  The two-dimensional electron gas residing in shallow InAs quantum wells
coupled to epitaxial aluminum is a widely utilized platform for exploration of
topological superconductivity. Strong spin-orbit coupling, large effective
$g$-factor, and control over proximity-induced superconductivity are important
attributes. Disorder in shallow semiconductor structures plays a crucial role
for the stability of putative topological phases in hybrid structures. We
report on the transport properties of 2DEGs residing 10nm below the surface in
shallow InAs quantum wells in which mobility may exceed 100,000 cm$^2$/Vs at
2DEG density n$_{2DEG}$$\leq$1$\times$10$^{12}$cm$^{-2}$ at low temperature.
