Plasmon Resonances in Nanohemisphere Monolayers

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Plasmon Resonances in Nanohemisphere Monolayers Cagri Ozge Topal, Hamzeh Mahmoud Jaradat, Sriharsha Karumuri, John F. O'Hara, Alkim Akyurtlu, and A. Kaan Kalkan J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b05934 • Publication Date (Web): 27 Sep 2017 Downloaded from http://pubs.acs.org on October 2, 2017

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The Journal of Physical Chemistry

Plasmon Resonances in Nanohemisphere Monolayers Ç. Özge Topal,a Hamzeh M. Jaradat,b Sriharsha Karumuri,a John F. O’Hara,c Alkim Akyurtlu,d and A. Kaan Kalkana,* a

Functional Nanomaterials Laboratory, Oklahoma State University, Stillwater, Oklahoma 74078

b

c

Department of Telecommunications Engineering, Yarmouk University, Irbid, Jordan 21163

Department of Electrical and Computer Engineering, Oklahoma State University, Stillwater, Oklahoma 74078

d

Department of Electrical and Computer Engineering, University of Massachusetts, Lowell, Massachusetts 01854

ABSTRACT: Plasmonic devices, consisting of nanoparticle monolayers, are conveniently fabricated by deposition techniques, wherein thermodynamics often favor the particle shape to be close to hemispherical. The present work investigates plasmon modes in Ag nanohemispheres (NHSs) using s- and p-polarized incident radiation at varying angles. The Ag NHSs, immobilized on nanoposts, resembling mushroom structures, allow for reduced substrate coupling and convenient resolution of the modes. Additionally, the modes are studied by in-situ extinction acquisitions during nanoparticle synthesis and elucidated by numerical simulations. It is revealed that the broken symmetry by asymmetric particle shape leads to dipolar modes parallel and normal to the base, which are significantly different in terms of energy, excitation dependence on polarization and particle-particle as well as particle-substrate couplings. In particular, the parallel mode offers distinct advantages in plasmonics applications over nanospheres. For example, its strong substrate coupling may benefit thin film photovoltaics by efficient light coupling. Higher field concentrations are induced at the sharp edges of a NHS that may enhance hot electron injection in a photocatalyst. Unlike in a spherical dimer, where the field intensity peaks in the middle of the gap, the maximum field in a NHS dimer gap occurs on the metal surface (i.e., at the edges), overlaying with the chemical enhancement. Hence, a higher surface enhancement factor is achieved in Raman scattering.

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Introduction Plasmonic devices, such as chemical sensors,1-5 surface-enhanced Raman scattering SERS) substrates,6-10 light-coupling layers in photovoltaics,11-15 and plasmonic photocatalysts16-18 are conveniently prepared by immobilization of metal nanoparticles (NPs) on a substrate. When NPs are synthesized directly on the substrate (e.g., vapor deposition, electrochemical reduction), the metal adatom surface diffusion length may be comparable or larger than the NP size. As a result, the NP can approach thermodynamic equilibrium and minimize the total surface energy resulting in the formation of a certain contact angle between the metal-ambient and substrateambient interfaces. The contact angle can be significantly less than 180°, that is, the metal wets the substrate. Hence, the particles may be truncated spheres rather than spheroids. In fact, in a number of reports the deposited NPs were characterized as close to hemispheres.2, 15, 16, 19-21 Additionally, nanohemispheres (NHSs) or nano-truncated-spheres may offer distinct advantages in plasmonics over nanospheres. For plasma oscillations parallel to the basal plane, the dipole center is close to the base allowing for a stronger substrate interaction. Second, higher field concentrations are induced at the sharp edges (i.e., lightening rod effect) leading to enhanced coupling with the substrate or adjacent NHSs. Indeed, recent numerical work on Ag NHS dimers has revealed superior field enhancement factors (over nanospheres) in the gap for edge-to-edge configuration with the excitation field being along the dimer axis.22 Hence, higher sensitivity molecular detection/sensing is anticipated. Compared with spheres, truncated spheres show higher diversity of localized surface plasmon modes due to broken symmetry as originally shown by Albella et al. with discrete dipole approximation simulations.23 They have studied Ga nanohemispheres (NHSs) deposited


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on sapphire substrates. More recently, Attanayake et al. comprehensively studied single and dimer Ag NHSs of radius 20 nm in vacuum using finite element simulations.22 In the present work, we experimentally investigate the plasmon modes in 2D Ag NHS ensembles of short-range order as excited by s- and p-polarized incident radiation at various angles. Although two different techniques were employed to synthesize the NPs on glass substrates, physical vapor deposition (PVD) in vacuum and electrochemical reduction in water, the NPs exhibit similar plasmonic characteristics, which verify the theoretical findings of the previous two reports.22, 23 Additionally, we provide new insights. Here, we focus on NHSs synthesized by electrochemical reduction, while results regarding NHSs synthesized by PVD are given in Supporting Information (SI). The reduction was performed by immersion of ultrathin (i.e., 4.5 nm thick) Ge films in AgNO3, where Ge functions as the reducing agent.6, 20 A unique feature of this Galvanic displacement technique is found to be consumption of Ge everywhere, except just below the center of NHSs, resulting in mushroom-like structures, as illustrated in Fig. 1a. NHSs are essentially immobilized on Ge nanoposts of uniform height from the glass substrate. Figure 1b provides a representative AFM image of those Ge posts after the Ag NHSs were dissolved and washed off in a mercury aliquot by amalgam formation. The AFM data of Fig. 1b confirms the expected average nanopost height of 4 nm, being very close to the Ge film thickness measured by quartz crystal microbalance. A useful attribute of the mushroom-like structure is separation of the hemisphere edges, the regions of highest field concentration, from the substrate. This separation allows reduced substrate coupling and damping. Hence, the extinction peaks are narrower and easier to resolve for different modes. We also employ finite integral time domain (FITD) simulations to complement our investigation of particle-substrate and particle-particle couplings as well as


