A platelet-to-pyramid shape transition under the influence of the adsorbate–substrate interfacial energy

Within the Tersoff approximation, we obtain an analytic expression for the elastic self-energy of a truncated hut which is more general than that of a truncated pyramid [C. Duport, C. Priester, J. Villain, in: Morphological Organization in Epitaxial Growth and Removal, World Scientific Series on Directions in Condensed Matter Physics, 1997, p. 73]. A pyramidal cluster studied previously can be treated as a square-based hut within the present formalism. The previous results [C. Duport, C. Priester, J. Villain, in: Morphological Organization in Epitaxial Growth and Removal, World Scientific Series on Directions in Condensed Matter Physics, 1997, p. 73; C. Duport, Université de Grenoble, Juin 1996; Phys. Rep. 324 (2000) 271] were obtained on the assumptions of neglecting the adsorbate–substrate interfacial energy and the equilibrium cluster forming with a square base. They predicted that when the volume of a cluster is above some critical value, it preferably forms as a pyramid rather than a platelet in the absence of other strained clusters. Instead, in this paper, we take the interfacial energy into account, based on the work by Korutcheva et al. [I. Markov, Crystal Growth for Beginners, Fundamentals of Nucleation, Crystal Growth Epitaxy, World Scientific, Singapore, 1995; Phys. Rev. B 61 (2000) 16890]. Besides, we start with the consideration of a hut cluster probably forming with a rectangular base instead of a square one [C. Duport, C. Priester, J. Villain, in: Morphological Organization in Epitaxial Growth and Removal, World Scientific Series on Directions in Condensed Matter Physics, 1997, p. 73; C. Duport, Université de Grenoble, Juin 1996]. By employing the derived analytic expression of the surface and elastic energies, we find that the two- to three- dimensional (2D–3D) transition with the inclusion of the adsorbate–substrate interfacial energy is quantitatively modified. It should provide more accurate predicted values of the critical volume in 2D–3D transitions. Furthermore, in the absence of other clusters on a substrate, a pyramid forms above the critical volume and calculations also show that at equilibrium a single cluster forms with a square base for a given cluster volume, which justifies the previous assumption [C. Duport, C. Priester, J. Villain, in: Morphological Organization in Epitaxial Growth and Removal, World Scientific Series on Directions in Condensed Matter Physics, 1997, p. 73; C. Duport, Université de Grenoble, Juin 1996; Phys. Rep. 324 (2000) 271].