Efficient phase-field simulation of quantum dot formation in a strained heteroepitaxial film

S. M. Wise; J. S. Lowengrub; J. S. Kim; W. C. Johnson

doi:10.1016/j.spmi.2004.08.029

Efficient phase-field simulation of quantum dot formation in a strained heteroepitaxial film

S. M. Wise, J. S. Lowengrub, J. S. Kim, W. C. Johnson

Research output: Contribution to journal › Conference article › peer-review

55 Citations (Scopus)

Abstract

A Cahn-Hilliard evolution equation possessing a source term is employed to study the morphological evolution of a strained heteroepitaxial thin film, during continuous mass deposition, on a substrate with an embedded coherent island. The elastic properties and the surface energy are anisotropic, with the surface energy anisotropy being strong enough to result in missing orientations and facets. A sophisticated finite-difference/multigrid method and an implicit time integration scheme are combined to make an efficient numerical method, one which enables numerically tractable computation in both two and three dimensions. Herein we present preliminary two-dimensional results demonstrating the utility of our finite difference/multigrid algorithms. The strain localization effects produced by a buried, coherent inclusion are shown to produce laterally organized quantum dots during the morphological evolution of the film.

Original language	English
Pages (from-to)	293-304
Number of pages	12
Journal	Superlattices and Microstructures
Volume	36
Issue number	1-3
DOIs	https://doi.org/10.1016/j.spmi.2004.08.029
Publication status	Published - 2004 Jul
Externally published	Yes
Event	European Materials Research Society 2004 - Strasbourg, France Duration: 2004 May 24 → 2004 May 28

Bibliographical note

Funding Information:
We thank Vittorio Cristini for helpful discussions. We are grateful to the U.S. National Science Foundation for the financial support of this work through the Center for the Design of Nanoscopic Materials, Grant DMR0080016.

Keywords

Anisotropy
Epitaxial strain
Self-assembly
Stress
Substrate
Surface diffusion
Thin film

ASJC Scopus subject areas

General Materials Science
Condensed Matter Physics
Electrical and Electronic Engineering

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10.1016/j.spmi.2004.08.029

Cite this

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title = "Efficient phase-field simulation of quantum dot formation in a strained heteroepitaxial film",

abstract = "A Cahn-Hilliard evolution equation possessing a source term is employed to study the morphological evolution of a strained heteroepitaxial thin film, during continuous mass deposition, on a substrate with an embedded coherent island. The elastic properties and the surface energy are anisotropic, with the surface energy anisotropy being strong enough to result in missing orientations and facets. A sophisticated finite-difference/multigrid method and an implicit time integration scheme are combined to make an efficient numerical method, one which enables numerically tractable computation in both two and three dimensions. Herein we present preliminary two-dimensional results demonstrating the utility of our finite difference/multigrid algorithms. The strain localization effects produced by a buried, coherent inclusion are shown to produce laterally organized quantum dots during the morphological evolution of the film.",

keywords = "Anisotropy, Epitaxial strain, Self-assembly, Stress, Substrate, Surface diffusion, Thin film",

author = "Wise, {S. M.} and Lowengrub, {J. S.} and Kim, {J. S.} and Johnson, {W. C.}",

note = "Funding Information: We thank Vittorio Cristini for helpful discussions. We are grateful to the U.S. National Science Foundation for the financial support of this work through the Center for the Design of Nanoscopic Materials, Grant DMR0080016. ; European Materials Research Society 2004 ; Conference date: 24-05-2004 Through 28-05-2004",

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AU - Wise, S. M.

AU - Lowengrub, J. S.

AU - Kim, J. S.

AU - Johnson, W. C.

N1 - Funding Information: We thank Vittorio Cristini for helpful discussions. We are grateful to the U.S. National Science Foundation for the financial support of this work through the Center for the Design of Nanoscopic Materials, Grant DMR0080016.

PY - 2004/7

Y1 - 2004/7

N2 - A Cahn-Hilliard evolution equation possessing a source term is employed to study the morphological evolution of a strained heteroepitaxial thin film, during continuous mass deposition, on a substrate with an embedded coherent island. The elastic properties and the surface energy are anisotropic, with the surface energy anisotropy being strong enough to result in missing orientations and facets. A sophisticated finite-difference/multigrid method and an implicit time integration scheme are combined to make an efficient numerical method, one which enables numerically tractable computation in both two and three dimensions. Herein we present preliminary two-dimensional results demonstrating the utility of our finite difference/multigrid algorithms. The strain localization effects produced by a buried, coherent inclusion are shown to produce laterally organized quantum dots during the morphological evolution of the film.

AB - A Cahn-Hilliard evolution equation possessing a source term is employed to study the morphological evolution of a strained heteroepitaxial thin film, during continuous mass deposition, on a substrate with an embedded coherent island. The elastic properties and the surface energy are anisotropic, with the surface energy anisotropy being strong enough to result in missing orientations and facets. A sophisticated finite-difference/multigrid method and an implicit time integration scheme are combined to make an efficient numerical method, one which enables numerically tractable computation in both two and three dimensions. Herein we present preliminary two-dimensional results demonstrating the utility of our finite difference/multigrid algorithms. The strain localization effects produced by a buried, coherent inclusion are shown to produce laterally organized quantum dots during the morphological evolution of the film.

KW - Anisotropy

KW - Epitaxial strain

KW - Self-assembly

KW - Stress

KW - Substrate

KW - Surface diffusion

KW - Thin film

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DO - 10.1016/j.spmi.2004.08.029

M3 - Conference article

AN - SCOPUS:9644302801

SN - 0749-6036

VL - 36

SP - 293

EP - 304

JO - Superlattices and Microstructures

JF - Superlattices and Microstructures

IS - 1-3

T2 - European Materials Research Society 2004

Y2 - 24 May 2004 through 28 May 2004

ER -

Efficient phase-field simulation of quantum dot formation in a strained heteroepitaxial film

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

Access to Document

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