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

TL;DR

This paper models epitaxial film growth considering a step height-dependent Ehrlich-Schwoebel barrier, revealing conditions for mounded surface formation and self-affine growth, with implications for surface morphology control.

Contribution

It introduces a novel model with a step height-dependent ES barrier, showing its effects on surface morphology and growth dynamics in epitaxial films.

Findings

Mounded morphologies occur with small barriers.

Self-affine growth observed without explicit barriers.

Surface structures depend on temperature and barrier strength.

Abstract

The formation of mounded surfaces in epitaxial growth is attributed to the presence of barriers against interlayer diffusion in the terrace edges, known as Ehrlich-Schwoebel (ES) barriers. We investigate a model for epitaxial growth using a ES barrier explicitly dependent on the step height. Our model has an intrinsic topological step barrier even in the absence of an explicit ES barrier. We show that mounded morphologies can be obtained even for a small barrier while a self-affine growth, consistent with the Villain-Lai-Das Sarma equation, is observed in absence of an explicit step barrier. The mounded surfaces are described by a super-roughness dynamical scaling characterized by locally smooth (faceted) surfaces and a global roughness exponent $\alpha>1$. The thin film limit is featured by surfaces with self-assembled three-dimensional structures having an aspect ratio (height/width) that may increase or decrease with temperature depending on the strength of step barrier.