Optical properties of metallic sodium tungsten bronzes: Analysis of free- and bound-electron contributions

Monitoring of the optical response of ${\mathrm{Na}}_{x}\mathrm{W}{\mathrm{O}}_{3}$ of varying stoichiometric ratio was performed by means of ellipsometry (from \ensuremath{\sim} 0.3 to 5.2 eV) and electromodulated reflectance (from 1.3 to 3 eV). The spectra of the real and imaginary part of the dielectric function were used to separate free-electron and bound-electron components, providing direct evaluation of the carrier-density to effective-mass ratio as well as of the carriers relaxation rate. Electroreflectance spectra gave evidence of major modulation structure associated with the plasma edge; this was explicitly analyzed with the help of ellipsometric data and shown to be compatible with the existence of a modulated transition layer at the metal-electrolyte interface. A smaller structure in the electroreflectance spectra, occurring at lower energies, was explained in terms of a band-population effect. Its discussion, together with the knowledge of free-electron parameters, allows a certain characterization of the conduction states, based on current theoretical band schemes for similar compounds.