Initial evolution of Kashchiev models of thin-film growth

The authors consider a continuum model of thin-film growth on an infinite perfect substrate. Multilayers grow by random-nucleation of islands, at fixed rate, followed by lateral expansion at constant speed. The focus is on the evolution of the film profile in the regime of small thicknesses. They present results for the layer coverages, the interface width, and the Bragg intensity oscillations, obtained by numerical integration of the original Kashchiev recursion relations. Asymptotically, the model shows Kardar-Parisi-Zhang universality scaling. Expressions for spatial correlation functions are also developed.