Electron-vacancy scattering in SrNbO$_3$ and SrTiO$_3$: A DFT-NEGF study

Oxygen vacancies are often attributed to changes in the electronic transport for perovskite oxide materials (ABO$_3$). Here, we use density functional theory (DFT) coupled with non-equilibrium Green's functions (NEGF) to systematically investigate the influence of O vacancies and also A and B-site vacancies, on the electronic transport as characterised by a scattering cross-section. We consider SrNbO$_3$ and n-type SrTiO$_3$ and contrast results for bulk and thin film (slab) geometries. By varying the electron doping in SrTiO$_3$ we get insight into how the electron-vacancy scattering vary for different experimental conditions. We observe a significant increase in the scattering cross-section (in units of square-lattice parameter, $a^2$) from ca. $0.5-2.5a^2$ per vacancy in SrNbO$_3$ and heavily doped SrTiO$_3$ to more than $9a^2$ in SrTiO$_3$ with 0.02 free carriers per unit cell. Furthermore, the scattering strength of O vacancies is enhanced in TiO$_2$ terminated surfaces by more than 6 times in lowly doped SrTiO$_3$ compared to other locations in slabs and bulk systems. Interestingly, we also find that Sr vacancies go from being negligible scattering centers in SrNbO$_3$ and heavily doped SrTiO$_3$, to having a large scattering cross-section in weakly doped SrTiO$_3$. We therefore conclude that the electron-vacancy scattering in these systems is sensitive to the combination of electron concentration and vacancy location.