First-principles embedded-cluster calculations of the neutral and charged oxygen vacancy at the rutile TiO$_2$(110) surface

TL;DR

This study uses advanced first-principles calculations to analyze the stability of oxygen vacancies on TiO2 surfaces, revealing that the doubly charged state is most stable and that vacancy concentrations increase in p-doped samples.

Contribution

It introduces a combined DFT and embedded-cluster approach to accurately assess charged surface defect stability in TiO2, highlighting the dominant +2 charge state.

Findings

The +2 charge state of oxygen vacancy is most stable.

Vacancy formation energy decreases with lower Fermi level.

Higher vacancy concentrations are expected in p-doped TiO2 surfaces.

Abstract

We perform full-potential screened-hybrid density-functional theory (DFT) calculations to compare the thermodynamic stability of neutral and charged states of the surface oxygen vacancy at the rutile TiO$_2$(110) surface. Solid-state (QM/MM) embedded-cluster calculations are employed to account for the strong TiO$_2$ polarization response to the charged defect states. Similar to the situation for the bulk O vacancy, the +2 charge state $V_{\rm O}^{2+}$ is found to be energetically by far most stable. Only for Fermi-level positions very close to the conduction band, small polarons may at best be trapped by the charged vacancy. The large decrease of the $V_{\rm O}^{2+}$ formation energy with decreasing Fermi-level position indicates strongly enhanced surface O vacancy concentrations for $p$-doped samples.