Quantitative modelling of the surface plasmon resonances of metal nanoclusters sandwiched between dielectric layers: the influence of nanocluster size, shape and organization

The effects of size, shape and organization on the surface plasmon resonances of Ag nanoclusters sandwiched between Si₃N₄ layers are studied by transmission electron microscopy and anisotropic spectroscopic ellipsometry. We present an easy-to-handle model that quantitatively links the nanostructure and optical response of the films, which are considered as dielectric/metal:dielectric/dielectric trilayers, with the central nanocomposite layer being an effective medium whose optical properties are described by an anisotropic dielectric tensor. The components of this tensor are calculated using a generalization of the Yamaguchi theory taking into account the real organization, size and shape distributions of ellipsoidal nanoclusters, whose electronic properties are assumed to reflect shape-dependent finite size effects. Using this model, it is shown that the optical response of the films in the visible range is dominated by the excitation of the surface plasmon resonance of the clusters along their in-plane long axis, while no surface plasmon resonance resulting from an excitation along their in-plane short axis can be observed due to damping effects. Moreover, the spectral position of this resonance appears to be mainly affected by the average shape of the clusters, and weakly by their size, their shape distribution and the electromagnetic interaction between them.