Electronic structure and optical properties of monoclinic HfO₂ with oxygen vacancy

The electronic structure and optical properties of monoclinic HfO₂ (m-HfO₂) with the consideration of oxygen vacancy were calculated using the plane-wave ultrasoft pseudopotential method based on the first-principles density functional theory (DFT). The results reveal that a new defect level at the conduction band edge is introduced for the defective m-HfO₂, and the 5d states of Hf atoms nearest to the oxygen vacancy make significant contribution to it. Furthermore, the dielectric functions and absorption coefficients of the perfect and defective m-HfO₂ were calculated and analyzed by means of the electronic structures, which were related to the defect levels. The calculated absorption coefficient shows that m-HfO₂ with oxygen vacancy exhibits an absorption band in the ultraviolet region.