Zinc-blende–wurtzite polytypism in semiconductors

The zinc-blende (ZB) and wurtzite (W) structures are the most common crystal forms of binary octet semiconductors. In this work we have developed a simple scaling that systematizes the T=0 energy difference \ensuremath{\Delta}${\mathit{E}}_{\mathrm{W}\mathrm{\ensuremath{-}}\mathrm{ZB}}$ between W and ZB for all simple binary semiconductors. We have first calculated the energy difference \ensuremath{\Delta}${\mathit{E}}_{\mathrm{W}\mathrm{\ensuremath{-}}\mathrm{ZB}}^{\mathrm{LDF}}$(AB) for AlN, GaN, InN, AlP, AlAs, GaP, GaAs, ZnS, ZnSe, ZnTe, CdS, C, and Si using a numerically precise implementation of the first-principles local-density formalism (LDF), including structural relaxations. We then find a linear scaling between \ensuremath{\Delta}${\mathit{E}}_{\mathrm{W}\mathrm{\ensuremath{-}}\mathrm{ZB}}^{\mathrm{LDF}}$(AB) and an atomistic orbital-radii coordinate R\ifmmode \tilde{}\else \~{}\fi{}(A,B) that depends only on the properties of the free atoms A and B making up the binary compound AB. Unlike classical structural coordinates (electronegativity, atomic sizes, electron count), R\ifmmode \tilde{}\else \~{}\fi{} is an orbital-dependent quantity; it is calculated from atomic pseudopotentials. The good linear fit found between \ensuremath{\Delta}${\mathit{E}}_{\mathrm{W}\mathrm{\ensuremath{-}}\mathrm{ZB}}$ and R\ifmmode \tilde{}\else \~{}\fi{} (rms error of \ensuremath{\sim}3 meV/atom) permits predictions of the W-ZB energy difference for many more AB compounds than the 13 used in establishing this fit. We use this model to identify chemical trends in \ensuremath{\Delta}${\mathit{E}}_{\mathrm{W}\mathrm{\ensuremath{-}}\mathrm{ZB}}$ in the IV-IV, III-V, II-VI, and I-VII octet compounds as either the anion or the cation are varied. We further find that the ground state of MgTe is the NiAs structure and that CdSe and HgSe are stable in the ZB form. These compounds were previously thought to be stable in the W structures.