On the Universal Scaling Behavior of the Distance Decay of Plasmon Coupling in Metal Nanoparticle Pairs: A Plasmon Ruler Equation

Localized surface plasmon resonances (LSPR) in lithographically fabricated gold (Au) nanodisc pairs are investigated using microabsorption spectroscopy and electrodynamic simulations. In agreement with previous work, we find that the fractional plasmon wavelength shift for polarization along the interparticle axis decays nearly exponentially with the interparticle gap. In addition, we find that the decay length is roughly about 0.2 in units of the particle size for different nanoparticle size, shape, metal type, or medium dielectric constant. The nearexponential distance decay and the interesting “universal” scaling behavior of interparticle plasmon coupling can be qualitatively explained on the basis of a dipolar-coupling model as being due to the interplay of two factors: the direct dependence of the single-particle polarizability on the cubic power of the particle dimension and the decay of the plasmonic near-field as the cubic power of the inverse distance. Using this universal scaling behavior, we are able to derive a “plasmon ruler equation” that estimates the interparticle separation between Au nanospheres in a biological system from the observed fractional shift of the plasmon band. We find good agreement of the interparticle separations estimated using this equation with the experimental observations of Reinhard et al. (Nano Lett. 2005, 5, 2246−2252). The unique interaction of metal nanoparticles with electromagnetic radiation is constituted by localized surface plasmons, which are coherent oscillations of the metal electrons in resonance with light of a certain frequency, i.e., the localized surface plasmon resonance (LSPR) frequency.1-6 The LSPR results in a strongly enhanced electric near-field localized at the particle surface, which forms the basis of surface-enhanced spectroscopy using metal nanoparticles.7,8 The plasmon oscillations also decay radiatively or nonradiatively, respectively, giving rise to strongly enhanced scattering (in the far-field) and absorption at the LSPR frequency.2,9,10 These optical properties have been utilized in optical technologies for chemical and biological imaging,11,12 sensing,13-15 and therapeutics.16-19 Many of the applications of metal nanoparticles are being realized from their assemblies and hence, recent studies have been focused on the assemblies/arrays of metal nanoparticles.20 These studies have established that the plasmonic properties are strongly dependent on interparticle interactions.21-29 The near-field on one particle has the ability to interact with that on an adjacent particle in close proximity, coupling the plasmon oscillations together.1,23,28,30,31 This interparticle plasmon coupling forms the basis of the intense enhancement of spectroscopic signals (e.g., SERS) from molecules adsorbed at nanoparticle junctions, providing the capability for single-molecule sensing and detection.32,33 Near-field coupling in ordered nanoparticle assemblies has also been exploited for electromagnetic energy transport and subwavelength photonic waveguiding.34-37 The coupled-particle LSPR occurs at a frequency that is shifted from the single-particle LSPR frequency. The assembly or aggregation of gold nanoparticles in solution results in a red-shift of the plasmon extinction wavelength maximum from that of isolated gold nanoparticle solution at ∼520 nm, as also evidenced by a visual color change from red to purple.22,38,39 As shown by the Alivisatos and Mirkin groups,40,41 by employing a biomolecular recognition event (e.g., DNA hybridization) to trigger the assembly of nanoparticles in solution, the spectral shift in the plasmon resonance can be employed to detect specific biomolecules including DNA and protein biomarkers for cancer and other diseases.13 The magnitude of the assembly-induced plasmon shift depends on the strength of the interparticle coupling, which, in turn, depends on the proximity of the individual nanoparticles. The plasmon shift thus gives a measure of the * Corresponding author. E-mail: [email protected]. Telephone: 404894-0292. Fax: 404-894-0294. † Georgia Institute of Technology. ‡ Miller Visiting Professor, University of California, Berkeley, California 94720. NANO LETTERS 2007 Vol. 7, No. 7 2080-2088 10.1021/nl071008a CCC: $37.00 © 2007 American Chemical Society Published on Web 06/19/2007 distance between the particles.39,42,43 Sonnichsen et al. and Reinhard et al. utilized this recently to design a “plasmon ruler” to measure nanoscale distances in biological systems on the basis of the spectral shift resulting from the coupling of two gold nanoparticles by a defined biomolecular binding scheme.42,44 The plasmon ruler has some distinct advantages over the fluorescence resonance energy transfer (FRET) technique traditionally used for distance measurement, viz. a longer distance range and better photostability of the optical probes.42,43 However, a major prerequisite for the application of the plasmonic ruler is the systematic calibration and standardization of the spectral shift as a function of the