Optical and mechanical properties of C, Si, Ge, and 3C-SiC determined by first-principles theory using Heyd-Scuseria-Ernzerhof functional

Accurately calculating the band gap and electronic state density distribution of crystals is significant in determining optical properties. First-principles calculations were based on the projector-augmented-wave method with the Perdew-Burke-Ernzerhof generalized gradient approximation functional, pure density functional theory (DFT) and Heyd-Scuseria-Ernzerhof (HSE) hybrid functional. Such calculations account for the lattice parameters, electronic structure, optical properties, and mechanical properties of materials, which include the diamond-C and zinc blende structure of Si, Ge, and 3C-SiC in this study. The results obtained with HSE calculations is more accurate than that of the pure DFT calculations, and consistent with previous experimental values. The band structure and density of states of Si, Ge, and 3C-SiC indicate that these materials are indirect band gap materials. Based on HSE calculation, the band gap of Si and 3C-SiC is in accordance with previous experimental values. The imaginary part of the analytical dielectric function, the refractive index, and the adsorption coefficient also matches previous experimental values. A corresponding relationship exists among the peak of the imaginary part of the analytical dielectric function, the refractive index, and the adsorption coefficient. The optical properties have a direct relationship with the distribution of the crystal band gap and electronic state density. The materials exhibit brittleness. Although 3C-SiC is not as hard and stiff as diamond, it is a better semiconductor than Si and Ge. The mechanical anisotropy of the four materials is inconspicuous. The anisotropy of diamond-C in terms of its Young's modulus is extremely inconspicuous.