  We evaluate the interplay between epitaxial strain and oxygen vacancy
formation in the perovskite-structure oxide lanthanum aluminate, LaAlO$_3$.
Using density functional theory within the GGA$+U$ approximation we calculate
the dependence of the oxygen vacancy formation energy on the biaxial strain
conditions. We find that the change in formation energy with strain is
negligible over the range of strain values usually accessible through coherent
epitaxial growth. Our findings suggest that experimental reports of different
oxygen vacancy concentrations in strained films result from extrinsic factors,
or from other impurities such as defect complexes.

Materials Science