We investigate an excitonic peak appearing in low-temperature photoluminescence of monolayer transition metal dichalcogenides (TMDCs), which is commonly associated with defects and disorder. First, to uncover the intrinsic origin of defect-related excitons, we study their dependence on gate voltage, excitation power, and temperature in a prototypical TMDC monolayer, $MoS_2$. We show that the entire range of behaviors of defect-related excitons can be understood in terms of a simple model, where neutral excitons are bound to ionized donor levels, likely related to sulphur vacancies, with a density of $7cdot10^{11} cm^{-2}$. Second, to study the extrinsic origin of defect-related excitons, we controllably deposit oxygen molecules in-situ onto the surface of $MoS_2$ kept at cryogenic temperature. We find that in addition to trivial p-doping of $3cdot10^{12} cm^{-2}$, oxygen affects the formation of defect-related excitons by functionalizing the vacancy. Combined, our results uncover the origin of defect-related excitons, suggest a simple and conclusive approach to track the functionalization of TMDCs, benchmark device quality, and pave the way towards exciton engineering in hybrid organic-inorganic TMDC devices.
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