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Shape and stability of self-assembled surface domains

Nature Materials volume 3, pages 95–98 (2004)Cite this article

Abstract

The shapes of two-dimensional (2D) nanostructures on surfaces are determined by their boundary energies1,2,3 as well as by long-range elastic, electrostatic or magnetic interactions. Although it is well known that long-range interactions can give rise to shape bifurcation4,5,6,7,8,9—an abrupt change in shape symmetry at a critical size—a general description of the evolution of shape with size, systematically incorporating both the azimuthal dependence of the boundary energy and long-range interactions, has been lacking. Here we show that unconstrained shape relaxation, including previously ignored boundary curvature, leads to a novel, continuous shape change from convex at small size to concave at large size. In addition to demonstrating a method to quantitatively determine the azimuthal dependence of the boundary energy, we show that the energy gain associated with boundary curvature relaxation is a key factor in stabilizing surface nanostructures. For 7×7 domains on Si(111), boundary curvature reduces the formation free-energy by up to 50%.

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Figure 1: Equilibrium domain shapes evolve as a function of size.
Figure 2: Domain boundary curvatures.
Figure 3: Calculated equilibrium shapes as a function of size.

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Acknowledgements

We are grateful to N. C. Bartelt, F. Leonard and M. C. Reuter for helpful discussions.

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Authors and Affiliations

  1. IBM Research Division, Thomas J. Watson Research Center, PO Box 218 Yorktown Heights, New York, 10598, USA

    G. E. Thayer, J. B. Hannon & R. M. Tromp

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  1. G. E. Thayer
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  2. J. B. Hannon
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  3. R. M. Tromp
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Correspondence to G. E. Thayer.

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The authors declare no competing financial interests.

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Thayer, G., Hannon, J. & Tromp, R. Shape and stability of self-assembled surface domains. Nature Mater 3, 95–98 (2004). https://doi.org/10.1038/nmat1050

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