Quasiparticle electronic structure of charged oxygen vacancies in TiO2

TL;DR

This study investigates the electronic structure of charged oxygen vacancies in rutile TiO2 using advanced computational methods, revealing the weak electron correlation and the stability of certain vacancy charge states as shallow donors.

Contribution

It introduces a combined G0W0@GGA+U scheme to better understand electron localization and vacancy states in TiO2, comparing hybrid functionals for accurate gap and defect state descriptions.

Findings

G0W0@GGA+U confirms weak electron correlation in TiO2.

Different charged vacancies show varying U-dependence.

Hybrid functionals, especially HSE06, accurately reproduce the band gap and defect states.

Abstract

We studied the oxygen vacancies($V_{O}$) in rutile TiO2 by using $G_0W_0$ approximation on top of GGA+$U$ as a method of choice to improve the gap. Since there is no extensive agreement regarding the characteristic of electron localization for $ TiO_2$, we examine combined $G_0W_0$@GGA+$U$ scheme in which both are conceptually one step toward better enumeration of the non locality of exchange-correlation potential . Our $G_0W_0$@GGA+$U$ results realize and confirm the weak nature of electron correlation in rutile $TiO_2$ and shows that the $U$-dependence of the energy gap in perfect bulk is slightly stronger than in defected sample. In addition, we studied the $U$- dependency of $V_O$ defect states and found that different charged vacancies shows different $U$-dependence . While the application of $G_0W_0$ correction would improve the quasiparticle gap and formation energies, however the $V_O$ states, in contrast to experiment, remains entangled with the conduction band. Finally, we used PBE0 and HSE06 hybrid functionals and found that these exchange-correlation functional particularly HSE06 that reproduced the real gap and provide desire description of the screening, properly disentangle the neutral and singly ionized $V_O$ from the conduction band . According to hybrid functional calculations, all vacancies are stabilized and $V_O$ with 2+ charge state is the most stable vacancy in the whole Fermi-level range inside the gap and hence $V_O$ acts as a shallow donor.