Stability and electronic structures of native defects in single-layer MoS 2

The atomic and electronic structures and stability of native defects in a single-layer ${\mathrm{MoS}}_{2}$ are investigated, based on density-functional theory calculations. Native defects such as a S vacancy (${V}_{\mathrm{S}}$), a S interstitial (${\mathrm{S}}_{i}$), a Mo vacancy (${V}_{\mathrm{Mo}}$), and a Mo interstitial (${\mathrm{Mo}}_{i}$) are considered. The ${\mathrm{S}}_{i}$ is found to have S-adatom configuration on top of a host S atom, and the ${\mathrm{Mo}}_{i}$ has Mo-${\mathrm{Mo}}_{i}$ split interstitial configuration along the $c$ direction. The formation energies of the native defects in neutral and charged states are calculated. For the charged states, the artificial electrostatic interactions between image charges in supercells are eliminated by a supercell size scaling scheme and a correction scheme that uses a Gaussian model charge. It is found that the ${V}_{\mathrm{S}}$ has a low formation energy of 1.3--1.5 eV in the Mo-rich limit condition, and the ${\mathrm{S}}_{i}$ has 1.0 eV in the S-rich limit condition. The ${V}_{\mathrm{S}}$ is found to be a deep single acceptor with the (0/$\ensuremath{-}$) transition level at 1.7 eV above the valence-band maximum (VBM). The ${\mathrm{S}}_{i}$ is found to be an electrically neutral defect. The Mo-related native defects of ${V}_{\mathrm{Mo}}$ and ${\mathrm{Mo}}_{i}$ are found to be high in formation energy above 4 eV. The ${V}_{\mathrm{Mo}}$ is a deep single acceptor and the ${\mathrm{Mo}}_{i}$ is a deep single donor, of which the (0/$\ensuremath{-}$) acceptor and (+/0) donor transition levels are found at 1.1 and 0.3 eV above the VBM, respectively.