A new approach to the continuum modeling of epitaxial growth: slope selection, coarsening, and the role of the uphill current

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. (C) 2002 Elsevier Science B.V. All rights reserved.