Disentangling the role of small polarons and oxygen vacancies in CeO2

The outstanding performance of cerium oxide $(\mathrm{Ce}{\mathrm{O}}_{2})$ as ion conductor or catalyst strongly depends on the ease of $\mathrm{C}{\mathrm{e}}^{4+}\ensuremath{\leftrightarrow}\mathrm{C}{\mathrm{e}}^{3+}$ conversion and oxygen vacancy formation. An accurate description of $\mathrm{C}{\mathrm{e}}^{3+}$ and oxygen vacancy is therefore essential to further progress in this area. Using the HSE06 hybrid functional, we investigate the formation and migration of small polarons $(\mathrm{C}{\mathrm{e}}^{3+})$ and their interaction with oxygen vacancies in $\mathrm{Ce}{\mathrm{O}}_{2}$, considering the small polaron and vacancy as independent entities. Oxygen vacancies are double donors and can bind up to two small polarons, forming a positively charged or neutral complex. We compute the electron self-trapping energy (i.e., energy gain when forming a small polaron), the small-polaron migration barrier, vacancy formation and migration energies, and vacancy-polaron binding energies. We find that small polarons weakly bind to oxygen vacancies, yet this interaction significantly contributes to the activation energy for hopping electronic conductivity. The results are compared with previous calculations and discussed in the light of available experimental data.