A Comparative Ab Initio Thermodynamic Study of Oxygen Vacancies in ZnO and SrTiO3: Emphasis on Phonon Contribution

Using a hybrid Hartree–Fock (HF)-DFT method combined with LCAO basis set and periodic supercell approach, the atomic, electronic structure and phonon properties of oxygen vacancies in ZnO and SrTiO3 were calculated and compared. The important role of a ghost basis function centered at the vacant site and defect spin state for SrTiO3 is discussed. It is shown that the use of hybrid functionals is vital for correct reproduction of defects basic properties. The Gibbs free energy of formation of oxygen vacancies and their considerable temperature dependence has been compared for the two oxides. These calculations were based on the polarizability model for the soft mode temperature behavior in SrTiO3. The supercell size effects in the Gibbs free energy of formation of oxygen vacancies in the two oxides are discussed. The major factors for the quite different behavior of the two oxides and the degree of electron delocalization nearby the oxygen vacancy have been identified.