Size dependence of the optical spectrum in nanocrystalline silver

We report a detailed study of the optical reflectance in sputter-deposited, nanocrystalline silver thin films in order to understand the marked changes in color that occur with decreasing particle size. In particular, samples with an average particle size in the 20 to 35 nm range are golden yellow, while those with a size smaller than 15 nm are black. We simulate the size dependence of the observed reflection spectra by incorporating Mie's theory of scattering and absorption of light in small particles, into the bulk dielectric constant formalism given by Ehrenreich and Philipp [Phys. Rev. $128,$ 1622 (1962)]. This provides a general method for understanding the reflected color of a dense collection of nanoparticles, such as in a nanocrystalline thin film. A deviation from Mie's theory is observed due to strong interparticle interactions.