Distinguishing impurity concentrations in GaAs and AlGaAs using very shallow undoped heterostructures

We have developed a method of fabricating very shallow, gateable, undoped two-dimensional electron gases (2DEG) and making very low resistivity contacts to these. We studied the evolution of mobility as a function of the depth of the 2DEG (from 310 to 30 nm). We extract quantitative information about the background impurity concentrations in GaAs and AlGaAs, the interface roughness, and the charge in the surface states. Surface charge sets an intrinsic limit to the mobility of very shallow 2DEGs. It is probably impossible to fabricate such shallow high-mobility 2DEGs using modulation doping due to the need to accommodate a spacer layer.