defects can be very fast when the defect states have a good overlap with the conduction or valence band Bloch states.

Quantum efficiencies of TMD light emitters and detectors that have been reported are extremely poor; in the .0001-.01 range [@Lopez13; @Ross14; @Yin12; @Steiner13; @Pablo14]. Similar quantum efficiencies for TMDs have been observed in photoluminescence experiments [@Fai10; @Feng10; @Wangb14]. Therefore, most of the electrons and holes injected electrically or optically in TMDs recombine non-radiatively. Given that the average radiative lifetimes of excitons in TMDs are in the range of hundreds of picoseconds to a few nanoseconds [@Wanga14], the non-radiative recombination or capture times in TMDs are expected to be of the order of a few picoseconds. Several experimental results on the ultrafast carrier dynamics in photoexcited monolayer MoS$_{2}$ do indeed point to non-radiative recombinaton and/or capture times in the few picoseconds range [@Shi13; @Korn11; @Lagarde14; @Wangb14]. The mechanisms by which electrons and holes recombine non-radiatively and/or are captured by defects, and the associated time scales, remain to be clarified. The results in this paper show that electrons and holes of excitons in TMDs can get captured by defects on very short times scales that are in the sub-picosecond to a 