Zone folding and subband dispersions in GaAs-AlxGa1-xAs(001) superlattices.

Abstract

We have used empirical pseudopotentials to show the form of the subband dispersions associated with superlattice conduction states derived from the principal and the secondary minima in several GaAs-${\mathrm{Al}}_{\mathrm{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathrm{x}}$As(001) superlattices. In particular, dispersions of interacting zone-center- and zone-edge-related states are shown and the zone-folding effect is demonstrated. We show that the zone-center--zone-edge mixing manifests itself in an intricate weaving of zone-center charge-density components through the charge densities of the zone-edge-related states. Along the superlattice axis, the zone-center charge density twists between each peak in the charge-density ``envelopes'' of the zone-edge-related states. This twisting is linked to the atomic layout within each layer and is the mechanism by which (mixed) zone-center- and zone-edge-related states are orthogonalized. Detailed comparison between results of the pseudopotential calculations and corresponding results obtained using Kronig-Penney-type analyses is made and a simple prescription is given in order to give a guide to the use of the simple model. The results suggest that in many cases the modified effective-mass Hamiltonian may be adequate for modeling hot-electron transport in superlattices, even in those consisting of ultrathin layers. We have made a thorough investigation of the role of the ``camel's-back'' structure at the bulk zone edges and have shown where the modified effective-mass procedures break down for zone-edge-related superlattice states.