Optical properties of copper clusters embedded in alumina: An experimental and theoretical study of size dependence

Optical properties of copper clusters of $3\text{to}5\mathrm{nm}$ in diameter, produced by laser vaporization and embedded in alumina, are investigated and compared to a semi-quantal model [based on time-dependent local-density approximation (TDLDA) and density functional theory (DFT)], including the absorption and screening properties of the ionic core background and the surrounding matrix. To begin with, the experiments show that the alumina trapped clusters are oxidized if codeposited at room temperature whereas they do remain metallic by holding the substrate temperature at $400°\mathrm{C}$. On the other hand, reducing under ${\mathrm{H}}_2\text{−}{\mathrm{N}}_2$ atmosphere of samples made at room temperature is an alternative to elaborate embedded metallic copper clusters. Consequently, the alumina matrix evaporated on a substrate at $400°\mathrm{C}$ is optically characterized and the oxidization level of the copper clusters is carefully investigated through x-ray photoelectron spectroscopy (XPS). Concerning the optical properties of the copper clusters, a strong damping and a broadening of the surface plasmon resonance (SPR) with decreasing size is observed, in good agreement with theoretical calculations. This damping, much more important than in gold clusters, is correlated to a strong coupling of the collective excitation with interband transitions. These results allow us to validate the semiquantal model for the three systems Au, Ag, and Cu, in which the size effects are ruled by the electronic spillout phenomenon, the surface of ineffective ionic core polarization and the local porosity at the metal/matrix interface. Lastly, the inhomogeneous effects such as size dispersion are shown to be of less importance compared to intrinsic size effects in the optical properties.