Electronic structures of - and a-silicon nitride

The electronic energy bands of $\ensuremath{\alpha}$ and $\ensuremath{\beta}$ phases of silicon nitride have been calculated using a first-principles orthogonalized linear combination of atomic orbitals method. The potential is constructed from a superposition of atomic charge densities. The basis functions are the atomiclike wave functions contracted from the site-decomposed atomiclike potentials. For $\ensuremath{\beta}\ensuremath{-}{\mathrm{Si}}_{3}{\mathrm{N}}_{4}$, detailed studies of augmenting the basis functions with Si $d$ orbitals and additional single Gaussian orbitals for both Si and N atoms, and for the pressurized structure are also performed. The valence bands are composed of mainly N orbitals and the conduction bands are dominated by Si orbitals. It is found that the inclusion of Si $d$ orbitals in the basis has little effect on the valence-band structures, but changes conduction bands substantially. The electronic structure of $\ensuremath{\beta}\ensuremath{-}{\mathrm{Si}}_{3}{\mathrm{N}}_{4}$ under pressure up to 29.1 kbars has no appreciable difference from that of ordinary $\ensuremath{\beta}\ensuremath{-}{\mathrm{Si}}_{3}{\mathrm{N}}_{4}$. Furthermore, the density of states of $\ensuremath{\alpha}\ensuremath{-}{\mathrm{Si}}_{3}{\mathrm{N}}_{4}$ is very similar to that of $\ensuremath{\beta}\ensuremath{-}{\mathrm{Si}}_{3}{\mathrm{N}}_{4}$. All these indicate that the electronic structure of silicon nitride is completely determined by the local short-range atomic structures.