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damping. Our experiments not only verify the theoretical results of Ref 22 in terms of mode energies and coupling between adjacent NHSs, but provide new insights on substrate/particle coupling and damping. The dipolar modes, which may be simply distinguished as parallel versus perpendicular to the NHS base, differ significantly in terms of energy, damping and couplings. Methods Details of the Ge film deposition, NP reduction and size determinations are given in the SI. Figures 1c and 1d depict plan and oblique SEM images of the Ag NPs synthesized, respectively. By SEM and AFM, the NPs were found to be close to hemispheres with basal diameter and height of 65±13 nm and 29±5, respectively (SI). Additionally, the average interparticle separation is derived as 2 nm (SI). The extinction spectra were acquired by a Cary 300 double-beam spectrometer using polarization filters (American Polarizers, APUV-UV linear polarizer) for both the reference and sample. The incidence angle was varied from 0 to 75° at intervals of 15° by rotation of the sample and reference. The details of substrate background subtraction in the extinction spectra are provided in the SI. The numerical simulations were carried out using the commercial software CST MICROWAVE STUDIO®, based on the FITD method. Unit cell boundary conditions are utilized in x- and y-directions. This configuration ensures that an infinite number of unit cells in both the x- and y-directions are taken into account in the simulation. Open Floquet ports were used as input and output ports to calculate transmission/reflection from/through the structure. The ports are placed at distances of Zmin from the base and Zmax from the top of the structure. The excitation plane wave source signal of 1 W is placed at the port located at Zmax which propagates along the negative z-direction. The frequency domain solver was then employed with


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tetrahedral meshing in order to extract reflection, transmission coefficients and the electric field distributions. Results and Discussion Experimental spectra: Representative experimental extinction spectra of the Ag NHSs are seen in Figs. 1e and 1f for various incidence angles, θ, and s- and p-polarizations, respectively (Fig. 1g). In the case of s-polarized incident radiation (Fig. 1e), the spectrum is dominated with a broad band at 482 nm with a weak shoulder at 362 nm. On the other hand, when incident radiation is p-polarized and oblique to the substrate plane (Fig. 1f), an additional extinction feature appears in UV which is resolvable to three Gaussians at 335, 344 and 362 nm (Fig. 1h). All three peaks increase in intensity with θ, while the 482 nm band attenuates. Similar spectral characteristics and trends are acquired for Ag NHSs vapor deposited on glass, as reported in the SI. In this case, however, certain resonances exhibit larger widths due to higher substrate coupling and cannot be resolved as conveniently. Therefore, we focus on the Ag NHSs reduced on Ge thin films. Numerical simulations: Figures 2a and 2b show the computed extinction spectra for a monolayer of Ag NHSs for s- and p-polarized incident radiation, respectively. Our numerical model consists of uniformly spaced NHSs in square lattice positioned on a 4.5 nm thick Ge layer standing on a semi-infinite glass domain. Although a triangular lattice is better representative of the synthesized Ag NHSs, a square unit cell enclosing a NHS in its center allows for computational stability and ease. As-deposited Ge films were characterized as amorphous by Raman spectroscopy. Therefore, the dielectric function of Ge is adopted as that for amorphous Ge.24 As inferred from Fig. 1b, a large fraction of the Ge film is consumed as reducing agent during Ag NHS synthesis


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(i.e., Galvanic displacement). Accordingly, we model the Ge layer as a porous medium and compute its dielectric function using dielectric mixing (i.e., Ge in vacuum) by zero-order effective medium approximation.25 The boundary conditions for the unit cell are employed to represent infinite repetition of NHSs in 2D. It is not a straightforward task to adopt an effective interparticle separation in our simulations. If a square cell is set with the experimentally measured average separation of 2 nm along the unit cell edge, then separation along the diagonal direction is 27 nm. Hence, adopting the polarization along the unit cell edge, as we do, maximizes and exaggerates the NHS-NHS coupling. This situation does not ideally represent the effective coupling in the experimental case, which is orientation-averaged (isotropic) due to disorder. As will be shown, separation of 8 nm (along the cell edge) and Ge filling factor (FF) of 0.05 yield an optimum match with experiment in terms of the parallel (to HS base) dipolar mode wavelength. Comparison with simulation: Here, we do not expect an exact match between experiment and simulation, especially for strongly coupled modes, as the experimental case of an ensemble involves short-range order against the ideal periodicity of the arrays, simulated. Our objective is to identify weakly coupled modes and major strongly coupled modes as well as compare the plasmon excitation trends (i.e., with incident angle/polarization, substrate/particle coupling) to gain insights. Nevertheless, a reasonable agreement is found between the measured (Figs. 1e and 1f) and simulated spectra (Figs. 2a and 2b, respectively) in terms of resonant wavelengths, extinction values and dependence on incident polarization and θ. We employed the dielectric function of bulk Ag in the simulations which does not take into account the electron scattering at NP surfaces.26 Due to the absence of this damping mechanism as well as heterogeneity in particle size, shape and separation (both distance and


