Growth rate of a crystal facet of arbitrary size and growth kinetics of vertical nanowires

We present a modification of the Kolmogorov-Johnson-Mehl-Avrami crystallization model to the case of a finite size crystal facet growing layer by layer. A general expression for the facet growth rate is derived that provides an asymptotic matching to the known limit cases of very small and very large facets. The derived expression is applied to the study of the growth kinetics of vertical nanowires in the vapor-liquid-solid growth mechanism. The presented model generalizes the Givargizov-Chernov theory of whisker growth, shows why the whiskers grow much faster than the nonactivated surface, and gives the dependence of the growth rate of nanowires on the diameter of drop of liquid alloy and the growth conditions.