First principles study of structural and electronic properties of cubic phase of ZrO₂ and HfO₂

We perform first-principles calculations founded on the hybrid density functional theory to investigate the electronic structure properties of c-ZrO₂ and c-HfO₂. The results indicate that PBE0 is better than HSE03/06 to improve the theoretical values of the band gaps. The similarities and differences between c-ZrO₂ and c-HfO₂ are described at PBE0 level, and the small differences between these two oxides may be caused by the difference in electronegativity. Then, a systematic study on the electronic structure properties of c-ZrO₂ surfaces is performed at PBE level. The results illustrate that (1 1 0) and (1 1 1)-O are the most stable surfaces, and both of them are insulating without any surface state in the energy gap. These are similar with the electronic properties of c-HfO ₂ surfaces. The optical band gaps for the surfaces of c-ZrO ₂, apart from (1 1 1)-O and (1 1 1)-OO surfaces, are considerably reduced in comparison to the c-ZrO₂ bulk. In addition, we also find that the optical band gaps for the surfaces of c-ZrO₂ are all indirect expect (1 1 0) surface.