  We demonstrate a method of making a very shallow, gateable, undoped
2-dimensional electron gas. We have developed a method of making very low
resistivity contacts to these structures and systematically studied the
evolution of the mobility as a function of the depth of the 2DEG (from 300nm to
30nm). We demonstrate a way of extracting quantitative information about the
background impurity concentration in GaAs and AlGaAs, the interface roughness
and the charge in the surface states from the data. This information is very
useful from the perspective of molecular beam epitaxy (MBE) growth. It is
difficult to fabricate such shallow high-mobility 2DEGs using modulation doping
due to the need to have a large enough spacer layer to reduce scattering and
switching noise from remote ionsied dopants.
