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

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 {Δ}Vdip(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 {Δ}VCC(r) (a ``central-cell'' correction). Whereas {Δ}Vdip(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 {Δ}VCC(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 Mg₂{X}IV$ with ${X}IV$=Si,Ge,Sn,Pb and ${Be}₂$C may be usefully regarded as ``filled tetrahedral structures'' (FTS's), i.e., consisting of a zinc-blende ${M}^{II{X}IV}$ substructure (for ${M}II=Be$,Mg) one of whose two inequivalent classes of tetrahedral interstitial sites is occupied by an additional ${M}II$ atom.Pursuing this FTS interpretation, we follow the continuous evolution of the electronic structure and total energy of Si into those of ${Mg}₂Si in terms of Δ{V}dip(r) and Δ{V}CC(r). Retention of Δ{V}dip(r$) alone causes the resulting material to be metallic (hence, generic Si antifluorite compounds are metals), whereas the effects of the central-cell perturbation for ${Mg}₂$Si largely compensate those of the dipole potential as far as the band structure is concerned, rendering ${Mg}₂Si a semiconductor. Results for our decomposition of antifluorite compounds into Δ{V}_{dip(r)+{{Δ}}{V}CC(r}$) 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.