Structural and electronic properties of cubic HfO2 surfaces

Using the first-principles method within the generalized gradient approximation, we have performed a systematic study on the structural and electronic properties of cubic HfO2 surfaces. We find that the most energetically favorable surfaces are (1 1 0) and (1 1 1) terminated with single oxygen layer, both of which are stoichiometric. The atomic relaxation in top layers of surface (1 1 1)-O and (1 1 0) exhibits very similar behavior, i.e. cations relax inward while anions outward. This could be well understood by the ionic feature of the Hf-O bond. Both of the two surfaces studied are insulating without any surface state in the energy gap.