Plasmon Spectroscopy for Subnanometric Copper Particles: Dielectric Function and Core–Shell Sizing

Abstract

In the last years, there has been a growing interest in the study of transition metal nanoparticles (Nps) due to their potential applications in several fields of science and technology. In particular, their optical properties are governed by the characteristics of the dielectric function of the metal, its size and environment. This work analyses the separated contribution of free and bound electrons on the optical properties of copper Nps. Usually, the contribution of free electrons to the dielectric function is corrected for particle size through the modification of the damping constant, which is changed as usual introducing a term inversely proportional to the particle’s radius to account for the extra collisions with the boundary when the size approaches the electronic mean free path limit (about 10 nm). For bound electron contribution, the interband transitions from the d-band to the conduction band are considered together with the fact that the electronic density of states in the conduction band must be made size-dependent to account for the larger spacing between electronic energy levels as the particle decreases in size below 2 nm. Taking into account these specific modifications of free and bound electron contributions to the dielectric function, it was possible to fit the bulk complex dielectric function, and consequently, determine optical parameters and band energy values such as the coefficient for bound electron contribution Q _bulk = 2 × 10²⁴, gap energy E _g = 1.95 eV, Fermi energy E _F = 2.15 eV, and damping constant for bound electrons γ _b = 1.15 × 10¹⁴ Hz. With both size-dependent contributions to the dielectric function, extinction spectra of copper Nps in the subnanometer radius range can be calculated using Mie’s theory and its behaviour with size can be analysed. These studies are applied to fit experimental extinction spectra of very small spherical core–shell Cu–Cu₂O Nps generated by ultrafast laser ablation of a solid target in water. Theoretical calculations for subnanometric core radius are in excellent agreement with experimental results obtained from core–shell colloidal Nps. From the fitting, it is possible determining core radius and shell thickness of the Nps, showing that optical extinction spectroscopy is a good complementary technique to standard high-resolution electron microscopy for sizing spherical nanometric-subnanometric Nps.