Unified approach to the linear optical properties of strained (Si)n/(Ge)m superlattices.

Abstract

The linear optical properties of (Si${)}_{\mathit{n}}$/(Ge${)}_{\mathit{m}}$ strained-layer superlattices (SLS's) grown on ${\mathrm{Si}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Ge}}_{\mathit{x}}$(001) substrates are studied within the framework of the tight-binding approximation. A systematic study of the influence of periodicity (n+m), composition (n/m), and strain of the superlattice on the ${\mathit{E}}_{1}$-like and ${\mathit{E}}_{2}$-like transitions of the dielectric function is presented. The near-gap absorption coefficient is calculated and the contribution of the pseudodirect transitions is investigated. The dielectric function ${\mathrm{\ensuremath{\varepsilon}}}_{2}$(\ensuremath{\omega}) of Si/Ge SLS's is compared with the average crystal dielectric function ${\mathrm{\ensuremath{\varepsilon}}}_{2}^{\mathit{a}}$(\ensuremath{\omega}), as well as to the mean value of the dielectric function of the constituent materials, ${\mathrm{\ensuremath{\varepsilon}}}_{2}^{\mathit{m}}$(\ensuremath{\omega}). For light polarization parallel to the growth plane, the dielectric functions of the SLS is better described by the ${\mathrm{\ensuremath{\varepsilon}}}_{2}^{\mathit{m}}$(\ensuremath{\omega}) spectrum, even for thin SLS's. For polarization along the growth axis it is closer to the ${\mathrm{\ensuremath{\varepsilon}}}_{2}^{\mathit{a}}$(\ensuremath{\omega}) spectrum and only for quite thick SLS's do we observe Ge-like and Si-like features. These results are also confirmed with the use of a decomposition technique of the SLS wave function.