LETTER pubs.acs.org/NanoLett
Shape Matters: Plasmonic Nanoparticle Shape Enhances Interaction with Dielectric Substrate Pablo Albella,† Borja Garcia-Cueto,† Francisco Gonzalez,† Fernando Moreno,† Pae C Wu,‡ Tong-Ho Kim,‡ April Brown,‡ Yang Yang,§ Henry O. Everitt,‡,§,|| and Gorden Videen*,^ Grupo de Optica, Departamento Física Aplicada, Universidad de Cantabria, 39005 Santander, Spain Department of Electrical and Computer Engineering, Duke University, Durham, North Carolina 27708, United States § Department of Physics, Duke University, Durham, North Carolina 27708, United States Army Aviation & Missile RD&E Center, RDMR-WS, Redstone Arsenal, Alabama 35898, United States ^ Army Research Laboratory, RMRD-CIE-S, 2800 Powder Mill Road, Adelphi, Maryland 20783-1197, United States †
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ABSTRACT: Numerical analyses of the ultraviolet and visible plasmonic spectra measured from hemispherical gallium nanostructures on dielectric substrates reveal that resonance frequencies are quite sensitive to illumination angle and polarization in a way that depends on nanostructure size, shape, and substrate. Large, polarization-dependent splittings arise from the broken symmetry of hemispherical gallium nanoparticles on sapphire substrates, inducing strong interactions with the substrate that depend sensitively on the angle of illumination and the nanoparticle diameter. KEYWORDS: UV plasmonics, nanoparticles, gallium, shape effects, substrate effects, nanoantenna
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he past decade has witnessed an explosion in the use of plasmonic metal nanoparticles for light localization and near-field enhancement applications such as surface enhanced Raman spectroscopy (SERS) and metal-enhanced fluorescence. Analyses of these plasmonic nanoparticles often consider isolated metallic spheroids in homogeneous environments,1 but few nanoplasmonic systems can be described this way.2 Multiparticle scattering is a rich and complex field, but insights may be gleaned from single-particle analysis, especially for commonly used systems composed of nonspherical metallic nanoparticles located on a substrate. Here the “substrate matters” because it reduces the symmetry of the scattering and supports an image dipole, shifting, broadening, and splitting the local surface plasmon resonance (LSPR) as pointed out recently for spherical and cubical nanoparticles.3,4 This interaction breaks the isotropic degeneracy of the laser-induced dipole into components that interact with Sand P-polarized light differently. The modest interaction between a spherical gold nanoparticle and its substrate was found to produce a polarization-dependent plasmon splitting as large as 0.47 eV for the substrate with the highest dielectric constant. Plasmonic sensors primarily use silver and gold nanoparticles for visible and near-infrared applications, but interest is growing to extend plasmonics into the ultraviolet (UV). Gallium, with a bulk plasmon resonance energy of 13.9 eV, was recently shown to be a good candidate for UV plasmonics because, unlike silver or aluminum, its slight oxidation minimally affects its optical properties over many months.5 7 Ga nanoparticles form from liquid droplets with a melting point of 30 C, so at room temperature they r 2011 American Chemical Society
produce a close-packed array of smooth truncated spheres whose mean radii and size distributions vary with growth conditions when deposited on a substrate. Their relatively monotonic, Drude-like optical properties in the region from 2 to 6 eV also make them an ideal metal for analytical investigations of the size and morphology dependence of reduced dimensional plasmon resonances. Surprisingly large (2 4 eV) polarization-sensitive splittings in the LSPR have been observed from hemispherical Ga nanoparticles on sapphire substrates. Figure 1 illustrates this splitting for three size distributions of Ga nanoparticles, synthesized on sapphire at room temperature by molecular beam epitaxy following the procedure outlined in refs 5 and 8. The complex pseudodielectric function Æεæ is measured in situ after deposition by grazing incidence (α = 70) spectroscopic ellipsometry. The imaginary components Ækæ of the spectra exhibit two LSPR features: a low-energy peak occurring in the red-visible part of the spectrum at 1 2 eV, and a high energy peak occurring in the UV region at 4 6 eV, both of which red shift as the mean nanoparticle size increases with increasing deposition time. Because such large splittings are always observed, regardless of the distribution of nanoparticle sizes, they must be a fundamental property of the nanoparticles themselves. The primary goal of this paper is to explore how the LSPR of an isolated hemispherical gallium nanoparticle on a sapphire Received: March 16, 2011 Revised: August 12, 2011 Published: August 17, 2011 3531
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Figure 1. Imaginary part of the pseudodielectric function Ækæ obtained using ellipsometric techniques (α = 70) of hemispherical Ga nanoparticles on sapphire substrates measured in situ following deposition by room temperature molecular beam epitaxy. The respective scanning electron microscope images and size distribution histograms for three samples of increasing mean nanoparticle size are also shown. The nanoparticle diameter is approximately twice the height. These data and analyses were produced using the techniques outlined in ref 5.
