NANO LETTERS
Strongly Interacting Plasmon Nanoparticle Pairs: From Dipole−Dipole Interaction to Conductively Coupled Regime
2004 Vol. 4, No. 9 1627-1631
Tolga Atay, Jung-Hoon Song, and Arto V. Nurmikko* DiVision of Engineering and Department of Physics, Brown UniVersity, ProVidence, Rhode Island 02912 Received May 25, 2004; Revised Manuscript Received July 19, 2004
ABSTRACT We have investigated the optical response of periodic arrays of metallic (gold) nanoparticles composed of a pair of particles on each lattice site. By varying the interparticle separation within the pairs from dielectric proximity to conductive contact on a nanometer scale, we observe an abrupt, large renormalization as well as a splitting of the surface plasmon polariton energy. These spectral anomalies are ascribed to a transition whereupon the interparticle dipole−dipole interaction is shunted and the plasmon polaritons exhibit multipolar behavior, including a very high local concentration of electromagnetic energy in the vicinity of their conductive contact.
The optical properties associated with plasmons in small metallic structures have been widely studied, ranging from chemically synthesized nanoparticles1-3 to recent work on precisely fabricated periodic arrays etched from thin gold and silver films by advanced lithographic techniques. The latter approach affords flexible control of the size, shape, and layout of arrays of nanoparticles in the ∼50-100 nm particle size range for a variety of metals so that their electromagnetic response can be studied in terms of the several distinct physical contributions that determine both linear and nonlinear optical properties.4,5 In planar metal nanoparticle arrays, it is well understood from classical electrodynamics how both the individual nanoparticle size/shape as well as the dimensions and geometry of the periodic lattice dictate the spectral response of the plasmon polaritons that can be readily excited by incident electromagnetic radiation from free space. One interesting case occurs when each lattice site is occupied by a pair of nanoparticles in close mutual proximity, whereupon the plasmon response is modified due to an additional contribution to the total energy by the pairwise induced dipole-dipole interaction.6,7 An unanswered experimental question, to our knowledge, is the change in the nature of the collective electron optical response when the interparticle separation is reduced to zero, i.e., when the dipole interaction is “shunted” and replaced by an (narrow) electrically conductive path connecting the pairs of particles. Earlier theoretical work has considered the case of bispherical * Corresponding author. E-mail:
[email protected]. 10.1021/nl049215n CCC: $27.50 Published on Web 08/12/2004
© 2004 American Chemical Society
surface plasmon modes of two interacting metal nanoparticles with decreasing dielectric spacing, in the absence of retardation effects, but these models lose their validity in the limit of physical contact between the spheres.8,9 From a different point of view, and drawing on the analogy to the Hertz contact problem for two elastic bodies, Nerkararyan and coworkers have solved the wave equation for two conductive spheres at exact point contact, to predict that a very large enhancement of the electromagnetic energy occurs in the immediate vicinity of this point contact.10 These authors have noted how localization of the plasmon modes is induced by the decrease of their wavelength toward the contact point and coined the phrase “superfocusing” to highlight the expected phenomena. In this work we show that the electromagnetic signature for a pair of metal nanoparticles can change quite dramatically as a conductive “bridge” is formed, resulting in a sharp and abrupt renormalization of the plasmon-polariton energy. The plasmon resonance in the transmission spectrum of light can shift and split by up to several hundred nanometers across the visible and near-infrared. For these experiments, samples were fabricated as periodic rectangular arrays of pairs of gold nanoparticles by high-resolution electron-beam lithography and liftoff techniques to create circular dots over a range of diameters (from 80 to 150 nm). We specifically focus in this work on relatively thin gold films (15-60 nm thickness range) so that the particle aspect ratio is akin to a “pancake” shape. Typical patterned areas were approximately 100 × 100 µm. Figure 1 illustrates the sample details as well as
Figure 1. (a) The arrays were fabricated on ITO coated glass substrates. Different samples with dot diameters ranging from 80 to 150 nm and heights from 15 to 60 nm were studied. For each sample, the lattice constants were fixed at 800 nm in the parallel direction to the pair axis and 400 nm in perpendicular. Series of arrays were fabricated with varying interparticle separation within pairs, all other parameters (diameter, thickness, and lattice constants) kept fixed. (b) The arrays were illuminated with polarized white light. The spectra were taken at normal incidence.
