Can Nanowires Coalesce?

Coalescence of nanowires and other three-dimensional structures into continuous film is desirable for growing low dislocation density III-nitride and III-V materials on lattice-mismatched substrates, and interesting from the fundamental viewpoint. Here, we develop a growth model for vertical nanowires which, under rather general assumptions on the solid-like coalescence process within the Kolmogorov crystallization theory, results in a morphological diagram for the asymptotic coverage of a substrate surface. The coverage is presented as a function of two variables, the material collection efficiency on the top nanowire facet a, and the normalized surface diffusion flux of adatoms from the NW sidewalls b. The full coalescence of nanowires is possible only when a=1 regardless of b. At a>1, which is usual for vapor-liquid-solid growth with a catalyst droplet, nanowires can only partly merge but never coalesce into continuous film. These results can be used for predicting and controlling the degree of surface coverage by nanowires and three-dimensional islands by tuning the surface density, droplet size, adatoms diffusivity, and geometry of the initial structures in the vapor-liquid-solid, selective area or self-induced growth processes in different epitaxy techniques.