# Asymptotic Analysis of the Shape and Composition of Alloy Islands in Epitaxial Solid Films

Mathematical Modelling of Natural Phenomena (2008)

- Volume: 3, Issue: 5, page 30-49
- ISSN: 0973-5348

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topBlanariu, M., and Spencer, B. J.. "Asymptotic Analysis of the Shape and Composition of Alloy Islands in Epitaxial Solid Films." Mathematical Modelling of Natural Phenomena 3.5 (2008): 30-49. <http://eudml.org/doc/222206>.

@article{Blanariu2008,

abstract = {
We consider the formation of solid drops
(“islands”) occurring in the growth of strained solid
films. Beginning from a detailed model for the growth of an alloy film
that incorporates the coupling between composition, elastic stress and
the morphology of the free boundary, we develop an asymptotic
description of the shape and compositional nonuniformity of small
alloy islands grown at small deposition rates. A key feature of the
analysis is a “thin domain” scaling in the island which enables
recasting the free boundary problem into a set of integrodifferential
equations for the shape and composition profile. The
integrodifferential system can be decomposed into two parts: one part
gives a single integrodifferential equation for the shape analogous to
that obtained for a single-component island determined by Shanahan and
Spencer (2002), and the other part gives the composition profile in
terms of the shape. Thus, the shape of an alloy island is identical to
that of a single-component island with the same system parameters, but
with a nonuniform composition that depends on the stress-composition
coupling and alloy solution thermodynamics. Finally, we characterize
the structure and magnitude of the compositional nonuniformity and
also interpret our theoretical results in the context of SiGe alloy
films.
},

author = {Blanariu, M., Spencer, B. J.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {free boundary problem; alloy film; quantum
dot; elasticity; compositional strain},

language = {eng},

month = {12},

number = {5},

pages = {30-49},

publisher = {EDP Sciences},

title = {Asymptotic Analysis of the Shape and Composition of Alloy Islands in Epitaxial Solid Films},

url = {http://eudml.org/doc/222206},

volume = {3},

year = {2008},

}

TY - JOUR

AU - Blanariu, M.

AU - Spencer, B. J.

TI - Asymptotic Analysis of the Shape and Composition of Alloy Islands in Epitaxial Solid Films

JO - Mathematical Modelling of Natural Phenomena

DA - 2008/12//

PB - EDP Sciences

VL - 3

IS - 5

SP - 30

EP - 49

AB -
We consider the formation of solid drops
(“islands”) occurring in the growth of strained solid
films. Beginning from a detailed model for the growth of an alloy film
that incorporates the coupling between composition, elastic stress and
the morphology of the free boundary, we develop an asymptotic
description of the shape and compositional nonuniformity of small
alloy islands grown at small deposition rates. A key feature of the
analysis is a “thin domain” scaling in the island which enables
recasting the free boundary problem into a set of integrodifferential
equations for the shape and composition profile. The
integrodifferential system can be decomposed into two parts: one part
gives a single integrodifferential equation for the shape analogous to
that obtained for a single-component island determined by Shanahan and
Spencer (2002), and the other part gives the composition profile in
terms of the shape. Thus, the shape of an alloy island is identical to
that of a single-component island with the same system parameters, but
with a nonuniform composition that depends on the stress-composition
coupling and alloy solution thermodynamics. Finally, we characterize
the structure and magnitude of the compositional nonuniformity and
also interpret our theoretical results in the context of SiGe alloy
films.

LA - eng

KW - free boundary problem; alloy film; quantum
dot; elasticity; compositional strain

UR - http://eudml.org/doc/222206

ER -

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