Nanoplasmonics: Classical down to the Nanometer Scale - Nano

Letter pubs.acs.org/NanoLett

Nanoplasmonics: Classical down to the Nanometer Scale Huigao Duan,†,§ Antonio I. Fernández-Domínguez,‡,§ Michel Bosman,†,§ Stefan A. Maier,*,‡ and Joel K. W. Yang*,† †

Institute of Materials Research and Engineering, A*STAR (Agency for Science, Technology and Research), 3 Research Link, Singapore 117602 ‡ Department of Physics, Imperial College London, London SW7 2AZ, United Kingdom S Supporting Information *

ABSTRACT: We push the fabrication limit of gold nanostructures to the exciting sub-nanometer regime, in which light−matter interactions have been anticipated to be strongly affected by the quantum nature of electrons in metals. Doing so allows us to (1) evaluate the validity of classical electrodynamics to describe plasmonic effects at this length scale and (2) witness the gradual (instead of sudden) evolution of plasmon modes when two gold nanoprisms are brought into contact. Using electron energy-loss spectroscopy and transmission electron microscope imaging, we investigated nanoprisms separated by gaps of only 0.5 nm and connected by conductive bridges as narrow as 3 nm. Good agreement of our experimental results with electromagnetic calculations and LC circuit models evidence the gradual evolution of the plasmonic resonances toward the quantum coupling regime. We demonstrate that down to the nanometer length scales investigated classical electrodynamics still holds, and a full quantum description of electrodynamics phenomena in such systems might be required only when smaller gaps of a few angstroms are considered. Our results show also the gradual onset of the charge-transfer plasmon mode and the evolution of the dipolar bright mode into a 3λ/2 mode as one literally bridges the gap between two gold nanoprisms. KEYWORDS: Plasmon coupling, charge transfer, quantum limit, EELS, LC circuit model

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defining smaller gaps and bridges, we instead observe evidence for the gradual evolution of the modes across this transition. The good agreement between experimental results, full electrodynamics simulations, and LC circuit models extends the validity of the classical description of plasmon resonances to the sub-1 nm regime and supports the theoretical prediction that quantum phenomena come into play only when gaps of several angstroms are considered.12 The ability to simultaneously measure the full-modal spectra and map the plasmon field distributions in user-defined structures with nanometer resolution has recently been achieved.17 Here, we fully utilize this capability by carefully performing systematic studies of plasmon coupling in metal nanostructures. We used a recently developed high-resolution electron-beam lithography process18 to pattern arrays of nanoprism pairs in the bowtie antenna configuration onto transmission electron microscope (TEM) membranes (see Methods in Supporting Information). In this top-down approach, we fabricated nanoprism pairs of uniform sizes with systematically decreasing gap/bridge widths down to nanometer dimensions. To avoid spectral broadening (due to

lasmon coupling in noble metal nanostructures separated by nanoscale gaps has the remarkable ability to funnel photon energy into deep subwavelength dimensions, resulting in an enhancement of electromagnetic fields by orders of magnitude.1 While this strong field enhancement in nanogaps is promising for surface-enhanced Raman scattering (SERS),2,3 nonlinear optics,4 fluorescence amplication,5 single-molecule sensing,6 and plasmonic nanorulers,7 more applications will be attained when one reduces the size of the nanogaps to the nanometer length scale. Importantly, as we approach the limit of the classical and enter the quantum regime, phenomena such as optical rectification8 and electrical excitation of plasmons9,10 would occur, which could further facilitate the future integration of plasmonics with electronics.11 One hallmark of the quantum regime is electron tunneling across a sub-nanometer gap that gives rise to a dipolar chargetransfer plasmon mode.12 Though theoretical predictions have been made for this mode, systematic experimental trends for the evolution of modes right up to the onset of this quantum regime have yet to be reported. Here we show experimental and simulation results from a systematic study of plasmon resonances between pairs of nanoprisms separated by gaps as small as 0.5 nm and connected by conductive bridges of only 3 nm width. Unlike previous reports of abrupt shifts in plasmon modes as soon as nanostructures come into contact,13−16 by © 2012 American Chemical Society

