Band structure of monolayer of graphene, silicene and silicon-carbide including a lattice of empty or filled holes

We have developed a pi-orbital tight-binding Hamiltonian model taking into account the nearest neighbors to study the effect of antidot lattices (two dimensional honeycomb lattice of atoms including holes) on the band structure of silicene and silicon carbide (SiC) sheets. We obtained that the band structure of the silicene antidot superlattice strongly depends on the size of embedded holes, and the band gap of the silicene antidot lattice increases by increasing of holes diameter. The band gap of SiC antidot lattice, except for the lattice of the small unit cell, is independent of the holes diameter and also depends on the distance between holes. We obtained that, the band gap of the SiC antidot lattice is the same as the band gap of the corresponding sheet without hole. Also, the electronic properties of the SiC antidot superlattice occupied either by carbon or by silicon atoms are investigated, numerically. Furthermore, we study the effect of occupation of graphene antidot by Si atoms and vice versa. Also, we have calculated the band structure of graphene and silicene antidot lattice filled by Si + C atoms. Finally, we compute the band structure of the SiC antidot lattice including the holes which are filled by C or by Si atoms. Really, in this paper we have generalized the method of paper([38]) about graphene antidot with empty holes to the cases of filled holes by different atoms and also to the case of silicene and silicon carbide antidot lattices.