# Plasmonics | Film-Coupled Nanoparticles

## Maximizing the Enhancement of the Optical Field

The strength of nearly any light-matter interaction can be increased by enhancing the local fields within the material. This enhancement effect is one of the most intriguing aspects of plasmonics, and one could argue that field enhancement remains unexploited, or at least under exploited. In the section that describes enhancement, we presented examples of surface plasmons and plasmon resonant nanoparticles, showing that interacting pairs of nanoparticles can produce locals fields hundreds of times--possibly even thousands of times--greater than the incident field. Yet, although plasmonic dimers and other clusters are capable of producing enormous field enhancements, those enhancements occur on the nanometer scale, requiring sub-nanometer control over the gap and other features of the enhancement region. In effect, while plasmonics might be nanoscience, robust and reliable structures that can leverage field enhancement require sub-nanometer tolerances.

How much field enhancement is enough? The answer to this question is complicated, since it depends on the particulars of the application being considered. The strength of nonlinear processes, for example, is proportional to higher powers of the field, so that enhancing the field to any extent possible is desirable. For example, wave mixing, harmonic generation, parametric up- or down-conversion, multiphoton absorption--the efficiency of all of these processes steadily increases as the field enhancement increases. On the other hand, field enhancement can also be used to modify the radiative characteristics of emitting molecules that interact with the local fields. For these applications, it may only be necessary to enhance the fields to the point that the radiative channel can compete with other non-radiative channels within the molecule. Still other applications, such as the creation of absorbing media, may require only modest enhancements to achieve their function.

Regardless of the application under consideration, it is important to obtain a robust and reliable platform that supports predictable field enhancements. Given the sensitivity of the enhancement to the gap thickness associated with dimers and other interacting clusters, the desired plasmonic platform should allow feature control to the sub-nanometer scale.

Interacting Nanospheres - One of the first plasmonic phenomena to be discovered was surface enhanced Raman scattering (SERS). In Raman scattering, a photon incident on a molecule excites vibrational modes that then scatter light at specific energies offset from the incident photon energy. Ordinarily this scattering is extremely weak and could never be observed from a small number of molecules. However, SERS is proportional to the fourth power of the local field, and is thus strongly enhanced in vicinity of interacting nanoparticles. Since the Raman spectrum of a molecule is unique, often terms a molecular fingerprint, it can serve as a useful probe of enhancement.

Every molecule has a Raman spectrum, and many types of molecules can also be adsorbed onto colloidal metal nanoparticles such as silver or gold and thus used as probes of enhancement. Since the SERS effect is weak, a weak enhancement--such as would be obtained from single spheres or nanoparticles--would not be expected to produce much of an effect in terms of detecting the Raman signal. In an experiment using the nanoparticle mapping technique described on this site, colloidal silver nanoparticles were coated with DPY (4,4'-dipyridyl), with their Raman spectra and physical characteristics (obtained using electron beam microscopy) compared (Mock et al., Plasmonics, 2010). As can be seen from the data in the figure below, single nanoparticles typically do not produce a measurable SERS signal.

For dimers--two interacting nanoparticles--we expect a large field enhancement to exist where the nanoparticles nearly touch. However, most colloidal methods used dont allow easy control over the dimer creation (just two particles as opposed to three or more), nor do they allow control of the gap thickness to the sub-nanometer level. In addition, there is no guarantee that the molecules of interest will actually end up in the very small enhancement volume between the nanoparticles. All of this uncertainty suggests that achieving a reliable field enhancement with dimers should be challenging. The apparent randomness in SERS enhancement, in fact, is common, as illustrated by the measurements shown below on nanoparticle pairs. Some of the dimers provide a SERS signal, while others do not, leaving one to speculate as to the cause of the variability.

## Film-Coupled Nanospheres

To fully leverage the field enhancement that nanoplasmonic structures can offer, it is clearly necessary to find a means of tightly controlling the surface quality and dimensions of the gap region. With many plasmonic systems, current methods of fabrication, including colloidal synthesis or nanolithography, are insufficient to unlock the full potential of field enhancement. One alternative system that addresses many of the essential issues is that of the film-coupled nanoparticle, shown schematically in the figure to the right.

The film-coupled nanoparticle system consists of a metal film, coated with a non-conducting spacer layer of dielectric material, with metal nanoparticles deposited on the spacer layer surface. From electromagnetic theory, charge distributions induced on the nanoparticle in turn induce image charges within the conducting layer. The configuration can be thought of as a nanoparticle interacting with its image nanoparticle, suggesting the properties of film-coupled nanoparticles should be similar to nanoparticle dimers. The film-coupled nanoparticle system, however, benefits from the strengths of planar fabrication and deposition; these techniques routinely allow thickness accuracy to the molecular scale.

The general optical properties of film-coupled nanospheres can be understood from simple electromagnetic image theory. In isolation, a plasmon resonant nanosphere's optical properties are close to those of an ideal polarizable dipole. As the nanosphere approaches a metal film, it induces an image dipole in the film that can be thought of as also scattering the incident field. For the component of the dipole perpendicular to the film, the image dipole is in the same direction and the two dipoles interfere constructively. There is also a red-shift in the resonance wavelength that increases as the nanosphere gets closer to its image. For the component of the dipole parallel to the film, the image dipole is in the opposite direction, and the two dipoles produce fields that cancel. The strength of the resulting scattered field is reduced and the resonance wavelength blue-shifted. The situation is illustrated in the diagram below.