Received: January 12, 2012 Revised: January 31, 2012 Published: February 7, 2012 1683

dx.doi.org/10.1021/nl3001309 | Nano Lett. 2012, 12, 1683−1689

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Figure 1. Geometry and plasmon resonances for single nanoprisms. (a) Schematics of the gold nanostructures investigated in this work: (i) Experimental configuration for measuring plasmon resonances using EELS: a focused electron beam excites plasmon resonances in gold nanostructures supported by a 30 nm thick SiNx membrane. (ii−iv) Top view of a single nanoprism as well as disconnected and connected nanoprisms. (b) Plasmon resonances of a single nanoprism with edge length ∼80 nm. (i) Experimental, background-subtracted, EELS spectra obtained from a single nanoprism with corner and edge excitations. (inset) HAADF STEM image of the nanoprism. (ii and iii) Simulated charge density (top), experimental EELS maps (medium), and simulated electric field distributions (bottom) for plasmon modes II and III, respectively.

Figure 2. Plasmon coupling of two nanoprisms with sub-5 nm gap (a, b) and bridge (c, d). (a) Experimental EELS spectra of two nanoprisms separated by a 3 nm gap. (b) Simulated charge distributions (top row), experimental EELS maps (middle row), and simulated electric-field distributions (bottom row) for various plasmon-resonance modes indicated in (a). (c) Experimental EELS spectra of connected nanoprisms with a 4 nm wide bridge. (d) Simulated charge distribution (top row), experimental EELS maps (middle row), and simulated electric-field distributions (bottom row) of the various plasmon-resonance modes indicated in (c).

ensemble averaging of spectra from multiple structures), we characterized individual pairs of nanoprisms in a scanning TEM (STEM) equipped with monochromated electron energy-loss spectroscopy (EELS). Details of the characterization can be found in the Methods section in Supporting Information. As a plasmon characterization technique, EELS has had a long history,19,20 and gradual improvements in instrumentation have

developed this near-field spectroscopy technique to the method of choice for observing plasmon resonances at the highest spatial resolution.21−23 The unique and crucial features of our EELS method used here are (1) the low-energy capability for characterizing plasmons down to 0.5 eV in energy, (2) high signal-to-noise ratios that enabled accurate determination of the resonant energies from the spectra,24 and (3) absolute plasmon 1684


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the quadrupolar mode at 2.14 eV, which does not appear to be significantly affected by plasmon coupling. Finally, peak iv, obtained for excitation at the edge, corresponds to the same dipolar dark mode as peak ii. Indeed, this coherent superposition of bright (i) and dark (iv) dipolar modes upon excitation at the edge of the dimer, and the sole appearance of the dipolar dark mode (ii) upon excitation in the center of the gap, is in agreement with previous observations for colloidal dimers.33 The plasmon modes for each spectral peak can be best identified by their characteristic simulated charge-density plots, shown in the top row of Figure 2b. Experimental plasmon maps are shown in the center row (also see Movie S2 in Supporting Information), above the numerical-simulation plots of their electric field−amplitude distributions. The large spectral separation between the bright (i) and dark (ii) modes results also in distinct plasmon maps. In particular, the bright mode yields stronger EELS signal at the outer nanoprism edges than at the gap region, and vice versa for the dark mode. The intensity of the EELS signal is dependent on the strength of the electric field component parallel to the trajectory of the excitation electron, i.e., Ez.34,35 Hence, it follows that the bright mode, which has strong in-plane fields Ex across the gap but weak Ez, yields a lower EELS signal than the dark mode, whose Ez components are stronger at the structure gap. Note that the EELS maps are not exactly the same as the simulated plots of their corresponding electric-field distributions. An EELS map is obtained by raster scanning the electron beam across the entire sample and plotting the number of electrons that lose its energy at the resonance energy, while a simulated plot shows the electric field distribution for this plasmon resonance as excited by an electron beam positioned at a single position. Figure 2c shows the experimental EELS spectra measured from connected nanoprisms with a 4 nm wide bridge (STEM image inset). Peaks ii and iii remain at the same spectral positions as in near-touching nanoprisms. However, peak i is now red-shifted by ∼0.84 to 0.5 eV, demonstrating the sudden appearance of a mode that supports the sloshing of charges from one prism to the other, i.e., the charge-transfer plasmon.13,14 For connected structures, we will now adopt the usual classification of longitudinal modes from antenna theory, where the charge-transfer plasmon would correspond to a λ/2 resonance. Further simulations and EELS measurements shown in Figure 2d indicate that the (dark) λ resonance (ii) and coupled quadrupolar (iii) plasmon modes in connected prisms have similar charge distributions, EELS maps, and electric field distributions as those for near-touching prisms. However, the low-energy λ/2 resonance Figure 2d(i) has a distinct charge and electric-field profile from the dipolar bright mode in Figure 2b(i). As charges are free to move between nanoprisms via the 4 nm wide conductive bridge, the λ/2 resonance in connected prisms corresponds to a single electric dipole, instead of two aligned dipoles in the case of disconnected geometries. The resulting resonant modes observed as a sweep in plasmon energy are also different, as can be seen by comparing Movie S2 (disconnected prisms) and Movie S3 (connected prisms). Finally, peak iv has an energy of 1.66 eV, which is very close to the dipolar dark mode of peak ii at 1.67 eV but is of a different origin as we explain below. To shed more light into the behavior of these modes, and also to investigate the mixing components leading to peak iv in the EELS spectra, we now turn to a systematic study of mode evolution with changes in geometry.

