and sampling distance of 2 or 0.6 nm/pixel were used for the analysis of a 30-nm-diameter single Ag nanoparticle or 20-nmdiameter Ag dimer, respectively. The EELS data in Fig. 1 and 3 were integrated over 4 × 4 (8 nm × 8 nm) or 3 × 6 (1.8 nm × 3.6 nm) pixels, respectively, at the region of interest, where the spectra at each point were recorded with an acquisition time of 30 ms. The background of each spectrum was removed by fitting with a power law for energies ranging from 1.0 to 2.0 eV. The obtained spectra were least-square fitted by the sum of several Gaussian functions for energies ranging from 2.0 to 4.0 eV. The MLLS fitting was used to obtain the individual intensity maps of each resonance mode. 2.3 DDA Simulations.

DDA simulations were performed with DDEELS ver. 2.1.43 The

dielectric function for Ag used in the present calculation was determined by Palik.44 The permittivity of silicate glass εglass was assumed to be 2.1, which was the same value used in the EELS calculation for the Au/SiO2 system.45) The dielectric function of Ag was then normalized by εglass to simulate the Ag nanospheres in glass. For calculations of the 20 (30)-nm-diameter Ag nanosphere, we used 5695 (19381) dipoles with a voxel size of 0.9 × 0.9 × 0.9 nm. The simulation of the Ag dimers used 11390 dipoles. The electric field outside the Ag nanospheres was calculated from the sum of the contributions from all dipoles neglecting the influence from retardation effects.

3. RESULTS AND DISCUSSION


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3.1 LSPR of a single Ag nanosphere.

First, we discuss the results of examination of

the LSPR mode of a single Ag nanosphere. Figure 1a is a high-angle annular dark-field (HAADF)-STEM image of Ag nanospheres dispersed in silicate glass, which shows that the Ag particles have sizes from 10 to 30 nm and are embedded in the glass. STEMEELS SI data were obtained for an Ag particle with a diameter of 30 nm and EELS spectra were extracted from the regions around point A (6 nm outside the edge of the nanosphere) and point B (6 nm inside the nanosphere) shown in Fig. 1b. These spectra are shown in Fig. 1c. HAADF-STEM images indicated that the glass surface was slightly etched after the acquisition of STEM-EELS SI data, but it was confirmed that there was no change in the low-loss spectra of the glass before and after the acquisition (Fig. S1). It was confirmed by the stereoscopic observation that this particle was completely embedded in the glass of 80 nm in thickness. The minimum distance between the carbon layer deposited on the top surface of the glass and the nanoparticle surface was approximately 20 nm. When the electron beam was incident on point A, a single peak was observed in the spectrum at around an energy loss of 3.1 eV. This peak is thought to originate from the LSPR of the Ag particle, and it coincided with the expected resonance energy because of the higher permittivity of the surrounding glass than that in vacuum. It was confirmed that there was less influence of the carbon layer deposited on the glass surface when the distance between the nanoparticle surface and the glass surface was greater than at 10 nm. Alternatively, when the electron beam was passed