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direction with respect to excitation field), the simulated resonances exhibit narrower widths. In particular, the ‘no substrate’ case (Figs. 2c and 2d) exhibits the sharpest resonances due to absence of electromagnetic coupling with the substrate. Figures 2e and 2f show the deconvoluted extinction peaks in the presence and absence of substrate, respectively, for ppolarized incident radiation for θ = 60°, where both parallel and vertical modes are excited. As seen in Figs. 2g and 2h, substrate coupling not only leads to shifts in the resonance frequencies, but also broadening of the linewidths due to energy transfer/dissipation. Finally, our simulated spectra for the investigation of particle-particle coupling (i.e., with varying interparticle separation) are provided in Figs. 2i and 2j. We will refer to Fig. 2 in the remainder of this article during our discussions. Mode assignments: Next, we would like to discuss the plasmon modes in Ag NHSs in light of our experimental and computational results so far. With the help of simulated electric field distributions in Figures 3 and 4, we identify and denote the modes from longer to shorter wavelength (i.e., 482, 373, 343 and 331 nm) as ‘dipolar parallel to the base’, D= , ‘dipolar perpendicular to the base’, D⊥1, multipolar, MP, and ‘dipolar perpendicular to the base’, D ⊥2 , respectively. Due to higher complexity of MP, a separate figure (Fig. 4) is devoted for this mode’s description. Additionally, MP is described by three videos in the SI which show phaseseries field maps of the XZ and YZ axial cross sections as well as XY base plane. In the field maps of Figs. 3 and 4 (as well as forthcoming Fig. 5), the dark vertical lines (in the z-direction) represent the unit cell boundaries in the substrate. Computations for the no-substrate case essentially reproduce the same modes (i.e., same field distributions) at 447, 367, 348 and 330 nm, respectively. Strikingly, D⊥1, MP and D ⊥2 exhibit virtually no substrate dependence, while D= is inferred to be strongly coupled to the substrate (e.g., as deduced from the spectral shift


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with Ge FF in Figs. 2g and 2h). Our computationally derived wavelengths of D⊥1, MP and D ⊥2 for an array of NHSs also agree precisely with those computationally solved for an isolated Ag NHS in vacuum,22 confirming the weak substrate as well as NP coupling for these modes. However, prior to elaborating on coupling effects, we would like to discuss the configurational differences between the modes and excitation dependence on incidence angle. Mode configurations: An isolated sphere has 3 dipolar plasmon modes corresponding to 3 orthogonal axes (i.e., normal modes). These normal modes are degenerate in a single energy due to symmetry. In a hemisphere on the other hand, the broken symmetry lifts the degeneracy of dipolar modes. Hence, dipolar modes at different frequencies are observed. We briefly name the two types of modes as ‘parallel’ ( D= ) and ‘perpendicular’ ( D⊥ ) with respect to the basal plane (and conveniently the substrate surface in case of immobilization). The energies of D= and D⊥ are different from each other as well as that of a sphere of equal volume due to shape-modified restoring force constants for the electron gas (equivalently polarizabilities). For a single Ag NHS (radius of 20 nm in vacuum), Ref. 22 reports 3 different resonances for D= excited in the case of parallel incident polarization (401, 380, 365 nm). We reproduced the computational results of Ref. 22 for single NHSs of the same geometry. However, the two shorter wavelength D= modes are weakly excited and their configurations are not clearly identified from the field profiles, which are overshadowed by that of the 401 nm mode. In our experimental case we observe this major parallel mode as a broad resonance band centered at 482 nm. It is redshifted due to particle as well as substrate couplings. It is also broadened due to distribution of particle size and interparticle distance. Reference 22 assigns the resonances at 343 and 373 nm (i.e., our MP and D⊥1) to “split perpendicular dipolar modes”. However, these assignments are based on field amplitude maps


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of an axial cross section and are not sufficient to describe these more complex modes. Particularly, the 343 nm mode has the highest degree of complexity and cannot be described simply as dipolar or quadrupolar. In Fig. 4, we describe this mode with phase-series field maps of the XZ axial cross section (essentially identical with that of the YZ axial cross section) and XY basal plane. These field distributions are derived from the simulation of a single NHS of 40 nm diameter in vacuum, for incidence angle of 90°, and at peak excitation of the mode (i.e., 350 nm). The simulation was performed using open boundaries with the source being a plane wave of 1 V/m magnitude. In Fig. 4, oscillating poles are seen at the edge perimeter (in the form of a ring), center base, and top. The charge distribution appears dipolar at 30° phase (Fig. 4b), while it is far from dipolar at 120° phase, where the charge at the base splits to opposite polarities at the edge periphery (ring) and center. Therefore, at best, this mode can be expressed as an expansion of multipoles oscillating with phase differences, hence the notation MP. Nevertheless, MP has a strong perpendicular dipole moment based on its increasing excitation with θ. On the other hand, the complexity of field patterns in Fig. 4 is not due to interference from D⊥1 and D ⊥2 . Based on the deconvoluted D⊥1 and D ⊥2 peaks in Fig. 2f, excitation of these modes are insignificant at the wavelength, for which MP reaches full resonance. Additionally, although the mode at 373 nm (Figs. 3b and 3e), D⊥1, is dipolar perpendicular, it is not a “split” mode in the sense that pole charge at the NHS base divides into two corners (while the opposite pole is concentrated at the apex). In reality, while the charge at the base is concentrated at the edges, it is interconnected in the form of a ring or donut as demonstrated by Fig. 5a with a couple of NHSs in the array. Here, the slight asymmetry along the x-axis is attributed to oblique incidence (i.e., θ = 75°). Unlike D⊥1, D ⊥2 involves relatively a


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more uniform distribution of the polar charge over the base of the NHS as inferred from Figs. 3c and 3f. Variation of excitation with incidence angle: As evident from Fig. 1e, D⊥1 and D ⊥2 are minimally excited in the presence of s-polarized radiation at any angle of incidence, θ. In addition, they are essentially not excited by p-polarized radiation at normal incidence (Fig. 1f). The common condition in these cases is the polarization of the incident field being parallel to the substrate. In both cases, the dipole moment induced by the field is orthogonal with the dipole moment associated with D⊥ . As a result, D⊥ modes are not excited, while D= is excited. In contrast, p-polarized radiation at oblique incidence has polarization vector having both parallel and perpendicular components to the substrate. Hence, the induced dipole moment has projections on both D⊥ and D= dipole moments. Therefore, both parallel and perpendicular modes are excited. With increasing θ, the perpendicular projection increases, while the parallel one decreases, explaining the systematic increase in D⊥ and simultaneous decrease in D= extinction peak intensities. MP is also inferred to have a strong perpendicular dipole moment based on its increasing excitation with θ. Substrate coupling: Another interesting plasmonic characteristic distinguishing NHSs from nanospheres is the stronger coupling of D= with the substrate. As such, D= systematically shifts from 467 to 577 nm as Ge FF is increased from 0.01 to 0.50 (Fig. 2g). For comparison, we simulated nanospheres of the same diameter, separation and substrate as the NHSs. In contrast, D= in nanospheres shifts only from 369 to 372 nm as Ge FF is increased from 0.01 to 0.50

