An extended computational approach for point-defect equilibria in semiconductor materials

Abstract Concentrations of intrinsic and extrinsic point defects in crystalline materials with a bandgap are typically calculated in a constant- μ approach from defect formation energies based on density functional theory. In this work, calculations of thermal and charge equilibria among point defects are extended to a constant- N approach. The two approaches for point-defect equilibria are comparatively demonstrated in the application to Mg 2 Si doped with Li, Na, and Ag, which is a lightweight and environmentally friendly thermoelectric candidate material. Our results reveal the systematic behavior of defect and carrier concentrations. The dopant atoms form interstitial defects at similar concentrations to substitutional defects at the Mg sites, resulting in significantly reduced free-carrier concentrations compared to the expected values. The developed procedures could be utilized to find an optimal avenue for achieving higher carrier concentrations, e.g., with regard to annealing temperature and the concentration of dopant atoms, in various semiconductors and insulators.