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through the edge of the nanosphere, a weak peak appeared around 3.4 eV in addition to the bulk plasmon peak observed at 3.8 eV. Furthermore, spectrum B was peak decomposed by the least squares method using three Gaussian functions with the peak energies of 3.1, 3.4 and 3.8 eV, respectively, as shown in Fig. 1c. The values of peak energy and FWHM of each component obtained by peak decomposition were summarized in Table.S1. The intensity distribution of three different resonance modes obtained by the multiple linear least squares (MLLS) fitting to the STEM-EELS SI data is shown in Fig. 1d. It can be seen that the resonance mode having a peak energy (Ep) of 3.1 eV (α-component) is maximum at the particle surface and exhibits an intensity distribution corresponding to the so-called surface plasmon, the intensity decreasing with distance from the particle. On the contrary, since the mode (γ-component) of Ep = 3.8 eV has intensity only inside the grain, this corresponds to the bulk plasmon. Finally, we discuss the feature of the resonance mode of Ep = 3.4 eV (β-component). Although it is obvious that this mode is a mode localized on the particle surface, its resonance energy has a higher value than the resonance mode represented by α-component. In other words, it can be considered that this mode is a higher order LSPR.27,33 In addition, compared to the mode with Ep = 3.1 eV, the intensity rapidly decreases as far from the particle surface. This clearly indicates that the higher order LSPR mode can be excited only when the electron beam passes near the surface of the particle. Similar resonance energies were obtained with completely embedded single Ag nanospheres. According to our measurements, no clear dependence on the depth of Ag nanospheres in the glass as shown in Fig. S2a. Also, there was no size dependence of the resonance energies was observed for Ag nanospheres of 20 nm to 30 nm in diameter (Fig. S2b). As long as the Ag nanospheres are more than 5 nm away from the glass


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surface, the influence of the surface carbon layer is considered to be almost negligible and the effect of the uniform medium is guaranteed. We performed a DDA simulation for an Ag nanosphere with a 30-nm diameter in silicate glass with a permittivity of 2.1. The optical absorption spectrum and EELS response when the electron beam enters at locations 1 and 30 nm away from the Ag nanosphere are plotted (Fig. 2a). A pronounced LSP peak appeared at 3.1 eV in every spectrum, whereas an apparent increase in loss intensity was seen around 3.4 eV only when the electron beam was incident 1 nm from the nanosphere edge. This increase in intensity was more conspicuous as the distance between the electron beam and nanosphere surface decreased, as shown in Fig. S3. Figure 2b presents the calculated electric field distribution around the nanosphere on the xy-plane (normal to the direction of incidence of the electron beam) and the magnitude of the electric field. Therefore, the direction of the electric field was parallel to the z axis. The electric field distribution corresponding to the peak at 3.1 eV was associated with a dipole with its moment along the x direction. That is, the calculation results indicated that the LSPR in the dipole mode was excited at 3.1 eV. In contrast, the electric field distribution corresponding to an energy of 3.4 eV was quite different between the cases of optical and electron beam excitation. In the case of optical excitation, a dipole-like electric field distribution was induced. Conversely, excitation by an electron beam produced an obviously different electric field distribution that was strongly biased to the right-hand


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side of the particle. When looking only at this side of the nanosphere, the electric field distribution corresponded to a field generated by a quadrupole rather than that produced by a dipole. To understand these electric field distributions, the two-dimensional electric field distribution calculated using dispersed point charges is shown in Fig. 3. Positive and negative electric charges were placed on the surface of the sphere individually for the dipole and in pairs for the quadrupole. Calculations with point charge are likely to localize the real charge distribution, but it is clear that the results of optical excitation reasonably reflect the electric field distribution of the dipole. Similarly, even under excitation by the electron beam, the resonance peak at 3.1 eV is related to the dipole. In contrast, even though the electric field intensity corresponding to a loss energy of 3.4 eV is asymmetric, the electric field distribution is consistent with that of the quadrupole. The reason why the electric field intensity becomes asymmetric can be explained by the simultaneous excitation of the quadrupole and dipole modes. In fact, the electric field calculated based on the charge distribution obtained by overlapping these two modes in phase well reproduced the electric field distribution around the Ag nanosphere obtained by the DDA simulation. Therefore, we concluded that the vibration mode localized on the surface at 3.4 eV (Fig. 1) is caused by the simultaneous excitation of higher order modes in addition to the dipole. Raza et al.42 has already observed multipole LSPR by STEM-EELS of an Ag nanosphere in an SiNx film. Their


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measurements were aided by the fact that the Ag nanospheres were embedded in a medium with higher permittivity than that of vacuum. The relative energy difference between two vibration modes increases by embedding a metallic nanosphere in a medium with high permittivity. As a result, we were able to easily distinguish to the resonance energy of the dipole and higher order vibration mode (Fig. S4); it is practically impossible to detect higher order vibration modes in the EELS measurements of Ag nanospheres in vacuum. 3.2 LSPR of an Ag nanosphere dimer.

