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We apply an Ising-type model to estimate the band gaps of the polytypes ofgroup IV elements (C, Si, and Ge) and binary compounds of groups: IV-IV (SiC,GeC, and GeSi), and III-V (nitride, phosphide, and arsenide of B, Al, and Ga).The models use reference band gaps of the simplest polytypes comprising 2--6bilayers calculated with the hybrid density functional approximation, HSE06. Wereport four models capable of estimating band gaps of nine polytypes containing7 and 8 bilayers with an average error of $\lesssim0.05$ eV. We apply the bestmodel with an error of $<0.04$ eV to predict the band gaps of 497 polytypeswith up to 15 bilayers in the unit cell, providing a comprehensive view of thevariation in the electronic structure with the degree of hexagonality of thecrystal structure. Within our enumeration, we identify four rhombohedralpolytypes of SiC -- 9$R$, 12$R$, 15$R$(1), and 15$R$(2) -- and perform detailedstability and band structure analysis. Of these, 15$R$(1) that has not beenexperimentally characterized has the widest band gap ($>3.4$ eV); phononanalysis and cohesive energy reveal 15$R$(1)-SiC to be metastable.Additionally, we model the energies of valence and conduction bands of therhombohedral SiC phases at the high-symmetry points of the Brillouin zone andpredict band structure characteristics around the Fermi level. The modelspresented in this study may aid in identifying polytypic phases suitable forvarious applications, such as the design of wide-gap materials, that arerelevant to high-voltage applications. In particular, the method holds promisefor forecasting electronic properties of long-period and ultra-long-periodpolytypes for which accurate first-principles modeling is computationallychallenging.

Band gaps of long-period polytypes of IV, IV-IV, and III-V semiconductors estimated with an Ising-type additivity model