Excess electron screening of remote donors and mobility in modern GaAs/AlGaAs heterostructures

In modern $\mathrm{GaAs}/{\mathrm{Al}}_x{\mathrm{Ga}}_{1\ensuremath{-}x}\mathrm{As}$ 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 layer, flanked by narrow AlAs layers which capture excess electrons from donors but leave each of them localized in a compact dipole atom with a donor. Still excess electrons can hop between host donors to minimize their Coulomb energy. As a result they screen the random potential of donors dramatically. We numerically model the pseudoground state of excess electrons at a fraction $f$ of filled donors and find both the mobility and the quantum mobility limited by scattering on remote donors as universal functions of $f$. We repeat our simulations for devices with additional disorder such as interface roughness of the doping layers, and find the quantum mobility is consistent with measured values. Thus, in order to increase the quantum mobility this additional disorder should be minimized.