itself).

In section II we describe our model giving the theoretical formalism and equations for the 2-impurity model. In section III we provide detailed results for mobility and quality along with discussion. We conclude in section IV with a summary of our findings along with a discussion of our approximations and of the open questions.

model and theory
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We assume a 2D electron (or hole) system at $T=0$ located at the $z=0$ plane with the 2D layer being in the x-y plane in our notation. The 2D system is characterized entirely by a carrier effective mass ($m$) defining the single-particle kinetic energy ($E_{\bf k}=\hbar^2k^2/2m$ with [**k**]{} as the 2D wave vector), a background lattice dielectric constant ($\kappa$) defining the 2D Coulomb interaction \[$V({\bf q}) = 2\pi
e^2/\kappa q$ with [**q**]{} as the 2D wave vector), and a 2D carrier density ($n$).

As discussed in the Introduction, we use a minimal 2-impurity model for the static disorder in the system characterized by three independent parameters: $n_R$, $d_R$, $n_B$. Here $n_R$ ($n_B$) is the effective 2D charged impurity density for the remote (background) impurities with the remote (background) impurities being distributed randomly in the 2D x-y plane at a distance ‘$d$’ 