Polaronic hole localization and multiple hole binding of acceptors in oxide wide-gap semiconductors

TLDR

In oxides, acceptor‑bound holes tend to localize asymmetrically on one of several equivalent oxygen ligands, a tendency that Hartree‑Fock theory over‑emphasizes while local‑density approximations spuriously delocalize them, due to opposite curvatures of the energy versus fractional occupation number. The study seeks to remove this localization bias by enforcing a generalized Koopmans condition that restores linear energy dependence on fractional occupation. This is accomplished by formulating a generalized Koopmans condition that sets the second derivative of energy with respect to occupation to zero. The corrected treatment reveals that nominal single acceptors on cation sites in ZnO, In₂O₃, and SnO₂ can bind multiple holes.

Abstract

Acceptor-bound holes in oxides often localize asymmetrically at one out of several equivalent oxygen ligands. Whereas Hartree-Fock (HF) theory overly favors such symmetry-broken polaronic hole localization in oxides, standard local-density (LD) calculations suffer from spurious delocalization among several oxygen sites. These opposite biases originate from the opposite curvatures of the energy as a function of the fractional occupation number $n$, i.e., ${d}^{2}E/d{n}^{2}<0$ in HF and ${d}^{2}E/d{n}^{2}>0$ in LD. We recover the correct linear behavior, ${d}^{2}E/d{n}^{2}=0$, that removes the (de)localization bias by formulating a generalized Koopmans condition. The correct description of oxygen hole localization reveals that the cation-site nominal single acceptors in ZnO, ${\text{In}}_{2}{\text{O}}_{3}$, and ${\text{SnO}}_{2}$ can bind multiple holes.