Alternating change of allowed and forbidden optical transitions in (Si)2m/(Ge)10-2m superlattices with (001) stacking.

Abstract

First-principles band-structure calculations predict that the symmetry of the wave function of the lowest and the second-lowest conduction-band states of the (Si${)}_{2\mathit{m}}$/(Ge${)}_{10\mathrm{\ensuremath{-}}2\mathit{m}}$ superlattice on the Ge(001) and the ${\mathrm{Si}}_{2\mathit{m}}$${\mathrm{Ge}}_{10\mathrm{\ensuremath{-}}2\mathit{m}}$ alloy (001) substrate alternates between ${\mathrm{\ensuremath{\Gamma}}}_{1}^{+}$ and ${\mathrm{\ensuremath{\Gamma}}}_{3}^{\mathrm{\ensuremath{-}}}$ as m increases from 1 to 4. Accordingly, the optical properties of the superlattice alternate, because the lowest-energy optical transition is allowed (forbidden) if the lowest conduction-band state has ${\mathrm{\ensuremath{\Gamma}}}_{3}^{\mathrm{\ensuremath{-}}}$ (${\mathrm{\ensuremath{\Gamma}}}_{1}^{+}$) symmetry. It is shown that first-order perturbation theory for the pseudopotentials accounts well for the general trend qualitatively.