Temperature dependence of mobility inAlxGa1

We calculate the mobility of a two-dimensional electron gas in ${\mathrm{Al}}_{\mathit{x}}$${\mathrm{Ga}}_{1\mathrm{\ensuremath{-}}\mathit{x}}$As/GaAs heterostructures for low temperatures. Remote impurity doping and homogeneous background doping is considered and a linear decrease of the mobility with increasing temperature is found. For remote doping the coefficient for the linear temperature dependence is strongly reduced. We argue that in heterostructures with ultrahigh mobility the relevant scattering is due to homogeneous background doping and the linear temperature dependence should be measurable.