Diffusion Boundary Condition at Surface Steps

TL;DR

This paper introduces a geometrical factor essential for accurately modeling adatom diffusion across surface steps, validated through theoretical derivation and numerical simulations on various lattice types.

Contribution

It derives and verifies a new geometrical factor for the diffusion boundary condition at surface steps, enhancing the understanding of adatom behavior at these features.

Findings

The factor is 1/π for different lattice geometries.

Theoretical formulation matches numerical simulation results.

Applicable to triangular, square, and hexagonal lattices.

Abstract

This Communication reports a geometrical factor that is necessary in the diffusion boundary condition across surface steps. Specifically, this factor relates adatom concentration to its spatial gradient at a surface step, and it describes the fraction of jump attempts that cross the step. In this Communication, the authors show that the factor is 1/\Pi using theoretical formulation and further verify the formulation using numerical simulations for triangular, square, and hexagonal surface lattices.