On the Stoney Formula for a Thin Film/Substrate System With Nonuniform Substrate Thickness

[+] Author and Article Information
X. Feng, Y. Huang

Department of Mechanical and Industrial Engineering, University of Illinois, Urbana, IL 61801

A. J. Rosakis

Graduate Aeronautical Laboratory, California Institute of Technology, Pasadena, CA 91125

J. Appl. Mech 74(6), 1276-1281 (Jan 14, 2007) (6 pages) doi:10.1115/1.2745392 History: Received October 18, 2006; Revised January 14, 2007

Current methodologies used for the inference of thin film stress through system curvature measurements are strictly restricted to stress and curvature states which are assumed to remain uniform over the entire film/substrate system. Recently Huang, Rosakis, and co-workers [Acta Mech. Sinica, 21, pp. 362–370 (2005); J. Mech. Phys. Solids, 53, 2483–2500 (2005); Thin Solid Films, 515, pp. 2220–2229 (2006); J. Appl. Mech., in press; J. Mech. Mater. Struct., in press] established methods for the film/substrate system subject to nonuniform misfit strain and temperature changes. The film stresses were found to depend nonlocally on system curvatures (i.e., depend on the full-field curvatures). These methods, however, all assume uniform substrate thickness, which is sometimes violated in the thin film/substrate system. Using the perturbation analysis, we extend the methods to nonuniform substrate thickness for the thin film/substrate system subject to nonuniform misfit strain.

Copyright © 2007 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 1

A schematic diagram of a thin film/substrate system with the cylindrical coordinates (r,θ,z)

Grahic Jump Location
Figure 2

(a) A schematic diagram of a thin film/substrate system with a step change in substrate thickness. (b) The normalized system curvatures κ̂rr=κrr∕κ0 and κ̂θθ=κθθ∕κ0, where κ0=6(Efhf∕1−νf)∕(1−νs∕Esh2)εm, Δh∕2h=0.1, νs=0.27, and Rin=R∕3.



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