Calculated Schwoebel barriers on Si(111) steps using an empirical potential

TL;DR

This study calculates Schwoebel barriers on Si(111) steps using an empirical potential, revealing significant barriers that influence step flow and electromigration, with implications for surface growth and sublimation processes.

Contribution

The paper provides the first detailed empirical calculation of Schwoebel barriers on Si(111) steps, linking potential energy correlations to local geometry and assessing their impact on electromigration.

Findings

Schwoebel barriers of 0.61 eV and 0.16 eV for specific steps

Barrier correlates with local atomic geometry

Upper bound on barrier and lower bound on electromigration force

Abstract

Motivated by the recent investigations on instabilities caused by Schwoebel barriers during growth and their effects on growth or sublimation by step flows, we have investigated, using the Stillinger-Weber potential, how this step edge barrier arises for the two high symmetry steps on 1$\times$1 reconstructed Si(111). Relative to a barrier of 0.97 $\pm$ 0.07 eV on the surface, we find additional (Schwoebel) barriers of 0.61 $\pm$ 0.07 eV and 0.16 $\pm$ 0.07 eV for adatom migration over the [$\overline{2}11$] and the [$\overline{1}\overline{1}2$] steps respectively. The adatom potential energy is found to be strongly correlated with that derived from the local geometry of atoms on the adatom-free surface or step edges. This correlation preserves a strict correspondence between the barrier determining features in the spatial variation of the adatom potential energy and the same derived from the local geometry for the Si(111) surface and the [$\overline{2}11$] step. It is therefore argued that the Schwoebel barrier on the [$\overline{2}11$] step is robust {\it i.e.} a feature that would survive in more satisfactory {\it ab initio} or tight binding calculations. Using a diffusion equation for the adatom concentration the relevance of the barrier to electromigration of steps has been explored. Data from such experiments on Si(111) has been used to place an upper bound on the Schwoebel barrier and a lower bound on the electromigration force.