Thermodynamics of carbon point defects in hexagonal boron nitride

We present a first-principles computational study of the thermodynamics of carbon defects in hexagonal boron nitride (hBN). The defects considered are carbon monomers, dimers, trimers, and larger carbon clusters, as well as complexes of carbon with vacancies, antisites, and substitutional oxygen. Our calculations show that monomers ($\text{C}_{\text{B}}$, $\text{C}_{\text{B}}$), dimers, trimers, and $\text{C}_{\text{N}}\text{O}_{\text{N}}$ pairs are the most prevalent species under most growth conditions. Compared to these defects, larger carbon clusters, as well as complexes of carbon with vacancies and antisites, occur at much smaller concentrations. Our results are discussed in view of the relevance of carbon defects in single-photon emission in hBN.