Coupled Plasmon Modes in an Ordered ... - APS Link Manager

VOLUME 84, NUMBER 25

PHYSICAL REVIEW LETTERS

19 JUNE 2000

Coupled Plasmon Modes in an Ordered Hexagonal Monolayer of Metal Nanoparticles: A Direct Observation Fabien Silly,1 Alexander O. Gusev,1 Abdelhafed Taleb,2 Fabrice Charra,1 and Marie-Paule Pileni2 1

CEA-Saclay, Service de Recherche sur les Surfaces et l’Irradiation de la Matière, F-91191 Gif-sur-Yvette Cedex, France 2 Laboratoire SRSI, URA CNRS 1662, Université Pierre et Marie Curie, BP 52, 4 place Jussieu, 75005 Paris, France and CEA-Saclay, Service de Chimie Moléculaire, F-91191 Gif-sur-Yvette Cedex, France (Received 2 February 2000) We report on the experimental observation of STM-induced photon emission in ultrahigh vacuum on a network of 4-nm silver spheres. The spheres are covered by a dielectric, electrically insulating, organic layer and deposited on Au(111). The bias-dependent spatial distribution of the photon emission rates reveals the electric-field distribution of the different coupled plasmon modes in this model. PACS numbers: 73.50.Gr, 73.40.Gk, 78.66.Vs

Nanoscaled systems consisting in self-assembled molecule, metal, or semiconductor quantum dot arrays are promising candidates for future electronic or photonic applications. Enhancements by several orders of magnitude of photophysical processes, like surface-enhanced raman scattering (SERS) [1], light emission from metal-oxidemetal tunnel junctions [2], or inelastic fast-electron scattering [3] have been observed at rough noble-metal surfaces. The amplification role played by localized optical plasma oscillation modes (plasmon modes) is now clearly established [4]. Most experimental studies on plasmon modes at surfaces were based on macroscopic measurements on rough surfaces. Insights in the microscopic mechanisms of plasmon-mediated processes can be gained by applying local diagnostic tools on model systems with well-controlled geometry. The tunnel current of a biased scanning tunneling microscope (STM) has been demonstrated to be able to excite highly local optical modes through inelastic electron tunneling. The detection of the photons emitted through the radiative decay of these modes offers valuable spatial and spectroscopic information on local optical excitations, and especially plasmon oscillation modes. Nanochemistry permits the fabrication of nearly perfect nanosized metal spheres. Such nanoparticles self-assemble into hexagonal monolayers identically replicated with a long-range order [5,6]. Such structures provide well-suited model systems to explore the original optical and electronic properties emerging at the nanometer scale. In this paper, we report STM-induced photon emission experiments on silver particles self-organized into 2D lattices on an atomically flat (111) gold surface. By analyzing the combined bias and spatial variations of the emission efficiency, we show the existence of several coupled plasmon modes, at different frequencies and with different spatial distributions. We tentatively assign these modes by comparison with the simplest case of bispherical plasmon modes: the metal spheres are sufficiently close to each other so that the coupling between the unperturbed spherical plasmon modes of the individual particles leads to the 5840

