Band alignment at surfaces and heterointerfaces of ${\mathrm{Al}}_2{\mathrm{O}}_3$, ${\mathrm{Ga}}_2{\mathrm{O}}_3$, ${\mathrm{In}}_2{\mathrm{O}}_3$, and related group-III oxide polymorphs: A first-principles study

The band alignments at nonpolar surfaces and heterointerfaces of ${\mathrm{Al}}_2{\mathrm{O}}_3$, ${\mathrm{Ga}}_2{\mathrm{O}}_3$, and ${\mathrm{In}}_2{\mathrm{O}}_3$ polymorphs, and three related group-III oxides, namely, ${\mathrm{Sc}}_2{\mathrm{O}}_3$, ${\mathrm{Y}}_2{\mathrm{O}}_3$, and ${\mathrm{La}}_2{\mathrm{O}}_3$, are investigated by using first-principles calculations. A non-self-consistent dielectric-dependent hybrid functional approach is adopted on top of semilocal density-functional calculations by using the Perdew-Burke-Ernzerhof functional tuned for solids (PBEsol) to accelerate the band alignment evaluation that involves surface and interface calculations. Among the five crystal structures considered, namely, corundum, β-gallia, κ-alumina, bixbyite (C-type rare earth), and A-type rare earth, the lowest energy phases are corundum, β-gallia, A-type rare earth, and bixbyite for ${\mathrm{Al}}_2{\mathrm{O}}_3$, ${\mathrm{Ga}}_2{\mathrm{O}}_3$, ${\mathrm{La}}_2{\mathrm{O}}_3$, and the others, respectively, within PBEsol calculations. The ionization potential typically decreases in the order ${\mathrm{Al}}_2{\mathrm{O}}_3$, ${\mathrm{Ga}}_2{\mathrm{O}}_3$, ${\mathrm{In}}_2{\mathrm{O}}_3$, ${\mathrm{Sc}}_2{\mathrm{O}}_3$, ${\mathrm{Y}}_2{\mathrm{O}}_3$, and ${\mathrm{La}}_2{\mathrm{O}}_3$ within the same crystal structure and surface termination. This tendency is enhanced by the atomic relaxation-induced surface dipoles, where smaller cations tend to relax toward the bulk side compared to O ions, while larger cations tend to relax toward the vacuum side. The ionization potential and electron affinity differences at unrelaxed surfaces are good indicators of the interfacial valence- and conduction-band offsets, respectively, for ${\mathrm{Al}}_2{\mathrm{O}}_3$/${\mathrm{Ga}}_2{\mathrm{O}}_3$ with a relatively small mismatch in the lattice parameters of the two phases.