Insights into the origin of robust ferroelectricity in HfO2 -based thin films from the order-disorder transition driven by vacancies

${\mathrm{Hf}\mathrm{O}}_{2}$-based ferroelectrics ($\mathrm{FE}\text{\ensuremath{-}}{\mathrm{Hf}\mathrm{O}}_{2}$) have triggered extensive research interest because they are promising materials for beyond-Moore electronic device applications. However, the origin of ferroelectricity in ${\mathrm{Hf}\mathrm{O}}_{2}$-based ferroelectrics remains elusive. Here, we demonstrate that the ordered oxygen vacancies (${\mathrm{V}}_{\mathrm{O}}$) in $\mathrm{FE}$-${\mathrm{Hf}\mathrm{O}}_{2}$ thin films contribute to ferroelectricity through the formation of a stable-polar phase. In $\mathrm{FE}$-${\mathrm{Hf}\mathrm{O}}_{2}$ thin films, oxygen vacancy (${\mathrm{V}}_{\mathrm{O}}$) defects induce local electric dipoles and the ordered ${\mathrm{V}}_{\mathrm{O}}$ distribution results in the stable-polar phases. Using first-principles calculations, a thermodynamically stable-polar phase ${M}_{1}$ with the spontaneous polarization of 27 \textmu{}C/${\mathrm{cm}}^{2}$ is predicted in monocliniclike ${\mathrm{Hf}}_{4}{\mathrm{Zr}}_{4}{\mathrm{O}}_{15}$ structures. Moreover, the predicted ${M}_{1}$ structures are directly visualized in ${\mathrm{Hf}}_{0.5}{\mathrm{Zr}}_{0.5}{\mathrm{O}}_{2\ensuremath{-}\ensuremath{\delta}}$ (HZO) ferroelectric thin films using spherical aberration (Cs)-corrected scanning transmission electron microscopy. The proposed mechanism for ${\mathrm{V}}_{\mathrm{O}}$-induced order-disorder ferroelectricity in $\mathrm{FE}$-${\mathrm{Hf}\mathrm{O}}_{2}$ opens a new pathway to explore the underlying physics of the ferroelectric characteristics in $\mathrm{FE}$-${\mathrm{Hf}\mathrm{O}}_{2}$.