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appearance of new coupled modes with different energies and delocalized electric field distributions. Silver nanoparticles were synthesized following the procedure described in detail in [5]: water-solution droplets in hexane are stabilized by a monolayer of bis(2-ethylhexyl)sulfosuccinate (AOT) as a surfactant, forming the so-called reverse micelles [6]. Two solutions with the same molar ratio W 苷关H2 O兴兾关AOT兴苷 40, corresponding to 12-nm micelles [7], are mixed. One contains 30% Ag(AOT) and 70% Na(AOT) and the other is made with hydrazine, N2 H4 , as a reducing agent with an overall concentration of 7 3 1022 M. 3.4-nm silver particles are formed with a rather large size distribution (43%). Dodecanethiol is then added (1 ml兾ml) and forms a monolayer at Ag-particle surface. Surfactant is removed by precipitation in ethanol. Repeated size-selective precipitation processes followed by centrifugation, as described in [5], yield a homogeneous clear hexane colloidal solution of 4-nm dodecanethiol-coated silver nanoparticles with a size distribution as low as 13%. Size dispersity and selfassembling ability were controlled by transmission electron microscopy (TEM) [8]. (111)-gold substrates were formed on mica following a known procedure [9]. After epitaxial growth of the 100-nm thick gold film on freshly cleaved mica plates, the substrates were submitted to argon-ion bombardment followed by annealing. This procedure yields typically 200-nm wide atomically flat terraces, as observed by STM. The particles were then deposited on this substrate by applying one droplet of solution, and immediately reintroducing the sample into UHV (10210 mbar). A quantitative Auger-electron spectrum analysis confirmed that only Ag, C, and S chemical elements are present on the surface with a S兾C ratio corresponding to that of dodecanethiol. A light collection optics has been adapted inside the UHV STM (Omicron). It consists in a f兾0.6 aspherical lens. The detection axis was close to the grazing incidence, at about 75± from the surface normal. Accounting for the sample shadow, the detection solid angle was about 0.35p sr, with incidences comprised between 90± © 2000 The American Physical Society



(grazing incidence) and 35± from the surface normal. The emitted light was focused through a viewport onto an avalanche photodiode (EGG, SPCM-AQ-15), operating in a photon-counting mode. The dark noise was of 35 cps. The detected optical wavelength range was 400–1000 nm. Photon maps were acquired simultaneously with topographic maps by recording photon counts at each pixel for a fixed acquisition time. The STM operated in a constant-current mode. Electrochemically formed Au tips were used, which were then cleaned and further sharpened in situ by electron bombardment, producing typical radii of no more than a few nanometers. A topographic STM image of a silver-nanosphere monolayer acquired at a tunnel current IT 苷 0.8 nA and a voltage VT 苷 2.3 V is shown in Fig. 1(A). The hexagonal arrangement and the size homogeneity of the particles are visible. The lattice constant, 6.1 nm, is consistent with 4.3 nm spherical particles, as observed by TEM [5], separated by a 1.8 nm gap formed by the dodecanethiol chains. Although insulating, this gap doesn’t appear directly in STM image because of the convolution with the spherical tip shape. Some area of the substrate remained uncovered, permitting one to measure a 5-nm height difference from the substrate to the top of the particles. Hence, the 4.3 nm particles are not in contact with the substrate, but are separated from it by the dodecanethiol chains. Thus, each particle is separated both from its neighbors and from the substrate by a dielectric and electrically insulating layer. This is confirmed by comparison of the current-voltage (I-V ) characteristics measured while the tip is located above the bare Au(111) substrate and the one measured above a silver nanosphere [see Fig. 1(B)]. Whereas the substrate presents an almost linear I-V relationship, which becomes only slightly superlinear above 1.0 nA, the particle characteristics exhibits a highly non-

FIG. 1. (A) Top-view STM image of a monolayer of selfassembled silver nanospheres deposited on a gold (111) substrate. The particles self-order in a compact hexagonal lattice. Scanned area: 50 3 50 nm; sample bias: Vt 苷 2.3 V; tunnelcurrent set point: Its 苷 0.8 nA. (B) Plot of current-voltage characteristics It 共Vt 兲 for a 4-nm Ag particle ( black curve) and for the bare Au substrate (gray curve). Both It 共Vt 兲 curves were measured for a height Z defined by a tunnel-current set point of 1.0 nA with a bias voltage of 1.0 V.