(spectra not shown here). The stronger substrate coupling of D= in NHSs may be simply explained by the dipole moment being located close to the basal plane and thus substrate. More precisely, the electric field lines from (+) to (−) pole have significant intersection with the


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substrate resulting in a larger interaction. On the other hand, in a nanosphere the dipole moment passes through the sphere center and is located above the substrate by a distance of its radius. Second, for D= in the NHS, the oscillating polar charges squeeze in the sharp edges forming more concentrated fields than those for a sphere. Figures 5b-5d illustrate penetration of these strong fields into the substrate at the edges for 3 different interparticle distances. Nevertheless, in our experimental case of mushroom nanostructures, these hot zones miss the Ge stems (posts) and penetrate into low dielectric-constant glass only. Additional evidence for strong substrate coupling for the D= mode is obtained from peak broadening (i.e., increased damping). While the FWHM is computed as 0.12 eV in vacuum, it dramatically increases to 0.41 and 0.47 eV on Ge (on glass) for FF of 0.05 and 0.5, respectively. The increased damping is due to both optical absorption and Ohmic losses associated with charge oscillations in the Ge film by strong plasmon coupling. In contrast, no significant energy shift of D ⊥1 , D ⊥2 and MP is found with FF (Fig. 2h), indicative of weak substrate coupling. Likewise, changes in the peak widths are negligible. This situation is expected for D⊥ modes , since electric field lines from (+) to (−) pole, that is from apex (or lateral surfaces) to base, have limited overlay with the substrate. As such, the field patterns simulated for D ⊥2 in Figs. 5e and 5f confirm insignificant substrate coupling. Similar characteristics are observed for D ⊥1 . Particle-particle coupling: To explore the impact of particle-particle coupling, we have conducted numerical simulations varying the interparticle separation, s, systematically. Figures 2i and 2j compare the extinction spectra for s = 2, 4, 8, 16 and 64 nm for p-polarized incident radiation at incidence angles of 0° and 75°, respectively. Corresponding field maps for different interparticle separations are given in Figs. 5b-5f.


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Coupled plasmon modes for adjacent NHSs may be examined in the context of plasmon hybridization model.27-29 Considering a NHS dimer, hybridization of D= occurs in 4 normal modes. These modes have oscillating dipoles being either parallel, DJ = (J-conjugation), or perpendicular, DH = (H-conjugation), to the interparticle axis. Further, each case has symmetric (in-phase) and antisymmetric (out-of-phase) combinations. In the absence of phase retardation, the antisymmetric modes are not excited by incident radiation because of zero total dipole moment. Compared with D = in a single NHS, DJ = is associated with a lower force constant (restoring force) per conduction electron mass due to dipole-dipole attraction and therefore the resonance shifts towards lower frequencies with decreasing NP separation (i.e., increasing attraction).28 An opposite trend occurs for DH = because of dipole-dipole repulsion. For our simulations, we observe D = shifting from 450 to 565 nm as s decreases from 64 to 2 nm in Fig. 2i, indicative of D J = characteristics being dominant. Our experimental data best match with the simulated case of s = 8 nm, where significant field coupling between NHSs is observed from Fig. 5b. Whereas, Fig. 5d indicates essentially no overlap of near fields between NHSs at s = 64 nm for D= resonance (450 nm). It has been well established that field concentrations in narrow gaps between plasmonic Ag NPs can exceed 2 orders of magnitude allowing for detection of SERS from single molecules (i.e., exceeding SERS electromagnetic enhancement factor of 108).30-32 In the presence of chemical enhancement, the SERS single molecule enhancement factors can approach 1012.6,7,30-32 As demonstrated by Figs. 5g and 5h, the distribution of enhanced field between two NHSs is unique. Unlike in the case of nanospheres, where the field intensity peaks in the middle of the gap,33 the maximum field between two NHSs occurs on the metal surface (i.e., at the edges), overlaying with the SERS chemical enhancement. A similar finding was shown by Attanayake


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et al. for NHS dimers.22 Hence, higher sensitivity molecular detection/sensing is anticipated with coupled NHSs than nanospheres. Unlike D = , D ⊥1 and D ⊥2 do not exhibit any notable coupling between NHSs. Since the dipole moment for D ⊥ is perpendicular to the dimer axis, hybridization involves Hconjugation. Accordingly, DH ⊥ modes are expected to shift to higher frequencies with decreasing interparticle distance as discussed above. Figure 2j confirms such spectral shift, but it is negligible. The wavelengths of the D ⊥ modes essentially remain constant and equal to those of a single Ag NHS as computed in Ref 22. Reference 22 also reports insignificant shift of DH ⊥ with particle separation in dimers. This insignificant level of coupling/hybridization for D ⊥ in NHS ensembles positioned on a plane is attributed to weak interaction of dipole moments, which are effectively positioned along the NHS symmetry axes and therefore separated by relatively larger distances. More precisely, for D ⊥ , the pole at the base of the NHS involves charge distribution either being uniform over the basal area or ring-shaped around the NHS edge. Therefore, the fraction of base pole charge, which is adjacent to the gap between the particles, is much lower compared to that in DJ = . Hence, coupling across the NHS gaps is weaker for both D ⊥ modes. This discussion is also valid for MP.

