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 redshift from the localized surface plasmon resonance (LSPR) of the isolated nanocrystals to that of an assembly reflects the 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 can be used to predict peak shifts for materials design. Here, we develop a unified scaling relationship that accounts for the unique properties of metal oxide plasmonic nanocrystals by considering the influence that dopants have not only on the LSPR frequency but also on the distribution of free electrons within the 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 when assembled into close-packed superlattices. This framework can be used to guide the design of plasmonic materials to realize specific optical characteristics based on the synthetically controllable attributes of the nanocrystal building blocks.