An accurate DFT-1/2 approach for shallow defect states: efficient calculation of donor binding energies in silicon

Accurate prediction of shallow donor electron binding energies is critical for device modeling, dopant activation, and donor-based quantum technologies. Traditional beyond-DFT approaches are prohibitively expensive for the large supercells needed to capture the extended, hydrogenic wavefunctions, while semi-local DFT underestimates band gaps and suffers from delocalization errors. We present a simple protocol for shallow donors based on the DFT-1/2 approximate quasiparticle correction that maintains the computational cost of standard DFT and enables supercells up to thousands of atoms. This approach provides a straightforward and reproducible workflow that delivers reliable donor binding energies with minimal computational overhead. Applied to group-V donors in Si, the method yields binding energies in close agreement with experiment. We found that, for Si:Bi, it is essential to include spin-orbit coupling to achieve near-experimental values with a difference of only 4 meV. For arsenic, the method yields excellent agreement with experiment, with a difference of only 0.3 meV. For antimony, the results match experiment to within 5 meV, and for phosphorus, the deviation is within 8 meV. To demonstrate its generality, we further validate the methodology by applying it to hydrogen donors in ZnO, confirming its broad applicability to semiconductor systems.