In reality, the coupling of D = does not really occur in the form of just J- or just Hconjugates. If an array of 4 particles is considered, each positioned at one corner of a square (i.e., the simplest array), the mode with the highest symmetry involves all 4 dipoles oscillating in phase along one of the square edges. Clearly, each dipole oscillation interacts with others as both J- and H-conjugates simultaneously in the same mode. More complex modes involve combinations of symmetric and antisymmetric oscillations as well as oscillations along the lattice diagonals. With increased number of dipoles in the array, the number/complexity of the modes


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increases. The majority of these modes are not excited, or are only weakly excited by incident radiation, as the mode patterns do not fit the excitation field patterns. Nevertheless, when the D= band is analyzed, combinations of multiple peaks are seen in Figs. 1h and 2e for both

experiment and simulation, respectively. Hence, excitation of different D= modes is inferred. We anticipate the highest intensity peak in Fig. 2e corresponds to D= with coherent coupled dipole oscillations everywhere in the array. This mode is strongly excited by normal incidence, where the excitation field is of uniform phase over the array. On the other hand, for oblique incidence, the phase of the excitation field changes over the array and is expected to excite modes with symmetric and antisymmetric combinations. As such, we observe new peaks for oblique angle incidence. Unfortunately, we cannot assign the deconvoluted peaks to specific modes, because the field patterns we obtain from our simulations are associated with overlapping resonances of different parallel modes. In addition, the complex coupled modes determined from our simulations may be symmetry-forbidden in the experimental ensembles because of disorder. The lack of long-range order in our Ag NHS ensembles is expected to limit the modes to shorter range, too. Additionally, the objective of our array simulations is to gain basic insights to explain our experimental results. Therefore, a detailed investigation of the array modes is the subject of a different work. Kinetics of NHS growth monitored by in-situ extinction: Instead, to elucidate the experimentally observed parallel modes, we have acquired the time-series extinction spectra of the NHSs with parallel polarization (i.e., normal incidence) while they are being synthesized in an optical cell. The SI provides the details of the experiment and background correction. This task has allowed for continuous monitoring of the modes, while the dipole-dipole coupling increases progressively with reduction time because of enlarging NHSs, increasing NHS density


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and decreasing interparticle distances. Subsequent to acquisitions, we have analyzed the spectral trends of the deconvoluted peaks. Such trends help characterize the modes as dipolar versus higher multipolar, uncoupled versus coupled (hybrid) or bonding (attractive) versus antibonding (repulsive) and identify the nanostructure associated with a mode. The simplicity of the electrochemical reduction, such that it can be performed in an optical cell, allows for in-situ acquisition of the Ag NHS growth kinetics. However, one must be careful and take into account progressive oxidation/dissolution of the Ge film (reducing agent) during the synthesis. The change of the dielectric environment around the NHSs impacts the modes, which have strong coupling with the substrate. Nevertheless, the same also provides an advantage to distinguish modes with strong versus weak substrate coupling. Figures 6a-d show only the spectra acquired at 5, 30, 60 and 90 s, beyond which extinction is observed to saturate. As displayed in each frame (a-d), the spectra can be most optimally fit to 5 Gaussians. Figures 6e and 6f provide the energy and integrated intensity of the peaks, as a function of time. Referring to Fig. 1h and recollecting our mode assignments, we focus on the lowest energy 3 peaks in Fig. 6. These are the peaks in the visible range (brown, blue, magenta), which constitute the D = band. Figure 6 also reveals two Gaussians in the UV, which spectrally match with D ⊥1 and MP. Although, the excitation field is expected to be parallel under normal incidence, and not excite D ⊥1 , the beam employed by the UV-Vis spectrometer is not strictly collimated. Additionally, the retarded fields of the neighboring NPs acting on a NP have vertical components. Hence, D ⊥1 can be excited, at least weakly. Similarly, we observe excitation of D ⊥1 in Figs. 1e and 1f under s-polarized radiation and ppolarized radiation of normal incidence, respectively, too (i.e., the shoulder peak at 362 nm). In contrast, excitation of D ⊥2 , is not observable with such weak perpendicular fields. To provide


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additional insight, the extinction spectrum of the sample, corresponding to 60 s reduction (Fig. 6c), is acquired at incidence angle of 45°. This case is seen in Fig. 6g, where the spectrum is now resolved to 6 Gaussians with the additional peak emerging at the highest energy, whose frequency matches with that of D ⊥2 . In Fig. 6, we code the modes with the same colors as in Fig 1h. The highest energy parallel mode (magenta) is assigned to D = associated with weaklycoupled or uncoupled NHSs, D =isolated . This situation occurs for NHSs farther (isolated) from others or for oscillations along the transverse axis of a dimer, trimer or tetramer (i.e., linear chains), which are again weakly coupled. For transverse oscillations in a linear chain, the dipole charges in NPs are separated by more than the average diameter and the coupling inside the chain (i.e., H-conjugation) is weak. Hence, frequency of the transverse mode is close to that for an isolated single particle.34, 35 Strikingly, a significant blueshift is seen for D =isolated (magenta) as well as the other two lower energy peaks (blue and brown) during Ag reduction. The blueshift is attributed to decreased coupling with the underlying Ge film. The Ge film serves as the reducing agent and hence diminishes because of oxidation and dissolution in water during the Galvanic displacement. This finding underscores the significant degree of substrate coupling in NHSs and how it can be avoided with immobilization of the NHSs on the nanoposts (i.e., mushroom structures). As described in the SI, the fraction of unconsumed Ge can be computed through baseline correction of the extinction spectra and thereby the amount of Ag reduced can also be quantified as in Fig. 6h. The lower energy D= bands, that is, the blue and brown Gaussians, are attributed to strongly-coupled longitudinal oscillations in dimers and higher order linear chains (e.g., trimers, tetramers), D =dimer and D =chain , respectively. In these coupled modes, the


