Revisiting semiconductor band gaps through structural motifs: An Ising model perspective

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We present an alternative perspective on semiconductor band-gap energies in terms of structural motifs, viewed through the lens of an Ising model as a means of quantifying the corresponding degree of lattice ordering. The validity of the model is demonstrated experimentally first through ${\mathrm{ZnSnN}}_{2}$ as an archetype ternary heterovalent semiconductor, in which variation of cation disorder enables the band gap to be tuned from above its equilibrium phase value, through zero, to negative values which correspond to inverted bands. The model is then applied to example binary compounds InN, GaN, and ZnO where anion-cation antisite defects form the basis for structural motifs, and we present experimental evidence that the same range of band-gap tuning is also possible for such materials. The case of alloys is treated by applying a three-spin Potts model to ${\mathrm{In}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{N}$. The Ising model also applies to elemental semiconductors, and is used to explain the wide range of reported values for silicon and nanoporous graphene in the context of vacancy-based structural motifs.