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The effect of thin
film/substrate radii on the Stoney formula for thin
film/substrate subjected to nonuniform axisymmetric misfit
strain and temperature
Xue Feng, Yonggang Huang, Hanqing Jiang, Duc Ngo and Ares J. Rosakis |
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Vol. 1 (2006), No. 6, 1041–1053
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Abstract |
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Current methodologies used for the inference of thin film stress through curvature measurements are strictly restricted to stress and curvature states which are assumed to remain uniform over the entire film/substrate system. There are recent studies of film/substrate systems subjected to nonuniform but axisymmetric misfit strain and temperature changes. The film stresses were found to depend nonlocally on system curvatures (that is, depend on the full-field curvatures). A very simple stress-curvature relation was established, but it is limited to thin film and substrate of same radius. We extend the analysis to thin film and substrate of different radii. Remarkably the same simple stress-curvature relation still holds regardless of the film/substrate radii mismatch. |
Keywords
thin film radius, nonuniform misfit strain, nonuniform
wafer curvatures, stress-curvature relations, nonlocal
effects, interfacial shears
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Milestones
Received: 27 December 2005
Accepted: 14 March 2006
Published: 1 October 2006
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Authors |
| Xue Feng | |
| Department of Mechanical and
Industrial Engineering University of Illinois Urbana, IL 61801 United States |
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| Yonggang Huang | |
| Department of Mechanical and
Industrial Engineering University of Illinois Urbana, IL 61801 United States |
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| Hanqing Jiang | |
| Department of Mechanical and
Aerospace Engineering Arizona State University Tempe, AZ 85287 United States |
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| Duc Ngo | |
| Department of Mechanical and
Industrial Engineering University of Illinois Urbana, IL 61801 United States |
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| Ares J. Rosakis | |
| Graduate Aeronautical
Laboratory California Institute of Technology Pasadena, CA 91125 United States |
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