Schwoebel-Ehrlich barrier: from two to three dimensions

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Abstract
The Schwoebel-Ehrlich barrier—the additional barrier for an adatom to diffuse down a surface step—dictates the growth modes of thin films. The conventional concept of this barrier is two dimensional (2D), with the surface step being one monolayer. We propose the concept of a three-dimensional (3D) Schwoebel-Ehrlich barrier, and identify the 2D to 3D transition, taking aluminum as a prototype and using the molecular statics method. Our results show that: (1) substantial differences exist between the 2D and 3D barriers; (2) the transition completes in four monolayers; and (3) there is a major disparity in the 3D barriers between two facets; further, alteration of this disparity using surfactants can lead to the dominance of surface facet against thermodynamics.