Morphology and plasmonic properties of self-organized arrays of ...

80 CHAPTER 5. MODELLING AND ANALYSIS OF THE OPT. PROP.5.2 2-dimensional arrays of gold nanoparticlesWe now focus on the optical modelling of the 2D arrays of gold NPs. The NP in sucharrays have non-spherical shape and are coherently aligned in either square or rectangularlattices. The LSP characteristics of the arrays depend both on intrinsic effect, like thesingle-NP shape, introducing anisotropic NP polarizability, and on the arrangement of theNPs in the arrays, possibly inducing anisotropic EM coupling between the NPs. In orderto separately assess the role of each effect, the experiments must be backed by appropriatemodel calculations of the LSP, that keep intrinsic and collective effects in due account.In general, due to the complexity of the involved systems, numeric methods are themost suitable to efficiently solve the optical properties of non-spherical particles; these include,for example, discrete dipole approximation [203, 204], T-matrix [205, 206] and finiteelements [207] models. Here, however, we approach the optical problem applying a simplermean field theory, based on effective medium approximations. Despite this approachbeing less rigorous than the aforementioned methods, it is much easier to implement, itcan include the main effects of the particles shape and of the presence of mutual interactions,and handles the presence of morphological disorder in a relatively straightforwardmanner.5.2.1 ModelThe 2D arrays of gold NPs are quite elaborated systems, presenting optically and morphologicallyanisotropic structures, facets tilted from the sample plane, and nearly-contactingmetallic particles with complex truncated shapes. In order to describe such systems, withoutresorting to unnecessary sophisticated computational methods, some simplificationsare therefore necessary. The major approximations we performed involve the followingparameters:• NP arrangement, fig. 5.5(a). We consider the ideal case where the substrates havea perfect ripple morphology; the NPs chains are then regularly spaced across theripples, with the same periodicity Λ of the substrate. Furthermore, following theobservation that the particles are partially aligned also between adjacent chains (seefig. 3.9), we also assume the NPs spacing along the chains to be well defined, so thatthe particles can be schematized arranged on a 2D rectangular lattice.• NP shape, fig. 5.5(b). The gold NPs are supported on the facets of the ripples,thus presenting a truncated shape tilted with respect to the plane of the sample.We simplify this geometry by considering non-truncated and non-tilted ellipsoids,having their principal axes either parallel or normal to the surface plane. This isnot a drastic approximation, because the annealing procedure is expected to smooththe NPs surface, while the tendency of gold to dewet suggests a low contact areabetween the NPs and LiF.• layers, fig. 5.5(c). The surface region of the Au/LiF nanostructures is complex.It is composed of several materials (LiF, gold, air), separated by interfaces withcomplex geometries (ripples, nanoparticles). In order to include in the model thecontributions of the most significant parameters, without complicating the model,we make extensive use of effective medium approximations (§1.2). Considering theprevious characterization of the LiF templates, we decompose the system in twomain parts, a substrate and a thin film. The substrate accounts for the optical