In modern GaAs/AlxGa1-xAs heterostructures with record high mobilities, a two-dimensional electron gas (2DEG) in a quantum well is provided by two remote donor δ layers placed on both sides of the well. Each δ layer is located within a narrow GaAs well, flanked by narrow AlAs layers which capture excess electrons from donors. We show that each excess electron is localized in a compact dipole atom with the nearest donor. Nevertheless, excess electrons screen both the remote donors and background impurities. When the fraction of remote donors filled by excess electrons f is small, the remote donor limited quantum mobility grows as f3 and becomes larger than the background impurity limited one at a characteristic value fc. We also calculate both the mobility and the quantum mobility limited by the screened background impurities with concentrations N1 in AlxGa1-xAs and N2 in GaAs, which allows one to estimate N1 and N2 from the measured mobilities. Taken together, our findings should help to identify avenues for further improvement of modern heterostructures.
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