substrate depends on nanoparticle radius, incidence angle, and polarization. We find that the nanoparticle’s hemispherical shape causes the large splitting, with orthogonal polarizations of incident light interacting with orthogonal dimensions of the nanoparticle to produce two widely separated LSPR features whose relative intensities depend on the angle of incidence and the amount of interaction with the substrate. The universality of this large splitting suggests that a theoretical analysis of light scattering by a single hemispherical nanoparticle on a substrate captures the essential behavior and can provide a basis to assess the potential for plasmonenhanced emission, detection, and Raman scattering in the UV.2,8 Consider a hemispherical Ga nanoparticle resting on a finite sapphire substrate (Figure 2), illuminated by a circularly or linearly polarized plane wave whose propagation direction in the X Y scattering plane is oriented at angle α with respect to the substrate normal. For linear S-polarized light, the electric field vector is perpendicular to the scattering plane and is always parallel to the substrate. For linear P-polarized light, the electric field vector lies within the scattering plane, so it has components both parallel and perpendicular to the substrate. The inset of
Figure 2 shows the experimentally measured and smoothed dielectric function for Ga in the range of 1 6 eV. In this range the imaginary part of the dielectric constant of sapphire can be neglected, and its real part is approximately constant at Re(ε) = 3.13. The horizontal line marks the value of Re(ε) = 2, whose intersection with Re(ε) for Ga predicts a UV LSPR energy of 4 eV for an isolated spherical particle of radius R , λ, where λ is the incident wavelength. The discrete dipole approximation (DDA) has been used for this analysis.9 12 Under this approximation the target is discretized into a finite array of N polarizable cells, each of which has the same optical properties as that of the target location. The cells acquire dipole moments in response to the local electric field. Each electric dipole is characterized by a polarizability tensor that depends on the interaction with all the other dipoles. DDA is a robust method whose accuracy has been confirmed by comparisons with analytical methods, including Lorenz Mie calculations of light scattering by a sphere, and with experimental results.13,14 Errors typically result from finite discretization of the scattering system and can be reduced by decreasing the cell size. 3532
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Figure 2. Scattering system composed of a hemispherical Ga particle (yellow) resting on a sapphire substrate (blue). Incident at an angle α from the normal, the light may be polarized perpendicular to (S-polarization) or within (P-polarization) the scattering plane. Inset: Real and imaginary part of the pseudodielectric constants smoothed from the experimentally obtained data for bulk Ga.
Figure 3. Spectral absorption efficiencies for four scattering geometries and five nanoparticle radii. The incident field is a plane wave linearly polarized at α = 0 (see Figure 2). (a) Isolated spherical Ga nanoparticle. (b) Spherical Ga nanoparticle located on a flat sapphire substrate. (c) Isolated hemispherical Ga nanoparticle. (d) Hemispherical Ga nanoparticle located on a flat sapphire substrate. Particle sizes are indicated in each figure: red (R = 20 nm), orange (R = 30 nm), green (R = 40 nm), violet (R = 50 nm), and blue (R = 60 nm).
In our DDA simulations, both the nanoparticle and the substrate must be discretized with a large number of dipoles (∼150,000). Both substrate thickness and total number of dipoles were optimized for all the cases analyzed in order to guarantee convergence in a reasonable amount of time without sacrificing accuracy. Furthermore, all results presented herein have been confirmed by finite-difference time-domain (FDTD) calculations. Typical errors in the scattering intensities are on the order of 1%. One of the benefits of the DDA is that calculations can be performed on any type of particle system that can be approximated by a discretized array. The only input parameters that are needed are the morphology of the system and the dielectric
constants at each cell location (see Figure 2). For two reasons we consider the spectral absorption efficiency of the particle system Qabs, defined as the absorption cross section divided by the crosssectional area of the scatterer. First, it correlates directly with the imaginary part of the pseudodielectric function measured in typical ellipsometric experiments.5 7 Second, for the range of nanoparticle radii of interest (20 60 nm), the extinction efficiency Qext is dominated by scattering Qsca, so Qabs = Qext Qsca more sensitively manifests multipolar effects, as will be seen in the following.15,16 It is important to emphasize that our analysis does not consider multiparticle interactions. In many situations, samples are composed of an ensemble of particles in which multiple 3533
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