Using first-principles density-functional-theory calculations, we find a strong position and thickness dependence of the formation energy of oxygen vacancies in ${\text{LaAlO}}_3\mid {\text{SrTiO}}_3$ $\left(\text{LAO}\mid \text{STO}\right)$ multilayers and interpret this with an analytical capacitor model. Oxygen vacancies are preferentially formed at $p$-type $\text{SrO}\mid {\text{AlO}}_2$ rather than at $n$-type $\text{LaO}\mid {\text{TiO}}_2$ interfaces; the excess electrons introduced by the oxygen vacancies reduce their energy by moving to the $n$-type interface. This asymmetric behavior makes an important contribution to the conducting (insulating) nature of $n$-type ($p$-type) interfaces while providing a natural explanation for the failure to detect evidence for the polar catastrophe in the form of core level shifts.

• Received 21 June 2010

DOI:https://doi.org/10.1103/PhysRevB.82.165127