the illumination/detection geometry. In particular, we concentrated on the development of fabrication techniques that enabled reasonably good control of the separation of particles within each pair with approximately 10 nm precision. We were able to produce series of array samples where the details of the impact of formation of the conductive contact could be spectroscopically investigated with varying interparticle separation, as one reaches the conductively coupled regime, and for a further gradually increased overlap and “fusion” of the particles. We note that the material science issues of reaching a precise point of contact between the particles are quite complex, including the likelihood of some mass transfer on nanometer scale by solid-state diffusion induced by very large concentration gradients. We will report on these investigations elsewhere, including the effects of thermal annealing on such nanostructures. The linear optical properties of the arrays were examined in polarized white light transmission (incoherent source), taken at normal incidence. As a “global overview” of the range of optical response encountered in our experiments, Figure 2 shows a partial snapshot selected from a series of spectra, with the optical field polarized along the interparticle axis, for a progression of samples where the separation between pairs of 130 nm diameter nanoparticles is varied (for a fixed lattice constant of 800 nm in the parallel direction to the pair axis, 400 nm perpendicular). An accompanying SEM image is shown for each representative particle pair, indicating their targeted edge-to-edge separation. Figure 2a emphasizes the regime where particle pairs are initially dielectrically separated but with this separation then reduced 1628
to zero. As long as the particle pairs lack a direct conductive interlink, their proximity produces a (negative) dipole-dipole coupling energy contribution so that the surface plasmon polariton resonance red shifts.6,7 Depending on the particle size and lattice constant, this red shift may reach ∼200 nm when the particles are brought to below ∼10 nm from each other (edge-to-edge separation). However, immediately upon physical contact, the dominant polariton resonance appears to “blue shift” abruptly, as shown in the third trace of Figure 2a, here to about 740 nm. (Such “jumps” in excess of 200 nm were observed in other samples of different size/ thickness.) We verified the abruptness and experimental consistency of the occurrence of these sudden spectral changes on samples obtained from different fabrication runs. The SEM images in Figure 2b show how the subsequent increase in the electrical connectivity between the nanoparticles creates, in effect, a plasmon polariton oscillator which includes the narrow conductive “neck” (note, e.g., the trace for a targeted 10 nm particle overlap). As the neck increases in its area, the associated spectral characteristics of the polariton show a clear contribution to the extinction coefficient at two distinct wavelengths, that is, the blue shifted component is accompanied by a longer wavelength infrared resonance. With the particle pair overlap increasing, this long wavelength resonance eventually dominates as the particles merge to a nearly ellipsoidal shape, consistent with earlier reports on single ellipsoidal particles with incident polarization along the major axis.11 Concentrating in the regime where initial conductive contact has occurred between pairs of particles, Figure 3 Nano Lett., Vol. 4, No. 9, 2004
Figure 2. Polarized transmission spectra in periodic arrays of pairwise interacting gold nanoparticles. The lattice constant is 800 nm in parallel direction to the pair axis, 400 nm perpendicular, and the dot height is 30 nm. (a) Pairs of particles approaching each other just reaching physical contact (labeled “0 nm” in the SEM image of a single particle pair). (b) Increasing the particle overlap from point contact (“0 nm”; shown again for reference) and the widening of the interconnection “neck” into an eventually single ellipsoidal single (anisotropic) plasmonic particle.
