the physics of quality versus mobility being discussed in this work. Many of our numerical results are, however, obtained by incorporating the appropriate quantitative effects of the quasi-2D layer thickness of the 2D carriers in calculating the mobility and the quality of the system within the 2-impurity model.

One last issue we need to discuss in the Introduction is the question of how to define the sample quality since it is obviously not a unique property and depends on the specific experiment being carried out. In order to keep things both simple and universal, we have decided to use the level broadening or the Dingle temperature as a measure of the sample quality. The level broadening $\Gamma$ is defined as $\Gamma = \hbar/2\tau_q$, where $\tau_q$ is the quantum scattering time (or the single particle relaxation time) in contrast to the mobility scattering time (or the transport relaxation time) $\tau_t$ which defines the conductivity ($\sigma$) or the carrier mobility ($\mu$) through $\sigma = ne^2\tau_t/m$ or $\mu =
ne \tau_t$. In general, $\tau_q \leq \tau_t$ with the equality holding for purely short-range disorder scattering. Thus, for pure $s$-wave $\delta$-function short-range scattering model, mobility and quality are identical for obvious reasons. For a 