Electronic structure of Sn/Ge superlattices

We present a theoretical study of the electronic structure of short-period ${\mathrm{Sn}}_{\mathit{m}}$ ${\mathrm{Ge}}_{\mathit{n}}$ strained-layer superlattices (SLS’s) grown along the [001] and [111] directions both on Ge and on zinc-blende-like SnGe. The total energies of SnGe and of ${\mathrm{Sn}}_2$/${\mathrm{Ge}}_2$ SLS’s as well as the band structures of various Sn/Ge SLS’s are calculated by means of the relativistic linear-muffin-tin-orbital method within the atomic-spheres approximation. The error in the excitation energies inherent in the local-density approximation is compensated by means of external potentials chosen such that the gaps of bulk Ge and α-Sn agree well with experiments. The total energy of Sn/Ge SLS’s increases with increasing concentration of homopolar bonds (Ge-Ge,Sn-Sn). The structural energy differences per formula unit are of the order of 0.1 eV. We have not found any direct-gap [001] SLS (with the exception of zinc-blende-type SnGe) but some of the [111] SLS’s have a direct gap. The ${\mathrm{Sn}}_1$/${\mathrm{Ge}}_3$ [111] SLS grown on Ge, for example, has a direct gap 0.22 eV. The Γ-Γ optical transitions in this SLS could have a considerable strength. The band structures of [001] SLS’s with both m and n even reflect the orthorhombic anisotropy of the SLS unit cell. Most of the results are successfully interpreted in terms of a tight-binding model.