Direct-band-gap structure of uniaxial-stressed ${\mathrm{Si}}_{\mathit{x}}$${\mathrm{Ge}}_{1\mathrm{-}\mathit{x}}$/Ge [111] strained-layer superlattices

The effects of both internal strain due to lattice mismatch and externally applied [111] uniaxial stress on ${\mathrm{Si}}_{\mathit{x}}$${\mathrm{Ge}}_{1\mathrm{-}\mathit{x}}$/Ge [111] superlattices are predicted. In an ${\mathit{N}}_{\mathrm{Si}}$×${\mathit{N}}_{\mathrm{Ge}}$ ${\mathrm{Si}}_{\mathit{x}}$${\mathrm{Ge}}_{1\mathrm{-}\mathit{x}}$/Ge [111] superlattice, the composition x can always be chosen so that the superlattice conduction-band minimum is Ge derived. Then the Ge conduction-band minimum at ${\mathbf{k}}_{\mathit{L}}$=(π/${\mathit{a}}_{\mathrm{Ge}}$) (1,1,1) can be folded to the zone center with suitable choices of ${\mathit{N}}_{\mathrm{Si}}$ and ${\mathit{N}}_{\mathrm{Ge}}$, permitting the crystal-momentum selection rule for luminescence to be satisfied for the folded (1,1,1) minimum in the superlattice. However, internal strains raise the energy of the folded (1,1,1) conduction-band minimum relative to the unfolded L minima at (1,-1,-1), (-1,1,-1), and (-1,-1,1), causing the unfolded minima to be the lowest-energy conduction-band states into which injected electrons thermalize—and reinstating the selection rules against luminescence. Nevertheless, application of a [111] uniaxial stress of sufficient magnitude will overcome the internal strain, will make the folded (1,1,1) L minimum (which has significant s character) the lowest-energy conduction-band minimum, and will cause the Ge quantum wells in the superlattice to luminesce. These results obtained with use of the zone-folding approximation also hold when the electronic structure of the superlattice is evaluated properly.