Next, we discuss the LSPR in an Ag

nanosphere dimer. An HAADF-STEM image of the Ag nanosphere dimer in silicate glass (Fig. 4a) indicated that the diameter of each nanosphere was approximately 20 nm. The spacing between the particles was determined to be 2 nm using the stereoscopic observation method (Fig. S5). Both Ag nanospheres were completely embedded in the glass of 50 nm in thickness, but the nanosphere on the right-hand side was located somewhat closer to the glass surface than that on the left. The distances between the right-hand nanosphere and bottom surfaces of the glass were about 10 nm, whereas the distance between the left-hand nanosphere and the bottom surface of the glass was estimated to be about 4 nm. In addition, a small Ag particle with a diameter of about 8 nm was also present and overlapped the side of the left-hand nanosphere. The distance between the left-hand nanosphere and small particle was approximately 3 nm. However, according to our DDA calculation, the presence of the small nanosphere


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should not strongly affect the LSP interactions in the Ag dimer (Fig. S6), so we considered these nanospheres an Ag dimer. The EELS data for this dimer obtained when the electron beam was incident on point A, B, and C in Fig. 4b are presented in Fig. 4c. A distinctly different LSPR mode was observed for the dimer compared with the behaviour of the single nanosphere. When the electron beam was incident on the outside of the dimer (point A) along the dimer axis, the LSPR energy of the Ag particles shifted slightly to 3.2 eV and a new peak appeared at 2.4 eV. When the electron beam was irradiated on the side of the dimer (point B), a single loss peak appeared at 3.2 eV. Moreover, a broad peak with shoulders at around 3.3 and 3.6 eV appeared when the electron beam was incident between the two Ag particles (point C). These mode separations based on the LSP interaction of two nanospheres have been observed by many researchers.23,26,27,30–32 Therefore, as same as in the case of a single particle, each spectrum was decomposed by the least squares method using four Gaussian functions with the peak energies of 2.4, 3.2, 3.3 and 3.6 eV, respectively. The values of peak energy and FWHM of each component obtained by peak decomposition were summarized in Table.S2. The results were shown in Fig. 4c. It can be seen from the figure that all spectra can be successfully reproduced as the sum of these four components. Here, the component having the peak energy of 3.2 eV could be confirmed in all spectra. However, as will be described later, since the electric field distribution at this energy varies depending on the electron beam incident position, they were distinguished as β-, β'- and β"-components for convenience. In particular, since the FWHM of β"-component is narrower than β- and β'-components, these modes are distinguished from


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each other (Table S2). Fig. 4d shows the intensity distribution of each resonance mode obtained by the MLLS fitting to the STEM-EELS SI data using the above-mentioned four Gaussian functions (α-, β-, γ- and δ-components determined in Table. S3). It was shown that the resonance mode corresponding to the lowest LSPR energy of 2.4 eV (α-component) appears only when electron beams were irradiated to both ends of the dimer. Although the resonance mode at Ep = 3.1 eV (β-component) tends to spread throughout the particles, the resonance modes having peaks at 3.3 eV and 3.6 eV (γ- and δ-component) tends to localize between the Ag nanospheres. In particular, the resonance mode at Ep = 3.6 eV (δ-component), which is the highest energy mode, was strongly localized at the centre of the dimer. In addition, all the resonance mode maps show asymmetrical intensity; in particular, the intensity is high outside the nanosphere on the right-hand side. The reason for this asymmetry may be that the nanosphere on the right is slightly larger and deeper from the glass surface that that on the left. Therefore, it is suggested that the carbon layer on the glass surface slightly affected to the result near the left side of the dimer. Except for this asymmetry, our observations are not greatly different from those in previous studies even though the Ag dimer was embedded in glass in our experiments. To clarify the origins of the observed modes, we performed a DDA simulation of an Ag dimer in silicate glass. In the present calculation, the diameter of the Ag nanospheres was 20 nm, the gap between them was 2 nm, and the permittivity of the glass medium was 2.1. Figure 5a shows the calculated optical absorption spectrum and EELS results for the Ag dimer. Under light illumination, LSPR signals appeared at 2.4


