Non-uniform, axisymmetric misfit strain

in thin films bonded on plate substrates/substrate systems: The relation between non-uniform film stresses and system curvatures

Yonggang Huang*, D. Ngo, A. J. Rosakis

*Corresponding author for this work

Research output: Contribution to journalArticle

22 Citations (Scopus)

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. By considering a circular thin film/substrate system subject to non-uniform, but axisymmetric misfit strain distributions in the thin film, we derived relations between the film stresses and the misfit strain, and between the plate system's curvatures and the misfit strain. These relations feature a local part which involves a direct dependence of the stress or curvature components on the misfit strain at the same point, and a non-local part which reflects the effect of misfit strain of other points on the location of scrutiny. Most notably, we also derived relations between the polar components of the film stress and those of system curvatures which allow for the experimental inference of such stresses from full-field curvature measurements in the presence of arbitrary radial non-uniformities. These relations also feature a non-local dependence on curvatures making a full-field measurement a necessity. Finally, it is shown that the interfacial shear tractions between the film and the substrate are proportional to the radial gradients of the first curvature invariant and can also be inferred experimentally.

Original languageEnglish (US)
Pages (from-to)362-370
Number of pages9
JournalActa Mechanica Sinica/Lixue Xuebao
Volume21
Issue number4
DOIs
StatePublished - Aug 1 2005

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Thin films
Substrates

Keywords

  • Interfacial shear
  • Non-local effect
  • Non-uniform misfit strain
  • Non-uniform wafer curvatures
  • Stress-curvature relation

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanical Engineering

Cite this

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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. By considering a circular thin film/substrate system subject to non-uniform, but axisymmetric misfit strain distributions in the thin film, we derived relations between the film stresses and the misfit strain, and between the plate system's curvatures and the misfit strain. These relations feature a local part which involves a direct dependence of the stress or curvature components on the misfit strain at the same point, and a non-local part which reflects the effect of misfit strain of other points on the location of scrutiny. Most notably, we also derived relations between the polar components of the film stress and those of system curvatures which allow for the experimental inference of such stresses from full-field curvature measurements in the presence of arbitrary radial non-uniformities. These relations also feature a non-local dependence on curvatures making a full-field measurement a necessity. Finally, it is shown that the interfacial shear tractions between the film and the substrate are proportional to the radial gradients of the first curvature invariant and can also be inferred experimentally.",
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AB - 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. By considering a circular thin film/substrate system subject to non-uniform, but axisymmetric misfit strain distributions in the thin film, we derived relations between the film stresses and the misfit strain, and between the plate system's curvatures and the misfit strain. These relations feature a local part which involves a direct dependence of the stress or curvature components on the misfit strain at the same point, and a non-local part which reflects the effect of misfit strain of other points on the location of scrutiny. Most notably, we also derived relations between the polar components of the film stress and those of system curvatures which allow for the experimental inference of such stresses from full-field curvature measurements in the presence of arbitrary radial non-uniformities. These relations also feature a non-local dependence on curvatures making a full-field measurement a necessity. Finally, it is shown that the interfacial shear tractions between the film and the substrate are proportional to the radial gradients of the first curvature invariant and can also be inferred experimentally.

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