Abstract
We develop a new approach to the macroscopic modeling of epitaxial growth, focusing on the slope selection and coarsening observed in spiral-mode growth. Our model distinguishes between the surface height and the surface adatom density. These quantities evolve by a coupled pair of partial differential equations: a Hamilton-Jacobi equation for the height, coupled to a nonlinear diffusion equation for the adatom density. The influence of the Ehrlich-Schwoebel barrier is included through an "uphill current" in the equation for adatom density. Our model predicts slope selection and coarsening - thus it offers a possible mechanism for these effects. The model predicts, in particular, that the coarsening rate depends mainly on the strength of the Ehrlich-Schwoebel barrier.
Original language | English (US) |
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Pages (from-to) | 237-257 |
Number of pages | 21 |
Journal | Physica D: Nonlinear Phenomena |
Volume | 161 |
Issue number | 3-4 |
DOIs | |
State | Published - Jan 15 2002 |
Keywords
- Ehrlich-Schwoebel barrier
- Epitaxial growth
- Slope selection
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics