Understanding band alignments in semiconductor heterostructures: Composition dependence and type-I–type-II transition of natural band offsets in nonpolar zinc-blendeAlxGa1−xN/AlyGa1−yNcomposites

The composition dependence of the natural band alignment at nonpolar ${\mathrm{Al}}_x{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}/{\mathrm{Al}}_y{\mathrm{Ga}}_{1\ensuremath{-}y}\mathrm{N}$ heterojunctions is investigated via hybrid functional based density functional theory. Accurate band-gap data are provided using Heyd-Scuseria-Ernzerhof (HSE) type hybrid functionals with a composition dependent exact-exchange contribution. The unstrained band alignment between zincblende (zb) ${\mathrm{Al}}_x{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}$ semiconductor alloys is studied within the entire ternary composition range utilizing the Branch-point technique to align the energy levels related to the bulklike direct ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{v}}\ensuremath{\rightarrow}{\mathrm{\ensuremath{\Gamma}}}_{\mathrm{c}}$ and indirect, pseudodirect, respectively, ${\mathrm{\ensuremath{\Gamma}}}_{\mathrm{v}}\ensuremath{\rightarrow}{X}_{\mathrm{c}}$ type transitions in zb-${\mathrm{Al}}_x{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}$. While the zb-GaN/${\mathrm{Al}}_x{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}$ band edges consistently show a type-I alignment, the relative position of fundamental band edges changes to a type-II alignment in the Al-rich composition ranges of zb-${\mathrm{Al}}_x{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}/\mathrm{AlN}$ and zb-${\mathrm{Al}}_x{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}/{\mathrm{Al}}_y{\mathrm{Ga}}_{1\ensuremath{-}y}\mathrm{N}$ systems. The presence of a direct-indirect band-gap transition at ${x}_{\mathrm{c}}=0.63$ in zb-${\mathrm{Al}}_x{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}$ semiconductor alloys gives rise to a notably different composition dependence of band discontinuities in the direct and indirect energy-gap ranges. Below the critical direct-indirect Al/Ga-crossover concentration, the band offsets show a close to linear dependence on the alloy composition. In contrast, notable bowing characteristics of all band discontinuities are observed above the critical crossover composition.