Energetics of carbon and oxygen impurities and their interaction with vacancies in cubic boron nitride

Abstract

We investigate, through first-principles calculations, the energetics of substitutional carbon and oxygen impurities as well as complexes involving these impurities and vacancies in cubic boron nitride $(c\ensuremath{-}\mathrm{BN}).$ The formation energies and the electronic and structural properties of these defects in their various charge states are investigated. We find that, under a boron-rich condition, both the carbon and the oxygen impurities at the nitrogen site $({\mathrm{C}}_{\mathrm{N}}$ and ${\mathrm{O}}_{\mathrm{N}})$ have formation energies comparable to or lower than those calculated for the vacancies, which are the lowest-energy intrinsic defects. Regarding defect complexes, we find that the donor character observed for the nitrogen vacancy ${(V}_{\mathrm{N}})$ can be compensated by the ${\mathrm{C}}_{\mathrm{N}}$ impurity in the formation of a ${V}_{\mathrm{N}}\ensuremath{-}{\mathrm{C}}_{\mathrm{N}}$ complex which has low formation energies. We also find that the ${V}_{\mathrm{B}}\ensuremath{-}{\mathrm{O}}_{\mathrm{N}}$ complex has low formation energies under n-type conditions. In contrast to the above mentioned complexes, we find that the ${V}_{\mathrm{B}}\ensuremath{-}{\mathrm{C}}_{\mathrm{B}}$ complex has high formation energies under a boron-rich condition, and shall only occur under a nitrogen-rich condition.