First-principles study of native point defects in hafnia and zirconia

A first-principles study of native point defects in hafnia $(\mathrm{Hf}{\mathrm{O}}_{2})$ and zirconia $(\mathrm{Zr}{\mathrm{O}}_{2})$ is carried out to identify dominant defects under different oxygen chemical potentials and Fermi levels. Oxygen vacancies and oxygen interstitials in both $\mathrm{Hf}{\mathrm{O}}_{2}$ and $\mathrm{Zr}{\mathrm{O}}_{2}$ show negative-$U$ behavior. It is shown that $\mathrm{Hf}{\mathrm{O}}_{2}$ is less prone to the formation of oxygen point defects than $\mathrm{Zr}{\mathrm{O}}_{2}$ under the same oxygen chemical potential. When the Fermi level is constrained to be within the band gap of silicon, the dominant defects are negatively charged hafnium or zirconium vacancies under intermediate to high oxygen chemical potential. We find no evidence for magnetic defects.