First principles total energy calculations within the density functional formalism have been used to investigate the electronic, mechanical, and optical properties of pseudocubic- Si 3 P 4 and Ge 3 P 4. Considering the technological importance of the Si/Ge -Group-V elements, we have concentrated mainly on the comparatively less studied, but energetically more favorable pseudocubic- Si 3 P 4 and Ge 3 P 4 structures of the Si and Ge phosphides. We find that the electronic band structures show that pseudocubic- Si 3 P 4 and Ge 3 P 4 are both indirect band semiconductors with very low density functional band gaps of 0.24 eV and 0.13 eV, respectively. We also calculate mechanical properties of the materials, such as the bulk modulus, elastic constants, shear modulus, and Vickers hardness of the two phosphides. We find that the bulk and shear modulus of pseudocubic- Si 3 P 4 and Ge 3 P 4 are 76.18 GPa and 58.37 GPa, and 59.99 GPa and 46.92 GPa, respectively. Pseudocubic- Si 3 P 4 and Ge 3 P 4 have low Vickers hardness, nearly 18.88 and 16.86 GPa, respectively. Moreover, optical parameters, including dielectric function, refractive index, optical absorption, energy loss function, and plasma frequency are also studied.
Electronic band structures of group-V two-dimensional materials