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Chalcogen vacancies in the semiconducting monolayer transition-metaldichalcogenides (TMDs) have frequently been invoked to explain a wide range ofphenomena, including both unintentional p-type and n-type conductivity, as wellas sub-band gap defect levels measured via tunneling or optical spectroscopy.These conflicting interpretations of the deep versus shallow nature of thechalcogen vacancies are due in part to shortcomings in prior first-principlescalculations of defects in the semiconducting two-dimensional (2D) TMDs thathave been used to explain experimental observations. Here we report results ofhybrid density functional calculations for the chalcogen vacancy in a series ofmonolayer TMDs, correctly referencing the thermodynamic charge transitionlevels to the fundamental band gap (as opposed to the optical band gap). Wefind that the chalcogen vacancies are deep acceptors and cannot lead to n-typeor p-type conductivity. Both the (0/$-1$) and ($-$1/$-$2) transition levelsoccur in the gap, leading to paramagnetic charge states S=1/2 and S=1,respectively, in a collinear-spin representation. We discuss trends in terms ofthe band alignments between the TMDs, which can serve as a guide to futureexperimental studies of vacancy behavior.

The deep-acceptor nature of the chalcogen vacancies in 2D transition-metal dichalcogenides