Structural and electronic properties of epitaxial thin-layer<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Si</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="normal">Ge</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="normal">n</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>superlattices

Abstract

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