16

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symmetric charge oscillations of the NPs are subject to attraction across the narrow gaps that account for decreased restoring force constants. Therefore, the resonances redshift with respect to D =isolated . Accordingly, the lowest energy peak is assigned to highest degree of attractive coupling (plasmon hybridization/bonding). The remarkably larger width of this band (Fig. 6g) is owed to heterogenous broadening due to multiple structures contributing to it, such as trimers, tetramers, etc. as well as distribution of gap lengths. Formation of dimers, trimers, and chains is also reported for PVD-deposited Ag NPs.10 The SEM image of Fig. 1c confirms the abundance of linear chain structures such as trimers and tetramers, while linear chains of 5 or more NHSs are rare. Figure 6i is a simple illustration of all modes and their associated nanostructures. Consistently, as seen from Fig. 6e, the observed blueshift for the parallel dipolar modes (magenta, blue, brown) is the slowest for D =chain (brown). The continuous blueshift of the D =chain during the course of NP synthesis is because of decreasing substrate coupling led by

consumption of Ge. Simultaneously, however, the particle-particle coupling in this mode continuously increases which has the opposite effect to redshift the plasmon resonance. As a result, the particle-particle coupling lessens the rate of the net blueshift. On the other hand, the blueshift is faster for D =dimer (blue) and the fastest for D =isolated (magenta) due to lower and no particle-particle couplings, respectively. No blueshift is observed for the modes in the UV, verifying the computational results (Fig. 2h), that is, insignificant substrate and particle-particle coupling for these modes ( D ⊥1 and MP). The intensity kinetics in Fig. 6f are consistent with the assignments of D =isolated , D =dimer and D =chain . Assuming homogenous nucleation, the density of the NPs is expected to increase with time. Accordingly, beyond 15 s, D =isolated starts to fade, as NHSs come closer and the


17


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Page 18 of 30

number of isolated NHs decreases, while D =dimer continues to rise due to formation of new dimers. With increased density and size of NPs over time, the probability of formation of trimers and chains increases leading to higher excitation of D =chain . As observed from Fig. 6f, the kinetics of D =chain lag behind D =dimer (i.e., slower rise and later saturation) suggesting the highest degree of coordination associated with this band; that is, formation of trimers and tetramers take longer time than that of dimers. Linewidths and damping: Finally, we would like to elaborate on the linewidths of the D= and D⊥ resonances. From Fig. 1h, FWHM of D =isolated , D =dimer and D ⊥2 are 0.40, 0.51 and 0.14 eV,

respectively. The D ⊥2 linewidth is significantly narrower, which is explained by the lack of substrate coupling (i.e., plasmon damping associated with energy lost to the substrate). Additionally, the distribution of interparticle distances does not lead to any heterogeneous broadening in D ⊥2 owing to absence of particle-particle coupling. Indeed, simulation in vacuum removes the impact of substrate coupling and size/distance distribution, where the linewidths for the major D= mode and D ⊥2 are found as 0.12 and 0.14 eV, respectively, verifying the explanation above. On the other hand, when substrate is included in the simulations, the major parallel mode broadens to FWHM of 0.41 eV while the linewidth for D ⊥2 remains constant at 0.14 eV. Hence, the simulations underscore the role of substrate coupling in increased damping, where D= is dramatically impacted but D ⊥2 is not susceptible at all. Speaking of D ⊥2 , it is intriguing why the experimental linewidth, 0.14 eV, is narrower than that numerically computed for a single NHS in vacuum by Reference 22, 0.19 eV, using the dielectric data of Palik.36 In the analytical solution, Drude damping, that is nonradiative damping, is embedded through the imaginary component of the dielectric function, ε2 . ε2 is


18

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derived experimentally from bulk crystalline Ag and takes into account electron scattering with electrons, phonons and bulk defects but not the NP surface. Accordingly, one would expect a higher Drude damping in the experimental case due to added interface damping. Therefore, it is inferred that the anomalously lower damping of D ⊥2 must be due to a photonic effect in the form of reduced radiative damping or subradiance. In fact, Zhou and Odom, in their investigation of cylindrical Ag NP arrays deposited on glass substrates, discuss suppression of radiative damping for the perpendicular-to-substrate (“out of plane”) plasmon mode, being equivalent to our D ⊥2 .37 According to Zhou and Odom, because the k-vector of the radiation emitted by D ⊥ is on the substrate plane, the emitted energy can be collected by neighboring particles as plasmons instead of radiation lost to the far field. Thereby, the radiative damping is suppressed accounting for a narrower linewidth. Conclusions Plasmonic devices, consisting of NP monolayers, are conveniently fabricated by deposition techniques, wherein thermodynamics generally favor the particle shape to be close to hemispherical. As experimentally verified and computationally elucidated in the present work, NHSs exhibit remarkably different plasmonic characteristics compared with nanospheres. The broken symmetry by asymmetric particle shape leads to dipolar modes parallel and normal to the base, which are significantly different in terms of energy, excitation dependence on polarization and electromagnetic coupling. In particular, the parallel mode offers distinct advantages in plasmonics over nanospheres. While the perpendicular mode exhibits essentially no substrate/particle coupling, the strong substrate coupling of the parallel mode may benefit thin film photovoltaics by efficient light coupling. Second, higher field concentrations are induced at the sharp edges of a NHS that may enhance hot electron injection to the substrate in a


19


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Page 20 of 30

photocatalyst. These higher field concentrations at the edges also account for enhanced coupling with adjacent NHSs. Unlike in a spherical dimer, where the field intensity peaks in the middle of the gap, the maximum field in a NHS dimer gap occurs on the metal surface (i.e., at the edges), overlaying with the chemical enhancement. Hence, higher enhancement factor SERS is anticipated with coupled NHSs. We monitor NP reduction in real time and infer the excited parallel modes are strongly coupled. The extinction associated with these coupled modes is resolved to two resonance bands, which we attribute to dimers and higher order chains (e.g., trimers, tetramers). The polarization dependence of the modes has interesting consequences. For example, if a NHS monolayer is employed as a SERS substrate, the coupled parallel mode(s) will be instrumental as explained above. Excitation and scattering of these modes dominantly involve parallel polarization, where a low numerical aperture lens will be more efficient than a high numerical aperture one. Similarly, the excitation dependence on incident angle should be taken into account in other plasmonic applications, employing NHSs.

