Influence of size-corrected bound-electron contribution on nanometric silver dielectric function. Sizing through optical extinction spectroscopy

Abstract

The study of metal nanoparticles (NPs) is of great interest due to their ability to enhance optical fields on the nanometric scale, which makes them interesting for various applications in several fields of science and technology. In particular, their optical properties depend on the dielectric function of the metal, its size, shape and surrounding environment. This work analyses the contributions of free and bound electrons to the complex dielectric function of spherical silver NPs and their influence on the optical extinction spectra. The contribution of free electrons is usually corrected for particle size under 10 nm, introducing a modification of the damping constant to account for the extra collisions with the particle's boundary. For the contribution of bound electrons, we considered the interband transitions from the d-band to the conduction band including the size dependence of the electronic density states for radii below 2 nm. Bearing in mind these specific modifications, it was possible to determine optical and band energy parameters by fitting the bulk complex dielectric function. The results obtained from the optimum fit are: Kbulk = 2 × 1024 (coefficient for bound-electron contribution), Eg = 1.91 eV (gap energy), EF = 4.12 eV (Fermi energy), and γb = 1.5 × 1014 Hz (damping constant for bound electrons). Based on this size-dependent dielectric function, extinction spectra of silver particles in the nanometric–subnanometric radius range can be calculated using Mie's theory, and its size behaviour analysed. These studies are applied to fit experimental extinction spectrum of very small spherical particles fabricated by fs laser ablation of a solid target in water. From the fitting, the structure and size distribution of core radius and shell thickness of the colloidal suspension could be determined. The spectroscopic results suggest that the colloidal suspension is composed by two types of structures: bare core and core–shell. The former is composed by Ag, while the latter is composed by two species: silver–silver oxide (Ag–Ag2O) and hollow silver (air–Ag) particles. High-resolution transmission microscopy and atomic force microscopy analysis performed on the dried suspension agree with the sizing obtained by optical extinction spectroscopy, showing that the latter is a very good complementary technique to standard microscopy methods.