Electronic structure and energetics of ${\mathrm{B}}_x{\mathrm{C}}_y{\mathrm{N}}_z$ layered structures

We investigate the relative stability and electronic structure of several ${\mathrm{B}}_x{\mathrm{C}}_y{\mathrm{N}}_z$ layered structures using first-principles calculations. The twenty structures we considered are derived from a graphite layer by placing carbon, nitrogen, or boron atoms on each site. Interestingly, a structure with ${\mathrm{B}}_3{\mathrm{C}}_2{\mathrm{N}}_3$ stoichiometry was found to be more stable than the eight $\mathrm{B}{\mathrm{C}}_2\mathrm{N}$ structures in our study. The BCN compositions we considered present a wide range of electronic behaviors. In general, we observe that structures with large values of the electronic band gap have a $\mathrm{B}∕\mathrm{N}$ $(x∕z)$ ratio of one.

Figure 1

${\mathrm{B}}_x{\mathrm{C}}_y{\mathrm{N}}_z$ layered structures considered in this work. Boron, carbon, and nitrogen atoms are represented by white, gray, and black circles, respectively.

Figure 2

(Color online) Formation energies per atom (in eV/atom) of the structures in Fig. 1, calculated using the bond-energy model of Eq. (2), vs the corresponding ab initio results.

Figure 3

(Color online) Electronic band gap $E_g$ as a function of the formation energy $E_f$ for the ${\mathrm{B}}_x{\mathrm{C}}_y{\mathrm{N}}_z$ structures of Fig. 1. Structures with $x=z$ $(\mathrm{B}∕\mathrm{N}=1)$ are indicated by open circles. The remaining structures are indicated by open triangles, for N-rich and B-rich cases.