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Native point defects from stoichiometry-linked chemical potentials in cubic boron arsenide

The presence of a point defect typically breaks the stoichiometry in a semiconductor. For example, a vacancy on an A-site in an AB compound makes the crystal B-rich. As the stoichiometry changes, so do the chemical potentials. While the prevalent first-principles methods have provided significant insight into characters of point defects in a transparent manner, the crucial connection between crystal stoichiometry and chemical potentials is usually not made. However, ad hoc choices for chemical potentials can lead to nonphysical negative formation energies in some Fermi level ranges, along with questions about charge balance. Herein, we formulate a canonical framework describing how the chemical potential of each element is directly linked to the composition of the crystal under (off-)stoichiometric conditions instead of the ad hoc assumption that the chemical potential is the elemental limit under a certain growth condition. Consequently, the chemical potential changes with the Fermi level within the band gap, and the formation energies are positive. Using such an approach, we present $ab$ $initio$ results for native point defects in BAs, a semiconductor with ultra-high room temperature thermal conductivity. We find that antisites are the constitutional defects in off-stoichiometric material, while B$_\mathrm{As}$ antisites and B vacancies dominate in the stoichiometric material. We further discuss the thermodynamic equilibrium and charge neutrality point in BAs in light of our stoichiometry-determined chemical potentials. As discussed, our work offers a more applicable and accessible approach to tackle defect formation energies in semiconductors, especially the ones with wide gap where negative formation energies are commonly seen.