Al-, Y-, and La-doping effects favoring intrinsic and field induced ferroelectricity in HfO₂: a first principles study

III-valent dopants have shown to be most effective in stabilizing the ferroelectric, crystalline phase in atomic layer deposited, polycrystalline HfO₂ thin films. On the other hand, such dopants are commonly used for tetragonal and cubic phase stabilization in ceramic HfO₂. This difference in the impact has not been elucidated so far. The prospect is a suitable doping to produce ferroelectric HfO₂ ceramics with a technological impact. In this paper, we investigate the impact of Al, Y, and La doping, which have experimentally proven to stabilize the ferroelectric Pca21 phase in HfO₂, in a comprehensive first-principles study. Density functional theory calculations reveal the structure, formation energy, and total energy of various defects in HfO₂. Most relevant are substitutional electronically compensated defects without oxygen vacancy, substitutional mixed compensated defects paired with a vacancy, and ionically compensated defect complexes containing two substitutional dopants paired with a vacancy. The ferroelectric phase is strongly favored with La and Y in the substitutional defect. The mixed compensated defect favors the ferroelectric phase as well, but the strongly favored cubic phase limits the concentration range for ferroelectricity. We conclude that a reduction of oxygen vacancies should significantly enhance this range in Y doped HfO₂ thin films. With Al, the substitutional defect hardly favors the ferroelectric phase before the tetragonal phase becomes strongly favored with the increasing concentration. This could explain the observed field induced ferroelectricity in Al-doped HfO₂. Further Al defects are investigated, but do not favor the f-phase such that the current explanation remains incomplete for Al doping. According to the simulation, doping alone shows clear trends, but is insufficient to replace the monoclinic phase as the ground state. To explain this fact, some other mechanism is needed