This dipole interaction picture can be easily confirmed experimentally using the darkfield microscopy techniques described elsewhere. Samples are fabricated by first depositing a layer of metal (gold or silver, for example) onto a glass substrate. Then, a spacer layer can be formed using organic polymers, or by atomic layer deposition (ALD). Either approach can yield extremely uniform spacer layers with thickness control down to about one or two tenths of a nanometer.

In the figure below, two sets of film-coupled gold nanospheres are compared, one with the nanospheres directly on top of a gold film, and the other with the nanospheres placed on a polymer spacer layer of thickness 23 nm. The nanospheres with the large spacer layer are far enough away from the metal film that they are essentially isolated, scattering light at the plasmon resonance wavelength corresponding to the isolated sphere (green). When the nanospheres are directly on the gold film, however, they interact strongly such that their radiative characteristics change drastically. Because the parallel dipole moments of the nanospheres and their images cancel, only the perpendicular components radiate, giving rise to the donut shaped images. Also, the perpendicular component of the dipole undergoes a substantial redshift, so that the ordinarily green nanospheres now appear as bright red. For this experiment, the spacer layer was formed using a layer-by-layer polymer assembly approach, with each layer adding about half a nanometer of thickness.

The polymer spacer layers provide remarkable uniformity over large areas, so that the characteristics of all of the nanospheres are very similar, as shown in the next set of darkfield images. As the spacer layer thickness is varied in steps of about 0.6 nanometers using the layer-by-layer assembly method, the appearance of the nanoparticles changes from red donuts to green dots. At all thicknesses, virtually all nanospheres scatter at the same wavelength and with the same pattern. Thus, using the film-coupled nanoparticle approach, control over the gap dimension can clearly be achieved with excellent reproducibility.

## Film-Coupled Nanospheres: Enhancement

Simple arguments based on the electromagnetic theory of images suggest that a nanosphere interacting with a film should be similar to two interacting spheres. But, those arguments were made with the assumption that the nanospheres scatter light roughly like point dipoles. We know that when two nanospheres become extremely close, the local field pattern changes considerably, becoming strongly localized within the gap region. If we want to leverage field enhancement using the film-coupled nanosphere system, it is important that the field distributions associated with the nanosphere nearly touching the film surface are also similar to two nearly touching nanospheres.

There are many ways to determine a solution to the film-coupled nanosphere, including full-wave numerical simulations. However, as with the case presented with nearly touching spheres, the transformation optics method of Aubry and Pendry can be applied to the film-coupled nanocylinder system, allowing simple analytical expressions that provide immediate insight. Using their approach, the expression for the resonance frequency of the system can be found as

${\left( {\sqrt \rho + \sqrt {1 + \rho } } \right)^4} = {\mathop{\rm Re}\nolimits} \left\{ {{{\left( {\frac{{\varepsilon \left( \omega \right) - 1}}{{\varepsilon \left( \omega \right) + 1}}} \right)}^2}} \right\}$

where ${\rho=g/d}$, and $d$ is the nanosphere diameter and $g$ is the gap between the nanosphere and the film. This equation can be used to include an infinite set of higher order resonances, but we are interested only in the lowest resonant mode here. As with the case of the two interacting nanospheres, we can use the above equation to create an approach curve for the system.

As was the case with the interacting nanocylinders, the plasmon resonance frequency undergoes an extreme shift as the gap between nanocylinder and film is around 10 nm or less, increasing without bound as the gap closes. These extreme shifts suggest that the nanocylinder-film interaction is indeed very strong, and one can expect the fields to be increasingly localized within the gap region.

The interaction effect can be visualized by plotting the fields (in this case, the perpendicular field component) for the film-coupled nanocylinder. When the gap between nanocylinder and film is large, the fields reside mostly in and around the cylinder, as if it were in isolation. While there are some fields in the metal film, they are relatively minor and do not impact the properties of the cylinder very much. As the sphere approaches the film, the fields between the cylinder and film begin to increase, until they are very strongly localized when the gap is on the scale of a few nanometers.

In general, the field in the enhanced region has a distribution that is strongest near the surface of the nanocylinder, and falls off somewhat towards the film. This would be similar for two interacting nanocylinders, for which the localized field would be relatively weaker at the midline between the nanocylinders, farthest from the surface charge distributions. As a function of the gap thickness, the enhancement of the local field follows a similar trend as the coupled nanocylinders, as shown in the figure below. The enhancement is not quite as large for the film-coupled nanocylinder system as for the two nanocylinders, but relatively large enhancements are available. Given the advantages in terms of systematic fabrication and reproducibility, the film-coupled nanocylinder system represents a reasonable tradeoff for leveraging field enhancement.

# Useful References

Electromagnetic enhancement effect caused by aggregation on SERS-active gold nanoparticles
J. J. Mock, S. M. Norton, S.-Y. Chen, A. A. Lazarides, D. R. Smith
Plasmonics 6, 113 (2010)

Distance-dependent plasmon resonant coupling between a gold nanoparticle and gold film
J. J. Mock, R. T. Hill, A. Degiron, S. Zauscher, A. Chilkoti, D. R. Smith
Nano Letters 8, 2245 (2008)

Plasmonic hybridization between nanowires and a metallic surface: A transformation optics approach
A. Aubry, D. Y. Lei, S. A. Maier, J. B. Pendry
ACS Nano 5, 3293 (2011)