Spiral growth limited by surface kinetics a self-consistent model

Abstract

A one-dimensional Stefan problem describing growth limited by surface processes is set and the time evolution of a spiral growing hillock calculated. The model is self-consistent in the sense that the critical surface supersaturation for the production of a new step, the slope and the growth rate of the hillock, strictly depend on a set of phenomenological parameters describing diffusion and matter exchange at the steps. The quasi-steady states calculated for several sets of values of the parameters, are illustrated and compared with classical models. Some criteria are proposed to correlate the features of the growth hillocks and the steps rates, to the kinetics.