  The defect stability in a prototypical perovskite oxide superlattice
consisting of SrTiO$_3$ and PbTiO$_3$ (STO/PTO) is determined using first
principles density functional theory calculations. Specifically, the oxygen
vacancy formation energies E$_v$ in the paraelectric and ferroelectric phases
of a superlattice with four atomic layers of STO and four layers of PTO
(4STO/4PTO) are determined and compared. The effects of charge state,
octahedral rotation, polarization, and interfaces on the E$_v$ are examined.
The formation energies vary layer-by-layer in the superlattices, with E$_v$
being higher in the ferroelectric phase than that in the paraelectric phase.
The two interfaces constructed in these oxide superlattices, which are
symmetrically equivalent in the paraelectric systems, exhibit very different
formation energies in the ferroelectric superlattices and this can be seen to
be driven by the coupling of ferroelectric and rotational modes. At equivalent
lattice sites, E$_v$ of charged vacancies is generally lower than that of
neutral vacancies. Octahedral rotations (a$^0$a$^0$c$^-$) in the FE
superlattice have a significant effect on the E$_v$, increasing the formation
energy of vacancies located near the interface but decreasing the formation
energy of the oxygen vacancies located in the bulk-like regions of the STO and
PTO constituent parts. The formation energy variations among different layers
are found to be primarily caused by the difference in the local relaxation at
each layer. These fundamental insights into the defect stability in perovskite
superlattices can be used to tune defect properties via controlling the
constituent materials of superlattices and interface engineering.
