From Wulff Kaishew' theorem to nanodots

Raymond Kern (1) , Pierre Müller (1)

1 CINaM - Centre Interdisciplinaire de Nanoscience de Marseille

This paper is devoted to professor R.Kaishew' 100 th birthday ceremony. It intends to illustrate his theorem especially when some inherent simplifying conditions are released (e.g amorphous substrate, stress free system). It is shown that some new insight was brought for the better understanding of present day arrays epitaxial dots, which are said to be promising tools in solid-state electronics. Introduction The paper will be divided in six parts: 1/ We first recall the somewhat long and tortuous genesis of the Wulff' theorem which at the end, clearly concerns the equilibrium shape (ES) of a freestanding crystal A. 2/ Kaishew' important achievement was to predict the ES of a crystal A sitting on a planar substrate B restricted to be amorphous and the system being stress-free. 3/ When releasing this limitation, allowing the substrate B to be crystalline too, epitaxial orientations may install. For coherent epitaxy high stress and strain appear not only in the contact area but spread out in A and B. Elastic energy has to enter in the formulation of the free energy, and has to be minimized (elastic relaxation) as well as the shape. The new theorem shows that ES is deeply modified by the relaxed elastic energy. 4/ Upon some critical size of the deposit crystal the stored elastic energy becoming too expensive, introduction of interfacial dislocations makes to release partially this energy par saccade. Consecutively, the ES retrogrades, at its proper rate, at each dislocation entrance. 5/ Due to (3) and (4) a dot A pilots, outside its contact area, a zone of nearly the same area where the non covered substrate B bears stress 1

Domaines: Physique [physics]; Matière Condensée [cond-mat]

Raymond Kern, Pierre Müller. From Wulff Kaishew' theorem to nanodots. Nanoscale phenomena and structures, 2008. ⟨hal-01967055⟩