far ($k_Fd \gg 1$) away from the 2D electron system due to the influence of the exponential $e^{-q d}$ factor in the Coulomb potential which restricts much of the scattering to $q \ll 1/z$, thus exponentially enhancing the importance of small-angle (i.e., small scattering wave vector) scattering. This then leads to $\tau_t \gg
\tau_q$ for scattering dominated by remote dopants (the two scattering times could differ by more than two orders of magnitude in high-mobility modulation-doped structures where $k_F d_R \gg 1$ is typically satisfied due to the far-away placement of the remote dopants in order to minimize large-angle resistive scattering processes) in 2D systems, but for the unintentional background impurities, which always satisfy $k_F d_B \ll 1$ by definition (since $d_B \approx 0$), the two scattering times are approximately equal. We note that the finite layer thickness of the 2D system puts a lower bound on how small $d_B$ can be, but this has no qualitative significance for our consideration.

Now, we immediately realize the crucial relevance of the 2-impurity model in distinguishing mobility (i.e., $\tau_t$) and quality (i.e., $\tau_q$) in 2D systems since it now becomes possible for one type of disorder (e.g., remote impurities) to control the 