Analytical modeling of localized surface plasmon resonance in heterostructure copper sulfide nanocrystals

Localized surface plasmon resonance (LSPR) in semiconductor nanocrystals is a relatively new field of investigation that promises greater tunability of plasmonic properties compared to metal nanoparticles. A novel process by which the LSPR in semiconductor nanocrystals can be altered is through heterostructure formation arising from solution-based cation exchange. Herein, we describe the development of an analytical model of LSPR in heterostructure copper sulfide-zinc sulfide nanocrystals synthesized via a cation exchange reaction between copper sulfide (Cu(1.81)S) nanocrystals and Zn ions. The cation exchange reaction produces dual-interface, heterostructure nanocrystals in which the geometry of the copper sulfide phase can be tuned from a sphere to a thin disk separating symmetrically-grown sulfide (ZnS) grains. Drude model electronic conduction and Mie-Gans theory are applied to describe how the LSPR wavelength changes during cation exchange, taking into account the morphology evolution and changes to the local permittivity. The results of the modeling indicate that the presence of the ZnS grains has a significant effect on the out-of-plane LSPR mode. By comparing the results of the model to previous studies on solid-solid phase transformations of copper sulfide in these nanocrystals during cation exchange, we show that the carrier concentration is independent of the copper vacancy concentration dictated by its atomic phase. The evolution of the effective carrier concentration calculated from the model suggests that the out-of-plane resonance mode is dominant. The classical model was compared to a simplified quantum mechanical model which suggested that quantum mechanical effects become significant when the characteristic size is less than ~8 nm. Overall, we find that the analytical models are not accurate for these heterostructured semiconductor nanocrystals, indicating the need for new model development for this emerging field.