Ensemble Inhomogeneity of Dielectric Functions in Cs-Doped Tungsten Oxide Nanoparticles

Ensembles of Cs-doped tungsten bronze nanoparticles (NPs) derived from breakdown process exhibit near-infrared absorption of localized surface plasmon resonance with highly broadened bandwidth. The dominant cause of this effect, after evaluating conventional factors such as particle size, shape, dipolar interactions, etc., has been identified as the ensemble inhomogeneity of dielectric functions of individual particles. A novel analysis method has been developed that can take into account the inhomogeneity of physical properties over a molar-order number of particles. Various variables to describe dielectric functions are numerically made scattered by randomly generated numbers, and Mie scattering wave, each with scattered variables, is calculated and integrated. The developed method successfully reproduced experimental absorption profiles. The analysis indicates that the dielectric functions are modified with a decrease in both plasma frequency and polaron transition energy and an increase in the band gap for NPs as compared with a bulk. These changes are considered to arise from the structural changes upon mechanical nanoparticulation via breakdown process, such as Cs-atom desorption from surface and decrease in oxygen vacancies.