Electronic structure of generic semiconductors: Antifluorite silicide and III-V compounds.

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The perturbation potential which transmutes a homopolar column-IV diamondlike semiconductor into either a heteropolar zinc-blende-like III-V or II-VI compound or an antifluorite semiconductor can be thought of as consisting of a sum of two terms: (i) a long-range Coulomb dipole potential \ensuremath{\Delta}${V}_{\mathrm{dip}(\mathrm{r}}$) associated with the different valence of the atoms of the compound relative to the atoms in the diamondlike system, and (ii) the remaining, short-range and primarily repulsive core pseudopotential \ensuremath{\Delta}${V}_{\mathrm{CC}(\mathrm{r}}$) (a ``central-cell'' correction). Whereas \ensuremath{\Delta}${V}_{\mathrm{dip}(\mathrm{r}}$) is common to all members of a given structural class (e.g., all III-V or all II-VI compounds or all antifluorite silicides), defining thereby generic semiconductors, the central-cell potential \ensuremath{\Delta}${V}_{\mathrm{CC}(\mathrm{r}}$) carries the specific signature of each atom, distinguishing therefore members of a given class from each other.Using self-consistent pseudopotential band theory within the local-density formalism, we calculate the band structures, equilibrium lattice constants, and electronic charge densities of a generic III-V compound and an antifluorite silicide, distinguishing those aspects of the electronic structure which are generic to a given class from those which are a consequence of the central-cell effects associated with given atoms. The antifluorite materials ${\mathrm{Mg}}_{2}$${\mathrm{X}}^{\mathrm{IV}}$ with ${X}^{\mathrm{IV}}$=Si,Ge,Sn,Pb and ${\mathrm{Be}}_{2}$C may be usefully regarded as ``filled tetrahedral structures'' (FTS's), i.e., consisting of a zinc-blende ${M}^{\mathrm{II}{X}^{\mathrm{IV}}}$ substructure (for ${M}^{\mathrm{II}=\mathrm{B}\mathrm{e}}$,Mg) one of whose two inequivalent classes of tetrahedral interstitial sites is occupied by an additional ${M}^{\mathrm{II}}$ atom.Pursuing this FTS interpretation, we follow the continuous evolution of the electronic structure and total energy of Si into those of ${\mathrm{Mg}}_{2}$Si in terms of \ensuremath{\Delta}${V}_{\mathrm{dip}(\mathrm{r}}$) and \ensuremath{\Delta}${V}_{\mathrm{CC}(\mathrm{r}}$). Retention of \ensuremath{\Delta}${V}_{\mathrm{dip}(\mathrm{r}}$) alone causes the resulting material to be metallic (hence, generic Si antifluorite compounds are metals), whereas the effects of the central-cell perturbation for ${\mathrm{Mg}}_{2}$Si largely compensate those of the dipole potential as far as the band structure is concerned, rendering ${\mathrm{Mg}}_{2}$Si a semiconductor. Results for our decomposition of antifluorite compounds into \ensuremath{\Delta}${V}_{\mathrm{dip}(\mathrm{r})+\mathrm{\ensuremath{\Delta}}{V}_{\mathrm{CC}(\mathrm{r}}}$) are compared with the more familiar transmutation of Si into a generic III-V or II-VI compound, where central-cell effects are found to be responsible for small variations in the lattice parameters within the III-V series.