K

Abstract

This is the second of a two-paper series in which we present a complete k\ensuremath{\cdot}p theory of semiconductor superlattices. In the first paper, the formal theoretical results are presented. Here, the numerical implementation of these results is described and they are used to investigate the electronic structure of ${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$${\mathrm{In}}_{\mathrm{x}}$As-${\mathrm{Al}}_{1\mathrm{\ensuremath{-}}\mathrm{y}}$${\mathrm{In}}_{\mathrm{y}}$As superlattices grown along the [100] direction. Three alloy composition pairs are considered: a lattice-matched case (x=0.53, y=0.52), a case where the Ga-containing layers are in biaxial tension with a 1% lattice mismatch (x=0.53, y=0.67) and a case where the Ga-containing layers are in biaxial compression with a 1% lattice mismatch (x=0.53, y=0.37). Our results for the superlattice energy band gap of the lattice-matched system are in good agreement with available experimental results. Calculations of subband energy dispersion for superlattice wave vectors both parallel and perpendicular to the growth axis are performed. These calculations show band-splitting and -mixing features not embodied within current envelope-function models which do not correctly describe the superlattice symmetry. However, these features are present in tight-binding models which do properly account for the superlattice symmetry. The origin of these band splitting and mixing features in the present k\ensuremath{\cdot}p theory is discussed.