Theoretical study on the electronic structure of (Si)m/(Ge)n superlattices.

Abstract

The electronic structures of (Si${)}_{\mathrm{m}}$/(Ge${)}_{\mathrm{n}}$ superlattices with (001) stacking were studied by using the linear-muffin-tin-orbital method. A simple scheme of a self-interaction correction was implemented in order to predict the semiconductor band gap quantitatively. As the ten-layer periodicity is particularly suitable for realizing direct-band-gap superlattices, we studied several modulated superlattices (Si${)}_{\mathrm{m}\ensuremath{'}}$/(Ge${)}_{\mathrm{n}\ensuremath{'}}$/(Si${)}_{\mathrm{m}\mathrm{\ensuremath{''}}}$/(Ge${)}_{\mathrm{n}\mathrm{\ensuremath{''}}}$$\stackrel{\mathrm{\ifmmode \dot{}\else \.{}\fi{}}}{\mathrm{ct}}$ with m\ensuremath{'}+n\ensuremath{'}+m\ensuremath{''}+n\ensuremath{''}+$\stackrel{\mathrm{\ifmmode \dot{}\else \.{}\fi{}}}{\mathrm{ct}}$=10. We found interesting variations in the symmetry of the conduction-band bottom state and also in the wave-function confinement in the Si layer with regard to the variation in the set of (m\ensuremath{'},n\ensuremath{'},m\ensuremath{''},n\ensuremath{''},...). These results were analyzed with simple models. The dipole transition probability was also estimated. Some calculations were also performed to discuss the alloying effects at the interface for the (Si${)}_{4}$/(Ge${)}_{4}$ superlattice on the Si substrate.