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eV when the polarization of the electric field was parallel to the dimer axis and 3.1 eV when the electric field polarization was orthogonal to the dimer axis. In addition, a broad peak was observed around 3 eV when the polarization was parallel to the dimer axis. In contrast, when the electron beam was incident on each location around the dimer, the calculated spectra corresponded well with the obtained experimental results. One important point is that the broader resonance mode from 3.3 to 3.6 eV excited when the electron beam was incident on the centre of the dimer (point C) was never excited by light illumination. Figure 5b shows the simulated energy loss probability maps at each LSPR peak energy. These calculated images also reproduce the experimental results well. As for experimental resonance mode map, the highest energy (3.6 eV) mode was strongly localized between the two Ag nanospheres. To clarify the LSPR interactions in the Ag dimer, we calculated the electric field distribution around the Ag dimer. Figure 6a shows this distribution in the direction parallel to the dimer axis (Ex) and in the vertical direction (Ey) when the electron beam was incident on the outside of the dimer (point A) at energy losses of 2.4 and 3.2 eV. The magnitude of the electric field (|E|) is also displayed. Similarly, the electric field distribution at 3.2 eV when the electron beam was incident on the side of the dimer (point B) is displayed in Fig. 6b, and those at 3.3and 3.6 eV when the electron beam was incident on the centre of the dimer (point C) are depicted in Fig. 6c. Using these figures, we discuss the vibration mode of the dimer at each loss peak.


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In Fig. 6a, the dimer axis coincides with the electric field of two dipoles oriented in the x direction at an energy loss of 2.4 eV; as a result, |E| is enhanced between the nanospheres of the dimer. That is, the LSPR mode at 2.4 eV corresponds to a longitudinal coupling (bonding) mode of two dipoles and is the same as the electric field enhancement observed when the light was incident along the dimer axis (Fig. S7 and S8). Conversely, for the energy loss of 3.2 eV, the electric field distribution was clearly different when the electron beam was incident on point A compared with that when the beam was incident on point B. When the electron beam was incident on the side of the dimer (point B), the electric field distribution involved two dipoles perpendicular to the dimer axis in parallel orientation. This coincides to a transverse antibonding mode of two dipoles in a metallic nanosphere dimer. Incidentally, we did not observe a pronounced peak corresponding to the transverse bonding mode in the present study. When considering the electric field generated by the electron beam, it is difficult to excite the transverse bonding mode directly. Because this mode can be excited only through the generation of induced dipole interactions between two nanospheres, its intensity is considered to be much smaller than that of other modes. Even when the loss energy was the same, the electric field distribution that appeared when the electron beam was incident on the outside of the dimer (point A) was specific. The electric field intensity was strongly biased toward the incident side of the electron beam and the directions of the electric field along the x axis were opposite on the two


