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 (e.g., hybrid functionals, GW) 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, practical 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, Si:X (X= P, As, Sb, Bi), 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 $\sim$ 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. Beyond its high accuracy, DFT-1/2 offers a significant practical advantage, providing a straightforward, reproducible, and transferable workflow that is less demanding than hybrid functional approaches while remaining fully generalizable to other shallow impurities in semiconductors.