Adatom Capture and Growth Rates of Nuclei

Abstract

A comprehensive treatment for the growth of cap- and disk-shaped nuclei on surfaces is developed. The results are important for a description of high-vacuum thin-film deposition, chemical-vapor deposition, electrodeposition, oxidation, and dropwise-condensation heat-transfer processes. The curvature effects of small nuclei on the adatom concentration field are included and shown to be negligible for nuclei appreciably larger than the critical size. The extent of the nucleation-exclusion zone surrounding a growing nucleus is shown to be strongly size dependent and initially much smaller than the adatom-capture zone. This obtains until the nucleus radius approaches the mean adatom-diffusion distance. Growth is considered to begin at the instant a nucleus exceeds the critical size. Analytical solutions and numerical integration have yielded results which are suitable for the evaluation of nuclei growth rates and growth times under most experimental conditions. This treatment also enables an evaluation of the adatom mean surface-diffusion distance and desorption energy to be made independent of the nucleation-rate model (classical or atomistic) chosen. Growth rates and times are shown to be essentially independent of the critical nucleus size for supersaturations greater than 100 and sizes greater than several times the critical. Growth on a substrate saturated with nuclei is also treated.