Ab initio calculation of the binding energy of impurities in semiconductors : application to Si nanowires

We discuss the binding energy Eb of impurities in semiconductors within density functional theory (DFT) and the GW approximation, focusing on donors in nanowires as an example. We show that DFT succeeds in the calculation of Eb from the Kohn-Sham (KS) hamiltonian of the ionized impurity, but fails in the calculation of Eb from the KS hamiltonian of the neutral impurity, as it misses most of the interaction of the bound electron with the surface polarization charges of the donor. We trace this deficiency back to the lack of screened exchange in the present functional