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.
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