The electronic energy bands of $\alpha$ and $\beta$ 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 $\beta -{\mathrm{Si}}_3{\mathrm{N}}_4$, 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 $\beta -{\mathrm{Si}}_3{\mathrm{N}}_4$ under pressure up to 29.1 kbars has no appreciable difference from that of ordinary $\beta -{\mathrm{Si}}_3{\mathrm{N}}_4$. Furthermore, the density of states of $\alpha -{\mathrm{Si}}_3{\mathrm{N}}_4$ is very similar to that of $\beta -{\mathrm{Si}}_3{\mathrm{N}}_4$. All these indicate that the electronic structure of silicon nitride is completely determined by the local short-range atomic structures.

• Received 10 November 1980

DOI:https://doi.org/10.1103/PhysRevB.23.5454