  The influence of atomic vacancy defects at different concentrations on
electronic properties of MoS$_2$ and WS$_2$ monolayers is studied by means of
Slater-Koster tight-binding model with non-orthogonal $sp^3d^5$ orbitals and
including the spin-orbit coupling. The presence of vacancy defects induces
localized states in the bandgap of pristine MoS$_2$ and WS$_2$, which have
potential to modify the electronic structure of the systems, depending on the
type and concentration of the defects. It is shown that although the
contribution of metal (Mo or W) $d$ orbitals is dominant in the formation of
midgap states, the sulphur $p$ and $d$ orbitals have also considerable
contribution in the localized states, when metal defects are introduced. Our
results suggest that Mo and W defects can turn the monolayers into p-type
semiconductors, while the sulphur defects make the system a n-type
semiconductor, in agreement with ab initio results and experimental
observations.
