  We present a novel two-step approach for the selective area growth (SAG) of
GaAs nanowires (NWs) by molecular beam epitaxy which has enabled a detailed
exploration of the NW diameter evolution. In the first step, the growth
parameters are optimized for the nucleation of vertically-oriented NWs. In the
second step, the growth parameters are chosen to optimize the NW shape,
allowing NWs with a thin diameter (45 nm) and an untapered morphology to be
realized. This result is in contrast to the commonly observed thick, inversely
tapered shape of SAG NWs. We quantify the flux dependence of radial
vapour-solid (VS) growth and build a model that takes into account diffusion on
the NW sidewalls to explain the observed VS growth rates. Combining this model
for the radial VS growth with an existing model for the droplet dynamics at the
NW top, we achieve full understanding of the diameter of NWs over their entire
length and the evolution of the diameter and tapering during growth. We
conclude that only the combination of droplet dynamics and VS growth results in
an untapered morphology. This result enables NW shape engineering and has
important implications for doping of NWs.

Mesoscale and Nanoscale Physics