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J. Phys. Chem. C 2008, 112, 6662-6666
Optical Properties of Gold Pyramidal Shells Kevin L. Shuford,*,† Jeunghoon Lee,‡ Teri W. Odom,‡,§ and George C. Schatz‡ Chemical Sciences DiVision, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6142, Department of Chemistry, Northwestern UniVersity, 2145 Sheridan Road, EVanston, Illinois 60208-3113, and Department of Materials Science and Engineering, Northwestern UniVersity, EVanston, Illinois 60208-3113 ReceiVed: January 17, 2008; In Final Form: February 14, 2008
We present an investigation of the optical properties of gold pyramidal shell nanoparticles. Theory shows a multiresonance spectrum at near-infrared wavelengths that is consistent with the measured extinction spectra of particles that are fabricated using a soft-lithography technique. In addition to electric dipole and electric quadrupole resonances, the calculations identify an unusual plasmon mode, which involves oscillation of the polarization perpendicular to the direction of both the incident polarization and wave vector. We show that this TE-like resonance can be suppressed by truncating the tip of the pyramid or by increasing the shell thickness without adversely affecting the in-plane dipole and quadrupole resonances.
1. Introduction Nanoparticles display interesting and unique characteristics that are strikingly different from either the microscopic or macroscopic regime. At optical frequencies, noble metals such as silver and gold support a collective oscillation of conduction electrons known as a surface plasmon excitation.1 This excitation can be thought of as the response of a sea of loosely bound charges to electromagnetic forces exerted by an applied field. This phenomenon generates intense resonances in optical spectra that are highly dependent upon particle characteristics such as size, shape, material, environment, and the orientation with respect to the incident field.2 Understanding how these variables affect plasmon excitations and controlling these properties are critical for developing nano-optic devices. The unique features of metallic nanostructures have produced several nanoparticle-based applications. For example, chemical and biological sensors take advantage of the intensity of plasmon resonances to yield extreme sensitivity and low limits of detection.3-6 The enormous field enhancements are ideal for many surface enhanced spectroscopies7 and in some cases have allowed for the detection of single molecules.8-11 Nanoparticle arrays can propagate electromagnetic energy, and so they have been proposed as waveguides capable of manipulating light below the diffraction limit.12,13 Medical applications for nanoparticles include imaging capabilities and treatment via tumor ablation.14-16 The majority of the preceding applications use particles with diameters less than 100 nm, sizes that are significantly smaller than the excitation wavelength. Under these conditions, the extinction spectra are often composed of a single peak, and the plasmon excitations are dipolar in character. Indeed, the lowest order response of small, spherical particles is exactly that of a dipole. As particles become larger or the shell structures become thinner, the anisotropy is increased and higher order polarizations are induced, which lead to more complex excitations. Rich * To whom correspondence should be addressed. † Oak Ridge National Laboratory. ‡ Department of Chemistry, Northwestern University. § Department of Materials Science and Engineering, Northwestern University.
spectra containing numerous peaks of varying intensities from the visible out to the near-infrared (NIR) are produced. Multipolar excitation has been observed for several shapes of nanoparticles including rectangular prisms,17 cylinders,18 triangular prisms,19,20 concentric spheres,21,22 and pyramidal shells.23 This paper presents the optical properties of gold pyramidal shell nanoparticles in solution. The fabricated particles are relatively large (ca. 300 nm in base diameter), have variable shell thickness (60-110 nm), and display complex multipolar excitations. This work builds upon a previous report on these structures encased in a polymer matrix,23 which primarily focused on the orientational dependence of the scattering properties at visible wavelengths. Here we report calculations and measurements out to NIR wavelengths, which show additional plasmon resonances with unusual properties. Theoretical results concerning the generation and manipulation of these resonances are presented in sections 3 and 4, and experimental verification is described in section 5. 2. Theory Figure 1 depicts the morphology of a pyramidal shell, which resembles a square pyramid with a rounded base. We generate the scattering target for our theoretical calculations using a multistep process in which initially we define a solid pyramid with a square base and equilateral faces. In the target frame, the square base is oriented in the x-y plane (z ) 0, axes normal to the edges of the square), and the apex is along the +z-axis. In the second step, a square pyramid with a shorter edge and the same symmetry axis is defined, and then this volume is removed from the larger pyramid. In the third step, we define a cylinder (z is the symmetry axis) with a diameter equal to the edge length of the larger pyramid and then remove any part of the shell framework that resides beyond the radius of the cylinder. The resulting structure is a pyramidal shell with a rounded base. Note that the particle cross section in the x-y plane near the base will be a shell with a circular outer surface and a square inner surface. We found that this structure most accurately represents the particles fabricated in ref 23. We have performed classical electrodynamics calculations using the discrete dipole approximation (DDA) to investigate
10.1021/jp8004844 CCC: $40.75 © 2008 American Chemical Society Published on Web 04/08/2008
Optical Properties of Gold Pyramidal Shells
J. Phys. Chem. C, Vol. 112, No. 17, 2008 6663
Figure 1. Schematic diagrams of the pyramidal shell nanoparticle (solid lines) used in the DDA calculations. From left to right, the views are from the side and from the top.