peak amplitudes, allowing a mutual comparison of peak heights and accurate observation of gradually increasing plasmon amplitudes for a series of geometries. Figure 1a illustrates the gold structures studied in this work. Schematics of the EELS measurement are shown in Figure 1a(i). The configurations of structures include a single nanoprism (ii) and nanoprism pairs separated by a small gap of size d (iii) or connected by a conductive bridge of width w (iv). We choose this prism geometry as it is widely used as “bowtie antennas” that focus photon energy into deep subwavelength volumes in a variety of applications.4,5,25−27 Furthermore, the sharp corners of these structures can support strong localized fields due to the “lightning-rod” effect. In our experiments, we studied the plasmon resonances in nanoprisms with systematically varied gap sizes (d) and bridge widths (w) for two sets of nanoprisms of length (l) of 80 and 40 nm. Experimental EELS spectra from a single nanoprism with 80 nm edge length are plotted in Figure 1b(i). A high-angle annular dark field (HAADF) STEM image of the corresponding sample is shown in the inset. The distinct spectra shown in blue and red lines are obtained by having the electron beam positioned at either the edge and or the corner of the prism, as indicated in the STEM image. Excitation at the sharp corner (red dot) gives rise to only one dominant resonance at 1.62 eV (peak I), which corresponds to the dipolar bright mode of the structure. Conversely, excitation at the edge (blue dot) leads to two resonance peaks, i.e., dipolar bright mode at 1.62 eV (I) and quadrupolar dark mode at 2.14 eV (II). Simulated charge density, experimental EELS maps, and simulated electric field distributions for these modes are shown in Figures 1b(ii) and 1b(iii), respectively (more details in Methods, Figure S1, and Movie S1 in Supporting Information). The differences in resonant energies between experimental and simulation might be caused by the use of perfect prism geometries and optical parameters of bulk gold in the simulations, which did not account for the imperfect geometries and surface scattering of electrons in the experimental nanoprisms. It has been reported that the details of the nanostructures (e.g., sharp corners and surface roughness) play an important role in plasmonic properties.28−30 However, the plasmon resonances of these lithographically defined nanoprisms are comparable to those reported previously for chemically synthesized single-crystalline silver nanoprisms.21 For example, the quality factor Q estimated for the dipolar bright mode (peak I) is comparably high at ∼8 (Q = E/ΔE, where E is the resonance energy at 1.62 eV and ΔE is the line width of ∼0.2 eV). Furthermore, the EELS map on this mode shows well-defined hot spots. Hence, the resultant structures (though polycrystalline) demonstrate strong resonances and are suitable for the purpose of our systematic studies, which benefit greatly from the lithographic control of lateral dimensions at sub-10 nm dimensions.17 The plasmon modes of closely spaced and touching nanoprisms are presented in Figure 2. Figure 2a shows an example of EELS spectra for nanoprisms separated by a 3 nm gap. The size of the nanoprisms is nominally the same as that in Figure 1b. But here, the effect of plasmon coupling31,32 can be clearly observed in peaks i and ii now having different energies compared to the degenerate peaks I and II in Figure 1b(i). Thus, peak i at 1.34 eV corresponds to the dipolar bright mode, while peak ii at 1.67 eV corresponds to the dipolar dark mode of the system. Note that for a tiny gap of only 3 nm strong plasmon coupling32 occurs that results in a substantial (∼0.33 eV) energy split between these modes. Peak iii originates from 1685


