Structural, electronic, and optical properties of defect-containing MX₂ monolayers from first principles

In this work, we investigate the role of defects on the modification of the structural, electronic, and optical properties of transition metal dichalcogenide (MX₂: M=Mo,W; X=S,Se) nanosheets. Using the cluster expansion formalism and density functional theory (DFT), we calculate the energetics and magnetic ordering of MX₂ monolayers with various concentrations of chalcogen vacancies. The energetically favorable structures with desired vacancy concentration are then investigated further to determine the effects on the electronic, magnetic, and optical properties including the exciton binding energies. The structures we obtained from cluster expansion are then used as training sets for our machine learning algorithm to predict large scale MX₂ monolayers with desired vacancy concentration. We employ classical molecular dynamic simulations to study in the effect of vacancy defect concentration on the structural deformation of freestanding MX₂ nanosheets and nanoribbons. We report that after certain vacancy concentration values, MX₂ monolayers deform from planar structures to buckled structures. This work not only provides insight into realistic (i.e. CVD grown) MX₂ monolayers, but also provides guidance for defect engineering for device applications of MX₂ structures.