Coupling kinetic Monte-Carlo and continuum models with application to epitaxial growth

Tim P. Schulze; Peter Smereka; E. Weinan

doi:10.1016/S0021-9991(03)00208-0

Coupling kinetic Monte-Carlo and continuum models with application to epitaxial growth

Tim P. Schulze, Peter Smereka, E. Weinan

Mathematics

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48 Scopus citations

Abstract

We present a hybrid method for simulating epitaxial growth that combines kinetic Monte-Carlo (KMC) simulations with the Burton-Cabrera-Frank model for crystal growth. This involves partitioning the computational domain into KMC regions and regions where we time-step a discretized diffusion equation. Computational speed and accuracy are discussed. We find that the method is significantly faster than KMC while accounting for stochastic fluctuations in a comparable way.

Original language	English (US)
Pages (from-to)	197-211
Number of pages	15
Journal	Journal of Computational Physics
Volume	189
Issue number	1
DOIs	https://doi.org/10.1016/S0021-9991(03)00208-0
State	Published - Jul 20 2003

All Science Journal Classification (ASJC) codes

Numerical Analysis
Modeling and Simulation
Physics and Astronomy (miscellaneous)
General Physics and Astronomy
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/S0021-9991(03)00208-0

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title = "Coupling kinetic Monte-Carlo and continuum models with application to epitaxial growth",

abstract = "We present a hybrid method for simulating epitaxial growth that combines kinetic Monte-Carlo (KMC) simulations with the Burton-Cabrera-Frank model for crystal growth. This involves partitioning the computational domain into KMC regions and regions where we time-step a discretized diffusion equation. Computational speed and accuracy are discussed. We find that the method is significantly faster than KMC while accounting for stochastic fluctuations in a comparable way.",

author = "Schulze, {Tim P.} and Peter Smereka and E. Weinan",

note = "Funding Information: The authors would like to acknowledge support through ONR Grant N00014-010100674 (W.E.). Additional support was provided by NSF Grant DMS 0103825 (T.P.S.) and DMS 0207402 (P.S.). We would also like to thank Eric Vanden-Eijnden for helpful discussions.",

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T1 - Coupling kinetic Monte-Carlo and continuum models with application to epitaxial growth

AU - Schulze, Tim P.

AU - Smereka, Peter

AU - Weinan, E.

N1 - Funding Information: The authors would like to acknowledge support through ONR Grant N00014-010100674 (W.E.). Additional support was provided by NSF Grant DMS 0103825 (T.P.S.) and DMS 0207402 (P.S.). We would also like to thank Eric Vanden-Eijnden for helpful discussions.

PY - 2003/7/20

Y1 - 2003/7/20

N2 - We present a hybrid method for simulating epitaxial growth that combines kinetic Monte-Carlo (KMC) simulations with the Burton-Cabrera-Frank model for crystal growth. This involves partitioning the computational domain into KMC regions and regions where we time-step a discretized diffusion equation. Computational speed and accuracy are discussed. We find that the method is significantly faster than KMC while accounting for stochastic fluctuations in a comparable way.

AB - We present a hybrid method for simulating epitaxial growth that combines kinetic Monte-Carlo (KMC) simulations with the Burton-Cabrera-Frank model for crystal growth. This involves partitioning the computational domain into KMC regions and regions where we time-step a discretized diffusion equation. Computational speed and accuracy are discussed. We find that the method is significantly faster than KMC while accounting for stochastic fluctuations in a comparable way.

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Coupling kinetic Monte-Carlo and continuum models with application to epitaxial growth

Abstract

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