Growth kinetics of planar nanowires

An approximate analytic equation is derived that describes the law of elongation of a semiconductor nanowire (NW) growing via the vapor–liquid–solid (VLS) mechanism in a substrate plane. Various growth regimes are theoretically analyzed as dependent on NW radius $R$ and epitaxial deposition conditions. It is established that the growth rate of planar NWs can be controlled either by the Gibbs–Thomson effect (in the case of small catalyst droplet dimensions) or by the diffusion of adatoms from the substrate surface (for increasing radius of the crystal). Dependence of the diffusion-controlled growth rate on radius $R$ obeys the $R^{-m}$ law, where the power exponent takes the values of 1, 3/2, or 2 depending on the character of surface diffusion.