The electronic, optical, and thermodynamical properties of tetragonal, monoclinic, and orthorhombic M₃N₄ (M=Si, Ge, Sn): A first-principles study

A detailed study of the M₃N₄ (M=Si, Ge, Sn) nitrides in their tetragonal, monoclinic and orthorhombic phases has been performed with the plane-wave pseudo-potential method combined with the quasi-harmonic approximation, including the phononic effects. We rationalize the main puzzle, i.e., the fundamental properties of these phases are unclear, by calculating the crystal structures, density of states, and optical properties. The direct band gaps of t-Ge₃N₄, m-Si₃N₄, and o-Ge₃N₄ benefit the opto-electrical properties. t-, m-, and o-Si₃N₄ can be used as refractive materials while m-M₃N₄ (M=Si, Ge, Sn) are optically transparent in the visible light region. Our results improve the understanding of the detailed electronic structures of all compounds, as well as the influences of electronic structure on their stabilities. Furthermore, we find that thermodynamic quantities are sensitive to structures and, therefore, depend on various temperature and pressure conditions.