First-principles calculations of structural and electronic properties of monoclinic hafnia surfaces

Abstract

We have carried out a systematic theoretical study of the surfaces of monoclinic hafnia $(\mathrm{Hf}{\mathrm{O}}_{2})$ using plane waves and density functional theory based on the generalized gradient approximation. The fully relaxed structures of the bulk phases of $\mathrm{Hf}{\mathrm{O}}_{2}$ are found to be in excellent agreement with experimental data, the monoclinic phase being the most stable. Simulations of the monoclinic phase surfaces indicate a large relaxation which reduces the total surface energy of all nine faces considered by between 23% and 36%, with a strong correlation between the unrelaxed and relaxed surface energies. Our calculations predict that the $(\overline{1}11)$ and (111) faces of the monoclinic phase have the lowest surface energies and are hence the most stable faces. An analysis of the total and partial electronic density of states of bulk monoclinic $\mathrm{Hf}{\mathrm{O}}_{2}$ reveals that the outer valence band significantly mixes the O $2p$ and Hf $5d$ atomic states indicating some covalency of the Hf-O bonds. The total density and partial density of states of the monoclinic surfaces exhibit a surface state corresponding to the surface O $2s$ states in the inner valence band region.