In2O3 is of particular interest as a wide-gap
transparent semiconductor oxide, in which the shallow donor defect
of the oxygen vacancy plays an important role in electronic properties.
Herein, we focus on the oxygen vacancy with various concentrations
in In2O3, where the distribution is found to
be crucial to the structural stabilities. For a specific supercell,
the formation energies of oxygen-vacancy pairs remarkably depend on
the distance between the two vacancies, which can be used to determine
the oxygen-vacancy distribution in the nonstoichiometric In2O3 structure. Interestingly, when two oxygen vacancies
share a same In atom, the structures are approximately stabilized
with the decreasing of distance. However, when two oxygen vacancies
are not attached to the same In atom, the structures become more stable
with the increasing of distance between vacancies. In addition, the
gap states induced by oxygen vacancies move toward the valence band
maximum (VBM) when the nearest distance between the two vacancies
decreases, which will have a great effect on the conductivity.