Structural, Electronic, and Thermodynamic Properties of Tetragonal t-Si_xGe_3-xN₄

The structural, mechanical, anisotropic, electronic, and thermal properties of t-Si₃N₄, t-Si₂GeN₄, t-SiGe₂N₄, and t-Ge₃N₄ in the tetragonal phase are systematically investigated in the present work. The mechanical stability is proved by the elastic constants of t-Si₃N₄, t-Si₂GeN₄, t-SiGe₂N₄, and t-Ge₃N₄. Moreover, they all demonstrate brittleness, because B/G < 1.75, and v < 0.26. The elastic anisotropy of t-Si₃N₄, t-Si₂GeN₄, t-SiGe₂N₄, and t-Ge₃N₄ is characterized by Poisson's ratio, Young's modulus, the percentage of elastic anisotropy for bulk modulus A, the percentage of elastic anisotropy for shear modulus A, and the universal anisotropic index A^U. The electronic structures of t-Si₃N₄, t-Si₂GeN₄, t-SiGe₂N₄, and t-Ge₃N₄ are all wide band gap semiconductor materials, with band gaps of 4.26 eV, 3.94 eV, 3.83 eV, and 3.25 eV, respectively, when using the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional. Moreover, t-Ge₃N₄ is a quasi-direct gap semiconductor material. The thermodynamic properties of t-Si₃N₄, t-Si₂GeN₄, t-SiGe₂N₄, and t-Ge₃N₄ are investigated utilizing the quasi-harmonic Debye model. The effects of temperature and pressure on the thermal expansion coefficient, heat capacity, Debye temperature, and Grüneisen parameters are discussed in detail.