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sides of the right-hand nanosphere. This distribution is clearly different from the electric field distribution of the dipole on the single nanosphere. Such an electric field distribution has already been discussed by Scholl et al.26 based on their EELS experiment on Ag nanosphere dimers; they called this mode “bonding quadrupolar”. That is, it is a structure in which two quadrupoles are placed so as to have different charge signs. Certainly, the electric field distribution of the bonding quadrupolar mode calculated based on the charge distribution proposed in their paper reproduced the distribution around the right-hand side nanosphere well (Fig. S9). It should be noted that a mode with the same electric field distribution also appeared at a peak energy of 3.0 eV under light illumination, as shown in Fig. S7. In other words, this quadrupolar bonding mode is not unique to electron beam irradiation, but is a bright mode that can be excited by light.46–48 Next, we discuss the instance when an electron beam was incident between the two nanospheres constituting the dimer (point C). What is expected from the geometric symmetry is that the charge distribution of each nanosphere is always symmetrical in the direction perpendicular to the dimer axis and the existence of the transverse vibration mode can be neglected. In contrast, the longitudinal charge distribution of the nanospheres is symmetrical with respect to the centre of the dimer, so that the antibonding longitudinal vibration mode is always excited. Both experimental and computational spectra confirmed that the energy loss had two shoulders at 3.3 and 3.6


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eV, consequently the electric field distribution at each energy was examined in detail. The calculated electric field distribution at a loss energy of 3.3 eV (Fig. 6c) shows that Ex was almost zero between the dimer whereas Ey was enhanced there regardless of whether the electron beam was incident between the two nanospheres. In addition, the x-component of the electric field around each nanosphere faced in the opposite direction. Obviously, this mode shows the feature of the longitudinal antibonding mode in which two dipoles with opposite directions face each other. This configuration is in good agreement with the LSPR antibonding mode in dimer reported by many authors.23,26,27,30–32 The trend of the electric field distribution at 3.6 eV (Fig. 6c) is very similar to the result for 3.3 eV, the x component of the electric field intensity was zero between the dimers and y component was enhanced there. One obvious difference is that the magnitude of the electric field at both ends of the dimer is relatively weak in the case for 3.6 eV. In addition, the electric field intensity in the direction perpendicular to the dimer axis (y direction) was more localized between the dimer. Furthermore, the x component of the electric field appears to split into two poles at both ends of the dimer. We discuss the differences in these electric field distributions of the longitudinal antibonding mode in the dimer. The expected interactions of the Ag dimer were obtained using a simplified twodimensional electrostatic field calculation of discrete point charges and are shown in Figure 7. As two Ag nanospheres in the antisymmetric dipole mode approach each


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other, their x components of the electric field between the particles cancel each other out as they are of opposite sign. In this instance, the electric field distribution around the dimer is almost in good agreement with the distribution at 3.3 eV in Fig. 6c. When two Ag particles behaving as a quadrupole are brought close together, the quadrupolar antibonding mode is excited. However, except for the vicinity of the centre of the dimer, most part of the electric field distribution created by the quadrupolar antibonding mode does not agree well with the previous DDA results. Therefore, as discussed in a single nanosphere, we considered the situation where the dipolar and quadrupolar antibonding modes are simultaneously excited in the dimer. The expected electric field were weak at both ends of the dimer and the x component of the electric field splitted into two poles at both ends of the dimer. In addition, the electric field distribution tended more localized at the dimer centre. These trends qualitatively agree with the electric field distribution predicted by the DDA simulation at an energy loss of 3.6 eV. Therefore, the reason why the broad peak excited at the beam position C is formed is suggested to be due to overlapping of the quadrupolar antibonding mode to the dipolar anti-bonding mode especially on the high energy side. As described above, we pointed out the possibility of the antibonding quadrupole interaction between two adjacent Ag nanospheres. This mode is never excited by light illumination, like the longitudinal antibonding dipolar mode. It should be possible to excite these modes by irradiating the electron beam on the centre of the two


