Using a hybrid density functional theory method combined with linear combination of atomic orbitals basis set and periodic supercell approach, the atomic, electronic structure, and phonon properties were calculated for SrTiO${}_3$ containing either Fe${}^{4+}$ substituting host Ti${}^{4+}$ ions or neutral oxygen vacancies $V_o$. For both defects, the Jahn–Teller effect occurs, thus reducing the cubic symmetry of a perfect crystal and leading to the appearance of both Raman- and infrared-active vibrational modes. The calculated phonon densities of states and group-theoretical analysis of defect-induced phonon frequencies were used for the interpretation of the relevant experimental data, once defect-induced local modes are identified. The temperature dependence of the $V_o$ formation energy based on the calculated Gibbs free energy was also compared with experiments, and the phonon contribution therein estimated.

• Received 17 November 2011

DOI:https://doi.org/10.1103/PhysRevB.85.174303