  We report on the growth and electrical characterization of modulation-doped
Al0.24Ga0.76As/AlxGa1-xAs/Al0.24Ga0.76As quantum wells with mole fractions as
low as x=0.00057. Such structures will permit detailed studies of the impact of
alloy disorder in the fractional quantum Hall regime. At zero magnetic field,
we extract an alloy scattering rate of 24 ns-1 per %Al. Additionally we find
that for x as low as 0.00057 in the quantum well, alloy scattering becomes the
dominant mobility-limiting scattering mechanism in ultra-high purity
two-dimensional electron gases typically used to study the fragile nu=5/2 and
nu=12/5 fractional quantum Hall states.
