First-principles study on energetics of c-BN(001) reconstructed surfaces

Total energies of cubic boron nitride (c-BN) (001) surfaces are systematically studied for various reconstructed configurations by the local density-functional approach with ultrasoft pseudopotentials. Stable phases as a function of nitrogen chemical potential are predicted theoretically. We examine the validity of the electron counting (EC) rule, which plays an important role for the study of the GaAs surfaces, and obtain supplemental factors to determine stable surface structures. The results of the total-energy minimization calculation demonstrate that the EC rule holds very well within the models that contain at most one layer with defects and no interlayer N-N and B-B bonds, and that next to the EC rule, the electrostatic energy has the most important role in determining stable structures. Furthermore, in the nitrogen-rich region, we found that the EC rule does not hold, because the energy difference between the N-B and N-N bonds is larger than the energy gain from using the EC model. We suggest that the important factors for determining stable structures of the c-BN(001) surface are N-B bond saturation, the EC rule, and electrostatic energy, whose effect decreases in this order. The difference between c-BN and GaAs surfaces is also discussed.