A \textit{first principles} investigation of point defects in monolayer, few-layer, and bulk WS$_{2}$*

We present the results of a systematic study of physics of point defects in 2D WS$_{2}$ materials conducted by means of density functional theory. First, we investigate the physics of point defects in monolayer (ML) WS$_{2}$. Second, we examine the impact of point defects on the physical properties of multi-layer defective WS$_{2}$ as a function of slab thickness. The studied point defects are: monovacancies, interstitials and anti-sites, and the considered physical properties include local geometry, defect formation energy, electronic structure and magnetism. Van der Waals interaction, spin-polarization and spin-orbit coupling effects are also incorporated in the calculations to ensure accurate results. In a ML WS$_{2}$, we predict that I$_{S}$ is the most favorable defect inside WS$_{2}$ having a low formation energy of 1.21 eV. W$_{S}$ and W$_{S2}$ anti-sites result in a total magnetic moment of 2 $\mu_{B}$. By studying ML, few-layer (up to 4 layers), and bulk WS$_{2}$ slabs we find that, all point defects cause only localized perturbation, thus have little influence on the thickness-dependent evolution of the physical properties. The depth-dependence of the defect formation energy is also found: V$_{S}$ prefers to stay on the surface, while V$_{W}$ prefers the slab center.