Formation Energies of Charged Defects in Transition Metal Dichalcogenides at Finite Temperature and Pressure

    While the formation energy of charged point defects is often used to estimate defect density in a material, the formation energies obtained from density functional theory usually have a 0 Kelvin reference that makes the defect densities far less accurate at finite temperature. The usual solution to this has been to perform finite-temperature density functional theory, but this process is known to be computationally expensive and not worthwhile for many cases. Here we demonstrate an alternative, wherein the 0 Kelvin density functional theory reference is maintained to reduce computational cost. We use the change in chemical potentials of Mo and Se and in molar free energy of MoSe₂ obtained from experimental data and apply the trends in temperature and pressure to the density functional theory reference to obtain defect formation energies for charged defects in freestanding monolayer MoSe₂. We then apply these formation energies to predict equilibrium defect concentrations in MoSe₂ as a function of temperature and pressure.