First-principles supercell calculations for simulating a shallow donor state in Si

We present first-principles simulations of As-doped Si carried out using several cubic supercells of up to 10 648 atoms. The 1s As donor level in each supercell splits into three states, which have A1A1, T2T2, and E   symmetries, respectively. The 1s(A1)1s(A1) wavefunction is well converged in the largest cell, and its spread is close to those of the effective-mass theories. However, the calculated binding energies are smaller than experimental values. This discrepancy would be due to the self-interaction error within the approximated exchange-correlation density functional used in this calculation. Therefore, we also show perturbative calculations based on an impurity potential without the self-interaction error to estimate the binding energies of the 1s(A1)1s(A1) donor state. The estimated binding energy in the largest supercell agrees well with the experimental value.