  We propose a dual-adatom diffusion-limited model for the growth of compound
semiconductor nanowires via the vapor-liquid-solid or the vapour-solid-solid
mechanisms. The growth is catalyzed either by a liquid or a solid nanoparticle.
We validate the model using experimental data from the growth of InAs nanowires
catalyzed by a gold nanoparticle in a molecular beam epitaxy reactor.
Initially, we determine the parameters (diffusion lengths, flux to the seed,
Kelvin effect) that describe the growth of nanowires under an excess of one of
the two beams (for instance, group III or group V atoms). The diffusion-limited
model calculates the growth rate resulting from the current of atoms reaching
the seed. Our dual-adatom diffusion-limited model calculates for a compound
semiconductor, the instantaneous growth rate resulting from the smallest
current of the two types of atoms at a given time. We apply the model to
analyze the length-radius dependence of our InAs nanowires for growth
conditions covering the transition from the As-limited to the In-limited
regime. Finally, the model also describes the complex dependence of the
transition between both regimes on the nanowire radius and length. This
approach is generic and can be applied to study the growth of any compound
semiconductor nanowires.
