Geodesic
Anisotropic surface energy formulations and their effect on stability of a growing thin film
Maciek D. Korzec1 ; Andreas Münch2 ; Barbara Wagner1
1Technische Universität Berlin, Germany
2Oxford University, UK
Interfaces and free boundaries, Tome 14 (2012) no. 4, pp. 545-567

Voir la notice de l'article provenant de la source EMS Press

DOI

In this paper we revisit models for the description of the evolution of crystalline films with anisotropic surface energies.We prove equivalences of symmetry properties of anisotropic surface energy models commonly used in the literature. Then we systematically develop a framework for the derivation of surface diffusion models for the self-assembly of quantum dots during Stranski-Krastanov growth that include surface energies also with large anisotropy as well as the effect of wetting energy, elastic energy and a randomly perturbed atomic deposition flux. A linear stability analysis for the resulting sixth-order semilinear evolution equation for the thin film surface shows that that the new model allows for large anisotropy and gives rise to the formation of anisotropic quantum dots. The nonlinear three-dimensional evolution is investigated via numerical solutions. These suggest that increasing anisotropy stabilizes the faceted surfaces and may lead to a dramatic slow-down of the coarsening of the dots.
DOI : 10.4171/ifb/291
Classification : 35-XX, 74-XX, 00-XX
Mots-clés : Anisotropic surface energy, high order partial differential equations, pseudospectral methods, surface diffusion

Maciek D. Korzec  1   ; Andreas Münch  2   ; Barbara Wagner  1

1 Technische Universität Berlin, Germany
2 Oxford University, UK 
Maciek D. Korzec; Andreas Münch; Barbara Wagner. Anisotropic surface energy formulations and their effect on stability of a growing thin film. Interfaces and free boundaries, Tome 14 (2012) no. 4, pp. 545-567. doi: 10.4171/ifb/291
@article{10_4171_ifb_291,
     author = {Maciek D. Korzec and Andreas M\"unch and Barbara Wagner},
     title = {Anisotropic surface energy formulations and their effect on stability of a growing thin film},
     journal = {Interfaces and free boundaries},
     pages = {545--567},
     year = {2012},
     volume = {14},
     number = {4},
     doi = {10.4171/ifb/291},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ifb/291/}
}
TY  - JOUR
AU  - Maciek D. Korzec
AU  - Andreas Münch
AU  - Barbara Wagner
TI  - Anisotropic surface energy formulations and their effect on stability of a growing thin film
JO  - Interfaces and free boundaries
PY  - 2012
SP  - 545
EP  - 567
VL  - 14
IS  - 4
UR  - http://geodesic.mathdoc.fr/articles/10.4171/ifb/291/
DO  - 10.4171/ifb/291
ID  - 10_4171_ifb_291
ER  - 
%0 Journal Article
%A Maciek D. Korzec
%A Andreas Münch
%A Barbara Wagner
%T Anisotropic surface energy formulations and their effect on stability of a growing thin film
%J Interfaces and free boundaries
%D 2012
%P 545-567
%V 14
%N 4
%U http://geodesic.mathdoc.fr/articles/10.4171/ifb/291/
%R 10.4171/ifb/291
%F 10_4171_ifb_291

Cité par Sources :