ASSOCIATED CONTENT Supporting Information Deposition of Ge films. Synthesis of Ag nanoparticles. Particle size and separation determination by SEM and AFM. Details of in-situ extinction measurements. Ag nanohemispheres synthesized by PVD. Description of the mode, MP, by three videos, showing phase-series field maps of the XZ and YZ axial cross sections as well as XY base plane. This material is available free of charge via the Internet at http://pubs.acs.org.


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AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]

Author Contributions COT performed the synthesis and acquisitions. HMJ and AA performed and analyzed the numerical solutions. SK acquired and analyzed the images (SEM/AFM) of the nanostructures. AKK and COT designed the experiments and analyzed the results. JFO contributed with discussions. AKK wrote the manuscript.

ACKNOWLEDGMENT AKK and COT acknowledge the funding by National Science Foundation, Award Number 1512157.

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TOC Graphic


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FIGURE 1

a

b Ag Ge Glass Substrate nm

e 1.0

s-polarized

0⁰ 15⁰ 30⁰ 45⁰ 60⁰ 75⁰

0.8 0.6 0.4

f

0.8 p-polarized

Extinction

d

c

0.6 0.4

0⁰ 15⁰ 30⁰ 45⁰ 60⁰ 75⁰

0.2

0.2

0.0 300 400 500 600 700 Wavelength (nm)

0.0 300 400 500 600 700 Wavelength (nm)

g

p

Nanoparticle

k

s

Ө

Substrate

h 0.5 Extinction

Extinction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58


0.4 0.3

335 nm 344 nm 362 nm 409 nm 482 nm 550 nm

Figure 1: Illustration of Ag NHSs on Ge nanoposts (a). AFM image showing the Ge nanoposts after Ag removal (b). Plan (c) and oblique (d, 45°) SEM images of the Ag NPs reduced on 4.5 nm thick Ge film. The scale bars are 500 nm. Extinction spectra of Ag NHSs reduced on Ge thin films at varying angle of incidence for s- and p-polarization (e) and (f), respectively. Definitions of incidence angle and s- and p-polarizations (g). Deconvoluted peaks of the extinction spectrum for p-polarized incidence at 60° (h).

p-polarized θ=60 °

0.2 0.1

z

0.0

x

1.5 2.0 2.5 3.0 3.5 4.0 Photon Energy (eV)



Extinction

a 1.0

Ag/Ge(FF=0.05)/glass s-polarized

0.8 0.6 0.4

0⁰ 15⁰ 30⁰ 45⁰ 60⁰ 75⁰

b

0.8 Ag/Ge(FF=0.05)/glass

Extinction

FIGURE 2

0.6

0.0 300 375 450 525 600 675 Wavelength (nm) Ag/vacuum, s-polarized 0⁰ 15⁰ 30⁰ 45⁰ 60⁰ 75⁰

Extinction

1.6 1.2 0.8

d 1.4

0.4 0.0 300 375 450 525 600 675 Wavelength (nm)

0.6 0.4

Extinction

330 nm 348 nm 367 nm 382 nm 431 nm 447 nm 467 nm

0.8 0.6 0.4

0⁰ 15⁰ 30⁰ 45⁰ 60⁰ 75⁰

675

Ag/vacuum p-polarized θ=60°

0.01 0.025 0.05 0.1 0.2 0.35 0.51

p-polarized θ=0°

0.0

1.5 2.0 2.5 3.0 3.5 4.0 Photon Energy (eV) FF Ag/Ge/glass

h 0.8 p-polarized 0.6 θ=75° 0.4

0.01 0.025 0.05 0.1 0.2 0.35 0.51

0.2

0.2

0.0 300 375 450 525 600 675 Wavelength (nm) s Ag/Ge(FF=0.05)/glass 1.0 2 nm

0.0 300 375 450 525 600 675 Wavelength (nm) 0.8 Ag/Ge(FF=0.05)/glass s

0.8 0.6 0.4

4 nm 8 nm 16 nm 32 nm 64 nm

p-polarized θ=0°

j

0.6

p-polarized θ=75°

0.4

2 nm 4 nm 8 nm 16 nm 32 nm 64 nm

0.2

0.2 0.0 300

Figure 2: Simulated extinction spectra of Ag NHSs. The incidence angle, polarization state and substrate information (Ge filling factor (FF) or vacuum) are given in each plot. Deconvoluted peaks in (e) and (f) are Lorentzian. Unless indicated, interparticle spacing, s, is 8 nm.

0.2

1.5 2.0 2.5 3.0 3.5 4.0 Photon Energy (eV) FF 1.0 Ag/Ge/glass 0.8

Ag/vacuum, p-polarized

1.2 1.0 0.8 0.6 0.4 0.2 0.0 300 375 450 525 600 Wavelength (nm)

f 1.0

Extinction

Extinction

i

0.5 0.4 0.3 0.2 0.1 0.0

Ag/Ge(FF=0.05)/glass p-polarized θ=60°

331 nm 343 nm 373 nm 425 nm 482 nm 519 nm

Extinction

Extinction

e 0.6

g

0.4

0⁰ 15⁰ 30⁰ 45⁰ 60⁰ 75⁰

0.0 300 375 450 525 600 675 Wavelength (nm)

Extinction

c 2.0

p-polarized

0.2

0.2

Extinction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

Page 26 of 30

400 500 600 700 Wavelength (nm)

0.0 300

400 500 600 700 Wavelength (nm)


Page 27 of 30

FIGURE 3

d

a

D= no substrate 447 nm

D= on Ge/glass 482 nm

e

b

Figure 3: Electric field maps (x-z cross section) characterizing 4 different plasmon modes in Ag NHSs on Ge (filling factor = 0.05) on glass (a-c) and no substrate (d-f), D=, DꞱ1, and DꞱ2, respectively from top to bottom. The incident radiation is p-polarized and at 75°, except in a and d, which are at 0°. Interparticle spacing for all cases is 8 nm.

