Electronic structure ofNaxWO3: A photoemission study covering the entire concentration range

Abstract

Angle-resolved and angle-integrated ultraviolet-photoemission-spectroscopy (UPS) investigations have been carried out over the entire concentration range $0<x<\mathrm{}1\mathrm{}$ of the sodium-tungsten-bronze system ${\mathrm{Na}}_x\mathrm{W}{\mathrm{O}}_3$. The results indicate that the rigid-band model used by several authors fails to explain the $x$ dependence of the electronic structure. For the metallic samples with $x\ge 0.3$, the top of the valence band and the bottom of the conduction band remain at 3 and 1 eV, respectively, and the width of the occupied part of the conduction band is independent of $x$. The peak amplitude at the Fermi level varies linearly with $x$ and does not follow the predicted dependence. A detailed comparison is made between the experimental results and the band-structure calculation of Kopp et al. Both the width of the valence band and the separation between the valence and conduction bands are too small in the calculation. Angle-resolved UPS measurements reveal a peak in the gap region for the metallic samples which disperses from 2.1 eV for ${\overrightarrow{\mathrm{k}}}_{\parallel }=0\mathrm{} \mathrm{to} 1.2$ eV for ${\overrightarrow{\mathrm{k}}}_{\parallel }$ along $\Gamma -M$. This feature is assigned to a surface state. The failure to detect localized gap states for the semiconducting samples is explained by band bending and a charge depletion layer caused by oxygen acceptor states at the surface. The fact that the work function $\phi$ decreases linearly with increasing $x$ indicates that there is no surface depletion of sodium as has been claimed earlier.