Multiscale modeling for epitaxial growth

Russel Caflisch

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Epitaxy is the growth of a thin film on a substrate in which the crystal properties of the film are inherited from those of the substrate. Because of the wide range of relevant length and time scales, multiscale mathematical models have been developed to describe epitaxial growth. This presentation describes atomistic, island dynamics and continuum models. Island dynamics models are multiscale models that use continuum coarse-graining in the lateral direction, but retain atomistic discreteness in the growth direction. Establishing connections between the various length and time scales in these models is a principal goal of mathematical materials science. Progress towards this goal is described here, including the derivation of surface diffusion, line tension and continuum equations from atomistic, kinetic models.

Original languageEnglish (US)
Title of host publicationInternational Congress of Mathematicians, ICM 2006
Pages1419-1432
Number of pages14
Volume3
StatePublished - 2006
Event25th International Congress of Mathematicians, ICM 2006 - Madrid, Spain
Duration: Aug 22 2006Aug 30 2006

Other

Other25th International Congress of Mathematicians, ICM 2006
CountrySpain
CityMadrid
Period8/22/068/30/06

Fingerprint

Island Model
Epitaxial Growth
Multiscale Modeling
Multiscale Model
Length Scale
Dynamic Model
Time Scales
Continuum
Substrate
Surface Diffusion
Coarse-graining
Materials Science
Epitaxy
Continuum Model
Kinetic Model
Thin Films
Lateral
Crystal
Mathematical Model
Line

Keywords

  • Adatom diffusion
  • Epitaxial growth
  • Gibbs-Thomson
  • Island dynamics
  • Kinetic Monte Carlo
  • Line tension
  • Renormalization group
  • Step edge
  • Step stiffness
  • Surface diffusion

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

Caflisch, R. (2006). Multiscale modeling for epitaxial growth. In International Congress of Mathematicians, ICM 2006 (Vol. 3, pp. 1419-1432)

Multiscale modeling for epitaxial growth. / Caflisch, Russel.

International Congress of Mathematicians, ICM 2006. Vol. 3 2006. p. 1419-1432.

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Caflisch, R 2006, Multiscale modeling for epitaxial growth. in International Congress of Mathematicians, ICM 2006. vol. 3, pp. 1419-1432, 25th International Congress of Mathematicians, ICM 2006, Madrid, Spain, 8/22/06.
Caflisch R. Multiscale modeling for epitaxial growth. In International Congress of Mathematicians, ICM 2006. Vol. 3. 2006. p. 1419-1432
Caflisch, Russel. / Multiscale modeling for epitaxial growth. International Congress of Mathematicians, ICM 2006. Vol. 3 2006. pp. 1419-1432
@inproceedings{50456f79d39c4f9db0428e93031d8888,
title = "Multiscale modeling for epitaxial growth",
abstract = "Epitaxy is the growth of a thin film on a substrate in which the crystal properties of the film are inherited from those of the substrate. Because of the wide range of relevant length and time scales, multiscale mathematical models have been developed to describe epitaxial growth. This presentation describes atomistic, island dynamics and continuum models. Island dynamics models are multiscale models that use continuum coarse-graining in the lateral direction, but retain atomistic discreteness in the growth direction. Establishing connections between the various length and time scales in these models is a principal goal of mathematical materials science. Progress towards this goal is described here, including the derivation of surface diffusion, line tension and continuum equations from atomistic, kinetic models.",
keywords = "Adatom diffusion, Epitaxial growth, Gibbs-Thomson, Island dynamics, Kinetic Monte Carlo, Line tension, Renormalization group, Step edge, Step stiffness, Surface diffusion",
author = "Russel Caflisch",
year = "2006",
language = "English (US)",
volume = "3",
pages = "1419--1432",
booktitle = "International Congress of Mathematicians, ICM 2006",

}

TY - GEN

T1 - Multiscale modeling for epitaxial growth

AU - Caflisch, Russel

PY - 2006

Y1 - 2006

N2 - Epitaxy is the growth of a thin film on a substrate in which the crystal properties of the film are inherited from those of the substrate. Because of the wide range of relevant length and time scales, multiscale mathematical models have been developed to describe epitaxial growth. This presentation describes atomistic, island dynamics and continuum models. Island dynamics models are multiscale models that use continuum coarse-graining in the lateral direction, but retain atomistic discreteness in the growth direction. Establishing connections between the various length and time scales in these models is a principal goal of mathematical materials science. Progress towards this goal is described here, including the derivation of surface diffusion, line tension and continuum equations from atomistic, kinetic models.

AB - Epitaxy is the growth of a thin film on a substrate in which the crystal properties of the film are inherited from those of the substrate. Because of the wide range of relevant length and time scales, multiscale mathematical models have been developed to describe epitaxial growth. This presentation describes atomistic, island dynamics and continuum models. Island dynamics models are multiscale models that use continuum coarse-graining in the lateral direction, but retain atomistic discreteness in the growth direction. Establishing connections between the various length and time scales in these models is a principal goal of mathematical materials science. Progress towards this goal is described here, including the derivation of surface diffusion, line tension and continuum equations from atomistic, kinetic models.

KW - Adatom diffusion

KW - Epitaxial growth

KW - Gibbs-Thomson

KW - Island dynamics

KW - Kinetic Monte Carlo

KW - Line tension

KW - Renormalization group

KW - Step edge

KW - Step stiffness

KW - Surface diffusion

UR - http://www.scopus.com/inward/record.url?scp=84878068734&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84878068734&partnerID=8YFLogxK

M3 - Conference contribution

VL - 3

SP - 1419

EP - 1432

BT - International Congress of Mathematicians, ICM 2006

ER -