Incorporating Dopant Effects in the Plasmon Ruler for Metal-Oxide Nanocrystal Superlattices

Plasmonic nanocrystals in close-packed assemblies exhibit collective optical resonance and strongly concentrated electric fields due to coupling. The spectral red-shift from the localized surface plasmon resonance (LSPR) of isolated nanocrystals to that of an assembly reflects coupling strength, which depends on nanocrystal characteristics and assembly structure. Scaling laws that relate these shifts to nanocrystal spacing are useful to systematically describe plasmon coupling and predict peak shifts for materials design. Here, we develop a unified scaling relationship that accounts for unique properties of metal-oxide plasmonic nanocrystals by considering the dopant influence on the LSPR frequency and free electron distribution within nanocrystals. We propose a rescaled plasmon ruler, adjusted for the presence of a dopant-dependent depletion layer, to describe the spectral shifts of colloidal indium tin oxide nanocrystals assembled into close-packed superlattices. This framework can guide designs of plasmonic materials to realize specific optical characteristics based on synthetically controllable attributes of nanocrystal building blocks.