  Localized electronic states formed inside the band gap of a semiconductor due
to crystal defects can be detrimental to the material's optoelectronic
properties. Semiconductors with lower tendency to form defect induced deep gap
states are termed defect tolerant. Here we provide a systematic first
principles investigation of defect tolerance in 29 monolayer transition metal
dichalcogenides (TMDs) of interest for nanoscale optoelectronics. We find that
the TMDs based on group VI and X metals form deep gap states upon creation of a
chalcogen (S, Se, Te) vacancy while the TMDs based on group IV metals form only
shallow defect levels and are thus predicted to be defect tolerant.
Interestingly, all the defect sensitive TMDs have valence and conduction bands
with very similar orbital composition. This indicates a bonding/anti-bonding
nature of the gap which in turn suggests that dangling bonds will fall inside
the gap. These ideas are made quantitative by introducing a descriptor that
measures the degree of similarity of the conduction and valence band manifolds.
Finally, the study is generalized to non-polar nanoribbons of the TMDs where we
find that only the defect sensitive materials form edge states within the band
gap.
