Insight on agglomerates of gold nanoparticles in glass based on surface plasmon resonance spectrum: study by multi-spheres T-matrix method

The formation of a localized surface plasmon resonance (SPR) spectrum of randomly distributed gold nanoparticles in the surface layer of silicate float glass, generated and implanted by UV ArF-excimer laser irradiation of a thin gold layer sputter-coated on the glass surface, was studied by the T-matrix method, which enables particle agglomeration to be taken into account. The experimental technique used is promising for the production of submicron patterns of plasmonic nanoparticles (given by laser masks or gratings) without damage to the glass surface. Analysis of the applicability of the multi-spheres T-matrix (MSTM) method to the studied material was performed through calculations of SPR characteristics for differently arranged and structured gold nanoparticles (gold nanoparticles in solution, particles pairs, and core-shell silver-gold nanoparticles) for which either experimental data or results of the modeling by other methods are available. For the studied gold nanoparticles in glass, it was revealed that the theoretical description of their SPR spectrum requires consideration of the plasmon coupling between particles, which can be done effectively by MSTM calculations. The obtained statistical distributions over particle sizes and over interparticle distances demonstrated the saturation behavior with respect to the number of particles under consideration, which enabled us to determine the effective aggregate of particles, sufficient to form the SPR spectrum. The suggested technique for the fitting of an experimental SPR spectrum of gold nanoparticles in glass by varying the geometrical parameters of the particles aggregate in the recurring calculations of spectrum by MSTM method enabled us to determine statistical characteristics of the aggregate: the average distance between particles, average size, and size distribution of the particles. The fitting strategy of the SPR spectrum presented here can be applied to nanoparticles of any nature and in various substances, and, in principle, can be extended for particles with non-spherical shapes, like ellipsoids, rod-like and other T-matrix-solvable shapes.