Mechanical, elastic, anisotropy, and electronic properties of monoclinic phase of m-Si_xGe_3-xN₄

The structural, mechanical, elastic anisotropic, and electronic properties of the monoclinic phase of m-Si₃N₄, m-Si₂GeN₄, m-SiGe₂N₄, and m-Ge₃N₄ are systematically investigated in this work. The calculated results of lattice parameters, elastic constants and elastic moduli of m-Si₃N₄ and m-Ge₃N₄ are in good agreement with previous theoretical results. Using the Voigt-Reuss-Hill method, elastic properties such as bulk modulus B and shear modulus G are investigated. The calculated ratio of B/G and Poisson's ratio v show that only m-SiGe₂N₄ should belong to a ductile material in nature. In addition, m-SiGe₂N₄ possesses the largest anisotropic shear modulus, Young's modulus, Poisson's ratio, and percentage of elastic anisotropies for bulk modulus A_B and shear modulus A_G, and universal anisotropic index A_U among m-Si_xGe_3-xN₄ (x=0, 1, 2, 3.) The results of electronic band gap reveal that m-Si₃N₄, m-Si₂GeN₄, m-SiGe₂N₄, and m-Ge₃N₄ are all direct and wide band gap semiconducting materials.