Polaron mobility in oxygen-deficient and lithium-doped tungsten trioxide

Electron localization and polaron mobility in oxygen-deficient as well as Li-doped monoclinic tungsten trioxide have been studied in the adiabatic limit in the framework of density functional theory. We show that small polarons formed in the presence of oxygen vacancy prefer the bipolaronic ${\text{W}}^{5+}\ensuremath{-}{\text{W}}^{5+}$ configuration, whereas the ${\text{W}}^{6+}\ensuremath{-}{\text{W}}^{4+}$ configuration is found to be metastable. Our calculations suggest that bipolarons are tightly bound by the vacancy and therefore largely immobile. On the contrary, polarons formed as a result of Li intercalation can be mobile; the activation energy for polaron jumping in this case varies between 98 and 124 meV depending on the crystallographic direction. The formation of ${\text{W}}^{5+}\ensuremath{-}{\text{W}}^{5+}$ bipolarons in ${\text{Li-WO}}_{3}$ is possible. When situated along $[001]$ the bipolaronic configuration is 8 meV lower in energy than two separate ${\text{W}}^{5+}$ polarons.