  We use first-principles calculations to investigate the stability of
bi-axially strained \textit{Pnma} perovskite CaMnO$_3$ towards the formation of
oxygen vacancies. Our motivation is provided by promising indications that
novel material properties can be engineered by application of strain through
coherent heteroepitaxy in thin films. While it is usually assumed that such
epitaxial strain is accommodated primarily by changes in intrinsic lattice
constants, point defect formation is also a likely strain relaxation mechanism.
This is particularly true at the large strain magnitudes ($>$4%) which
first-principles calculations often suggest are required to induce new
functionalities. We find a strong dependence of oxygen vacancy defect formation
energy on strain, with tensile strain lowering the formation energy consistent
with the increasing molar volume with increasing oxygen deficiency. In
addition, we find that strain differentiates the formation energy for different
lattice sites, suggesting its use as a route to engineering vacancy ordering in
epitaxial thin films.
