Oxygen Vacancy Chain Formation in TiO2 under External Strain for Resistive Switching Memory

The electronic structure and vacancy formation energy of rutile TiO2 with ordered oxygen vacancies were calculated using the density functional theory with on-site Coulomb corrections between Ti 3d orbital and O 2p orbital (LDA+Ud+Up). The calculated band gaps are about 3 eV, using LDA+Ud+Up, and a hybrid functional proposed by Heyd–Scuseria–Ernzerhog. The ordered oxygen vacancies were introduced along the [001] direction within a 3×3×4 supercell of rutile TiO2-x that consisted of 72 Ti and 136 O atoms. Biaxial strain was induced in the rutile TiO2 along the x- and y-directions up to ±5%. The lowest formation energy of ordered oxygen vacancies was found in 5% compressive strain and deemed as a thermodynamically favorable structure.