Migration and capture processes in heterogeneous nucleation and growth: I. Theory

Abstract

Atoms adsorbed and migrating on a substrate surface may be lost by desorption, by nucleation, or by capture by existing nuclei. A random diffusion capture relation recently given by Halpern for the desorption controlled case is extended to conditions of competitive capture by assuming a uniformly distributed probability of loss. This corresponds to uniform depletion of the adatom population. Using this capture relation, the number density, sizes and area coverage of nuclei have been calculated as a function of time for a range of desorption rates, migration rates and incidence rates. The results are compared with localised depletion models which have predicted saturation densities of nuclei. When most incident atoms are captured, the maximum density of nuclei before coalescence, n max, has a similar temperature dependence to the localised depletion saturation density but is about two orders of magnitude higher. When desorption is initially more probable than capture, the nucleation rate falls faster than the growth rate and consequently n max falls substantially lower than the saturation values given by treatments which neglect growth.