TY - JOUR
T1 - A new approach to the continuum modeling of epitaxial growth
T2 - Slope selection, coarsening, and the role of the uphill current
AU - Lo, Tak Shing
AU - Kohn, Robert V.
N1 - Funding Information:
This work was supported by DARPA and NSF. We are indebted to Weinan E and Tim Schulze for many useful discussions. We also thank the anonymous referees for helpful suggestions and references.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2002/1/15
Y1 - 2002/1/15
N2 - 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.
AB - 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.
KW - Ehrlich-Schwoebel barrier
KW - Epitaxial growth
KW - Slope selection
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U2 - 10.1016/S0167-2789(01)00371-2
DO - 10.1016/S0167-2789(01)00371-2
M3 - Article
AN - SCOPUS:0037080419
SN - 0167-2789
VL - 161
SP - 237
EP - 257
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
IS - 3-4
ER -