Short-range ordered 2D nanoholes: Lattice-model and novel insight into the impact of coordination geometry and packing on their propagating-mode transmittance features

Optically thin perforated gold films, fabricated using template colloidal masks self-assembled by following an elsewhere described simplified colloidal lithography protocol, are presented and discussed with the aim to develop a theory of short-range ordered nanoholes without straightforwardly extending concepts strictly related to periodic nanoholes. By Scanning Electron Microscopy (SEM) analysis of the evolution of nanohole short-range ordering and spatial coordination geometry under increasing interhole average spacing (dNN), unprecedented differences in the spectroscopic response are pointed out with respect to periodic systems. First, the dependence of the wavelength of a propagating plasmon mode on dNN is demonstrated to deviate from the linear relationship predicted by the grating-coupling picture developed for periodic arrays. Second, dNN cannot be straightforwardly interpreted as the counterpart of the lattice constant of periodic nanoholes, which demands to introduce a conceptually more rigorous periodicity-like length-scale. Once the impact of these findings on setting the operating parameters of a nanohole distribution is demonstrated, they are related, experimentally and by using a theoretical model developed by the authors, to the changes of the local coordination geometry (from quasi-hexagonal to quasi-square packing through mixed hexagonal-square coordination) induced by varying dNN over a wide interval. Autocorrelation analysis of SEM images is exploited to estimate a short-range periodicity-like length-scale, as a conceptual advance for laying the foundation of the concept of short-range ordered nanohole lattices and for deeper insight into the spectral response. As discussion is based on realistic, rather than simulated, evolution of colloidal arrangements, the formulated interpretative model accounts for realistic effects impacting transmission resonances.