  In this study, we use DFT calculations to investigate the electronic and
structural properties of MoX$_2$ (X = S, Se, Te) monolayers doped with
substitutional Sb atoms, with a central focus on the Sb(Mo) substitution. In
MoS$_2$, we observe that this substitution is energetically favored under S
rich conditions, where the S$_2$ gaseous phase is likely to be present. This
result is compatible with a recent experimental observation in Sb-doped MoS$_2$
nanosheets grown by CVD. A similar behavior is found in MoSe$_2$, but in
MoTe$_2$ the Sb(Mo) substitution is less likely to occur due to the possible
absence of gaseous Te phases in experimental setups. In all cases, several
impurity-induced states are found inside the band gap, with energies that span
the entire gap. The Fermi energy is pinned a few tenths of eV above the top of
the valence band, suggesting a predominant $p$-type behavior. The orbital
nature of these states is investigated with projected and local density of
states calculations, which reveal similarities to defect states induced by
single Mo vacancies as well as their rehybridization with the $5s$ orbital from
Sb. Additionally, we find that the band gap of the doped systems is increased
in comparison with the pristine materials, in contrast with a previous
calculation in Sb-doped MoS$_2$ that predicts a gap reduction with a different
assignment of valence band and impurity levels. We discuss the similarities,
discrepancies, and the limitations of both calculations. We also speculate
possible reasons for the experimentally observed redshifts of the A and B
excitons in the presence of the Sb dopants in MoS$_2$. We hope that these
results spark future investigations on other aspects of the problem,
particularly those concerning the effects of disorder and electron-hole
interaction, and continue to reveal the potential of doped TMDCs for
applications in optoelectronic devices.
