Point defect formation at finite temperatures with machine learning force fields

Abstract: Point defects dictate the properties of many functional materials. The standard approach to modelling the thermodynamics of defects relies on a static description, where the change in Gibbs free energy is approximated by the internal energy. This approach has a low computational cost, but ignores contributions from atomic vibrations and structural configurations that can be accessed at finite temperatures. We train a machine learning force field (MLFF) to explore dynamic defect behaviour using $\mathrm{Te_i^{+1}}$ and $\textit{V}{\mathrm{_{Te}^{+2}}}$ in CdTe as exemplars. We consider the different entropic contributions (e.g., electronic, spin, vibrational, orientational, and configurational) and compare methods to compute the defect free energies, ranging from a harmonic treatment to a fully anharmonic approach based on thermodynamic integration. We find that metastable configurations are populated at room temperature and thermal effects increase the predicted concentration of $\mathrm{Te_i^{+1}}$ by two orders of magnitude -- and can thus significantly affect the predicted properties. Overall, our study underscores the importance of finite-temperature effects and the potential of MLFFs to model defect dynamics at both synthesis and device operating temperatures.