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

TL;DR

This paper evaluates the calculation of impurity binding energies in semiconductors using DFT and GW methods, highlighting the strengths and limitations of DFT in different scenarios, especially for nanowires.

Contribution

It demonstrates the effectiveness of DFT for ionized impurities but reveals its shortcomings for neutral impurities due to missing surface polarization effects.

Findings

DFT accurately calculates E_b for ionized impurities from the KS Hamiltonian.

DFT fails to accurately compute E_b for neutral impurities because of missing surface polarization interactions.

The deficiency is linked to the lack of screened exchange in current functionals.

Abstract

We discuss the binding energy E_b 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 E_b from the Kohn-Sham (KS) hamiltonian of the ionized impurity, but fails in the calculation of E_b 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 functionals.