Localisation effects caused by the remote donors in modulation-doped quantum wells

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Abstract
In modulation-doped quantum wells (QWS) electrons are introduced into the QW by doping only the barrier region with an undoped spacer layer nearest the quantum well. The electrons flow into the QW forming a two-dimensional (2D) gas which is separated from the ionised donors by the spacer layer. The authors have developed a theoretical model to determine the size and scale of potential fluctuations 2 eta created in the 2D electron gas in the QW by the random distribution of ionised donors modelled as a 2D sheet. The interaction is through a 2D statistically screened coulomb interaction. The size of the fluctuations grow as square root Ns where Ns is the two-dimensional density of ionised donors which compares with a 2D level Fermi energy EFE which grows as n2D, where n2D is the two-dimensional density of electronics. They show that for EFE< eta all electrons are localised at low temperature, while for EFE< eta there are both localised and free electrons. This behaviour manifests itself in experimental results of mobility measurements using persistent photoconductivity which exhibit a mobility edge. Photoluminescence results where the oscillator strength for the localised electrons is suppressed compared with free electrons recombining with the few photo-excited localised holes also support this theory since the fluctuations separate the localised electrons and holes in real space.