Electronic structure and energetics of sapphire (0001) and (11¯02) surfaces

Abstract

Electronic structure and energetics of (0001) and (11¯02) surfaces of sapphire, α-${\mathrm{Al}}_2$ ${\mathrm{O}}_3$, were calculated using the self-consistent-field discrete variational (DV) method in the local-density framework. Clusters of a size of 70–120 atoms embedded in the semi-infinite host lattice were used to model the sapphire free surfaces. Calculations were performed on all possible terminating (0001) and (11¯02) surfaces obtained from cleaving a sapphire single crystal. The energetic calculations show that the surface with the lowest cleavage energy is terminated with an Al layer for the (0001) surface, while it is terminated with an O layer for the (11¯02) surface. The concept of the surface building block, useful in determining the surface atomic termination, was proposed. Two unoccupied surface bands derived from the top-layer Al atoms are found within the bulk band gap at 2 and 8 eV below the conduction-band minimum (CBM) for the (0001) surface. For the (11¯02) surface, the occupied valence states derived from 2p states of the top-layer O atoms are found ∼4.0 eV below the CBM, which may explain the 4.7-eV energy-loss feature found experimentally on a sapphire (11¯02) surface.