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Figure 3. Systematic EELS study of plasmon modes excited by an electron beam positioned at the center of the pair structures and at the corner of the single prism. (a) Representative HAADF STEM images of the experimental samples with different junction geometries used for the measurements. (b) Enlarged images of the particles with 0.5 nm gap and 3 nm bridge. (c) Experimental EELS spectra of the dark modes of structures with different gap and bridge sizes. (d) Simulated spectra of the dark modes for different gap sizes and bridge widths. The gap sizes and bridge widths are measured from the HAADF STEM images of the structures.

We start our systematic studies by looking at the dipolar dark modes of a dozen different structures with systematically varied gap/bridge dimensions. The constant spectral position of this mode then demonstrates the reproducibility of the resonant response across multiple nominally identical prisms. Figure 3 plots the EELS and simulated spectra for the dipolar dark mode (cf. Figure 2, peak ii) due to excitations at the center of the structures. Figure 3a shows representative HAADF STEM images of the experimental structures used for the measurements, and Figure 3b shows enlarged images for the particles with 0.5 nm gap and 3 nm bridge. The complete STEM images of all nanoprism samples can be found in Figure S2 of the Supporting Information. The experimental EELS spectra in Figure 3c were obtained from structures with different gap sizes (d) and bridge widths (w, indicated as negative values). The resonant peaks in the nanoprism pairs are nearly identical and slightly blue-shifted (∼0.05 eV) relative to the isolated prism. The energies of these plasmon resonances range from 1.64 to 1.68 eV, with no observable trend. Numerical simulations shown in Figure 3d corroborate that the spectral position of the dark dipolar modes indeed remains almost constant when the junction geometries are changed, with a mere ∼0.05 eV blue shift as the gap size decreases and negligible shift as the bridge width varies. The small ∼2% deviation of the resonance energy demonstrates both the excellent lithographic control on structure geometry and reliability of the EELS measurements.

Figure 4 presents the spectra obtained from excitation at the outer edges of the nanoprisms. The experimental EELS spectra are shown in Figure 4a for structures with junction sizes as indicated for each spectrum using the same notation as in Figure 3. The various plasmon modes are labeled from set 1 to 5 as detailed below. The results from numerical simulations are displayed in Figure 4b showing agreement with experiment. This agreement in the systematic trends demonstrates that classical electromagnetic calculations are capable of capturing the essential physics of the system even down to 0.5 nm gaps and 3 nm bridges. The fact that we did not observe the charge transfer mode even for our nanoprism pair with 0.5 nm gap supports previous prediction that full quantum calculations would necessarily be required only when gaps of several angstroms are considered.12 Our calculations reproduce not only qualitatively, but also quantitatively, the dependence of the energy position of the various plasmon modes on the nanostructure geometry without fitting parameters. As the gap is decreased, we observe the red-shifting of the dipolar bright mode (set 1) and the nearly constant-energy dipolar dark (set 2) and quadrupolar modes (set 5). The spectral position of peaks in set 1 varies from 1.62 to 1.25 eV, for nanostructures ranging from single to closely spaced nanoprisms with a gap of ∼0.5 nm, translating to a wavelength tunability of ∼230 nm. Upon the formation of a conductive bridge, we observe the appearance of the dipolar charge-transfer mode (set 3) 1686


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Figure 4. Systematic EELS study of plasmon modes excited by an electron beam incident at the structure edge. (a) Experimental EELS spectra of plasmonic modes of nanoprism pairs with different gap and bridge sizes. (b) Simulated EELS spectra of plasmon modes of the experimentally measured structures in (a), confirming the systematic shifting trends of the plasmon modes. The minus sign in bridge widths was intentionally used here for the convenience of plotting the data in the following coordinate graph. The columns shown at the right side of (a) and (b) are magnified spectra covered by the light blue strips. (c) Simulations to distinguish plasmon modes with symmetric vs asymmetric charge density distributions using two simultaneous electron beams. Spectrum from a single-beam excitation is composed of spectra from the symmetric and antisymmetric excitations. The width and height of the bridge used for this simulation were 3 and 5 nm, respectively.

