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Description
We investigate the mechanism of hole diffusion across leaky amorphous TiO$_2$ (am-TiO$_2$) layers. Through $\textit{ab initio}$ molecular dynamics simulations, we construct an atomistic model of am-TiO$_2$ consistent with the experimental characterization. We first demonstrate oxygen vacancies impossibly occur in am-TiO$_2$, which can be assimilated by the amorphous structure upon structural rearrangement. Hence, their role in hole diffusion is ruled out. In contrast, O-O peroxy linkages are formed in pristine am-TiO$_2$ upon injection of excess holes, with an associated defect level at 1.25 eV above the VBM. We show that such linkages can provide a viable mechanism for hole diffusion in am-TiO$_2$, as illustrated by a diffusion path of 1.2 nm with energy barriers lower than 0.5 eV in our model.