A dual-concentration level-set method for BCF step flow with asymmetric Ehrlich–Schwoebel kinetics: formulation and stability analysis
Journal
Journal of Crystal Growth
Journal Volume
693
Start Page
128711
ISSN
00220248
Date Issued
2026-10-15
Author(s)
Abstract
A sharp-interface level-set method is presented for the Burton–Cabrera–Frank (BCF) step-flow model with the Ehrlich–Schwoebel (ES) barrier. A dual-concentration formulation is introduced in which two concentration fields evolve on the upper and lower terraces of each step, explicitly permitting a concentration jump across the step and enabling precise implementation of asymmetric attachment kinetics kup and kdown. Unlike diffuse-interface approaches, atomic steps are treated as true discontinuities, eliminating the need for asymptotic matching, interface regularization, or remeshing. Reinitialization is avoided by employing a local quasi-distance function that maintains a unit gradient near each step without an auxiliary PDE. The method is validated against the exact quasi-steady analytic BCF solution for periodic step trains, faithfully reproducing the concentration profile and step velocity on reasonable meshes. Closed-form linear stability parameters, derived directly from the analytic fluxes, serve as quantitative benchmarks for both longitudinal (step-bunching) and transverse (meandering) modes, including the full short-wave dispersion relation. Systematic variation of the attachment ratio kup/kdown reproduces the classic ES instabilities in quantitative agreement with these benchmarks: inverse ES (kup>kdown) produces the predicted step-pairing and bunching mode, while forward ES (kup
Subjects
BCF step flow
Level set method
Stability analysis
Step bunching
Step meandering
Publisher
Elsevier B.V.
Type
journal article