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linear characteristics, indicating the existence of the Coulomb blockade typical of a two-tunnel barrier system: one between the tip and the particle and another between the particle and the substrate. As expected, the two curves cross each other at the regulation set point, IT 苷 1 nA and VT 苷 1 V. A closeup (26 3 10 nm2 ) of a self-assembled domain is presented in Figs. 2 and 3. The topography (A) and the photon map (B) were recorded simultaneously. Figures 2 and 3 were recorded on the same area successively using different biases: in Fig. 2 Vt 苷 2.1 V and in Fig. 3 Vt 苷 2.5 V. In both cases, the tunnel current was set to It 苷 3.5 nA. To compare, even though the topography is quite the same, save for slight drift on the right, the photon maps exhibit a drastic change in the photon emission efficiency. Figure 2 shows that at the lower bias (2.1 V), light emission is below our detection limit (35 cps) when the tip is located above the top of the particle and appears gradually when the tip is moved towards the side. A maximum of emission is reached between particles. In contrast, when a bias of 2.5 V is applied, the maximum of photon emission is detected on the top of the particle. The emission decreases progressively when the tip is moved towards the side. The junction between particles is now a minimum of emission. One can notice, however, that the emission rate measured at this minimum at Vt 苷 2.5 V is still as large as that measured at the same location at Vt 苷 2.1 V, where it is a maximum of emission. Since both set-point current and bias voltage are kept constant during the scan, variations in photon-emission

FIG. 2. Simultaneously recorded STM topography (A) and photon map (B). Scan area 26 3 10 nm, sample bias Vs 苷 2.1 V, It 苷 3.5 nA. Graph (C) presents topography cross section, which goes through the summit of particle and junction between particles alternatively following the dotted line in (A). Emission intensity is maximized between the particles.

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FIG. 3. STM topography (A) and photon map (B) following Fig. 2, same scan area, but sample bias Vs 苷 2.5 V, It 苷 3.5 nA. Graph (C) presents topography cross section, which goes through the summit of particle and junction between particles alternatively following the dotted line in (A). Light emission varies like topology; emission is maximum at the summit and minimum at the junction between particles.

rate reflect changes in the quantum efficiency of photon emission through inelastic electron tunneling. Although a complete theoretical description of this process involves the quantization of electromagnetic field [10], a more intuitive semiclassical treatment is possible, by considering the excitation of electromagnetic modes by a highly localized classical current distribution at frequency v as an electromagnetic source term [11]. As a matter of fact, dc current of a biased tunnel junction is accompanied with ac current the spectrum of which extends up to the cutoff frequency vC 苷 eVT 兾h. ¯ The emitted power is then proportional to the square of a matrix element Mif , product of the ac tunnel current vector by a function representing the amplification due to the local amplitude of the electric field of the excited plasmon mode at the junction location. The intensity of the ac tunnel current at frequency v depends on the tunneling matrix element between final and initial electron quantum states. Assuming weak variation of this matrix element with the energy difference between final and initial state leads to a dependence on dc junction resistance R0 only [12]. Hence, the observed changes in photon emission rate during constant-current scanning reflect mainly the spatial variations of the local electric-field profile of the excited plasmon mode at the location of the ac exciting current. Thus, recording the photon emission rate yields a map of the amplitude of the excited plasmon mode. One must keep in mind, however, that the presence of the gold tip may influence the observed plasmon modes. As shown by tunnel spectroscopy, the STM current 5842

