Absorption peak decomposition of an inhomogeneous nanoparticle ensemble of hexagonal tungsten bronzes using the reduced Mie scattering integration method.

Recent optical analyses of cesium-doped hexagonal tungsten bronze have accurately replicated the absorption peak and identified both plasmonic and polaronic absorptions in the near-infrared region, which have been exploited in various technological applications. However, the absorption peaks of tungsten oxides and bronzes have not generally been reproduced well, including those of the homologous potassium- and rubidium-doped hexagonal tungsten bronzes that lacked evidence of polaronic subpeaks. The present study reports a modified and simplified Mie scattering integration method which incorporates the ensemble inhomogeneity effect and allows precise peak decomposition and determination of the physical parameters of nanoparticles. The decomposed peaks were interpreted in terms of electronic structures, screening effect, and modified dielectric functions. The analysis revealed that the plasma frequencies, polaron energies, and the number of oxygen vacancies decrease in the dopant order Cs → Rb → K. The coexistence of plasmonic and polaronic excitations was confirmed for all the alkali-doped hexagonal tungsten bronzes.