Atomic and electronic structures of R2O3(ZnO)3 (R=Al, Ga, and In), which are included in homologous series of compounds, are investigated using first-principles calculations based on density functional theory. Three models with different R atom arrangements in the five-fold and four-fold coordination sites are examined. Al and Ga prefer the five-fold coordination sites. The formation energies are much larger than those of the competing phases, ZnR2O4, with a normal spinel structure. On the other hand, In2O3(ZnO)3 shows no clear site preference and can be more stable than the spinel at high temperatures when configurational entropy contribution is taken into account. Electronic states near the conduction band bottom are mainly composed of Zn-4s orbital in Al2O3(ZnO)3, while the contributions of Ga-4s and In-5s are comparable to Zn-4s in Ga2O3(ZnO)3 and In2O3(ZnO)3.
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