the optical properties of these gold pyramidal shell nanoparticles. DDA20,24,25 has been used extensively for similar calculations on metallic nanoparticles, and thus only the salient points of the method are reproduced here. The target pyramid is represented by a square array of point dipoles. Each dipole oscillates in response to the total field at that position, which is composed of an incident plane wave, and the fields generated by all of the other dipoles in the array. The induced polarization at each site is N
[
Pj ) Rj Einc j -
AjkPk ∑ k*j
]
(1)
where R is the polarizability, Einc is the incident field, and A is a dipole interaction matrix. The polarizability is assigned on the basis of experimentally determined values for the dielectric constant of gold26 and using a lattice dispersion relationship27 that makes the dipole array reproduce exact electrodynamics for an infinite size object with a sufficiently fine dipole lattice. The field radiating from each of the other dipoles in the array is given by
AjkPk )
{
exp(ikrjk) rjk
3
k2rjk × (rjk × Pk) +
1 - ikrjk rjk2
×
[rjk2Pk - 3rjk(rjk‚Pk)]
}
(2)
The system of coupled dipole equations can be formulated as a large matrix equation and solved iteratively to calculate the induced polarizations. The latter are then used to calculate the nanoparticle extinction cross section via the optical theorem:
Cext )
4πk |E |
inc 2
N
Im{Einc ∑ j ‚Pj} j)1
(3)
This procedure must be repeated at all wavelengths of interest, as this is a frequency domain method. 3. Results Figure 2A displays the calculated spectrum of pyramidal shell nanoparticles in solution with a 300 nm diameter base and a 60 nm shell thickness. This spectrum is an average of three important orientations discussed in detail below. Previous studies23 have determined that these orientations represent the relevant classes of excitations that occur in pyramidal shells well, and an average of them produces results in good agreement with experimentally measured spectra. The large size and thin shell structure of the particle lead to higher order polarizations, which generate many resonances. There are four features present
Figure 2. Extinction spectra of gold pyramidal shells (300 nm diameter, 60 nm shell thickness) in water. (A) Spectrum obtained by averaging over orientations. (B) Spectra of three different orientations: propagation vector k and polarization vector E are parallel to the base (solid line); k is perpendicular to the base and E is parallel to the base (dashed line); k is parallel to the base and E is perpendicular to the base (dotted line).
at approximately 580, 780, 990, and 1170 nm, corresponding to a shoulder and three resolved peaks. We found that the spectra of these particles were extremely sensitive to their diameter and shell thickness. As the particle size increased or the shell thickness decreased, the existing resonances red-shifted and new resonances were introduced. Figure 2B shows spectra calculated for three relevant orientations that contribute to the averaged extinction (Figure 2A). The solid trace corresponds to when both the propagation vector k and incident polarization vector E are parallel to the base. The dashed line corresponds to k perpendicular to the base and E parallel to the base. Note that these two orientations have the same polarization vector but perpendicular propagation directions; thus, they both generate plasmon excitations that are primarily in-plane (i.e., the electrons oscillate parallel to the base plane). The dotted line in Figure 2B represents when k is parallel to the base and E is perpendicular to the base. This orientation produces primarily out-of-plane excitations, where the electrons oscillate perpendicular to the base plane. These resonances occur throughout the optical regime and are generally less intense than the in-plane modes. With the exception of the peak at 590 nm, the out-of-plane modes do not add any significant new structure to the averaged spectrum. Out-of-plane excitations can contribute to the experimentally observed spectrum, but the major features are dominated by the in-plane modes. For this reason, we do not examine orientations with E perpendicular to the basal plane in great detail and concentrate upon orientations where E is parallel to the base. The goal of this paper is to examine the nature of the resonances that lead to peaks in the spectra from 700 to 1400 nm. The in-plane modes dominate these wavelengths and show three peaks of varying intensities. We first focus on the solid trace in Figure 2B since it contains all three resonances, where both k and E are parallel to the plane containing the base. Figure 3 displays vector plots of the nanoparticle polarization, which are spatial maps of the induced dipole moments. These polarizations also determine the electric field patterns outside of the particle surface; however, these are not considered here. Figure 3A clearly shows a pattern consistent with a quadrupole source arrangement, and thus we label the peak at 781 nm a
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Figure 3. Vector plots of the induced polarization for a pyramidal shell nanoparticle (300 nm diameter, 60 nm shell thickness). The propagation direction k and incident polarization E are labeled in the figure. (A-C) Polarizations in the base oriented in the x-y plane (z ) 0). (D) Polarization in the y-z plane (x ) 0). Only 40% of the dipoles are displayed for clarity.
