Asymmetry in crystal facet dynamics of homoepitaxy by a continuum model

Journal Article (Journal Article)

In the absence of external material deposition, crystal surfaces usually relax to become flat by decreasing their free energy. We study analytically an asymmetry in the relaxation of macroscopic plateaus, facets, of a periodic surface corrugation in 1+1 dimensions via a continuum model below the roughening transition temperature. The model invokes a continuum evolution law expressed by a highly degenerate parabolic partial differential equation (PDE) for surface diffusion, which is related to the nonlinear gradient flow of a convex, singular surface free energy with a certain exponential mobility in homoepitaxy. This evolution law is motivated both by an atomistic broken-bond model and a mesoscale model for crystal steps. By constructing an explicit solution to this PDE, we demonstrate the lack of symmetry in the evolution of top and bottom facets in periodic surface profiles. Our explicit, analytical solution is compared to numerical simulations of the continuum law via a regularized surface free energy.

Full Text

Duke Authors

Cited Authors

  • Liu, JG; Lu, J; Margetis, D; Marzuola, JL

Published Date

  • June 1, 2019

Published In

Volume / Issue

  • 393 /

Start / End Page

  • 54 - 67

International Standard Serial Number (ISSN)

  • 0167-2789

Digital Object Identifier (DOI)

  • 10.1016/j.physd.2019.01.004

Citation Source

  • Scopus