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Comptes Rendus Physique
Volume 16, n° 8
pages 741-757 (octobre 2015)
Doi : 10.1016/j.crhy.2015.08.002
Instability-driven quantum dots
Instabilité et boîtes quantiques

Jean-Noël Aqua a, , Thomas Frisch b
a Institut des nanosciences de Paris, UPMC (Université Paris-6), CNRS, UMR 7588, 4, place Jussieu, 75005 Paris, France 
b Institut Non Linéaire de Nice, Université de Nice Sophia Antipolis, UMR, CNRS 6618, 1361, routes des Lucioles, 06560 Valbonne, France 

Corresponding author.

When a film is strained in two dimensions, it can relax by developing a corrugation in the third dimension. We review here the resulting morphological instability that occurs by surface diffusion, called the Asaro–Tiller–Grinfel'd instability (ATG), especially on the paradigmatic silicon/germanium system. The instability is dictated by the balance between the elastic relaxation induced by the morphological evolution, and its surface energy cost. We focus here on its development at the nanoscales in epitaxial systems when a crystal film is coherently deposited on a substrate with a different lattice parameter, thence inducing epitaxial stresses. It eventually leads to the self-organization of quantum dots whose localization is dictated by the instability long-time dynamics. In these systems, new effects, such as film/substrate wetting or crystalline anisotropy, come into play and lead to a variety of behaviors.

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Un film qui subit une pression selon deux dimensions peut relaxer cette contrainte en ondulant dans la troisième dimension. Nous analysons ici l'instabilité morphologique qui en résulte grâce à la diffusion de surface, l'instabilité d'Asaro–Tiller–Grinfel'd (ATG), en particulier sur le système paradigmatique silicium/germanium. L'instabilité est régie par l'équilibre entre la relaxation élastique liée à l'évolution de la surface, et son coût en énergie de surface. Nous nous focalisons ici sur sa manifestation aux échelles nanométriques dans les systèmes épitaxiés, quand un film cristallin est déposé sur un substrat de paramètre de maille différent, induisant une contrainte élastique bi-axiale. Cette évolution débouche aux temps longs sur l'auto-organisation de boites quantiques dont la localisation est dictée par la dynamique aux temps longs. Dans ces systèmes, des nouveaux effets entrent en jeu, comme le mouillage entre le film et son substrat ou l'anisotropie cristalline, et débouchent sur une diversité de comportements nouveaux.

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Keywords : Strained film, Morphological instability, Epitaxy

1  Note that when coarsening is limited by attachment/detachment one finds   [[95]].
2  A weakly non-linear analysis coupled with singular   wetting interactions lead to   [[27]].

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