Sub-band populations and the spatial distribution of electrons in GaAs/(Al,Ga)As modulation-doped quantum wells

Abstract

High-field Hall and Shubnikov-de Haas (SDH) measurements on modulation-doped GaAs/(Al,Ga)As quantum well (QW) structures have been interpreted on a model in which an asymmetric potential distribution across the QW causes a well-width-dependent spatial separation of the probability densities of electrons in different sub-bands. In narrow wells, <150 AA, this effect is small, and the electron distribution can be considered as a single two-dimensional electron gas (2DEG) extending throughout the well, with a low mobility characteristic of the inverted (GaAs on (Al,Ga)As) interface. In the wide well samples, >or approximately=450 AA, the electron density in the lowest sub-band is spatially concentrated near to the inverted interface, while the second sub-band has a peak density close to the normal, high mobility, interface; the electrons in these sub-bands thus have different mobilities, and magnetoresistance effects characteristic of parallel conduction in two distinct 2DEG channels are observed. For intermediate thickness wells, approximately=250-300 AA, the two sub-band populations are close to those in the corresponding wide well samples, but because of the increased spatial overlap of the wavefunctions, the mobilities in the two subbands are similar. This results in a characteristic 'beating' phenomenon in the SDH curves. This model is shown to accord with published self-consistent calculations for modulation-doped quantum wells.