Continuum limit of a step flow model of epitaxial growth

Robert Kohn, T. S. Lo, N. K. Yip

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

Abstract

We examine a class of step flow models of epitaxial growth obtained from a Burton-Cabrera-Frank (BCF) type approach in one space dimension. Our goal is to derive a consistent continuum model for the evolution of the film surface. Away from peaks and valleys, the surface height solves a Hamilton-Jacobi equation (HJE). The peaks are free boundaries for this HJE. Their evolution must be specified by boundary conditions reflecting the microscopic physics of nucleation. We investigate this boundary condition by numerical simulation of the step flow dynamics using a simple nucleation law. Our results reveal the presence of special structures in the profile near a peak; we discuss the relationship between these structures and the continuum equation. We further address the importance of evaporation for matching the local behaviour near the peak to the solution of the continuum equation.

Original languageEnglish (US)
Title of host publicationMaterials Research Society Symposium - Proceedings
EditorsE Stach, E Chason, R Hull, S Bader
Pages285-291
Number of pages7
Volume696
StatePublished - 2002
EventCurrent Issues in Heteroepitaxial Growth Stress Relaxation and Self Assembly - Boston, MA, United States
Duration: Nov 26 2001Nov 29 2001

Other

OtherCurrent Issues in Heteroepitaxial Growth Stress Relaxation and Self Assembly
CountryUnited States
CityBoston, MA
Period11/26/0111/29/01

Fingerprint

Epitaxial growth
Nucleation
Boundary conditions
Evaporation
Physics
Computer simulation

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials

Cite this

Kohn, R., Lo, T. S., & Yip, N. K. (2002). Continuum limit of a step flow model of epitaxial growth. In E. Stach, E. Chason, R. Hull, & S. Bader (Eds.), Materials Research Society Symposium - Proceedings (Vol. 696, pp. 285-291)

Continuum limit of a step flow model of epitaxial growth. / Kohn, Robert; Lo, T. S.; Yip, N. K.

Materials Research Society Symposium - Proceedings. ed. / E Stach; E Chason; R Hull; S Bader. Vol. 696 2002. p. 285-291.

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

Kohn, R, Lo, TS & Yip, NK 2002, Continuum limit of a step flow model of epitaxial growth. in E Stach, E Chason, R Hull & S Bader (eds), Materials Research Society Symposium - Proceedings. vol. 696, pp. 285-291, Current Issues in Heteroepitaxial Growth Stress Relaxation and Self Assembly, Boston, MA, United States, 11/26/01.
Kohn R, Lo TS, Yip NK. Continuum limit of a step flow model of epitaxial growth. In Stach E, Chason E, Hull R, Bader S, editors, Materials Research Society Symposium - Proceedings. Vol. 696. 2002. p. 285-291
Kohn, Robert ; Lo, T. S. ; Yip, N. K. / Continuum limit of a step flow model of epitaxial growth. Materials Research Society Symposium - Proceedings. editor / E Stach ; E Chason ; R Hull ; S Bader. Vol. 696 2002. pp. 285-291
@inproceedings{37b070e3d22b4adda2275765d0b201f5,
title = "Continuum limit of a step flow model of epitaxial growth",
abstract = "We examine a class of step flow models of epitaxial growth obtained from a Burton-Cabrera-Frank (BCF) type approach in one space dimension. Our goal is to derive a consistent continuum model for the evolution of the film surface. Away from peaks and valleys, the surface height solves a Hamilton-Jacobi equation (HJE). The peaks are free boundaries for this HJE. Their evolution must be specified by boundary conditions reflecting the microscopic physics of nucleation. We investigate this boundary condition by numerical simulation of the step flow dynamics using a simple nucleation law. Our results reveal the presence of special structures in the profile near a peak; we discuss the relationship between these structures and the continuum equation. We further address the importance of evaporation for matching the local behaviour near the peak to the solution of the continuum equation.",
author = "Robert Kohn and Lo, {T. S.} and Yip, {N. K.}",
year = "2002",
language = "English (US)",
volume = "696",
pages = "285--291",
editor = "E Stach and E Chason and R Hull and S Bader",
booktitle = "Materials Research Society Symposium - Proceedings",

}

TY - GEN

T1 - Continuum limit of a step flow model of epitaxial growth

AU - Kohn, Robert

AU - Lo, T. S.

AU - Yip, N. K.

PY - 2002

Y1 - 2002

N2 - We examine a class of step flow models of epitaxial growth obtained from a Burton-Cabrera-Frank (BCF) type approach in one space dimension. Our goal is to derive a consistent continuum model for the evolution of the film surface. Away from peaks and valleys, the surface height solves a Hamilton-Jacobi equation (HJE). The peaks are free boundaries for this HJE. Their evolution must be specified by boundary conditions reflecting the microscopic physics of nucleation. We investigate this boundary condition by numerical simulation of the step flow dynamics using a simple nucleation law. Our results reveal the presence of special structures in the profile near a peak; we discuss the relationship between these structures and the continuum equation. We further address the importance of evaporation for matching the local behaviour near the peak to the solution of the continuum equation.

AB - We examine a class of step flow models of epitaxial growth obtained from a Burton-Cabrera-Frank (BCF) type approach in one space dimension. Our goal is to derive a consistent continuum model for the evolution of the film surface. Away from peaks and valleys, the surface height solves a Hamilton-Jacobi equation (HJE). The peaks are free boundaries for this HJE. Their evolution must be specified by boundary conditions reflecting the microscopic physics of nucleation. We investigate this boundary condition by numerical simulation of the step flow dynamics using a simple nucleation law. Our results reveal the presence of special structures in the profile near a peak; we discuss the relationship between these structures and the continuum equation. We further address the importance of evaporation for matching the local behaviour near the peak to the solution of the continuum equation.

UR - http://www.scopus.com/inward/record.url?scp=0036048865&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0036048865&partnerID=8YFLogxK

M3 - Conference contribution

VL - 696

SP - 285

EP - 291

BT - Materials Research Society Symposium - Proceedings

A2 - Stach, E

A2 - Chason, E

A2 - Hull, R

A2 - Bader, S

ER -