Relationship between ferroelectric polarization and stoichiometry of HfO2 surfaces

We used density functional theory to assess the stability of nonpolar tetragonal (P42/nmc) HfO2(110) reconstructed surfaces and the effect of polarization on the stability of the corresponding surfaces of polar orthorhombic (Pca21) HfO2(001). The models consisted of nine-formula-unit-thick slabs with two-formula-unit surface unit cells. We determined an oxygen-terminated surface reconstruction to be the most stable surface for the nonpolar HfO2 slab, with one oxygen atom per formula unit on both sides of the slab (1.0-O/1.0-O). For the same surface composition, the ferroelectric displacements in the polar orthorhombic slab result in band bending that leads to the migration of charge carriers to the surface (with sign opposite to that of the surface polarization charge) which metallizes the surface to eliminate or reduce the net out-of-plane dipole. Ionic passivation also is effective at screening the polarization charge, which therefore alleviates band bending, leading to stabilization. This is achieved via a nonstoichiometric surface reconstruction, in which the most stable positively polarized side is oxygen-terminated with 1.5 oxygen atoms per formula unit, while the negatively polarized side has one oxygen atom per formula unit (P+:1.5-O/P-:1.0-O). This work establishes a link between the stability of the surface reconstruction and the ferroelectric polarization in HfO2, which is important for the technological need to control ferroelectric performance at the nanoscale.