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nanospheres forming the dimer; however, excitation of the quadrupolar antibonding mode is still restricted by certain conditions. One condition is that the distance between the two nanospheres needs to be sufficiently small. To excite the multipolar mode in one nanosphere, it is necessary to irradiate the neighbouring nanosphere with the electron beam. That is, to simultaneously excite multipolar modes in two nanospheres, they need to be adjacent to each other. More important condition, which was determined by observing the interaction of multipolar LSP modes, is that the resonance energies of the dipolar and multipolar modes need to separate as far enough. Normally this condition is not satisfied in the EELS measurement of the Ag nanosphere dimer exposed in a vacuum. Figure 8 shows the simulated EELS results for Ag nanosphere dimers in glass and vacuum. In vacuum, it is obvious that the LSP resonance peak appears on the higher energy side than in the glass, although the trends of both spectra are almost same. The significant difference between in the glass and the vacuum is the spread of the resonance peak when the electron beam is incident on position C. As mentioned above, the Ag nanosphere dimer in the glass has a broad absorption peak ranging from 3.3 to 3.6 eV, whereas in the vacuum only a single peak appears at 3.6 eV. Figure 9 shows the calculation results for the electric field distribution at the energy loss of 3.6 eV in both media. The difference between the two electric field distributions was clearly shown. The electric field distribution around the Ag nanosphere dimer placed in the vacuum


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well agrees with the electric field distribution predicted by the resonance energy of 3.3 eV in the glass. It shows that the anti-bonding dipolar mode is the observable LSPR interaction in vacuum. The same as the case for a single nanosphere, it is practically impossible to detect the signal from the high-order coupling mode in the EELS measurements of the Ag nanosphere dimer in vacuum. In other words, by embedding Ag nanospheres in a medium with a high permittivity, the possibility was indicated that the interaction of their higher order LSPR modes could be detected by EELS. Note that the accumulation of contaminants during electron beam scanning may affect EELS measurements.23 In this study, we believe the change in the Ag surface condition during the EELS measurements was effectively suppressed by embedding the Ag nanospheres in glass. This is another advantage for analyzing the LSPR interactions between nanostructures using EELS.

4. CONCLUSIONS We investigated the LSPR behaviour in a single Ag nanosphere and Ag nanosphere dimer embedded in silicate glass by STEM-EELS. By irradiating the Ag nanosphere with an electron beam, a multipole mode was excited at high energy in addition to the dipole mode. EELS analysis of the Ag dimer revealed the presence of some LSPR coupling modes. When the electron beam was incident on the outside of the Ag dimer, a longitudinal bonding mode of two dipoles formed and its resonance energy shifted to the lower energy than the LSPR signal of the single nanosphere. In contrast, when the electron beam was incident between the Ag nanospheres


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of the dimer, two more modes appeared at higher energies than the resonance energy of a single Ag nanosphere. Analysis of the electric field distribution around the Ag dimer suggested that these modes had the nature of the classical longitudinal antibonding LSPR mode of two dipoles. Furthermore, the DDA simulation suggested the possibility that the mode on the highest energy may include a negligible contribution of an antibonding-type quadrupolar interaction. This study suggested that by embedding Ag nanospheres in a medium with much higher permittivity, the LSPR coupling in high-order modes can be conceivably observed.


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Fig. 1 a HAADF-STEM image of Ag nanospheres in silicate glass and b magnified image of an Ag nanosphere. c EELS data acquired from point A and B indicated in b. The least-squared fit of the sum of three Gaussian functions (,  and ) is also plotted. d Intensity maps of each resonance mode for  (Ep = 3.1 eV),  (Ep = 3.4 eV) and  (Ep = 3.8 eV) components obtained by MLLS fitting.


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Fig. 2 Results of DDA simulation for a single Ag nanosphere. a Optical absorption spectra and EELS maps of the Ag nanosphere and b calculated electric field distribution around the nanospheres on the xy-plane (normal to the electron-beam incident direction) and the magnitude of the electric field at each energy.


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Fig. 3 Two-dimensional electric field distribution calculated by dispersed point charges as dipole, quadrupole, and their superimposition.


