Electronic structure of [001]- and [111]-growth-axis semiconductor superlattices

Abstract

A k⋅p theory is used to investigate the electronic structure of semiconductor superlattices grown along the [001] and [111] axes. The present work considers the case of ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{In}}_{\mathrm{x}}$As-${\mathrm{Al}}_{1\mathrm{-}\mathrm{y}}$ ${\mathrm{In}}_{\mathrm{y}}$As superlattices. We specifically treat three alloy composition pairs: a lattice-matched case (x=0.53, y=0.52), a case where the Ga-containing layers are in biaxial tension with a 0.8% lattice mismatch (x=0.53, y=0.64), and a case where the Ga-containing layers are in biaxial compression with a 1.5% lattice mismatch (x=0.53, y=0.30). We analyze the effects of the growth axis on the electronic structure of the superlattice from a consideration of the subband dispersion both parallel and perpendicular to the growth direction. Apart from point-group symmetry considerations, a major factor which differentiates the electronic structure of [001]- and [111]-growth-axis superlattices is the presence of large (exceeding 100 kV/cm) internal strain-induced electric fields in strained-layer superlattices grown along the [111] axis. These internal electric fields are directed along the [111] growth axis and are generated by the internal strain because the constituent semiconductors are piezoelectric. In [001]-growth-axis strained-layer superlattices, the orientation of the lattice-mismatch-induced strains is such that these fields are not present. We demonstrate that the strain-induced electric fields result in sizeable Stark shifts on the superlattice electron and hole subbands and lead to a substantial reduction of the superlattice band gap. Moreover, these strain-induced internal electric fields modify the superlattice wave functions and cause a spatial separation of electrons and holes within the confining superlattice layers. This latter effect greatly modifies the interband optical matrix elements. It also leads to a screening of the strain-induced internal electric fields by photogenerated free carriers which causes nonlinear (i.e., intensity-dependent) optical response of [111]-growth-axis strained-layer superlattices.