Figure 3. Polarized transmission spectra, emphasizing the regime of conductive overlap between the particles (the values indicate approximate overlap, in reference to “0 nm” referring to the point contact of the particle pairs). The SEM images illustrate details of geometry. (Particle size 150 nm and height 30 nm.)
shows the above-described spectral behavior in more detail for another fabricated array with individual particle diameter of 150 nm and a lattice constant of 800 nm in parallel to the pair axis, 400 nm perpendicular. The line width of the long wavelength resonance is clearly broader, implying larger Nano Lett., Vol. 4, No. 9, 2004
damping. A summary of the wavelength position of the spectral resonances for this particular array is shown in Figure 4a over the entire range from finite dielectric separation to conductive overlap. Note that the spectral separation between the two components remains approximately constant in the latter regime. Upon thermal annealing of the samples at 400 °C for 10 min, the behavior shown in Figures 2-4 is maintained, except for an overall small blue shift in all sets of spectra. This is due to some rounding of the corners of the “pancakes” as evident from their electron microscope images. Finally, Figure 5 shows the transmission spectra recorded with optical fields polarized perpendicular to the interparticle axis, from which we note the relative insensitivity of the plasmon polariton response over the large range of changes in the local “architecture” of the particle pair. Here, only a small blue shift is observed with the spacing/ overlap changes, as reported earlier in the regime of dielectrically separated particle pairs.6 In interpreting the observed effects in the conductively coupled particle regime, we note that the optical response in single small spherical metallic particles was theoretically analyzed already some time ago by estimating the contributions by different multipolar orders for plasmon polariton contributions. The charge distributions for dipole, quadrupole, and multipole modes are illustrated in Figure 4b for a single spherical particle. Kreibig and co-workers in particular12 showed how, for isolated silver nanospheres with a diameter up to about the 100 nm range, the quadrupole contribution, in particular, effectively competes with the dipolar polariton mode for both the absorptive and scattering cross-sections. While the (Mie) scattering contribution in our periodic arrays is less important, we believe that the idea of a competition between dipole and quadrupole modes is applicable to the 1629
Figure 4. (a) Measured spectral positions of the polariton resonances (maximum extinction), as a function of particle separation, in the regime of dielectric separation (right side in the figure) and conductive overlap (left side). (b) Pictorial illustration of charge distributions for dipole, quadrupole, and multipole modes for a single spherical particle.
Figure 5. Spectra for perpendicular polarization over the entire pair separation regime.
present case, once the conductive contact between particles in each pair is established. In terms of the summary data of Figures 3 and 4, once this link is established (thereby “shorting” the dipole-dipole interaction), the relative crosssections of the dipole and quadrupole plasmon polariton 1630
modes are dictated by the degree of particle overlap. Clearly, at the instance of “point contact” the geometry and symmetry of the “dumbbell” can favor the quadrupole mode, while at the opposite limit of merging the particles to a single ellipsoidal cylinder, the dipole mode establishes its dominance. We emphasize that the interest in this work was on “flat” particles due to potential applications; for aspect ratios that correspond to tall cylinders or spherical pairs of particles, the quadrupole/dipole contributions will have different ratios. We also note that detailed electromagnetic wave analysis of the geometries considered here are quite challenging; indeed as already pointed out, prior theoretical work on the bispherical (dielectrically separated) particles was unable to reach into the regime of conductive point contact. The physically most interesting regime, where the pairs of nanoparticles form a narrow, conducting link for interparticle plasmon coupling, has potentially useful consequences in terms of concentration of very large optical fields in the spatial region of the interconnection “neck”. As already noted, recent work has suggested that anomalous plasmon field enhancement effects occur at contacting surfaces between metal spheres (or cylinders), leading to “superfocusing” of electromagnetic energy. We have tested this hypothesis crudely by subjecting the arrays to illumination by ultrashort (100 fs) laser pulses, tuned to the quadrupole plasmon resonance. In this case, the height of each particle is 17 nm with a diameter of 150 nm. With moderate excitation levels that have no permanent impact on simple single-particle gold arrays, such photoexcitation is seen to lead readily to an irreversible physical break of the “neck” as seen in Figure 6a. We speculate that that local concentration of absorbed optical energy creates such mechanical breaking perhaps by THz acoustic shock waves that are generated as a result of the rapid thermal expansion/ contraction that arises from transient heating/cooling in the vicinity of the particle interconnection. Figure 6b shows the transmission spectra of the pairs before and after the fs pulse illumination. The studied sample area was limited by a small pinhole to a diameter of 10 µm in order to ensure that all the “necks” of the particle pairs were broken, as monitored by SEM. Now the plasmon resonance is dramatically split into two peaks when the particles are separated by a small gap (
