Optical functions of discontinuous aluminum films: intraband and interband contributions to particle resonance absorption

Abstract

We have developed a comprehensive optical model that accounts for the continuous evolution of the effective optical functions of discontinuous Al (particle) films in the vicinity of the resonance absorption feature as a function of the particle size. We obtain unprecedented agreement between the calculated and experimental results for both real and imaginary parts of the effective dielectric functions of particle films that are from 1 to 6 nm in thickness. The experimental studies rely on a unique rapid-scanning multichannel ellipsometer to collect (ψ,Δ) spectra from 1.3 to 4.0 eV during Al particle-film growth by evaporation and sputtering onto SiO2/c–Si substrates. In a least-squares regression analysis the effective dielectric functions that we obtained experimentally are fitted to a generalized Maxwell-Garnett effective-medium theory with three free parameters. Two parameters describe the particle-film morphology. The third parameter is the mean free path, which we assume to be common to electrons that participate in both intraband and interband transitions. From the modeling we find that the optical functions of the particles themselves are remarkably independent of size and shape as well as of the method of preparation. This is presumably because scattering at defects that are internal to the particles determines the electron relaxation time. The simplifying assumption regarding particle-film morphology (i.e., identical spheroids) does not appear to compromise these conclusions. From the overall study we conclude that the crystalline quality of substrate-supported metallic particles as small as 0.5 nm in radius can be assessed solely from noninvasive real-time spectroscopic ellipsometry measurements.