Modulation doped GaAs-AlGaAs quantum well based structures are usually used to achieve very high mobility 2-dimensional electron (or hole) gases. Usually high mobilities ($>10^{7}{rm{cm}^{2}rm{V}^{-1}rm{s}^{-1}}$) are achieved at high densities. A lo
ss of linear gateability is often associated with the highest mobilites, on account of a some residual hopping or parallel conduction in the doped regions. We have developed a method of using fully undoped GaAs-AlGaAs quantum wells, where densities $approx{6times10^{11}rm{cm}^{-2}}$ can be achieved while maintaining fully linear and non-hysteretic gateability. We use these devices to understand the possible mobility limiting mechanisms at very high densities.
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 funct
ion 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.
