Migration of Holstein Polarons in Anatase TiO2

A simple yet reliable valence bond theory was applied to ascertain the effective size and shape for the electron and hole polarons in bulk anatase TiO2 by examining the extent of polaron charge delocalization. It was found that the electron polaron is approximately 2 times as large as its hole counterpart, leading to a faster electron diffusion than hole hopping with regard to the electronphonon coupling strength. Moreover, the oblate hole polaron exhibits a pronounced directional heterogeneity in migration, whereas the nearly spherical electron polaron tends to diffuse along all possible lattice directions. In light of the notable delocalization characteristics of both polarons, their migration should proceed in an adiabatic manner, and their rates can be calculated by the Arrhenius equation. It turns out that our calculated polaron mobilities at 300 and 1300K are both in excellent agreement with experimental values, justifying our novel approach for Holstein polaron modeling in crystalline semiconductors.