Journal of Crystal Growth 193 (1998) 257—270 Equilibrium shape of epitaxially strained crystals (Volmer—Weber case) P. Mu¨ller*, R. Kern Centre de Recherche sur les Me & canismes de la Croissance Cristalline 1 , Campus de Luminy, Case 913, F-13288 Marseille Cedex 9, France Received 2 March 1998; accepted 5 May 1998 Abstract Three-dimensional epitaxial deposits when accomodated on a mismatched substrate only reach an equilibrium state for a given shape and a given strain distribution in the deposit A and in the substrate B. The aim of this paper is to formulate the equilibrium shape ratio r"h/l (height over lateral size ratio) of a crystal A epitaxially coherently strained on a substrate B where the natural misfit is m. Whereas for a structureless substrate Wulff—Kaishew’s theorem tells that r"r  is constant depending only on the wetting of B by A, the new theorem shows that when mO0, whatever its sign, r increases with size so that self similarity is lost. This size dependence originates in the fact that epitaxial strain acts against wetting and thus leads to a thickening of the equilibrium shape. The greater the parameters m, r  and K (the substrate/deposit stiffness) the larger the shape ratio r. For a collection of crystals, and when close enough, crystals interact by substrate deformation so that their shapes deviate from that of isolated crystal. In spite of this elastic shape effect other behaviors are only slightly changed. (a) The nucleation barrier G* practically is not influenced by the elastic energy provided the nucleus is small or G*+k¹. (b) Gibbs—Thomson’s equation stays close to the usual one where elastic energy is omitted (m"0). As a consequence a collection of epitaxially strained crystals have an Ostwald ripening without any anomaly. All these results only hold for Volmer—Weber coherent epitaxy.  1998 Elsevier Science B.V. All rights reserved. 1. Introduction 1.1. Equilibrium shape The equilibrium shape of a free crystal is that which mimimizes the total surface free energy  for a given volume [1—3]. It is given by the Wulff * Corresponding author. Fax: # 33 91 41 89 16; e-mail: muller@crmc2.univ-mrs.fr.  Associe´ aux Universite´s Aix—Marseille II et III. theorem [4]: the equilibrium shape is the inner envelope of the planes perpendicular to directions n and proportional to distances (n) measured from a point called Wulff point. There is an activation barrier G  to overpass to obtain the equilibrium shape, which is one third of the total surface energy of the crystal [3]. Quite different is the case of supported crystals since, as shown independently by Kaishew [5] then Winterbottom [6], the equilib- rium shape of a supported crystal is modified by the influence of the substrate. For a structureless substrate, or strictly isomorphous species, these 0022-0248/98/$ — see front matter  1998 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 9 8 ) 0 0 5 0 8 - 9