Universal Polaronic\nBehavior in Elemental Doping of\nMoS<sub>2</sub> from First-Principles

Elemental doping\nof two-dimensional (2D) semiconductors\nis crucial\nfor manipulating their electrical and optical properties and enhancing\nthe performance of advanced 2D devices. However, doping methods, such\nas ion implantation and chemical vapor deposition, can produce various\noutcomes extensively, depending on the chemical environment. We systematically\nstudy the elemental doping of the monolayer MoS<sub>2</sub> by using\ndensity-functional theory calculations, which identify thermally stable\nsites among atomic substitutions, surface adsorption, and lattice\ninterstitials of 27 elemental dopants, along with their formation\nenergies and charge transition levels. By adopting the Koopmans-compliant\nhybrid functionals, the hydrogenic states predicted by semilocal functionals\ntransform into localized polaronic states, which universally exhibit\ndeep transitions located 1.0 eV away from the band edges. This polaronic\nbehavior persists even in bulk MoS<sub>2</sub>, which suggests impurity\nconduction as the predominant carrier conduction mechanism. Our study\noffers fundamental insights into elemental doping in MoS<sub>2</sub>, which could be essential for doping transition metal dichalcogenides\nand similar 2D semiconductors.