Surface currents and slope selection in crystal growth

TL;DR

This paper investigates the slope-dependent surface current during crystal growth, linking it to adatom movement probabilities and analyzing conditions for slope selection, with applications to step edge barriers and steering effects.

Contribution

It provides a unified framework for understanding slope-dependent currents in epitaxial growth, emphasizing the combined effects of different mechanisms rather than separate contributions.

Findings

Current proportional to average adatom travel distance

Slope selection occurs when asymmetry delta vanishes

Application to step edge barriers and steering effects

Abstract

We face the problem to determine the slope dependent current during the epitaxial growth process of a crystal surface. This current is proportional to delta=(p+) + (p-), where (p+/-) are the probabilities for an atom landing on a terrace to attach to the ascending (p+) or descending (p-) step. If the landing probability is spatially uniform, the current is proved to be proportional to the average (signed) distance traveled by an adatom before incorporation in the growing surface. The phenomenon of slope selection is determined by the vanishing of the asymmetry delta. We apply our results to the case of atoms feeling step edge barriers and downward funnelling, or step edge barriers and steering. In the general case, it is not correct to consider the slope dependent current j as a sum of separate contributions due to different mechanisms.