Band structure and optical properties of Si-Si1-xGex superlattices.

Abstract

We report the band structure and optical properties of Si-${\mathrm{Si}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Ge}}_{\mathrm{x}}$ superlattices calculated by k\ensuremath{\cdot}p theory using the envelope-function approximation. In this paper we have demonstrated that direct-band-gap Si-${\mathrm{Si}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{Ge}}_{\mathrm{x}}$ superlattices can be achieved by a suitable choice of layer thicknesses. We have presented detailed results for Si-${\mathrm{Si}}_{0.5}$${\mathrm{Ge}}_{0.5}$ superlattices grown on ${\mathrm{Si}}_{0.75}$${\mathrm{Ge}}_{0.25}$ buffer layers with layer thicknesses in the range from 4 to 24 monolayers. Our calculations indicate that the optical absorption strengths can vary by 3--4 orders of magnitude even for layer thickness variations as small as 1--2 monolayers. Thus, it is important to control the layer thicknesses to a monolayer accuracy to obtain the enhanced optical absorption strengths. Although these optical absorption strengths are 3--4 orders of magnitude larger than bulk Si or Ge, they are still 3 orders of magnitude smaller than the absorption strengths due to direct transitions in materials such as GaAs.