Peculiarities of silicon-donor ionization and electron scattering in pseudomorphous AlGaAs/InGaAs/GaAs quantum wells with heavy unilateral $\delta$-doping

The influence of the concentration of silicon donors on the electron-transport properties of pseudomorphous Al$_{0.25}$Ga$_{0.75}$As/In$_{0.2}$Ga$_{0.8}$ As/GaAs quantum wells (QWs) in heterostructures with heavy unilateral $\delta$-doping by Si atoms was studied in a broad temperature interval (2.1–300 K). High electron mobility (up to 35700 cm$^2$/(V s)) at $T$ = 4.2 K was observed at a 2D (sheet) electron density of 2 $\times$ 10$^{12}$ cm$^{-2}$ in the QW. A band mechanism limiting the ionization of donors at an increased level of doping is described. The nonmonotonic variation of electron mobility with increasing silicon concentration is explained. A growth in the mobility is related to increase in the Fermi momentum and screening, while the subsequent decay is caused by tunneling-induced degradation of the spacer layer with decreasing potential of the conduction band in the region of $\delta$-Si layer. It is shown that the effect is not related to filling of the upper subband of dimensional quantization.