  We performed density functional theory (DFT) calculations on epitaxially
strained hafnia. We demonstrate the stabilization of the ferroelectric
($Pca2_{1}$) phase from the antiferroelectric ($Pbcn$) in bulk hafnia in the
presence of electric field. We found that the polar ($Pca2_{1}$) phase can be
efficiently stabilized with an adequate choice of film orientation. We show
that for a (010)-oriented Pbcn, the ferroelectric $Pca2_{1}$ phase can be
reached with a relatively small electric field ($\mid\varepsilon\mid\geq 150$
KV/m). We thus provide a simple explanation to the experimental observation of
polarization enhancement through electric field cycling, or wake-up effect, as
a ferroelectric phase transition driven by electric field. We find, in
contrast, that stress free pure hafnia does not become ferroelectric for any
reasonable electric field. So we explain the wake up effect and stabilization
of ferroelectric pure hafnia as coming from a combination of epitaxial strain
under applied electric field perpendicular to the film. We find that strain (or
doping) primarily destabilizes the baddeleyite structure, so that the
antiferroelectric Pbcn and ferroelectric phases can form.
