  First-principles calculations based on Density functional theory (DFT) and
Heyd, Scuseria and Ernzerhof (HSE) adopt PBE approximation-a new version of the
generalized gradient approximation (GGA). It has studied lattice parameter,
electronic structure, optical properties and mechanical properties of
materials, including diamond-C and zinc-blende structure of Si, Ge, 3C-SiC. The
result of HSE calculation is obviously superior to DFT calculation and accord
well with the existing experimental values. It indicates that they are indirect
bandgap materials from the figure of band structure and density of states. The
bandgap which it calculated using HSE accords well with the existing
experimental values except Ge. In the calculation of optical property, it shows
that they correspond with the existing experimental values from the imaginary
part of analytical dielectric function to the refractive index and adsorption
coefficient. It demonstrates that they exists the corresponding relationship
among the peak of the imaginary part of analytical dielectric function, the
refractive index and adsorption coefficient. The optical property has a direct
relationship with the distribution of crystal bandgap and electronic state
density. From the results of mechanical properties it can know that they are
brittle materials. Though the hardness and stiffness of 3C-SiC is lower than
diamond, it is superior to the materials of Si, Ge as excellent semiconductor
materials. In addition, the mechanical anisotropy of four materials is
inconspicuous; the anisotropy of Diamond-C is very inconspicuous from
anisotropic properties of Young modulus.
