  Selective area growth (SAG) of nanowires and networks promise a route toward
scalable electronics, photonics and quantum devices based on III-V
semiconductor materials. The potential of high-mobility SAG nanowires however
is not yet fully realized, since interfacial roughness, misfit dislocations at
the nanowire/substrate interface and non-uniform composition due to material
intermixing all scatter electrons. Here, we explore SAG of highly
lattice-mismatched InAs nanowires on insulating GaAs(001) substrates and
address these key challenges. Atomically smooth nanowire/substrate interfaces
are achieved with the use of atomic hydrogen (a-H) as an alternative to
conventional thermal annealing for the native oxide removal. The problem of
high lattice mismatch is addressed through an In$_x$Ga$_{1-x}$As buffer layer
introduced between the InAs transport channel and the GaAs substrate. The Ga-In
material intermixing observed in both the buffer layer and the channel is
inhibited via careful tuning of the growth temperature. Performing scanning
transmission electron microscopy and x-ray diffraction analysis along with
low-temperature transport measurements we show that optimized In-rich buffer
layers promote high quality InAs transport channels with the field-effect
electron mobility over~10000~cm$^2$V$^{-1}$s$^{-1}$. This is twice as high as
for non-optimized samples and among the highest reported for InAs selective
area grown nanostructures.
