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Article Dans Une Revue Journal of Crystal Growth Année : 1998

Equilibrium shape of epitaxially strained crystals (Volmer-Weber case)

Kern Raymond
  • Fonction : Auteur

Résumé

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.
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Dates et versions

hal-01967026 , version 1 (04-01-2019)

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  • HAL Id : hal-01967026 , version 1

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Pierre Müller, Kern Raymond. Equilibrium shape of epitaxially strained crystals (Volmer-Weber case). Journal of Crystal Growth, 1998, 193, pp.257 - 270. ⟨hal-01967026⟩
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