A longwave model for strongly anisotropic growth of a crystal step

TL;DR

This paper develops a continuum, strongly nonlinear model for the anisotropic growth of a crystal step, analyzing stability, nonlinear dynamics, and coarsening behavior under various conditions.

Contribution

It introduces a novel longwave PDE model for strongly anisotropic crystal step growth, incorporating non-negligible desorption and deriving coarsening laws.

Findings

Step stability depends on stiffness orientation and anisotropy strength.

Formation and coarsening of hill-and-valley structures observed.

Coarsening laws are established for different orientations and parameters.

Abstract

A continuum model for the dynamics of a single step with the strongly anisotropic line energy is formulated and analyzed. The step grows by attachment of adatoms from the lower terrace, onto which atoms adsorb from a vapor phase or from a molecular beam, and the desorption is non-negligible (the "one-sided" model). Via a multi-scale expansion, we derived a longwave, strongly nonlinear, and strongly anisotropic evolution PDE for the step profile. Written in terms of the step slope, the PDE can be represented in the form similar to a convective Cahn-Hilliard equation. We performed the linear stability analysis and computed the nonlinear dynamics. Linear stability depends on whether the stiffness is minimum or maximum in the direction of the step growth. It also depends nontrivially on the combination of the anisotropy strength parameter and the atomic flux from the terrace to the step. Computations show formation and coarsening of a hill-and-valley structure superimposed onto a large-wavelength profile, which independently coarsens. Coarsening laws for the hill-and-valley structure are computed for two principal orientations of a maximum step stiffness, the increasing anisotropy strength, and the varying atomic flux.