A multiscale method for epitaxial growth

Yi Sun, Russel Caflisch, Bjorn Engquist

Research output: Contribution to journalArticle

Abstract

In this paper we investigate a heterogeneous multiscale method (HMM) for interface tracking and apply the technique to the simulation of epitaxial growth. HMM relies on an efficient coupling between macroscale and microscale models. When the macroscale model is not fully known explicitly or not accurate enough, HMM provides a procedure for supplementing the missing data from a microscale model. Here we design a multiscale method that couples kinetic Monte-Carlo (KMC) simulations on the microscale with the island dynamics model based on the level set method and a diffusion equation. We perform the numerical simulations for submonolayer island growth and step edge evolutions on the macroscale domain while keeping the KMC modeling of the internal boundary conditions. Our goal is to get comparably accurate solutions at potentially lower computational cost than for the full KMC simulations, especially for the step flow problem without nucleation.

Original languageEnglish (US)
Pages (from-to)335-354
Number of pages20
JournalMultiscale Modeling and Simulation
Volume9
Issue number1
DOIs
StatePublished - 2011

Fingerprint

Epitaxial Growth
Multiscale Methods
Epitaxial growth
Kinetic Monte Carlo
microbalances
Kinetics
kinetics
simulation
Monte Carlo Simulation
Interface Tracking
Island Model
Level Set Method
Dynamic models
Nucleation
Missing Data
Boundary conditions
Diffusion equation
dynamic models
Computational Cost
Dynamic Model

Keywords

  • Epitaxial growth
  • Heterogeneous multiscale method
  • Interface tracking
  • Island dynamics
  • Kinetic Monte-Carlo
  • Level set method

ASJC Scopus subject areas

  • Chemistry(all)
  • Modeling and Simulation
  • Ecological Modeling
  • Physics and Astronomy(all)
  • Computer Science Applications

Cite this

A multiscale method for epitaxial growth. / Sun, Yi; Caflisch, Russel; Engquist, Bjorn.

In: Multiscale Modeling and Simulation, Vol. 9, No. 1, 2011, p. 335-354.

Research output: Contribution to journalArticle

Sun, Y, Caflisch, R & Engquist, B 2011, 'A multiscale method for epitaxial growth', Multiscale Modeling and Simulation, vol. 9, no. 1, pp. 335-354. https://doi.org/10.1137/090747749
Sun, Yi ; Caflisch, Russel ; Engquist, Bjorn. / A multiscale method for epitaxial growth. In: Multiscale Modeling and Simulation. 2011 ; Vol. 9, No. 1. pp. 335-354.
@article{6d0f951b1e524a8981801c069bc8c414,
title = "A multiscale method for epitaxial growth",
abstract = "In this paper we investigate a heterogeneous multiscale method (HMM) for interface tracking and apply the technique to the simulation of epitaxial growth. HMM relies on an efficient coupling between macroscale and microscale models. When the macroscale model is not fully known explicitly or not accurate enough, HMM provides a procedure for supplementing the missing data from a microscale model. Here we design a multiscale method that couples kinetic Monte-Carlo (KMC) simulations on the microscale with the island dynamics model based on the level set method and a diffusion equation. We perform the numerical simulations for submonolayer island growth and step edge evolutions on the macroscale domain while keeping the KMC modeling of the internal boundary conditions. Our goal is to get comparably accurate solutions at potentially lower computational cost than for the full KMC simulations, especially for the step flow problem without nucleation.",
keywords = "Epitaxial growth, Heterogeneous multiscale method, Interface tracking, Island dynamics, Kinetic Monte-Carlo, Level set method",
author = "Yi Sun and Russel Caflisch and Bjorn Engquist",
year = "2011",
doi = "10.1137/090747749",
language = "English (US)",
volume = "9",
pages = "335--354",
journal = "Multiscale Modeling and Simulation",
issn = "1540-3459",
publisher = "Society for Industrial and Applied Mathematics Publications",
number = "1",

}

TY - JOUR

T1 - A multiscale method for epitaxial growth

AU - Sun, Yi

AU - Caflisch, Russel

AU - Engquist, Bjorn

PY - 2011

Y1 - 2011

N2 - In this paper we investigate a heterogeneous multiscale method (HMM) for interface tracking and apply the technique to the simulation of epitaxial growth. HMM relies on an efficient coupling between macroscale and microscale models. When the macroscale model is not fully known explicitly or not accurate enough, HMM provides a procedure for supplementing the missing data from a microscale model. Here we design a multiscale method that couples kinetic Monte-Carlo (KMC) simulations on the microscale with the island dynamics model based on the level set method and a diffusion equation. We perform the numerical simulations for submonolayer island growth and step edge evolutions on the macroscale domain while keeping the KMC modeling of the internal boundary conditions. Our goal is to get comparably accurate solutions at potentially lower computational cost than for the full KMC simulations, especially for the step flow problem without nucleation.

AB - In this paper we investigate a heterogeneous multiscale method (HMM) for interface tracking and apply the technique to the simulation of epitaxial growth. HMM relies on an efficient coupling between macroscale and microscale models. When the macroscale model is not fully known explicitly or not accurate enough, HMM provides a procedure for supplementing the missing data from a microscale model. Here we design a multiscale method that couples kinetic Monte-Carlo (KMC) simulations on the microscale with the island dynamics model based on the level set method and a diffusion equation. We perform the numerical simulations for submonolayer island growth and step edge evolutions on the macroscale domain while keeping the KMC modeling of the internal boundary conditions. Our goal is to get comparably accurate solutions at potentially lower computational cost than for the full KMC simulations, especially for the step flow problem without nucleation.

KW - Epitaxial growth

KW - Heterogeneous multiscale method

KW - Interface tracking

KW - Island dynamics

KW - Kinetic Monte-Carlo

KW - Level set method

UR - http://www.scopus.com/inward/record.url?scp=79955898138&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79955898138&partnerID=8YFLogxK

U2 - 10.1137/090747749

DO - 10.1137/090747749

M3 - Article

AN - SCOPUS:79955898138

VL - 9

SP - 335

EP - 354

JO - Multiscale Modeling and Simulation

JF - Multiscale Modeling and Simulation

SN - 1540-3459

IS - 1

ER -