Morphology, ordering, stability, and electronic structure of carbon-doped hexagonal boron nitride

We present theoretical studies of morphology, stability, and electronic structure of monolayer hexagonal CBN alloys with rich content of h-BN and carbon concentration not exceeding 50 %. Our studies are based on the bond order type of the valence force field to account for the interactions between atomic constituents and Monte Carlo method with Metropolis algorithm to establish equilibrium distribution of atoms over the lattice. We find out that the phase separation into graphene and h-BN domains occurs in the majority of growth conditions. Only in N-rich growth conditions, it is possible to obtain quasi uniform distribution of carbon atoms over boron sublattice. We predict also that the energy gap in stoichiometric C$_x$(BN)$_{1-x}$ alloys exhibits extremely strong bowing.