The electronic and optical properties of the new cubic spinel nitrides $c-{\mathrm{Si}}_3{\mathrm{N}}_4,$ $c-{\mathrm{Ge}}_3{\mathrm{N}}_4,$ and that of the predicted double nitrides $c-{\mathrm{SiGe}}_2{\mathrm{N}}_4$ and $c-{\mathrm{GeSi}}_2{\mathrm{N}}_4$ are studied by a first-principles method. They are all semiconductors with band gaps between 1.85 and 3.45 eV and a bulk modulus between 258 and 280 GPa. From the total-energy calculations, it is shown that $c-{\mathrm{SiGe}}_2{\mathrm{N}}_4$ should be a stable compound while $c-{\mathrm{GeSi}}_2{\mathrm{N}}_4$ could be metastable. The compound $c-{\mathrm{SiGe}}_2{\mathrm{N}}_4$ is of particular interest because of a favorable direct band gap of 1.85 eV and a conduction-band effective mass of 0.49. The crystal has a very strong covalent bonding character as revealed by the calculated Mulliken effective charge and bond order. The strong covalent bonding in $c-{\mathrm{SiGe}}_2{\mathrm{N}}_4$ is attributed to the optimal arrangement of the cations. The smaller Si ion occupies the tetrahedrally coordinated $\mathrm{}\left(8a\right)\mathrm{}$ site and the larger Ge ion occupies the octahedrally coordinated $\mathrm{}\left(16d\right)\mathrm{}$ site.

• Received 13 November 2000

DOI:https://doi.org/10.1103/PhysRevB.63.245110