Nanosphere lithography: Surface plasmon resonance spectrum of a periodic array of silver nanoparticles by ultraviolet-visible extinction spectroscopyand electrodynamic modeling

In this paper we measure the optical extinction spectrum of a periodic arra y of silver nanoparticles fabricated by nanosphere lithography (NSL) and pr esent detailed comparisons of the results with predictions of electrodynami c theory. The silver nanoparticles are small (similar to 100 nm) compared t o the wavelength of light but too large to have their optical properties de scribed adequately with a simple electrostatic model. We make use of the di screte dipole approximation (DDA), which is a coupled finite element method . With the DDA one can calculate the extinction of light as a function of w avelength for particles of arbitrary size and shape. We show that NSL-fabri cated Ag nanoparticles can be modeled without adjustable parameters as trun cated tetrahedrons, taking their size and shape parameters directly from at omic force microscopy (AFM) measurements and using literature values of the bulk dielectric constants of silver. These AFM measurements are presented as part of this paper, and the resulting theoretical line shapes and peak w idths based on the AFM-derived parameters are in good agreement with measur ed extinction spectra. The peak width measured as the full width at half-ma ximum (fwhm) is approximately 100 nm, or 0.35 eV, which corresponds to an e lectron-hole pair lifetime of 2 fs. The combined effects of particle-partic le and particle-substrate interactions red-shift the surface plasmon resona nce by only about 10 nm versus a single isolated particle. By use of AFM-de rived parameters that have been corrected for tip-broadening and by inclusi on of an estimate for the effects of particle-particle and particle-substra te interaction, the discrepancy between the theoretical and experimental ex tinction peak maxima is approximately 25 nm, which is significantly smaller than the plasmon width. This residual difference between theory and experi ment is due to shortcomings of the truncated tetrahedron geometry in descri bing the actual shape of the particles, errors in the literature values of the bulk dielectric constants, and experimental uncertainty due to slight h eterogeneities in nanoparticle structure.