中国物理B ›› 2008, Vol. 17 ›› Issue (8): 3008-3013.doi: 10.1088/1674-1056/17/8/041

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Morphologies of epitaxial islands on a lattice-misfitted substrate

周旺民1, 尹姝媛2, 汪建平3, 王崇愚4   

  1. (1)College of Mechanical {\& Electrical Engineering, Zhejiang University of Technology, Hangzhou 310032, China;Department of Mechanical Engineering, West Branch of Zhejiang University of Technology, Quzhou 324000, China; (2)College of Science, Zhejiang University of Technology, Hangzhou 310023, China; (3)Department of Mechanical Engineering, West Branch of Zhejiang University of Technology, Quzhou 324000, China; (4)Department of Physics, Tsinghua University, Beijing 100084, China
  • 收稿日期:2007-12-20 修回日期:2008-03-26 出版日期:2008-08-20 发布日期:2008-08-20
  • 基金资助:
    Project supported by the National Natural Science Foundation of China (Grant No 90101004).

Morphologies of epitaxial islands on a lattice-misfitted substrate

Wang Jian-Ping(汪建平)a), Zhou Wang-Min(周旺民)b)a)†, Wang Chong-Yu(王崇愚)c), and Yin Shu-Yuan(尹姝媛)d)   

  1. a Department of Mechanical Engineering, West Branch of Zhejiang University of Technology, Quzhou 324000, China; b College of Mechanical & Electrical Engineering, Zhejiang University of Technology, Hangzhou 310032, China; c Department of Physics, Tsinghua University, Beijing 100084, China; d College of Science, Zhejiang University of Technology, Hangzhou 310023, China
  • Received:2007-12-20 Revised:2008-03-26 Online:2008-08-20 Published:2008-08-20
  • Supported by:
    Project supported by the National Natural Science Foundation of China (Grant No 90101004).

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摘要： Under certain growth conditions for systems with a film/substrate lattice misfit, the deposited material is known to aggregate into island-like shapes. We have obtained an analytical expression of the total free energy, which consists of strain energy, surface energy and interfacial energy of a coherent island/substrate system, and the change of equilibrium aspect ratio versus the volume of the island and the misfit of lattices in the system, which provides a broad perspective on island behaviour. These then were used to study the equilibrium shapes of the system. The results show that in order to minimize the total free energy, a coherent island will have a particular height-to-width aspect ratio, called equilibrium aspect ratio, that is a function of the island volume and misfit. The aspect ratio is increased with increasing island volume at a fixed misfit, and with increasing misfit strain between the island and substrate at a fixed island volume. Moreover, the effect of misfit dislocation on the equilibrium shape of the island is also examined. The results obtained are in good agreement with experiment of observations and thus can serve as a basis for interpreting the experiments.

关键词: epitaxial island, free energy, equilibrium shape

Abstract: Under certain growth conditions for systems with a film/substrate lattice misfit, the deposited material is known to aggregate into island-like shapes. We have obtained an analytical expression of the total free energy, which consists of strain energy, surface energy and interfacial energy of a coherent island/substrate system, and the change of equilibrium aspect ratio versus the volume of the island and the misfit of lattices in the system, which provides a broad perspective on island behaviour. These then were used to study the equilibrium shapes of the system. The results show that in order to minimize the total free energy, a coherent island will have a particular height-to-width aspect ratio, called equilibrium aspect ratio, that is a function of the island volume and misfit. The aspect ratio is increased with increasing island volume at a fixed misfit, and with increasing misfit strain between the island and substrate at a fixed island volume. Moreover, the effect of misfit dislocation on the equilibrium shape of the island is also examined. The results obtained are in good agreement with experiment of observations and thus can serve as a basis for interpreting the experiments.

Key words: epitaxial island, free energy, equilibrium shape

中图分类号:  (Thin film structure and morphology)

  • 68.55.-a
61.72.Hh (Indirect evidence of dislocations and other defects (resistivity, slip, creep, strains, internal friction, EPR, NMR, etc.)) 68.35.Gy (Mechanical properties; surface strains) 68.35.Md (Surface thermodynamics, surface energies) 68.55.Ln (Defects and impurities: doping, implantation, distribution, concentration, etc.) 68.60.Bs (Mechanical and acoustical properties)