Vol. 1, No. 6, 2006

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ISSN: 1559-3959
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

Vol. 1 (2006), No. 6, 1041–1053
Abstract

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
Milestones
Received: 27 December 2005
Accepted: 14 March 2006
Published: 1 October 2006
Authors
Xue Feng
Department of Mechanical and Industrial Engineering
University of Illinois
Urbana, IL 61801
United States
Yonggang Huang
Department of Mechanical and Industrial Engineering
University of Illinois
Urbana, IL 61801
United States
Hanqing Jiang
Department of Mechanical and Aerospace Engineering
Arizona State University
Tempe, AZ 85287
United States
Duc Ngo
Department of Mechanical and Industrial Engineering
University of Illinois
Urbana, IL 61801
United States
Ares J. Rosakis
Graduate Aeronautical Laboratory
California Institute of Technology
Pasadena, CA 91125
United States