of the system. In high-mobility 2D GaAs-AlGaAs-based systems of interest in the current work, there are at least six distinct scattering mechanisms of varying importance arising from different physical sources of disorder in the system. These are: Unintentional background charged impurities in the 2D GaAs conducting layer; remote dopant impurities in the insulating AlGaAs layer (which are necessary for introducing 2D carriers to form the 2DEG); short-range interface roughness at the GaAs-AlGaAs interfaces; short-range disorder in the insulator AlGaAs layer arising from alloy disorder (and neutral defects); unintentional background charged impurities in the insulating AlGaAs barrier regime; random charged impurities at the GaAs-AlGaAs interface. This is obviously a highly complex situation where the complete disorder distribution will have many independent parameters, and in general, there is no reason to expect a unique relationship between mobility and quality since mobility could be dominated by one type of disorder (e.g., background unintentional charged impurities) and quality may be dominated by a different type of disorder (e.g., remote dopants far from the 2D layer).

It is clear from the above discussion that the minimal disorder model capable of capturing the mobility versus quality dichotomy in high-quality 2D semiconductor structures is a “2-impurity” model 