Electronic structure of indium oxide using cluster calculations

We report first-principles electronic-structure calculations of ${\mathrm{In}}_2{\mathrm{O}}_3$ using the discrete variational $X\alpha$ method on model clusters. The computation has been made up to the model cluster composed of 163 atoms in order to see the size effect. The In-O bond is found to be predominant in ${\mathrm{In}}_2{\mathrm{O}}_3,$ and both O-O and In-In bonds are much weaker. Antibonding interaction between $\mathrm{O}-2p$ with nearly filled $\mathrm{In}-4d$ orbitals near the top of the valence band is noticed. Valence-band structure by XPS is well reproduced by the calculation. Unoccupied $\mathrm{In}-5\mathrm{sp}$ orbitals show wide spatial distribution over the third In shell. Direct interaction between $\mathrm{In}-5\mathrm{sp}$ orbitals is found to be important in the excited states. When an oxygen vacancy is present, a vacancy level appears in between the band gap. The vacancy level is composed of $\mathrm{In}-5\mathrm{sp}$ orbitals hybridized with $\mathrm{O}-2p$ orbitals, which exhibits a strong In-In bonding interaction. The occupation of the vacancy level due to the localization of electrons to the oxygen vacancy thus results in the reinforcement of the In-In bond strength. This is suggested to be the electronic mechanism for the stability of the oxygen vacancies in the ${\mathrm{In}}_2{\mathrm{O}}_3$ crystal.