quadrupole excitation. Note that this assignment is consistent with previous studies of pyramidal shell particles.23 The quadrupole designation is also reflected by the lack of a resonance when k is perpendicular and E is parallel to the base (Figure 2B, dashed line). Under these conditions, the symmetric field distribution perpendicular to k leads to a suppression of this excitation, similar to the surface selection rules noted for cylindrical particles.18 Figure 3B displays a pattern consistent with a dipole arrangement, and therefore we label the peak at 1203 nm a dipole excitation. The vast majority of the vectors indicate a uniform polarization pointing from one side of the base toward the opposing side of the base. Some dipoles do not strictly follow this pattern, which can be attributed to factors such as this resonance being a weaker, less defined excitation, or a mixing of modes from other close lying excitations. It should be noted that most excitations will contain a mixture of many modes and that our labeling convention reflects the dominant order that contributes to an observed excitation. We have examined the polarization plots in several planes parallel to the base, and all show similar arrangements. Interestingly, the induced polarization at 1047 nm (Figure 3C) displays a complex arrangement of dipoles oriented in many directions. This peak is unusual in that it occurs in a range of wavelengths that lie between well-defined quadrupole and dipole modes. A complicated multipole pattern appears along the polarization direction. The dipoles at the outer edges point in the opposite direction when compared to the dipoles on the inner edges, which creates the appearance of nodal planes at (125 nm of the ordinate. Figure 3D shows the polarization in a perpendicular plane for the same excitation and wavelength. Close inspection reveals that the exterior dipoles align parallel to each other, so that this mode can be thought of as primarily a dipole mode that oscillates out of the base plane of the pyramid and perpendicular to both the polarization E and wave vector
k. There are also admixtures of other types of excitations at 1047 nm. In particular, the dipoles near the exterior surfaces of the shell are aligned, while those in the interior of the shell are oppositely aligned, as would arise from a higher multipole. Further details on the physical meaning of this excitation are presented below. 4. Discussion The most interesting plasmon excitation is the middle resonance that occurs at ∼1000 nm. We have identified this excitation as a mode that induces out-of-plane polarization even when the incident field vector is parallel to the basal plane. If this interpretation is indeed correct, we expect that altering the region near the apex would disrupt this mode, but not the other modes. We have tested this hypothesis by shearing off the apex parallel to the base and recalculating the optical properties. Figure 4 shows extinction spectra of pyramidal shell nanoparticles that are truncated by various amounts. Increasing the amount of truncation (that is, decreasing the effective height) leads to a suppression of the middle resonance and red-shifts the in-plane dipole and quadrupole excitations. This effect is consistent with the truncated pyramidal shell behaving as a ringshaped particle and displaying typical trends expected upon decreasing the height. We can thus effectively eliminate the outof-plane mode near 1000 nm by removing spatial regions near the apex, which is a structural requirement for the particle to support this excitation. In addition, we have found that certain conditions are necessary to generate this type of unique resonance. The unusual out-of-plane multipole observed in the vector plots (Figure 3C,D) results from coupling of excitations on the inner and outer shells in directions perpendicular to the polarization and wave vectors. This coupling arises only when the shell thickness is thin enough for the incident field to excite both surfaces in
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Figure 4. Extinction spectra of truncated gold pyramidal shells (300 nm diameter, 60 nm shell thickness). Both the propagation direction and incident polarization are parallel to the base. The solid, dotted, and dashed lines correspond to effective particle heights of 100, 75, and 50 nm, respectively.
Figure 6. (A) SEM images of gold pyramidal shells. (B) Experimental and (C) calculated extinction of 300 nm pyramidal particles with 60 nm (solid lines) and 110 nm (dotted lines) shell thicknesses. Figure 5. Extinction spectra of pyramidal shells (300 nm in diameter) with two different thicknesses. Both the propagation direction and incident polarization are parallel to the base. The solid and dotted lines correspond to shell thicknesses of 60 and 110 nm, respectively.
