Theoretical study of subband levels in semiconductor heterostructures

We present an envelope-function approach designed to describe a large class of weakly inhomogeneous semiconductors. This model is a generalization of Kane’s eight-band k⋅p model with remote-band effects included in second-order perturbation theory. It is used to study subband levels of single and multiple quantum wells fabricated by layers of GaAs and ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Al}}_{\mathrm{x}}$As. The dependence of these levels on variations of input parameters such as effective masses and band offsets, as well as sample parameters such as alloy concentration and layer thickness, is investigated. Comparison of our results with experimental data on single GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Al}}_{\mathrm{x}}$As quantum wells demonstrates that experimental uncertainties in sample length and alloy concentration do not allow a unique determination of the band offsets. For recent data on quasiparabolic wells, we find that the level splittings for electrons and holes cannot always be explained by a unique choice for the offsets. However, in agreement with previous observations, we find that these structures favor nearly symmetric band offsets.