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Metal Nanostructures for Optical Sensing and Signaling
Jim Adleman, Demetri Psaltis

Abstract. The aim of this research is to develop devices based upon two dimensional arrays of metallic nanoparticles, with an optical signatures that are tunable and can measure changes their environment. We have synthesized silver nanoparticles of 3-6 nm in diameter. We have measured resonant scattering from solutions and 2D arrays of these particles throughout the visible spectrum. The resonance of these particles is due to the motion of the ‘free’ electrons in the cluster.

We attempt to modify the shape of this resonance by distorting the shape of the electron cloud of the particle with an external field. To study this effect we spin coat silver nanoparticles on to clear conductive substrates in order to apply large fields both along the direction of propagation and the direction of polarization of light that passes through our devices. Non-linear interaction between nanoparticles which can be tuned by applied fields would make it possible to switch electromagnetic energy confined to a nanometer scale at optical frequencies. This would be very useful in the design of optical switches for computing, and arrays of nanoparticle based sensors that could be used to measure chemical or physical changes in a given environment.

We also are attempting electrical tuning of the metal insulator transition in silver nanoparticles. When a lattice of sufficiently identical nanospheres is compressed so that the electron spillout from individual crystals overlap, the electron states become delocalized across the whole lattice. This gives the lattice the characteristics of a thin metal film. We propose to use external fields to re-localize these electrons to single sites in the lattice. This would allow the film to switch between a metallic state with a flat absorption curve and an insulating state with a resonant absorption curve.

The effects of electromagnetic fields on very small particles have many interesting properties that can be exploited to create sensors, switches and modulators. For optical frequencies, the interaction of light and matter can be analyzed using Maxwell’s equations in the formalism of the vector wave equations. The classical optical properties are essentially determined by two sets of parameters. One is the geometry of the system being studied, or the boundary conditions of the problem. The second is the material properties of the system, as specified by the complex permittivity and permeability (e and m) of the object being studied. These quantities are functions of the frequency of the electromagnetic field.

For instance, in metallic spheres smaller than the wavelength of visible light, there exists a ‘plasma resonance frequency’ at which the permittivity of the sphere is negative, and the extinction cross section of the particle is extremely large [1]. This phenomenon is called plasma resonance, because it is at this frequency that the electromagnetic field can excite charge density waves in the free electrons of the metal. The extinction of such a particle resembles a Gaussian curve with a peak at the plasma resonance frequency. Nonspherical particles change the boundary conditions, and can shift the extinction peak throughout the spectrum, or create multiple, smaller resonance peaks due to asymmetry [2]. The strong dependence on the resonance with shape can be used in sensor applications to determine when certain chemicals have bonded to nanoparticles [3].

Since the resonance of a metallic nanostructure is based upon the movement of the free electrons in the crystal, Coulomb forces between nearby particles cause significant changes to the individual extinction curve [4]. We have been attempting to modify the resonance of ensembles of nanoparticles by applying large external fields. By applying electric fields great enough to produce deviations of the electrons from equilibrium on the order of the particle size, we expect to introduce nonlinearity.

Figure 1. Absorption of two batches of Ag nanospheres in chloroform

In order to study these effects, we have synthesized metallic nanoparticles passivated with dodecanethiol by means of a reduction reaction based on the recipe given by Collier et al [5]. These nanoparticles have a resonance in the visible at around 430 nm. We can evaporate a solution of these particles on a substrate to create monolayers of variable packing density on substrates in order to measure the resonance of the particles and the effect of the inter-particle coupling. We can apply a field across a monolayer of particles sandwiched between two clear conducting (ITO) plates. We are currently attempting to measure an electro-optic effect caused by this applied field.

We would like to extend these experiments to measurements of mixing between different frequencies. By placing nanoparticles of different sizes very close to each other, we could monitor how the driving one particle at its resonant frequency affects the resonance of the other particle. This geometry would be useful in attempting to design optical gates that could perform computation.