phase. To investigate whether a thicker shell could also support this resonance, we increased the shell thickness of the pyramid. Figure 5 shows that as the shell thickness increased from 60 to 110 nm, the out-of-plane resonance disappeared. Also, as the shell thickness increased, both the in-plane dipole and quadrupole resonances blue-shifted because of the decrease in effective aspect ratio. The presence of a resonance mode that oscillates perpendicular to the incident polarization and wave vectors is qualitatively related to transverse electric (TE) modes that are found for spherical particles, so we will use the designation “TE-like” to label this resonance even though this designation is not rigorous for a low-symmetry particle such as we are considering. Such modes are often associated with magnetic properties, and thus we examined the magnetic dipole properties of the pyramid modes. We calculated the induced magnetic moments associated with all the resonances in Figure 2 by summing the cross product of the induced polarization vector of each DDA dipole and the position vector relative to a selected origin. We considered several choices for the origin, but the conclusions from these calculations did not depend on where the moment was calculated. We found that the resonance near 1000 nm did not exhibit a magnetic moment significantly different from the other modes. We conclude that the low symmetry of the pyramidal shell produces a mixing of the magnetic and electric character of the modes such that all excitations have a similar magnetic character, which impedes the emergence of a dominant magnetic mode. 5. Experimental Studies To test these predictions, we fabricated gold pyramidal shells with different thicknesses using PEEL (phase-shifting photoli-
thography, etching, electron-beam deposition, and liftoff).23,28 We concentrated and dispersed the pyramids into solution and then measured their extinction spectra out to NIR wavelengths. SEM images of the particles are shown in Figure 6A. The experimental spectra (Figure 6B), obtained from a ∼2 pM suspension of pyramids in D2O by a Cary 5000 UV-vis-NIR double-beam spectrophotometer, show several resonances between 600 and 1400 nm from pyramids with 60 and 110 nm shell thicknesses. As the shell thickness is increased from 60 to 110 nm, the central resonance is suppressed, and the other in-plane excitations are shifted to shorter wavelengths, in agreement with simulations. Figure 6C depicts the calculated, orientationally averaged extinction for the same particle morphologies. Theory and experiment agree reasonably well on the plasmon frequencies, but there are some discrepancies in the intensities. This result is expected considering the slight variations in the fabricated particles and the extreme sensitivity of extinction with shell thickness. In general, the calculations appear to overestimate the intensity of some resonances, which could be due to factors such as the assumed particle morphology, or the chosen dielectric constant at those wavelengths. Overall, experiment and theory are in good agreement and show the same trends. In particular, experimental measurements confirm the three-peak resonance structure that theory predicts for shell thicknesses of 60 nm and verify the effect on the optical spectrum upon increasing the shell thickness. 6. Conclusions We have presented a detailed investigation of the optical properties of gold pyramidal shells out to NIR wavelengths. The extinction spectra displayed numerous resonances upon photoexcitation that are consistent with multipolar excitation of a large (>100 nm) particle with a thin shell structure. Calculations predicted and measurements confirmed the existence of a new TE-like plasmon mode with major components that oscillate perpendicular to the direction of the incident
6666 J. Phys. Chem. C, Vol. 112, No. 17, 2008 polarization and wave vectors. Truncating the apex of the structure or increasing the shell thickness eliminates this excitation. The sensitivity of this out-of-plane mode to truncation provides a unique platform for sensing applications based on nanoparticle structural changes induced by analyte binding. For example, a “sandwich” assay in which a multidentate analyte molecule (such as a protein) binds together two fragments of a pyramid (the “base” and the “tip”) could induce the out-ofplane resonance. Since the change in tip size required to quench the resonance is only about 25 nm, this assay could be implemented using a relatively small fragment particle in solution; that is, a tip could bind to a pyramid base structure patterned and fixed on a surface. Acknowledgment. K.L.S. was supported by the Wigner Fellowship Program and the Division of Chemical Sciences, Biosciences, and Geosciences, Office of Basic Energy Sciences, U.S. Department of Energy, under Contract DE-AC0500OR22725 with Oak Ridge National Laboratory, managed and operated by UT-Battelle, LLC. GCS thanks DOE Grant DEFG02-02-ER15487 and Materials Research Science and Engineering Center (NSF Grant DMR-0520513) at Northwestern University for support of this research. G.C.S. and T.W.O. thank NSF Grant DMR-0705741. T.W.O. and J.L. were supported in part by the Center of Cancer Nanotechnology Excellence (CCNE) initiative of the National Institutes of Health’s National Cancer Institute under Award U54CA119341. References and Notes (1) Bohren, C. F.; Huffman, D. R. Absorption and Scattering of Light by Small Particles; Wiley: New York, 1983. (2) Kelly, K. L.; Coronado, E.; Zhao, L. L.; Schatz, G. C. J. Phys. Chem. B 2003, 107, 668. (3) Taton, T. A.; Mirkin, C. A.; Letsinger, R. L. Science 2000, 289, 1757.
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