The electronic properties of tetrahedral intermetallic compounds IV. The determination of valence bands by a method of linear combination of bond orbitals

Abstract

The linear combination of bond orbitals (l.c.b.o.) method is used to calculate the valence bands of the tetrahedral crystals BN, AlP, GaAs, InSb, CdTe, C (diamond), Si, Ge and grey tin. The l.c.b.o. method, which is mathematically similar to the atomic orbital tight-binding approximation, is described for the zinc-blende form of boron nitride. It is assumed that two adjacent atoms B and N are joined by a partly covalent bond. An electron in such a bond is represented by the localized σ-type bond orbital Ψ = N -1/2 (Φ N +λΦ B ) The periodicity of the crystal is taken into account by forming Bloch functions from these bond orbitals. A fourthorder secular determinant is obtained. This determinant is resolved for the (100) and (111) directions of the Brillouin zone; but for more general points in k-space it is only solved under more restrictive conditions. In the present general discussion, overlap integrals are neglected. The valence bands of a purely covalent diamond-type crystal are easily obtained from those of a partly covalent zinc-blende type crystal by replacing the two different kinds of atom by one common type. Where possible the valence bands obtained with the l.c.b.o. method are compared with the results of other calculations, and with experimental values, though at present none of the widths of the valence bands of these crystals is known accurately. But our forms of the valence bands in the (100) and (111) directions are found to agree well with results previously obtained by the orthogonalized plane wave method. For all the solids studied the maximum of the valence band is at k = (0, 0, 0) and is of p -character, being triply degenerate.