Epitaxial island shapes

We have discussed certain aspects of self-assembly of quantum dots from thin solid films epitaxially grown on solid substrates. We have considered two principle mechanisms of instability of a planar film that lead to the formation of quantum dots the one associated with epitaxial stress and the one associated with the anisotropy of the film surface energy. We have focused on the case of particularly thin hlms when wethng interactions between the film and the substrate are important and derived nonlinear evolution equations for the him surface shape in the small-slope approximahon. We have shown that wetting interachons between the him and the substrate damp long-wave modes of instability and yield the short-wave instability spectrum that can result in the formahon of spahally-regular arrays of islands. We have discussed the nonlinear evoluhon of such arrays analyhcally, by means of weakly nonlinear analysis, and numerically, far from the instability threshold and have shown... 

Fig. 8.39. Low energy electron microscopy images showing transitions in shape of epitaxial SiGe islands deposited on a Si(OOl) substrate. Reproduced with permission from Ross et al. (1999).

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