On the stoney formula for a thin film/substrate system with nonuniform substrate thickness

X. Feng*, Y. Huang, A. J. Rosakis

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

96 Scopus citations

Abstract

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/sub strate 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. Meek, 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.

Original languageEnglish (US)
Pages (from-to)1276-1281
Number of pages6
JournalJournal of Applied Mechanics, Transactions ASME
Volume74
Issue number6
DOIs
StatePublished - Nov 1 2007

Keywords

  • Interfacial shears
  • Nonlocal stress-curvature relations
  • Nonuniform misfit strain
  • Nonuniform substrate thickness
  • Thin films

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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