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

TL;DR

This paper introduces a practical DFT-1/2 method for accurately calculating shallow donor binding energies in silicon, achieving near-experimental results with low computational cost and broad applicability.

Contribution

The authors develop a simple DFT-1/2 protocol that accurately predicts donor binding energies in silicon, outperforming traditional methods in efficiency and ease of use.

Findings

Binding energies closely match experimental values for P, As, Sb, Bi donors.

Including spin-orbit coupling improves accuracy for Bi donors.

Method is computationally efficient and transferable to other shallow impurities.

Abstract

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.