Deep and Shallow Gap States in Reduced and n-Type Doped m-ZrO₂

Monoclinic zirconium dioxide (m-ZrO₂) is a wide-band-gap functional oxide with many applications. Understanding the role of intrinsic defects and dopants is important for improving the properties of m-ZrO₂ relevant to its applications. In this work, we characterize the electronic states and energy levels of oxygen vacancies (V_O’s) and n-type Nb, Ta, Rb, H, and F dopants in the bulk and at the majority (1̅11) surface of m-ZrO₂, using accurate dielectric-dependent hybrid functional calculations. Our results show that V_O’s generally behave as deep donors with the excess electrons localized at the vacant O sites in the form of F centers, in agreement with previous studies. In contrast, surface V_O’s at two-fold coordinated oxygen sites show a rather shallow (1+/0) transition level. Shallow levels are also obtained for adsorbed hydrogen (H_ads) and fluorine substituting an oxygen atom (F_O) either in the bulk or at the surface, whereas Nb and Ta form deep levels.