Issue Eur. Phys. J. Appl. Phys. Volume 37, Number 1, January 2007 Page(s) 33 - 37 Section Surfaces, Interfaces and Films DOI 10.1051/epjap:2006134 Published online 22 November 2006

Eur. Phys. J. Appl. Phys. 37, 33-37 (2007)
DOI: 10.1051/epjap:2006134

Equilibrium shapes of coherent islands in heteroepitaxial systems

W. Zhou^{1, 2}, C. Cai¹, S. Yin³ and C. Wang<sup>4

1</sup>  College of Mechanical and Electrical Engineering, Zhejiang University of Technology, Hangzhou 310032, China
²  Department of Mechanical Engineering, West Branch of Zhejiang University of Technology, Quzhou 324000, China
³  College of Science, Zhejiang University of Technology, Hangzhou 310032, China
⁴  Department of Physics, Tsinghua University, Beijing 100084, China

wangminzhou@sohu.com

(Received: 21 May 2006 / Accepted: 6 September 2006 / Published online: 22 November 2006)

Abstract
An analytical expression of the free energy consisting of the strain energy, surface energy and interfacial energy for the coherent island/substrate system, as well as the evolving relations of aspect ratio against volume of the island and misfit of the system, which provides a broad perspective on island behavior, is obtained, and used to study the equilibrium shapes of the systems. Under certain growth conditions in systems with a film/substrate lattice misfit, deposed material is known to aggregate into islandlike shapes with geometries having triangular shaped cross-sections. A two-dimensional model assuming liner elastic behavior is used to analyze an isolated triangular shaped island with elastic properties similar to those of the substrate assumed to be semi-infinite. The results show that in order to minimize the total free energy, a coherent island will adopt a particular height-to-width aspect ratio that is a function of only the island volume. The effect of a misfit dislocation on the equilibrium shape of an island is in passing examined. These can serve as a basis for interpretation of experiments.

PACS
68.55.Jk - Structure and morphology; thickness; crystalline orientation and texture.
62.25.+g - Mechanical properties of nanoscale materials.
68.35.-p - Solid surfaces and solid-solid interfaces: Structure and energetics.
68.65.Hb - Quantum dots.

© EDP Sciences 2006

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