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/$-$) 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/$-$) acceptor and (+/0) donor transition levels are found at 1.1 and 0.3 eV above the VBM, respectively.

• Received 15 July 2013
• Revised 17 March 2014

DOI:https://doi.org/10.1103/PhysRevB.89.205417