  Using high quality undoped GaAs/AlGaAs heterostructures with optically
patterned insulation between two layers of gates, it is possible to investigate
very low density mesoscopic regions where the number of impurities is well
quantified. Signature appearances of the scattering length scale arise in
confined two dimensional regions, where the zero-bias anomaly (ZBA) is also
observed. These results explicitly outline the molecular beam epitaxy growth
parameters necessary to obtain ultra low density large two dimensional regions
as well as clean reproducible mesoscopic devices.