interparticle separation.43 While the distance dependence of FRET is well established,45 there have been few quantitative studies on the distance dependence of plasmon coupling.21,23,27,43 The decay of electromagnetic fields in nanostructures is also fundamentally interesting from the point of view of plasmonics.30,34 The electron beam lithography technique, which provides the ability to produce metal nanoparticle structures with controlled dimensions and spacing, has already been shown by Aussenegg and Krenn to be extremely powerful for such studies.23,46-48 Recently, Su et al. studied plasmon coupling in lithographically produced elliptical gold nanoparticle pairs and observed that the plasmon shift decays almost exponentially as a function of the interparticle separation.21 Gunnarsson et al.27 further verified this near-exponential behavior in a system of Ag nanodisc pairs. A fundamental model explaining the distance dependence of plasmon coupling is lacking, however, which is the goal of the present work. Here, we study the plasmon resonances of lithographically fabricated pairs of Au nanodiscs for different interparticle separations. The polarization dependence of the plasmon coupling is clearly evident, in line with an earlier study by Rechberger et al.23 The exponential-like decay of the plasmonic shift with interparticle gap for polarization along the interparticle axis is also observed. Discrete dipole approximation simulations of the nanodisc pairs verify the observation of Su et al. that the near-exponential trend of the plasmon shift with respect to the interparticle gap becomes independent of the nanodisc diameter when the shift and separation gap are scaled respectively by the singleparticle plasmon wavelength and the nanodisc diameter.21 We further find that the decay constant measured for our Au-based system matches very well with that of the Ag system studied earlier.27 The decay constant is calculated also to be similar for nanoparticles of different shape as well as for different dielectric media. Thus, the distance decay of interparticle plasmon coupling manifests a universal scaling behavior, the origin of which we explain on the basis of a simple dipolar-coupling model. Au Nanodisc Array Fabrication. Au nanodisc pairs were fabricated using electron beam lithography (EBL). Quartz slides (Technical Glass Products, Inc.) cleaned in piranha solution (1 part 30% H2O2 and 3 parts H2SO4) for 1.5 h at 80 °C and dried in air were spin-coated with 65 nm PMMA 950k electron-sensitive resist followed by curing at 180 °C for 3 min. In order to render the substrate conductive, it was coated with a 10 nm gold layer in a thermal evaporator. The pattern for the nanodisc array was written on the substrate using the JEOL JBX-9300FS EBL system. The gold layer was then etched with an aqueous solution of KI and I2 followed by development in 1:3 methyl isobutyl ketone/ isopropyl alcohol for 180 s. The patterned substrate was then washed in isopropyl alcohol for 30 s and dried in pure N2. A thin 0.4 nm Cr layer was deposited on the substrate in an electron beam evaporator in order to improve the adhesion of the subsequent Au layer deposited to a 25 nm thickness at a rate of 0.5 Å/s. Finally, the PMMA resist and the overlaying Au layer is removed by lift-off in hot acetone (∼63 °C). Following this procedure, we fabricated twodimensional 80 μm × 80 μm arrays of 88 nm diameter Au nanodiscs with an interparticle center-to-center spacing of 300 nm between the particle rows and a center-to-center spacing of 600 nm between particles within each row. In each subsequent sample, every second particle row is shifted closer to the previous row to give different arrays of particle pairs with interparticle edge-to-edge separation gap varying as 212, 27, 17, 12, 7, and 2 nm. The patterns were imaged by scanning electron microscopy (SEM) on a LEO 1530 thermally-assisted field emission SEM, Zeiss/LEO. A representative image of the array with an interparticle gap of 12 nm is shown in Figure 1. Optical spectra of the nanodisc pairs were obtained on the substrate using a SEE 1100 microabsorption spectrophotometer in the transmission mode under polarized light excitation using a 20× objective. The area examined was 8 × 8 μm2. Polarized Microabsorption. LSPR spectra of lithographically fabricated Au nanodisc pair arrays with different internanodisc separation gap s ) 212, 27, 17, 12, 7, and 2 nm were obtained by microabsorption spectroscopy (Figure 2a,c). Two different polarization directions of the incident light were chosen, i.e., one parallel to the interparticle axis (Figure 2a) and the other perpendicular (Figure 2c) to the axis. The spectral behavior is in sharp contrast for the two polarization directions, as already observed by Tamaru et al.,49 Rechberger et al.,23 and Maier et al.30 Under parallel polarization, the plasmon resonance strongly red-shifts as the interparticle gap is reduced. Conversely, there is a very weak blue-shift with decreasing gap for orthogonal polarization. The resonance shift results from the electromagnetic coupling of the single-particle plasmons, the polarization dependence of which can be