Confined Capillary Stresses During the Initial Growth of Thin Films on Amorphous Substrates

[+] Author and Article Information
S. P. A. Gill

Department of Engineering, Leicester University, University Road, Leicester, LE1 7RH, UK

H. Gao

Division of Mechanics and Computation, Department of Mechanical Engineering, Stanford University, Stanford, CA 94305

V. Ramaswamy, W. D. Nix

Department of Materials Science and Engineering, Stanford University, Stanford, CA 94305

J. Appl. Mech 69(4), 425-432 (Jun 20, 2002) (8 pages) doi:10.1115/1.1469001 History: Received March 15, 2001; Revised December 10, 2001; Online June 20, 2002
Copyright © 2002 by ASME
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In-situ curvature versus nominal thickness for a Pt film deposited on a SiO2 substrate
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(a) The problem geometry, (b) the loading on the island and substrate due to current capillarity and capillarity history
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A simplified model of the problem as a beam subject to a pure bending moment
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Variation in α-parameters with the relative island size, R0/L. The parameter remains approximately constant for small island sizes but there is a pronounced edge-effect as the island perimeter approaches the edge of the island catchment area. This effect is most obvious in the case of the current capillarity loading (type A). The effect with other loading types is similar to that shown for loading types B and H. The constant values quoted for α in Table 1 are weighted averages over the growth period of the island, ∫01α(η)η3dη, where η=R0/L and a constant volumetric growth rate is assumed.
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The geometrical parameter αT varies with island size R0 given a constant surface layer thickness b
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A comparison of the areal fraction model of (3.5) with experimental data (1). The best correlation is obtained with a grain radius of L≈40 Å.
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Comparison between the substrate curvature obtained from the finite element analysis, κ, and that predicted by the Stoney formula, κs, with varying substrate thickness D. It can be seen that the two models converge for large substrate thicknesses above 100 times the film thickness t0.
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Comparison between compressive stress curvature predictions of (4.2) and experimental results (1). All three models are of the correct order of magnitude. The models are only valid before an appreciable amount of island coalescence occurs and tensile stresses start developing in the film. The experimental data indicates that this is around 5 Å.
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The deformation mechanism (exaggerated) due to the current capillarity forces acting on an elastically stiff island generates a negative curvature. If the island is elastically much softer than the substrate then the current capillarity can generate a positive curvature.




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