Limit to two-dimensional mobility in modulation-doped GaAs quantum structures: How to achieve a mobility of 100 million

Considering scattering by unintentional background charged impurities and by charged dopants in the modulation doping layer as well as by GaAs acoustic phonons, we theoretically consider the practical intrinsic (phonons) and extrinsic (background and dopants) limits to carrier mobility in modulation-doped AlGaAs-GaAs two-dimensional (2D) semiconductor structures. We find that reducing background impurity density to 10(12) cm(-3) along with a modulation doping separation of 1000 A or above will achieve a mobility of 100 x 10(6) cm(2)/V s at a carrier density of 3 x 10(11) cm(-2) for T = 1 K. At T=4(10) K, however, the hard limit to the 2D mobility would be set by acoustic phonon scattering with the maximum intrinsic mobility being no higher than 22(5) x 10(6) cm(2)/V s. Detailed numerical results are presented as a function of carrier density, modulation doping distance, and temperature to provide a quantitative guide to experimental efforts for achieving ultrahigh 2D mobilities.