The Effect of Strain Orientation on Structural Coordination and Phase Stability of Ferroelectric HfO₂

Ferroelectric hafnium oxide (HfO₂) has garnered renewed interest in nonvolatile memory technologies. The phase transition from the stable monoclinic P2₁/c phase to the metastable ferroelectric Pca2₁ phase is influenced by various factors, including strain, doping, and oxygen vacancies. The stability of the Pca2₁ phase has birthed numerous findings but remains challenging due to the interdependence of these intrinsic and extrinsic factors. First-principles calculations show that biaxial compressive strain in the (111) orientation significantly enhances the stability of the ferroelectric phase, even at lower yttrium doping levels and oxygen vacancy concentrations, compared to the conventional (110) orientation. Here, we investigate the impact of strain orientation on structural coordination, including bond lengths and atom displacements, and discuss how structural coordination, in turn, affects phase stability. The cumulative effects of dopants and oxygen vacancies on structural coordination and ferroelectric properties in the (111) orientation are also analyzed.