Mobility of the two-dimensional electron gas in DA-$p$HEMT heterostructures with various $\delta$–$n$-layer profile widths

The effect of the silicon-atom distribution profile in donor $\delta$-layers of AlGaAs/InGaAs/AlGaAs heterostructures with donor–acceptor doping on the mobility of the two-dimensional electron gas is studied. The parameters of the $\delta$-layer profiles are determined using the normal approximation of the spatial distributions of silicon atoms, measured by secondary-ion mass spectroscopy. It is shown that the standard deviation $\sigma$ of the $\delta$-layer profile can be reduced from 3.4 to 2.5 nm by the proper selection of growth conditions. Measurements of the magnetic-field dependences of the Hall effect and conductivity show that such a decrease in $\sigma$ allowed an increase in the mobility of the two-dimensional electron gas in heterostructures by 4000 cm$^2$/(V s) at 77 K and 600 cm$^2$/(V s) at 300 K. The mobility calculation taking into account filling of the first two size-quantization subbands shows that an increase in the mobility is well explained by a reduction in the Coulomb scattering at ionized donors due to an increase in the effective thickness of the spacer layer with decreasing $\sigma$ of the $\delta$-layer profile.