Equilibrium densities of intrinsic defects in transition metal diselenides of molybdenum and tungsten

Point defects are thermodynamically stabilized in all crystalline materials, with increased densities negatively impacting the properties and performance of transition metal dichalcogenides (TMDs). While recent point defect reduction methods have led to considerable improvements in the optoelectronic properties of TMDs, there is a clear need for theoretical work to establish the lower limit of defect densities, as represented by thermal equilibrium. To that end, an ab initio and thermodynamic analysis of the equilibrium densities of intrinsic point defects in MoSe2 and WSe2 is presented. The intrinsic defect formation energies at the limits of the selenium and metal-rich regimes are determined by density functional theory (DFT) and then augmented with elemental chemical potential functions to determine temperature- and pressure-dependent formation energies. Equilibrium defect densities are determined for MSe, SeM, vM, and vSe, where M and v, respectively, represent the metal and the vacancy, as a function of synthesis temperature and pressure. The effects of vibrational free energy contributions and treatment of the DFT exchange–correlation potential are found to be non-negligible. Calculated equilibrium densities are several orders of magnitude below reported defect densities in TMDs made by chemical vapor deposition, chemical vapor transport, and flux methods, thereby establishing that current synthesis methods are either kinetically limited or impurity dominated.