Dependences of the transport scattering time and quantum lifetime on the two-dimensional electron gas density in modulation-doped single GaAs quantum wells with AlAs/GaAs short-period superlattice barriers

The dependences of the transport scattering time $\tau_t$, quantum lifetime $\tau_q$, and their ratio $\tau_t/\tau_q$ on the density $n_e$ of the electron gas in modulation-doped single GaAs quantum wells with AlAs/GaAs short-period super-lattice barriers are investigated. The experimental dependences are explained in terms of electron scattering by remote ionized donors with an effective two-dimensional concentration $n^*_R$ and background impurities with a three-dimensional concentration $n_B$. An expression for $n^*_R(n_e)$ is obtained including the contribution of X-valley electrons localized in AlAs layers to the suppression of scattering by the random potential of remote donors. It is shown that the experimentally observed abrupt increase in $\tau_t$ and $\tau_q$ with an increase in $n_e$ above a certain critical value $n_{ec}$ is related to a decrease in $n^*_R$. It is established that the drop in $\tau_t/\tau_q$ observed for electron densities $n_e>n_{ec}$ occurs because scattering by the random potential of background impurities in this two-dimensional system with a decrease in $n^*_R$ limits an increase in $\tau_t$ more considerably than an increase in $\tau_q$.