Small polarons and their interaction with donor centers in Titania*

The use of TiO$_{2}$ in photocatalysis, photosensitized solar cells, and memristors strongly depends on the behavior of conduction-band electrons, prompting a more profound understanding of conduction mechanisms. The reported results for the behavior of excess electrons in TiO$_{2}$ are contradictory. High carrier mobilities, characteristic of delocalized electrons, have been observed in Hall measurements, whereas optical spectra indicate the presence of localized, small polarons. Using first-principles calculations based on a hybrid functional we study the formation of small polarons, comparing it to delocalized electrons in the conduction band of TiO$_{2}$. From the calculated configuration coordinate diagram and migration energy barriers, we discuss the coexistence of small polarons with delocalized electrons, and address how the observed behavior depends on the type of experiment being conducted. The interaction of small polarons with intrinsic defects such as the oxygen vacancy and donor impurities will also be discussed.