Based on density functional methods, relative stabilities between monoclinic, tetragonal, and cubic phases of ${\text{HfO}}_2$ with cation dopants or oxygen vacancies are investigated. It is found that dopants such as Si, Ge, Sn, P, Al or Ti with ionic radii smaller than Hf stabilize the tetragonal phase but destabilize the cubic phase. In contrast, larger dopants such as Y, Gd or Sc favor the cubic phase. The ionized oxygen vacancies compensating trivalent dopants greatly stabilize both cubic and tetragonal phases. Microscopic explanations on the results are also given. The metastable phase favored by each dopant is in good agreement with experimental data. Our results can serve as a useful guide in selecting dopants to stabilize a specific phase.

• Received 11 March 2008

DOI:https://doi.org/10.1103/PhysRevB.78.012102