Analytical solution of generalized Burton--Cabrera--Frank equations for growth and post--growth equilibration on vicinal surfaces

TL;DR

This paper develops an analytical approach to solve generalized Burton--Cabrera--Frank equations for vicinal surface growth, incorporating microscopic step boundary conditions and analyzing effects like the Schwoebel barrier.

Contribution

It introduces a novel perturbative analytical method for nonlinear equations in surface growth, directly linking microscopic boundary conditions to macroscopic behavior.

Findings

Analytical solutions for coupled adatom and dimer kinetics.

Impact of diffusion barriers on growth and equilibration.

Quantitative insights into the Schwoebel effect during surface processes.

Abstract

We investigate growth on vicinal surfaces by molecular beam epitaxy making use of a generalized Burton--Cabrera--Frank model. Our primary aim is to propose and implement a novel analytical program based on a perturbative solution of the non--linear equations describing the coupled adatom and dimer kinetics. These equations are considered as originating from a fully microscopic description that allows the step boundary conditions to be directly formulated in terms of the sticking coefficients at each step. As an example, we study the importance of diffusion barriers for adatoms hopping down descending steps (Schwoebel effect) during growth and post-growth equilibration of the surface.