explained on the basis of a simple dipole-dipole coupling model. The dipole-dipole interaction is attractive for parallel polarization, which results in the reduction of the plasmon frequency (red-shift of the plasmon band), while that for the orthogonal polarization is repulsive, resulting in the increase in the plasmon frequency (blue-shift).23,50 The interparticle interactions are clearly stronger for parallel polarization, as seen from the larger wavelength shifts. In fact, under parallel polarization, at extremely small interparticle gaps, i.e., s ) 2 nm, a new shoulder appears at shorter wavelengths, similar to earlier studies on pairs of Ag nanodisc27 and Au nanorods50 with nearly touching particles. It must be noted that this new band is attributed to higher-order interactions, possibly the quadNano Lett., Vol. 7, No. 7, 2007 2081 rupole mode,27,51 and cannot be explained by the dipolar interaction model. The shift in the plasmon extinction maximum is plotted against the interparticle edge-to-edge separation gap for the parallel polarization in Figure 3a. Note that the plasmon maximum for s ) 212 nm (particles spaced enough to assume minimal coupling) has been used as the reference for calculation of the shift. Because these spectra are from an ensemble of particle pairs rather than single particle pairs, the data point for s ) 2 nm was not included due to the significant dispersion in the lithographic fabrication of such a small gap. The plot of the plasmon shift versus the Figure 1. Representative SEM image of the array of nanodisc pairs used in the present study, having an interparticle edge-to-edge separation gap of 12 nm, showing the homogeneity of the sample. The inset shows a magnified image of a single nanodisc pair clearly showing the interparticle gap. Each nanodisc has a diameter of 88 nm and thickness of 25 nm. Images of arrays with other interparticle gaps are not shown. Figure 2. (a,c) Microabsorption and (b,d) DDA-simulated extinction efficiency spectra of Au nanodisc pairs for varying interparticle separation gap for incident light polarization direction (a,b) parallel and (c,d) perpendicular to the interparticle axis. 2082 Nano Lett., Vol. 7, No. 7, 2007 interparticle gap follows nearly an exponential decay with a decay length of 15.5 nm ( 3.0 nm. DDA Simulations. The discrete dipole approximation (DDA) method52 was used to simulate the LSPR spectra of the Au nanodisc pairs. The DDA method has been demonstrated by the Schatz group to be suitable for optical calculations of the extinction spectrum and the local electric field distribution in metal particles with different geometries and environments.2,53 While DDA has limitations in calculating electromagnetic fields around particles,54,55 we are interested in the extinction properties of the particle pairs, which are simulated quite well by DDA, as established by the work of the Schatz group, including recent calculations of lithographically prepared silver nanodisc pairs.27 As argued earlier by Rechberger et al.,23 it is reasonable to consider in the calculations a single particle pair instead of the entire 2-D array. This is because the individual particle pairs in the experiment, especially for the smaller gap samples, are separated from each other well enough (much larger than 2.5 particle diameters)21 to have any significant near-field coupling between different pairs. This ensures that only the interaction with the pair partner is important.23 The results of discrete dipole approximation simulations of a pair of Au nanodiscs are shown for the light polarization direction parallel to the interparticle axis (Figure 2b) and that perpendicular to the axis (Figure 2d). In our calculations, each nanodisc was approximated by a cylinder of diameter 86.5 nm and height 25.5 nm, with the cylinder axis normal to the substrate. The dielectric constant of the surrounding medium m used was 1.0 for air, however, the most accurate treatment would require the consideration of the dielectric properties of the substrate, which consists of a quartz slide covered by a very thin chromium layer. The simulation assumes idealized isotropic cylinders with homogeneous sizes and interparticle gaps, which deviates from the true experimental situation. Our calculations also do not include a parameter to account for experimental inhomogeneities. All these factors contribute to the deviations of the DDA results from the experimental spectra. Nevertheless, the features of the experimental data are clearly reproduced in our simulation. The plasmon band for the disc pair with the maximum separation, i.e., s ) 208 nm (which is close to 2.5 particle diameters),21,30 closely matches the isolated nanodisc plasmon maximum (not shown) at ∼561 nm. With decreasing interparticle gap, a strong red-shift is seen for parallel polarization, along with increase in the extinction efficiency similar to the experimental observation. When the gap reaches around 2 nm, a small shoulder emerges around 550 nm similar to the experimental case. For perpendicular polarization, only a weak blue-shift of the plasmon band with decreasing gap is seen along with a decrease in the extinction