Interparticle Coupling Effects on Plasmon Resonances of Nanogold Particles

The collaborative oscillation of conductive electrons in metal nanoparticles results in a surface plasmon resonance that makes them useful for various applications including biolabeling. We investigate the coupling between pairs of elliptical metal particles by simulations and experiments. The results demonstrate that the resonant wavelength peak of two interacting particles is red-shifted from that of a single particle because of near-field coupling. It is also found that the shift decays approximately exponentially with increasing particle spacing and become negligible when the gap between the two particles exceeds about 2.5 times the particle short-axis length. Noble metal nanoparticles, usually of Ag or Au, are well known for their strong interactions with visible light through the resonant excitations of the collective oscillations of the conduction electrons within the particles. As a result, local electromagnetic fields near the particle can be many orders of magnitude higher than the incident fields, and the incident light around the resonant-peak wavelength is scattered very strongly. This local-field enhancement and strong scattering have been proven to be very unique for biomolecular manipulation, labeling, and detection.1,2 The enhanced electric fields are confined within only a tiny region of the nanometer length scale near the surface of the particles and decay significantly thereafter. This localized field enhancement provides a field gradient that is much greater than that of any far-field optical tweezers; therefore, it may be possible to trap single molecules or other nanoparticles in regions near an elliptical metal nanoparticle or tip3-5 or between two nanoparticles.6 It has also been shown that the emission properties of fluorescent molecules under the influence of this enhanced field are changed dramatically. As an example, the radiative decay rates and quantum yields of weakly fluorescent species can increase significantly. Even multiphoton absorptions and fluorescence excitations have been shown to be possible.7,8 The recent discovery of single-molecule sensitivity of Raman scattering enhanced by resonantly excited metal nanoparticles has caused a renewed interest in surface-enhanced Raman scattering (SERS) and its application to molecular detection.9-11 In typical SERS experiments, a collection of colloidal particles of various sizes are induced to aggregate, and those aggregates that happen to be resonantly excited by the illuminating laser are called “hot spots”. Therefore, from a practical point of view, it is very important to be able to fabricate optimally designed plasmon configurations of interacting nanoparticles. The resonant frequency of a metal nanoparticle is known to be dependent on its size, shape, material properties, and surrounding medium.12-14 When a cluster of metal nanoparticles are placed in close proximity to one another, such as in SERS experiments, the coupling between particles becomes very important.11,15-17 In this paper, we focus our study on the effects of near-field interparticle coupling on the particle plasmon resonances, especially the shift of the plasmon resonant wavelength as a function of particle separation. As expected, the experimental and simulation results indicate that the resonant wavelength of two coupled particles in close proximity is significantly red-shifted from that of the individual particles. This shift decays approximately exponentially with increasing particle spacing. It is also found that the exponential decay of the peak shift with the particle gap is size-independent because the shift and gap are scaled respectively by the peak wavelength and * Corresponding author. E-mail: [email protected]. NANO LETTERS 2003 Vol. 3, No. 8 1087-1090 10.1021/nl034197f CCC: $25.00 © 2003 American Chemical Society Published on Web 06/21/2003 particle sizes. The scaled decay function is particle-shapedependent in the sense that the decay length depends on particle shapes. We note that the shift drops to zero when the gap between the two particles reaches about 2.5 times the particle size. The gold nanoparticles were prepared on quartz substrates by electron-beam lithography (EBL) and the standard liftoff process, which allows for the accurate placement of the particles on designed locations. To reduce charging effects during the EBL, 10-nm-thick indium tin oxide (ITO) films were sputtered on the quartz substrates. Polymathylmethaacrylate (PMMA) films (100 nm thick) were spin-coated on this ITO-quartz glass, which was used as a positive photoresist for e-beam lithography. The samples were examined by a scanning electron microscopy (Hitachi) to characterize the size and shape of these nanoparticles. Evanescent light produced by a collimated light beam undergoing total internal reflection (TIR) is utilized to excite the particle plasmons. The excited collective electron oscillations within the particles then radiate electromagnetic waves of the same frequency into the far field, whereby the collection and spectral measurement take place. In our experiments, a collimated light beam delivered by a multimode optical fiber from a 75-W Xe white-light source is incident on a right-angle prism at an angle resulting in total internal reflection. The samples are situated on the top surface of the prism, and index-matching oil is used between the touching surfaces of the sample substrate and the prism, which ensures that all stray scattering light due to surface defects and dust particles is minimized, leading to very high dark-field contrast. The scattered light from the metal nanoparticles is collected by an optical microscope with a 50× long-working-distance objective and forms an image at the image plane. At this image plane, a small aperture is located to select individual particles or pairs of particles and serves to block the scattered light from the surrounding particles and substrate. The emerging light is then imaged onto the entrance slit of an SPEX 270M grating spectrometer system with a thermal electrically cooled charge-coupled device (CCD) detector (Princeton Instruments). The detailed experimental setup has been described in a previous paper.12 To demonstrate the control of the plasmon resonant wavelength of single particles, we first fabricated well-separated gold nanoparticles of various sizes. Usually, a thin, 5-nm Cr layer is deposited before the Au deposition to promote the adhesion between Au and the quartz substrates. The vertical thickness of the particles is kept at 30 nm in our study. As shown in Figure 1a, the particles are slightly elongated, and the ratio between the long and short axes is about 1.55. To study the coupling effects of two particles on their common plasmon resonance, we have also fabricated particle pairs with various interparticle spacing and sizes. We denote a line connecting two centers of coupled particles as the x axis. It was determined that the particle short axis is tilted about 7° from the x axis. The purpose of fabricating tilted elliptical particle pairs is to see the effect of the tilt angle on plasmon couplings. For measurements of both single particles and particle pairs, the polarization of the incidentlight electric field is selected parallel to the x axis. In the EBL process, the individual particles or particles pairs are well separated from each other; therefore, multiparticle interference effects or so-called long-range dipole interactions on the spectrum measurements are eliminated. Figure 1a presents some typical measured scattering spectra of single nanoparticles with the short axis varying from 84 to 104 nm and with a long/short axis ratio about 1.55. Owing to the TIR dark-field illumination and the strong plasmon-resonance-associated scattering, individual nanoparticles can be easily identified and distinguished from dust. It is clear that the plasmon-resonant-peak wavelength is shifted significantly to larger values with increasing particle size. A plot of the peak resonant wavelength as a function of particle size indicates a good linear relationship (Figure 1b), in agreement with Mie scattering theory. The effect of particle size on the peak resonant wavelength results from two different mechanisms depending on the particle size range. For small particles with diameters of less than 10 nm, known as the quasi-static regime, the effects of phase retardation and multiple modes can be neglected. Whereas Mie theory gives a constant resonant frequency independent of particle size if the bulk dielectric constant is used, the size effect in the quasi-static regime comes from the dependence of the permittivity on particle size because of quantum confinements. For larger particles with diameters greater than 10 nm, such as in our case, the quantum confinement effect or size dependence of dielectric coefficients becomes negligible, and the role of phase retardation effects comes into play. The peak red-shift observed in our experiments is a fully electrodynamic effect due to phase Figure 1. (a) Scattering spectra of elliptical Au particles with shortaxis lengths of 84, 91, 96, 102, and 104 nm. The long/short axis aspect ratio is kept at about 1.55. (b) Measured plasmon resonant wavelength as a function of the particle short-axis length. 1088 Nano Lett., Vol. 3, No. 8, 2003 retardation. With this linear relationship between resonance frequency and size, it is easy for a researcher to design the target illumination wavelength of hot spots in SERS ap-