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Fig. 4 a HAADF-STEM image of Ag nanospheres in silicate glass and b magnified image of an Ag dimer. c EELS data acquired from point A, B and C in b. The leastsquared fits of the sum of four Gaussian functions (, ,  and ) are also plotted. d Intensity maps of each resonance mode for  (Ep = 2.4 eV),  (Ep = 3.2 eV),  (Ep = 3.3 eV) and  (Ep = 3.6 eV) components obtained by MLLS fitting.


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Fig. 5 Results of DDA simulation for an Ag nanosphere dimer. a Optical absorption spectra and EELS maps of the Ag dimer and b simulated energy loss probability maps at energy losses of 2.4, 3.1, 3.3, and 3.6 eV.


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Fig. 6 Calculated electric field distribution around an Ag nanosphere dimer on the xyplane (normal to the electron-beam incident direction) and the magnitude of the electric field. a Electron beam incident outside the dimer at energy losses of 2.4 and 3.1 eV. b Electron beam incident on the side of the dimer at an energy loss of 3.1 eV. c Electron beam incident between two nanospheres at energy losses of 3.3 and 3.6 eV.


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Fig. 7 Two-dimensional electric field distribution calculated from dispersed point charges as antibonding dipoles, antibonding quadrupoles, and their superimposition.


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Fig. 8 DDA simulation of EELS maps of an Ag nanosphere dimer. a In glass and b in vacuum.


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Fig. 9 Calculated electric field distribution around an Ag nanosphere dimer on the xyplane and the magnitude of the electric field. a In glass and b in vacuum.


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ASSOCIATED CONTENT Supporting Information. Influence of irradiation damage of silicate glass during the EELS measurements, influences of nanosphere size and depth position on LSPR energy, peak decomposition of EEL spectra, relationship between intensity of multipolar excitation and electron beam position, effects of medium on LSPR energy, determination of the relative position of Ag nanospheres, influence of the small Ag nanosphere near the Ag dimer on dimer behavior, two-dimensional model for dipole– dipole interactions in the metal nanosphere dimer, electric field near an Ag nanosphere dimer excited by light illumination (PDF) AUTHOR INFORMATION Corresponding Author *[email protected] Author Contributions N.S. conceived and designed the experiments, performed most of the experiments and analyses, and wrote the paper. S.M. assisted in the STEM observation and DDA calculations. Y.K. conducted the DDA calculations. M.W. prepared the samples. All of the authors discussed the results and contributed to the manuscript.


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ACKNOWLEDGMENT We gratefully acknowledge member of the High-Voltage Electron Microscope Laboratory, Hokkaido University, K. Ohkubo, R. Oota, T. Tanioka, Y. Yamanouchi, A. Yokohira and E. Obari, for their technical support in STEM operations and sample preparations. Part of this work was conducted at Hokkaido University, supported by the “Nanotechnology Platform” Program of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan. This work was also supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI (Grant Number 18K0487208). REFERENCES 1. Maier, S. A.; Kik, P.G.; Atwater, H.A.; Meltzer, S.; Harel, E.; Koel, B.E.; Requicha, A.A. Local detection of electromagnetic energy transport below the diffraction limit in metal nanosphere plasmon waveguides. Nature Mater. 2003, 2, 229–232. 2. Maier, S. A.; Kik, P. G.; Atwater, H. A. Optical pulse propagation in metal nanosphere chain waveguides. Phys. Rev. B 2003, 67, 205402. 3. Fevrier, M.; Gogol, P.; Aassime, A.; Megy, R.; Delacour, C.; Chelnokov, A.; Apuzzo, A.; Blaize, S.; Lourtioz, J.M.; Dagens, B. Giant coupling effect between metal nanosphere chain and optical waveguide. Nano Lett. 2012, 12, 1032–1037. 4. Crozier, K.B.; Sundaramurthy, A.; Kino, G.S.; Quate, C.F. Optical antennas: Resonators for local field enhancement. J. Appl. Phys. 2003, 94, 4632–4642.


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“TOC Graphic”


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Interaction of Localized Surface Plasmons of a Silver Nanosphere

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