Two-dimensional hexagonal layers of $A_{N}B_{8-N}$ compounds on semiconductors

Using the parabolic model of the electronic spectrum of the substrate and the low-energy approximation of the dispersion law for two-dimensional hexagonal compounds $A_{N}B_{8-N}$, the density of states of an epitaxial layer has been investigated as a function of the band gap of the substrate, the band gap of the graphene-like compound in a free-standing state, their mutual arrangement, and the dimensionless “layer–substrate” coupling constant $C$. It has been shown that, when the coupling constant $C$ exceeds critical values, the density of states of the epitaxial layer undergoes qualitative changes. Both flat and buckled epitaxial layers have been considered. Estimates of the charge redistribution due to the transformation of the density of states of the graphene-like compound have been presented.