In addition, we are developing models of the linear response of nanoparticle assemblies based on both analytical models such as Mie scattering, and numerical methods. We have chosen the Multiple Multipole (MMP) technique as a computational method. MMP is a frequency domain technique based on matching boundary conditions. It is a useful technique for nanometer size electromagnetic simulation, since time domain techniques scale poorly as size decreases [6]. We are currently implementing the algorithm and checking its predictions against both analytic and experimental results.

We are also developing ways to control the placement of nanocrystals on substrates. It would be advantageous to be able to line up the nanocrystals in lines and grids for sensor and switching arrays. To this end, we are working with the nanolithography group here at Caltech to design nanometer sized channels which can be filled with these particles. These channels could act as submicron wave guides, or as an array of chemical sensors. By monitoring the local optical signature of the channel, we may be able to detect changes in concentration of the particles or chemicals adsorbed to their surface.

Metal Insulator Transition:
The particles we have produced are also suitable to perform the metal insulator transition. Collier et al showed that a lattice of these particles, if sufficiently ordered, could take on the character of a continuous metal film [5]. These films were made by floating the particles on water and allowing them to self organize into a regular two dimensional ‘super-lattice’. By applying pressure as shown below, the spacing between the particles could be controlled.

They observed that when the inter-particle spacing was large, light reflected from the film was characteristic of the classical resonant scattering as described above. However, as the spacing was decreased beyond a critical point, the film took on a metallic sheen, and the resonant peak disappeared and was replaced by a flat absorption that was consistent with a thin continuous metal film. The explanation for this effect is that the electrons of each particle have some extent outside the classical boundaries of the sphere. As the spheres are compressed, their electron wave functions overlap and quantum exchange can occur. For films with a high degree of order, the film can make a transition from an insulating system, where electrons are localized to the individual sites in the lattice, to a metallic state, where the electrons are able to tunnel through the potential barriers and are delocalized across the whole film.

Remacle et al have characterized this system using a simplified quantum mechanical model that uses a Hamiltonian that is in the basis of the lattice sites. [7]

Here the diagonal elements represent the site energies of the system, and the off diagonal elements represent coupling between the adjacent sites in the lattice. This coupling is brought about by the overlap of the wave functions of electron in the original sites. The coupling is a perturbation that causes the electrons to delocalize, and produces the behavior observed by Collier upon compression of the nanoparticle film. Remacle concludes that delocalization occurs when the average strength of the coupling, b is significant compared to the variation of the site energies, .

We propose to demonstrate similar films where the coupling can be tuned electrically rather than mechanically. By constructing a film of silver nanoparticles that has been compressed just to the point of the metal transition, and sandwiching it between two conductive plates, we should be able to apply fairly strong fields perpendicular to the plane of the film. The effect of these fields would be to change the angular dependence of the electron wave functions, shifting the probability of having an electron near the equator of the particle, and reducing the overlap of adjacent particles. By tuning this field the value of the overlap integral between sites, _, could be reduced and the film could be toggled into the insulator regime.

Figure 2. SEM image of packing of silver particles on a silicon substrate

References
[1] Bohren, C.F.; Huffman, D.R. Absorption and Scattering of Light by Small Particles; John Wiley & Sons: New York, 1983. p326.

[2] Bohren & Huffman, p 356.

[3] Shipway, A.N.; Katz, E.; Wilner, I. Chemphyschem 1(1):18-52 AUG 4 200

[4] Rechberger, W.; Hohenau, A. Leitner, A.; Krenn, J.R.; Lamprecht, B.; Aussenegg, F.R.; Optics Communications, 220 (2003) 137-141.

[5] Collier C.P.; Saykally R.J.; Shiang J.J.; Henrichs S.E.; Heath J.R.; Science 277 (5334): 1978-1981 SEP 26 1997

[6] Hafner, C. The Generalized Multipole Technique for Computational Electromagnetics. Artech House Inc.: Boston, 1990.

[7] Remacle, F.; Collier, C.P.; Markovich G.; Heath, J.R.; Banin, U.; Levine, R.D. J. Phys. Chem. B 1198, 102, 7727-7734.