corresponding to a λ/2 resonance over the connected structure. The increasing height of this peak going from the narrowest 3 nm bridge to 5 nm bridge suggests the gradual appearance of this mode. This gradual appearance of the charge-transfer mode that is only observable for bridge widths of less than 5 nm is again reproduced in the systematic study for 40 nm nanoprisms as shown in Figure S3c (Supporting Information). To the best of our knowledge, this is the first systematic study of the optically accessible (bright) plasmon mode for conductive bridges down to sub-5 nm widths. As the bridge width increases from 3 to 17 nm, the energy of this mode increases from 0.48 to 0.79 eV, translating to a wavelength tunability of ∼1000 nm. This blue shift can be interpreted as a reduction of kinetic inductance of the bridge, as captured in the LC circuit model discussed later. Careful analysis reveals that set 4 consists of resonant peaks from two distinct plasmon modes. Two features of this set differentiate it from being solely the dipolar dark mode of set 2. For one, its spectral position is very close to set 2, but unlike set 2, which does not show any systematic shift, set 4 blue-shifts with increasing bridge width (see top right panel in Figure 4a). Second, while set 2 has a weak EELS peak, set 4 begins with a much stronger peak for the narrowest bridge that weakens as the bridge widens. To identify the distinct plasmon modes in set 4, we simulated the idealized cases of two in-phase electron beams incident simultaneously at opposite edges of the nanostructure, as shown in the schematics in Figure 4c. This unique approach

allows plasmon modes with symmetric and antisymmetric charge distributions to be distinguished, as shown in Figure 4c(i−iv). The resulting spectra and charge distributions in Figure 4c reveal that set 4 is a combination of λ (i) and 3λ/2 (ii) resonant modes. Furthermore, the similarity of the charge distributions of the bright dipolar mode and the 3λ/2 mode (cf. Figure 2b(i) and Figure 4c(ii)) suggests the gradual transition from one mode to the other at the point of electrical contact between the prisms. Finally, the simulations show also that set 5, which arises from the hybridization of the quadrupolar modes, also consists of two resonant modes as shown by peaks iii and iv and their associated charge densities in Figure 4c. To develop a physical intuition for the multiple phenomena observed above, we used LC circuit models,36,37 as shown in Figure 5a,b. We then compared the predictions from the circuit models to the resonance energies of sets 1 to 4 as a function of the gap and bridge sizes in Figure 5c. We modeled each nanoprism as a simple LC tank oscillator circuit, the gap between nanoprisms as a capacitor, and the bridge as another tank oscillator (see details in the Supporting Information). We used the mathematical forms obtained from the LC model and fitted them to the data in Figure 5c. For simplicity, the capacitance of the gap was set to be inversely proportional to the gap size, and the inductance of the bridge as dominated by the kinetic inductance of the conductor was inversely proportional to the bridge width. 1687


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the bridge and the electrostatic energy of the accumulated charge at the nanoprisms. Intuitively, as the bridge widens, a larger number of electrons participate in electrical conduction of the bridge, hence storing more kinetic energy to result accordingly in the observed blue-shift, as shown in the fit in Figure 5a. Therefore, all essential features of our observations can be explained via this intuitive model. In conclusion, in this work we shed light on the evolution of plasmon modes at the transition regime from a disappearing gap to a conductive bridge between two metal nanoprisms. Using high-resolution electron-beam lithography, we demonstrate the fabrication of nanoprisms with varying gap and bridge widths. By systematic reduction of the gap to 0.5 nm size and narrowing the bridge to 3 nm width, we observe for the first time the gradual appearance of the charge-transfer plasmon mode and identify higher-order antenna modes. Furthermore, the good agreement between experiment and simulation demonstrates the validity of classical electromagnetism even at the single nanometer length scales. We expect that further reduction in the gap size and optimization of the plasmonic structures by improving the crystallinity and avoiding the Cr adhesion layer could lead to the appearance of the quantum regime of plasmon resonances, in which the charge-transfer plasmon and the gapped dipolar bright modes may be seen to be simultaneously supported on the same structure. The understanding gained in this work will be useful in the development of future plasmonic devices that operate in this quantum regime.

