First principles studies were carried out for $lpha$-Ga2O3 and $lpha$-Ir2O3 to investigate their electronic band structures. The lattice parameters of $lpha$-Ga2O3 and rutile-structured IrO2 were in good agreement with experimental results. We presented calculated lattice parameters of $lpha$-Ir2O3. HSE06 hybrid functional was used for calculations of their electronic band structures. $lpha$-Ir2O3 was found to have an indirect bandgap of 2.62 eV and the valence and conduction bands were formed by d-electrons. By leveling $Gamma$ point of oxygen 2p electron energy, the band alignment of $lpha$-Ga2O3/$lpha$-Ir2O3 heterostructures is expected to be a type-II staggered structure.
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