Theoretical analysis of non-catalytic growth of nanorods on a substrate

A theoretical analysis explaining the whole process of the growth of nanorods on a substrate without a catalyst is presented. Prior to the growth of the nanorods, the reaction precursors form nuclei on the substrate. The nuclei undergo cluster migration caused by the surface diffusion of adatoms on the substrate, and this migration continues until the mean free time of the adatoms is larger than surface diffusion time. The most probable mechanism by which cluster migration takes place is the one that leads to the minimization of the cluster free-energy, namely the migration of six adatoms into one fixed adatom. This cluster migration continues during several (typically smaller than 6) consecutive nuclei growth steps. After the process of cluster migration comes to an end, the nuclei grow in an isotropic manner by collection of the adatoms, until the nucleus reaches the thermodynamic size limit. The one-dimensional growth of nanorods on the nuclei, which is associated with the critical radius, begins when the reactant dose is smaller than a certain value, which is determined by the thermodynamic size limit and the mass transport parameter. The mass transport of the reaction precursors leads to the expansion of the radius and elongation of the height of the nanorods, and the growth rate of the height is greater than that of the radius. This difference in the growth rate causes the aspect ratio to increase with increasing growth time. By comparing the experimental data in the literature (ZnO nanorods), the presented analysis explains well the noncatalytic growth of nanorods on a substrate.