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The formation of mounded surfaces in epitaxial growth is attributed to thepresence of barriers against interlayer diffusion in the terrace edges, knownas Ehrlich-Schwoebel (ES) barriers. We investigate a model for epitaxial growthusing a ES barrier explicitly dependent on the step height. Our model has anintrinsic topological step barrier even in the absence of an explicit ESbarrier. We show that mounded morphologies can be obtained even for a smallbarrier while a self-affine growth, consistent with the Villain-Lai-Das Sarmaequation, is observed in absence of an explicit step barrier. The moundedsurfaces are described by a super-roughness dynamical scaling characterized bylocally smooth (faceted) surfaces and a global roughness exponent $\alpha>1$.The thin film limit is featured by surfaces with self-assembledthree-dimensional structures having an aspect ratio (height/width) that mayincrease or decrease with temperature depending on the strength of stepbarrier.

Modelling of epitaxial film growth with a Ehrlich-Schwoebel barrier dependent on the step height