Semiconductor-to-metal transition in WO3−x: Nature of the oxygen vacancy

Hybrid functional density functional theory calculations of the oxygen vacancy (V${}_{\mathrm{O}}$) in monoclinic bulk WO${}_{3}$ provide a coherent rationalization for the strong dependence of WO${}_{3\ensuremath{-}x}$ electronic properties on the V${}_{\mathrm{O}}$ concentration and of the semiconductor-to-metal transition, a phenomenon intimately connected to the electrochromic effect. Different V${}_{\mathrm{O}}$ centers containing W${}^{4+}$, W${}^{5+}$, and W${}^{6+}$ species are expected to coexist. Optical transition levels are 0.7--1.0 eV below the conduction band minimum, in agreement with experiments. The complex nature of V${}_{\mathrm{O}}$ in WO${}_{3}$ can only be detected with methods that properly describe band gaps and polaronic distortions at defect sites.