Transport in two-dimensional modulation doped semiconductor structures
  We develop a theory for the maximum achievable mobility in modulation-doped 2D GaAs-AlGaAs semiconductor structures by considering the momentum scattering of the 2D carriers by the remote ionized dopants which must invariably be present in order to create the 2D electron gas at the GaAs-AlGaAs interface. The minimal model, assuming first order Born scattering by random quenched remote dopant ions as the only scattering mechanism, gives a mobility much lower (by a factor of 3 or more) than that observed experimentally in many ultra high-mobility modulation-doped 2D systems, establishing convincingly that the model of uncorrelated scattering by independent random remote quenched dopant ions is often unable to describe the physical system quantitively. We theoretically establish that the consideration of spatial correlations in the remote dopant distribution can enhance the mobility by (up to) several orders of magnitudes in experimental samples. The precise calculation of the carrier mobility in ultra-pure modulation-doped 2D semiconductor structures thus depends crucially on the unknown spatial correlations among the dopant ions in the doping layer which may manifest sample to sample variations even for nominally identical sample parameters (i.e., density, well width, etc.), depending on the details of the modulation-doping growth conditions. 
S. Das Sarma, E. H. Hwang, S. Kodiyalam, L. N. Pfeiffer, and K. W.   West
cond-mat.mes-hall cond-mat.mtrl-sci