Stability of charged sulfur vacancies in 2D and bulk MoS2 from plane-wave density functional theory with electrostatic corrections

Two-dimensional (2D) semiconducting transition metal dichalcogenides such as\nMoS$_2$ have attracted extensive research interests for potential applications\nin optoelectronics, spintronics, photovoltaics, and catalysis. To harness the\npotential of these materials for electronic devices requires a better\nunderstanding of how defects control the carrier concentration, character, and\nmobility. Utilizing a correction scheme developed by Freysoldt and Neugebauer\nto ensure the appropriate electrostatic boundary conditions for charged defects\nin 2D materials, we perform density functional theory calculations to compute\nformation energies and charge transition levels associated with sulfur\nvacancies in monolayer and layered bulk MoS$_2$. We investigate the convergence\nof these defect properties with respect to vacuum spacing, in-plane supercell\ndimensions, and different levels of theory. We also analyze the electronic\nstructures of the defects in different charge states to gain insights into the\neffect of defects on bonding and magnetism. We predict that both vacancy\nstructures undergo a Jahn-Teller distortion, which helps stabilize the sulfur\nvacancy in the $-1$ charged state.\n