Electronic structure of boron nitride sheets doped with carbon from first-principles calculations

Using density functional theory with local and non-local exchange and correlation (XC) functionals, as well as the Green's function quasiparticle (GW) approach, we study the electronic structure of hexagonal boron nitride ($h$-BN) sheets, both pristine and doped with carbon. We show that the fundamental band gap in two-dimensional $h$-BN is different from the gap in the bulk material, and that in the GW calculations the gap depends on the interlayer distance (separation between the images of the BN layers within the periodic supercell approach) due to the non-local nature of the GW approximation, so that the results must be extrapolated to infinitely large separations between the images. We further demonstrate by the example of carbon substitutional impurities that the local and hybrid XC functionals give a qualitatively correct picture of the impurity states in the gap. Finally, we address the effects of many important parameters, such as the choice of chemical potential, and atom displacement cross sections for the substitutional process during electron-beam-mediated doping of $h$-BN sheets with carbon atoms. Our results shed light on the electronic structure of pristine and doped $h$-BN and should further help to optimize the postsynthesis doping of boron nitride nanostructures stimulated by electron irradiation.