Determination of size and concentration of copper nanoparticles dispersed in glasses using spectroscopic ellipsometry

For the generation of particular optical properties the melt of a commercially manufactured glass is doped with copper compounds. The glass obtained is opaque black at the usual thickness and looks dark red after making it into bulbs of incandescent lamps. It is generally assumed that copper particles cause this colouring. A proof in a spectrophotometric way fails due to the very high absorbance even for a sample thickness below 20 μm. It will be shown that in these cases spectroscopic ellipsometry is a suitable method of investigation. The pseudo-optical constants of this material were determined as a function of wavelength in the range from 350 nm to 700 nm by ellipsometric measurements. They can be reproduced very well by those of a model that consists of a roughness layer situated on a substrate of glass containing spherical copper particles with a Gaussian size distribution with R̄= 6.5 nm and σ = 0.24R̄ and a volume concentration of 2.4 × 10-3. For this modelling the dielectric function of the roughness layer was approximated by Bruggeman effective-medium theory and that of the copper-containing glass substrate was calculated on the basis of the theory of Gans and Happel. The results were verified by transmission electron microscope investigations.