Disorder-induced electron and hole trapping in amorphous TiO2

Thin films of amorphous $(\mathrm{a})\text{--}{\mathrm{TiO}}_{2}$ are ubiquitous as photocatalysts, protective coatings, photo-anodes, and in memory applications, where they are exposed to excess electrons and holes. We investigate trapping of excess electrons and holes in the bulk of pure amorphous titanium dioxide, $\mathrm{a}\text{--}{\mathrm{TiO}}_{2}$, using hybrid density-functional theory (h-DFT) calculations. Fifty 270-atom $\mathrm{a}\text{--}{\mathrm{TiO}}_{2}$ structures were produced using classical molecular dynamics and their geometries fully optimized using h-DFT simulations. They have the density, distribution of atomic coordination numbers, and radial pair-distribution functions in agreement with experiments. The calculated average $\mathrm{a}\text{--}{\mathrm{TiO}}_{2}$ band gap is $3.25\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ with no states splitting into the band gap. Trapping of excess electrons and holes in $\mathrm{a}\text{--}{\mathrm{TiO}}_{2}$ is predicted at precursor sites, such as elongated Ti--O bonds. Single electron and hole polarons have average trapping energies $({E}_{T})$ of $\ensuremath{-}0.4\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$ and $\ensuremath{-}0.8\phantom{\rule{0.16em}{0ex}}\mathrm{eV}$, respectively. We also identify several types of electron and hole bipolaron states and discuss their stability. These results can be used for understanding the mechanisms of photo-catalysis and improving the performance of electronic devices employing $\mathrm{a}\text{--}{\mathrm{TiO}}_{2}$ films.