Low field mobility of 2-d electron gas in modulation doped AlxGa1−xAs/GaAs layers

We derive a simple analytical formula for the low field electron mobility which uses the 2-d degenerate statistics of the 2-d electron gas. This takes into account the finite width of the depletion layer in (Al,Ga)As for the scattering by remote donors, scattering by the interface charge, and the polar-optical and acoustic deformation potential and piezoelectric scattering. The largest measured value of mobility is determined by scattering due to interface charge in some cases. The ultimate value of the mobility which may be achieved is limited by the acoustic deformation potential and piezoelectric scattering at about 6.5×106 cm2/V s for an interface carrier density of the 2-d electron gas ns0 ≂4×1011 cm−2. Our results agree very well with experimental data obtained in our laboratory as well as other laboratories.