The formation of mounded surfaces in epitaxial growth was attributed to the presence of barriers against interlayer diffusion in the terrace edges, known as Ehrlich–Schwoebel barriers. A model for epitaxial growth was investigated by using an Ehrlich–Schwoebel barrier which was explicitly dependent upon the step height. The model had an intrinsic topological step barrier even in the absence of an explicit Ehrlich–Schwoebel barrier. It was shown that mounded morphologies could be obtained even for a small barrier while a self-affine growth, consistent with the Villain–Lai–Das Sarma equation, was observed in the absence of an explicit step barrier. The mounded surfaces were described by a super-roughness dynamical scaling characterized by locally smooth (faceted) surfaces and a global roughness exponent α > 1. The thin film limit was featured by surfaces with self-assembled three-dimensional structures having an aspect ratio (height/width) that may increase or decrease with temperature depending upon the strength of the step barrier.

Modelling of Epitaxial Film Growth with an Ehrlich–Schwoebel Barrier Dependent on the Step Height. F.F.Leal, S.C.Ferreira, S.O.Ferreira: Journal of Physics - Condensed Matter, 2011, 23[29], 292201