Size effect in the optical properties of small metallic particles: A solvable model for cubic symmetry

Abstract

A solvable tight-binding model for the electronic states of cubic crystals of arbitrary size is used to compute the real and the imaginary part of the dielectric function of metallic particles. Two types of microscopic processes are discussed: first-order transitions between electronic states and second-order transitions due to collisions with vibrational states and impurities. Interband and intraband transitions are both taken into account fors andp bands. The results display very strong size effects due to the lack of translational symmetry and to the presence of surface states; the Lorentz-Drude behaviour of the bulk metal is approached as the number of atoms in the particles increases. The size effects in the optical functions of the metallic particles are shown to depend on the environment and this is made to account for the basic features in the optical properties, in particular for the resonance plasma absorption. The case of silver particles in a glassy environment is investigated, experimental trends of the optical absorption with varying particle sizes are explained and reasonable agreement with experimental data is obtained.