Mechanistic insights into polarization modulation of ferroelectric HfO ₂ under strain and oxygen vacancies

As an emerging ferroelectric material, HfO 2 has attracted considerable interest in ferroelectric memory applications due to its outstanding polarization properties. However, in practical devices, its polarization fatigue behavior is strongly influenced by external stress and oxygen vacancies. In this work, first-principles calculations are employed to elucidate the physical mechanisms by which oxygen vacancies and external stress affect the polarization characteristics of HfO 2 . Intrinsic ferroelectric HfO 2 (f-HfO[Formula: see text] is a wide-band-gap semiconductor, exhibiting an indirect band gap of 4.5[Formula: see text]eV and a spontaneous polarization of 0.502 C/m 2 . The valence band near the Fermi level is dominated by O2p orbitals. Defect formation energy analysis reveals that 4-coordinated oxygen vacancies are more energetically favorable than 3-coordinated vacancies. Nevertheless, the trap state introduced by a 3-coordinated oxygen vacancy lies closer to the conduction-band minimum, making it more detrimental to the electronic and ferroelectric properties. Under strain applied along the [Formula: see text] direction, the band gap of f-HfO 2 displays a convex parabolic dependence, whereas its polarization follows a concave parabolic trend, decreasing initially and then gradually recovering. This polarization behavior is consistent with that of 4-coordinated oxygen, suggesting that the ferroelectric polarization of f-HfO 2 is primarily governed by the displacement of 4-coordinated oxygen atoms. Moreover, the polarization associated with 4-coordinated oxygen exceeds that of intrinsic f-HfO 2 across the strain range, with more pronounced variation under compression than under tension. These results underscore the pivotal role of oxygen vacancies in determining the ferroelectric behavior of HfO 2 under mechanical deformation. A deeper understanding of oxygen-vacancy dynamics in HfO 2 -based ferroelectrics is therefore essential for guiding material design and enhancing device performance.