Stark shifts in GaAs-Ga1−xAlxAs finite-length superlattices

We report full-scale pseudopotential calculations of the electronic structure of a typical finite-length superlattice of GaAs-${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Al}}_{\mathrm{x}}$As under the influence of a strong [(0–5)×${10}^5$ V ${\mathrm{cm}}^{\mathrm{-}1}$] external field. This enables us to present for the first time a microscopic three-dimensional picture of localization (probability densities), over a distance of over 400 Å along the growth axis and spanning the range of energies over which ballistic electrons are injected. Since the local velocity is proportional to probability density distribution, our results constitute velocity–field-energy maps for evaluation of band-structure effects upon transport parameters. We find that for fields above (1–2)×${10}^5$ V ${\mathrm{cm}}^{\mathrm{-}1}$ the energy separation, localization, and width of Stark resonances reflects the level-crossing-induced momentum mixing. This band-structure effect lies outside the simple models of Stark phenomena and strongly reflects the structural parameters. However, the width of the level crossing is dominated by the momentum composition of zero-field wave functions. We predict a strong link between the width of Stark resonances and interface quality.