Mobility and quantum mobility of modern GaAs/AlGaAs heterostructures

In modern GaAs/${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ heterostructures with record high mobilities, a two-dimensional electron gas (2DEG) in a quantum well is provided by two remote donor $\ensuremath{\delta}$ layers placed on both sides of the well. Each $\ensuremath{\delta}$ 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 ${f}^{3}$ and becomes larger than the background impurity limited one at a characteristic value ${f}_{c}$. We also calculate both the mobility and the quantum mobility limited by the screened background impurities with concentrations ${N}_{1}$ in ${\mathrm{Al}}_{x}{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ and ${N}_{2}$ in GaAs, which allows one to estimate ${N}_{1}$ and ${N}_{2}$ from the measured mobilities. Taken together, our findings should help to identify avenues for further improvement of modern heterostructures.