DꞱ1 no substrate 367 nm

DꞱ1 on Ge/glass 373 nm

f

c

DꞱ2 on Ge/glass 331 nm

DꞱ2 no substrate 330 nm 6.25e6 0

4.38e7

3.13e7 1.88e7

x

5.63e7

V/m

z 1.00e8 9.38e7 8.13e7 6.88e7

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58




1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

Page 28 of 30

FIGURE 4

0°

0°

30°

30°

60°

60°

90°

90°

120°

120°

150°

150°

Figure 4: Description of the MP mode with phase-series field maps of XZ axial cross section (left column) and XY base plane (right column). The phase-series maps are shown in intervals of 30° from 0° to 150° which are antisymmetric with those from 180° to 330°, respectively.


Page 29 of 30

FIGURE 5

a

b

V/m 8.00e8 7.38e8 6.38e8 5.38e8

4.38e8 3.38e8 2.38e8 1.38e8

0

1.73e8

y

8.09e8 7.18e8 6.27e8 5.36e8 4.45e8 3.55e8 2.64e8

V/m 9.00e8

0

x

s = 8 nm θ = 75° 373 nm

c

z

s = 2 nm θ = 0° 565 nm

x

d

V/m 8.00e8 7.38e8

V/m 8.00e8 7.38e8

6.38e8

6.38e8

5.38e8

5.38e8

4.38e8

4.38e8

3.38e8

3.38e8

2.38e8

2.38e8

1.38e8

1.38e8

0

0

z

s = 8 nm θ = 0° 485 nm

z

s = 64 nm θ = 0° 450 nm

x

e

x

f

V/m 8.00e8 7.38e8

V/m 8.00e8 7.38e8

6.38e8

6.38e8

5.38e8

5.38e8

4.38e8

4.38e8

3.38e8

g

3.38e8

2.38e8

2.38e8

1.38e8

1.38e8

0

0

z

s = 2 nm θ = 75° 331 nm

h

V/m

Figure 5: Simulated field amplitude maps for Ag NHS arrays on Ge on glass (FF = 0.05). The incident radiation is ppolarized. The interparticle distance (s), incidence angle (θ), and excitation wavelength are provided in each figure. a) xy-plane intersecting the base of two NHSs during resonant excitation of DꞱ1. A ring-like distribution of the pole charge at the hemisphere base is inferred. b-f) xzplanes, cross-sectioning Ag NHSs at the center for various interparticle spacings. Resonant excitation of D= (b-d) and DꞱ2 (e,f). g,h) xy-planes intersecting the bases of two NHSs during resonant excitation of D= for two different interparticle separations. Corresponding field enhancement factor profiles along the dimer as well as dipole axis (x-axis) are given.

x

V/m

8.00e9 7.19e9 6.38e9 5.58e9 4.77e9 3.96e9 3.15e9 2.34e9 1.54e9

4.49e9 3.99e9 3.48e9 2.98e9 2.47e9 1.97e9 1.46e9 9.60e8

y

z

s = 8 nm θ = 75° 331 nm

x

5.00e9

y

0

s = 8 nm θ = 0° 485 nm -60 -40 -20

E/Eo

100 80 60 40 20 0

0

x

x

E/Eo

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58


0

x(nm)

20

40

60

240 200 160 120 80 40 0

s = 4 nm θ = 0° 521 nm -60 -40 -20

0

20

40

60

x(nm)



FIGURE 6

b 0.5

Experiment Fit

0.2

Extinction

Extinction

a 0.1

0.4 0.3 0.2 0.1

0.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Photon Energy (eV)

0.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Photon Energy (eV)

d 0.8 Extinction

f

2.8 2.4 2.0

0.5

1.6 30

0.2 0.1

60 90 120 150 Time (s)

0

30

60 90 120 150 Time (s)

30

60 90 120 150 Time (s)

h 100

0.5 0.4 0.3 0.2 0.1 0.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Photon Energy (eV) D 2

+

D dim er − +

−

60 40 20 0

−−

Figure 6: a-d) In-situ extinction spectra of Ag NHSs in 2 mM AgNO3 solution during synthesis. Only the spectra acquired at 5, 30, 60, 90 s of immersion are shown, respectively. The spectra are fit to 5 Gaussians. e,f) Time evolution of peak energy and integrated intensity, respectively, at 5 s intervals. g) Extinction spectrum of 60 s immersion sample acquired at θ = 45°. In (a-g) same color coding is used to trace the peaks. h) (1 − 𝐾 𝑡 )/(1 − 𝐾𝑠 ) as described in the text. i) Illustration of mode configurations and associated nanostructures. The mode assignments to the peaks are made with the color coding used in (a-g). The arrows indicate the orientation of the dipole moments, associated with the modes.

80

0

D isolated +

D 1

MP

−− ++

+

0.3

0.0 0

g 0.6

i

0.4

Ag Reduction (%)

1.2

0.4

0.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Photon Energy (eV)

e 3.6 3.2

0.6

0.2

Intensity (eV)

0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0 1.0 1.5 2.0 2.5 3.0 3.5 4.0 Photon Energy (eV)

Peak Energy (eV)

Extinction

c

Extinction

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

Page 30 of 30

+

+

−

−

+ −

D chain +

− +

− +

−

+

− +

− +

− +

−


Plasmon Resonances in Nanohemisphere Monolayers

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