An application of multigrid methods for a discrete elastic model for epitaxial systems

Caflisch, Russel E.; Lee, Y.-J.; Shu, Shi; Xiao, Yingxiong; Xu, Jinchao

doi:10.1016/j.jcp.2006.04.007

Cited by 7 publications

(7 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This greatly reduces the extent of the computational domain, with no loss of accuracy [19]. Second, we apply an algebraic multigrid method to solve the strain equations, that greatly accelerates the computations [9]. Similar methods have been developed and implemented by Smereka and Russo [38].…”

Section: Numerical Simulations For Thin Filmsmentioning

confidence: 99%

Growth, Structure and Pattern Formation for Thin Films

Caflisch¹

2008

J Sci Comput

View full text Add to dashboard Cite

An epitaxial thin film consists of layers of atoms whose lattice properties are determined by those of the underlying substrate. This paper reviews mathematical modeling, analysis and simulation of growth, structure and pattern formation for epitaxial systems, using an island dynamics/level set method for growth and a lattice statics model for strain. Epitaxial growth involves physics on both atomistic and continuum length scales. For example, diffusion of adatoms can be coarse-grained, but nucleation of new islands and breakup for existing islands are best described atomistically. In heteroepitaxial growth, mismatch between the lattice spacing of the substrate and the film will introduce a strain into the film, which can significantly influence the material structure, for example leading to formation of quantum dots. Technological applications of epitaxial structures, such as quantum dot arrays, require a degree of geometric uniformity that has been difficult to achieve. Modeling and simulation may contribute insights that will help to overcome this problem. We present simulations that combine growth and strain showing the structure of nanocrystals and the formation of patterns in epitaxial systems.

show abstract

Section: Numerical Simulations For Thin Filmsmentioning

confidence: 99%

Growth, Structure and Pattern Formation for Thin Films

Caflisch¹

2008

J Sci Comput

View full text Add to dashboard Cite

show abstract

“…An effective numerical method for solving the atomistic strain equations using an algebraic multigrid method was developed in [4]. Moreover an artificial boundary condition can be imposed in the substrate close to the interface with the film, to greatly accelerate the computation [10].…”

Section: Discrete Elasticitymentioning

confidence: 99%

Growth and Pattern Formation for Thin Films

Caflisch

2008

Progress in Industrial Mathematics at ECMI 2006

View full text Add to dashboard Cite

Summary.Epitaxy is the growth of a thin film by attachment to an existing substrate in which the crystalline properties of the film are determined by those of the substrate. In heteroepitaxy, the substrate and film are of different materials, and the resulting mismatch between lattice constants can introduce stress into the system. We have developed an island dynamics model for epitaxial growth that is solved using a level set method. This model uses both atomistic and continuum scaling, since it includes island boundaries that are of atomistic height, but describes these boundaries as smooth curves. The strain in the system is computed using an atomistic strain model that is solved using an algebraic multigrid method and an artificial boundary condition. Using the growth model together with the strain model, we simulate pattern formation on an epitaxial surface.

show abstract

“…The Fouriermultigrid algorithm developed in Russo and Smereka (2006b) helps with this (see also Caflsich et al, 2006), but we find we can do better using approximate local calculations centered on the locations of the atom being moved. Whenever an atom is added or removed from the lattice, we implement an efficient iterative technique based on successive over-relaxation to update the displacement field in a sequence of nested domains until a convergence criteria is satisfied.…”

Section: Introductionmentioning

confidence: 99%