  We designed and performed low temperature DC transport characterization
studies on two-dimensional electron gases confined in lattice-matched
In$_{0.53}$Ga$_{0.47}$As/In$_{0.52}$Al$_{0.48}$As quantum wells grown by
molecular beam epitaxy on InP substrates. The nearly constant mobility for
samples with the setback distance larger than 50nm and the similarity between
the quantum and transport life-time suggest that the main scattering mechanism
is due to short range scattering, such as alloy scattering, with a scattering
rate of 2.2 ps$^{-1}$. We also obtain the Fermi level at the
In$_{0.53}$Ga$_{0.47}$As/In$_{0.52}$Al$_{0.48}$As surface to be 0.36eV above
the conduction band, when fitting our experimental densities with a
Poisson-Schr\"odinger model.
