Insights into the facet- and direction-dependent photoelectric properties of anatase and rutile TiO2

In general, the photoelectric properties of $\mathrm{Ti}{\mathrm{O}}_{2}$ are highly dependent on its crystal directions and facets. However, the impact of initial momentum distributions, group velocity distributions, and spatial transport properties of photoexcited carriers on the anisotropic photoelectric properties needs more study. In this work, we have thoroughly investigated these issues at the atomic and electronic scales for anatase and rutile $\mathrm{Ti}{\mathrm{O}}_{2}$ with homemade code. It is meaningful to find that anatase and rutile $\mathrm{Ti}{\mathrm{O}}_{2}$ mainly produce high-energy electrons and holes upon photoexcitation, respectively, which is beneficial for the efficient separation of carriers in the heterojunction system of anatase and rutile $\mathrm{Ti}{\mathrm{O}}_{2}$. In addition, it is found that for both anatase and rutile $\mathrm{Ti}{\mathrm{O}}_{2}$, the initial momentum and group velocity distribution of the photoexcited carriers is highly anisotropic, and anatase $\mathrm{Ti}{\mathrm{O}}_{2}$ has a better directionality than rutile as a whole. Moreover, the transport properties of carriers in group velocity space also exhibit high anisotropy. Notably, the crystal directions with excellent transport properties are consistent with the group velocity distribution of carriers in anatase $\mathrm{Ti}{\mathrm{O}}_{2}$, which indicates the beneficial transport and accumulation of photoexcited carriers. In contrast, the crystal directions with excellent transport properties are inconsistent with the preferable group velocity distribution of carriers in rutile $\mathrm{Ti}{\mathrm{O}}_{2}$, which may result in unfavorable carrier transport and accumulation properties. These results provide not only valuable thoughts for understanding related experimental phenomena but also theoretical guidance for effectively collecting carriers in $\mathrm{Ti}{\mathrm{O}}_{2}$.