Ehrlich-Schwoebel barrier controlled slope selection in epitaxial growth

TL;DR

This paper investigates how the Ehrlich-Schwoebel barrier influences slope selection during epitaxial growth, revealing the critical role of incorporation mechanisms and providing analytical and simulation insights into mound formation and slope stability.

Contribution

It demonstrates the impact of the Ehrlich-Schwoebel barrier and incorporation mechanisms on mound formation and slope selection, with analytical solutions and simulation validation.

Findings

Stable slope formation depends on incorporation mechanisms.

Analytical saturation profile derived for infinite step edge barrier.

Temperature effects on slope are governed by the Ehrlich-Schwoebel barrier.

Abstract

We examine the step dynamics in a 1+1 dimensional model of epitaxial growth based on the BCF-theory. The model takes analytically into account the diffusion of adatoms, an incorporation mechanism and an Ehrlich-Schwoebel barrier at step edges. We find that the formation of mounds with a stable slope is closely related to the presence of an incorporation mechanism. We confirm this finding using a Solid-On-Solid model in 2+1 dimensions. In the case of an infinite step edge barrier we are able to calculate the saturation profile analytically. Without incorporation but with inclusion of desorption and detachment we find a critical flux for instable growth but no slope selection. In particular, we show that the temperature dependence of the selected slope is solely determined by the Ehrlich-Schwoebel barrier which opens a new possibility in order to measure this fundamental barrier in experiments.