Structural and electronic properties of epitaxial thin-layerSinGensuperlattices

We examine theoretically structural and electronic properties of thin ${\mathrm{Si}}_{\mathrm{n}}$ ${\mathrm{Ge}}_{\mathrm{n}}$ superlattices for n=1, 2, 4, and 6, grown on (001)-oriented substrates. The increased repeat distance along the growth direction leads to folding of conduction-band states to the Γ point of the superlattice Brillouin zone, resulting in a significant reduction in the minimum direct band gap. Transitions to these folded-in states have nonzero dipole matrix elements because of (i) atomic relaxation, leading to the accommodation of distinct Si-Si and Ge-Ge bond lengths and (ii) the superlattice ordering potential. Our calculations show that superlattices grown pseudomorphically on a Si substrate remain indirect-band-gap structures, with a minimum gap from Γ to Δ (near the X point) of the fcc Brillouin zone. We find, however, that increasing the lattice parameter $a_s$ of the substrate will further reduce the direct band gap. For $a_s$≳ā, where ā is the average of the lattice constants for Si and Ge, we predict a nearly direct band gap: For ${\mathrm{Si}}_6$ ${\mathrm{Ge}}_6$ the indirect band gap for $a_s$=ā is only ∼0.01 eV smaller than the direct band gap. The lowest conduction-band states in this case are localized on the Si sublattice.