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flows through two tunnel barriers, one between tip and particle, the other between particle and substrate. When the tip is scanned over one given particle, only the first one is modified. The variations in photon emission rate observed then, e.g., in Fig. 3, show that the excitation tunnel current is mainly the one taking place between tip and particle. This indicates that the bias is mainly applied to this junction, the second one presenting a less pronounced tunnel barrier. These variations also show that the emission rate is sensitive to the neighboring of the junction at a distance at least of the order of particle radius. So, even if the close proximity of the tip and the particle yield an enhancement of the plasmon mode amplitude within a small area beneath the tip [13], this amplitude has nonnegligible contributions that are extended over larger distances, of the order of particle size. We are then led to consider coupled plasmon modes involving several particles. Notice that the lowest-energy unperturbed plasmon mode of an isolated silver sphere is of 2.9 eV [13], by far larger than the excitation biases applied here, up to 2.5 V. The full calculation of coupled plasmon modes in a 2D hexagonal network of particles would require tedious numerical computations. Some insights can be gained by considering how the plasmon modes of two spheres couple when those are brought close together. An exact calculation shows that, even at small distances compared with sphere radii, the dominant component to the low-energy coupled plasmon modes are the dipolar (l 苷 1) plasmon modes of the unperturbed spheres [14]. The lowest-energy coupled mode (mode 1) involves the unperturbed modes polarized along the axis formed by the center of the spheres (m 苷 0), oscillating in-phase. The maximum field amplitude is in the region between the spheres. The next mode in energy (mode 2) involves the unperturbed modes polarized perpendicularly to the axis (m 苷 61), oscillating out-of-phase, thus forming a node of electric field in the region between the spheres. Although the generalization of this simple model to our complex system is not straightforward, our experimental results suggest that the nature of the plasmon modes excited at the lowest bias VT 苷 2.0 V are similar to mode 1. They are very likely polarized in-plane, and the particles in the vicinity of the tip oscillate in-phase. When the apex is located over the top of a sphere, the tunnel current is perpendicular to the plasmon electric field and its excitation is inefficient. This is consistent with the low emission rate observed there (see Fig. 2). At larger biases, we observe an increase of the emission rate over the top of the spheres, indicating that plasmon modes with vertically polarized electric fields are excited. Then, we observe a minimum of emission rate between particles, indicating a reduced electric field, similarly to mode 2 of the two-spheres system. The microscopic polarization influences both the polarization and the emission direction of the radiated light. The vertically polarized (m 苷 0)-like plasmon mode radiates p-polarized (TM) light with maximum intensity near the grazing incidence and with a symmetrical azimuthal



distribution, which is well adapted to our detection geometry. The polarization state of the light radiated by the (m 苷 61)-like plasmon mode is more complicated because of the two-dimensional multiple orientations of the possible bispherical axes and because of the influence of the tip and of the substrate on mode symmetry. At a given tip location, the polarization should depend on the azimuthal angle of emission. Owing to the large collection solid angle, which was necessary for imaging with sufficient counting rates, such mixed polarizations are washed out in the present experiments. In summary, we have studied the effects of local geometry on the photon emission process in a two tunneljunction system consisting of an etched gold tip, a monolayer of close-packed silver nanospheres, and a gold film under UHV. This technique has permitted an analysis of the coupled plasmon modes of a hexagonal network of silver spheres, as a function of excitation energy. More complex structures, such as periodic ordered systems in three dimensions, can be fabricated. The understanding of the collective excitations in such a system may lead to a control of field distribution and finally of the optical and photophysical properties.

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[1] M. Moskovits, Rev. Mod. Phys. 57, 783 (1985). [2] J. Lambe and S. L. McCarthy, Phys. Rev. Lett. 37, 923 (1976). [3] P. E. Batson, Ultramicroscopy 9, 277 (1982). [4] F. J. García-Vidal and J. B. Pendry, Phys. Rev. Lett. 77, 1163 (1996). [5] A. Taleb, C. Petit, and M. P. Pileni, Chem. Mater. 9, 950 (1997). [6] P. J. Durston, J. Schmidt, and R. E. Palmer, Appl. Phys. Lett. 71, 2940 (1997). [7] M.-P. Pileni, J. Phys. Chem. 97, 6961 (1993). [8] A. Taleb, C. Petit, and M. P. Pileni, J. Phys. Chem. 102, 2214 (1998). [9] Y. Golan, L. Margulis, and I. Rubinstein, Surf. Sci. 264, 312 (1992). [10] B. N. J. Persson and A. Baratoff, Phys. Rev. Lett. 68, 3224 (1992). [11] P. Johansson, R. Monreal, and P. Apell, Phys. Rev. B 42, 9210 (1990). [12] R. W. Rendell and D. J. Scalapino, Phys. Rev. B 24, 3276 (1981). [13] A. Taleb, V. Russier, A. Courty, and M. P. Pileni, Phys. Rev. B 59, 13 350 (1999). [14] M. Schmeits and L. Dambly, Phys. Rev. B 44, 12 706 (1991).

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