Theoretical study of the electronic structure of the Si 3N 4(0 0 0 1) surface

Abstract

Density functional theory has been applied to a study of the electronic structure of the ideally-terminated, relaxed and H-saturated (0 0 0 1) surfaces of β-Si 3N 4 and to that of the bulk material. For the bulk, the lattice constants and atom positions and the valence band density of states are all in good agreement with experimental results. A band gap of 6.7 eV is found which is in fair accord with the experimental value of 5.1–5.3 eV for H-free Si 3N 4. Using a two-dimensionally-periodic slab model, a π-bonding interaction is found between threefold-coordinated Si and twofold-coordinated N atoms in the surface plane leading to π and π* surface-state bands in the gap. A surface-state band derived from s-orbitals is also found in the gap between the upper and lower parts of the valence band. Relaxation results in displacements of surface and first-underlayer atoms and to a stronger π-bonding interaction which increases the π–π* gap. The relaxed surface shows no occupied surface states above the valence band maximum, in agreement with recent photoemission data for a thin Si 3N 4 film. The π* band, however, remains well below the conduction band minimum (but well above the Fermi level). Adsorbing H at all dangling-bond sites on the ideally-terminated surface and then relaxing the surface and first underlayer leads to smaller, but still finite, displacements in comparison to the clean relaxed surface. This surface is more stable, by about 3.67 eV per H, than the clean relaxed surface.