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Measuring the surface stress polar dependence

Nature Materials volume 4, pages 238–242 (2005)Cite this article

Abstract

Although measurements of the polar dependence of the surface free energy are easily available, measurements of the whole polar dependence of the surface stress of a crystal do not exist. Here, we present a procedure that allows the experimental determination of this dependence. For this purpose, electromigration was used to control the kinetic faceting of surface orientations that belong to the equilibrium shape of the crystal, and for each destabilized surface, the period of faceting as well as the crystallographic angles of the appearing facets were measured by atomic force microscopy. The data obtained lead to a set of equations whose mathematical solution, compatible with physical constraints, gives access to the surface stress polar dependence of the whole crystal, and thus to a better understanding of surface stress properties.

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Figure 1: Equilibrium shape and corresponding γ-plot of silicon obtained at 1,373 K from a 3D silicon bulb.
Figure 2: Stereographic representation of the vicinal faces under study.
Figure 3: AFM image of a hill-and-valley structure obtained after annealing a (118) vicinal surface in ultrahigh-vacuum conditions at 1,373 K over 150 h.
Figure 4: Temporal evolution of the wavelength λ (a) and the crystallographic angle β (b) for all the studied vicinal faces.
Figure 5: Schematic representation of the mechanism of kinetic faceting.
Figure 6: Surface stress polar dependence.

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Acknowledgements

We acknowledge J. Fuhr, G. Tréglia, R. Kern and S. Olivier for helpful discussions and J. P. Astier for the AFM images.

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Authors and Affiliations

  1. Centre de Recherche sur la Matière Condensée et les Nanosciences, CNRS, Associated to Université de la Mediterranée and Université Paul-Cezanne Aix-Marseille III, Campus de Luminy, case 913, Marseille, F-13288 Cedex 9, France

    J. J. Métois, A. Saúl & P. Müller

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  1. J. J. Métois
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  2. A. Saúl
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Correspondence to P. Müller.

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Métois, J., Saúl, A. & Müller, P. Measuring the surface stress polar dependence. Nature Mater 4, 238–242 (2005). https://doi.org/10.1038/nmat1328

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