Figure 5. Quantitative analysis of the plasmon modes. (a) Schematic of a coupled-capacitor model to explain the plasmon coupling in two nanoprisms with a gap size of d. (b) Schematics of a coupled-inductor/ capacitor model to explain the plasmon resonance in two connected nanoprisms with a bridge of w. (c) Plots showing the systematic shifting trend of different plasmon modes as a function of the gap size and bridge width. The data points were extracted from the EELS spectra in Figure 4. The solid lines are the fitting curves with coupledcapacitor (for gapped structures) and coupled-inductor/capacitor models.

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ASSOCIATED CONTENT

S Supporting Information *

Methods (fabrication, characterization, and simulation), Figures S1−S3, and Movies S1−S3. This material is available free of charge via the Internet at http://pubs.acs.org.

Solving for the resonant conditions for these circuits, the trends in both set 1 (gapped bright dipolar mode) and set 4 (3λ/2 mode) are achieved by impedance-matching the gap/ bridge circuit to that of the nanoprisms, as shown by the fits in Figure 5a. At this resonance, the resulting potential drop across the gap/bridge is twice in magnitude but opposite in sign to those across the nanoprisms, in agreement with both the large fields in the gap/bridge region and the corresponding charge distributions for these modes. In the case of the dipolar dark mode (set 2), like charges from each nanoprism move toward the gap/bridge. Hence, similar to how charging two parallel capacitor plates with like charges results in 0 V across the capacitor, no electric potential is sustained across the gap/bridge. This condition is met in the circuit model as a resonance condition of the tank oscillators of the nanoprisms, operating 180° out of phase with each other. As the nanoprism oscillators are independent of the gap/bridge sizes, the circuit model predicts a constant resonant energy of the form E2 = ℏω0 = ℏ/(L0C0)1/2, as shown by the horizontal lines in Figure 5c, which generally agrees with the experimental results. In reality, L0 and C0 do vary slightly due to charge and field redistributions as the gap/bridge sizes change. These details are captured by the full electromagnetic simulations that indicate a slight slight blue-shift in the dark mode with decreasing gap size that tracks the experimental results, as shown in Figure 5a. Finally, the charge-transfer plasmon (set 3) can be understood in the LC circuit model as the resonance condition for the tank oscillator that models the bridge. Here the energy oscillates between the kinetic energy of the electrons flowing in

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (J.K.W.Y.); s.maier@ imperial.ac.uk (S.A.M.). Author Contributions §

These authors contributed equally to this work.

Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Agency of Science, Technology and Research (A*STAR) in Singapore and the Leverhulme Trust and the Engineering and Physical Sciences Research Council (EPSRC) in the UK. Patterning was done at SNFC’s shared Elionix ELS-7000 SEBL system in A*STAR. We thank Jie Deng and Hong Liu for technical assistance, Paul Thomas (Gatan UK), Timothy Petersen (Monash, Melbourne), and Markus Heidelmann (Jülich and RWTH Aachen) for EELS data processing scripts and finally Javier Aizpurua (CSIC) and Karl K. Berggren (MIT) for valuable discussions. H.D., M.B., and J.K.W.Y. designed the experiments. H.D. fabricated the samples. M.B. performed the EELS characterization. A.I.F.-D. and S.A.M. did the numerical simulations and developed the LC circuit model. All authors analyzed the data and wrote the manuscript. 1688


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(34) García de Abajo, F. J.; Kociak, M. Phys. Rev. Lett. 2008, 100, 106804. (35) Hohenester, U.; Ditlbacher, H.; Krenn, J. R. Phys. Rev. Lett. 2009, 103, 106801. (36) Engheta, N.; Salandrino, A.; Alù, A. Phys. Rev. Lett. 2005, 95, 095504. (37) Engheta, N. Science 2007, 317, 1698−1702.

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Nanoplasmonics: Classical down to the Nanometer Scale - Nano

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