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

A k 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 Ga₁-ₗInₗAs-Al₁-ₘInₘAs 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.