Interaction and multiscale mechanics

  • 제1권1호
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  • Pages.123-142
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  • 2008
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  • 1976-0426(pISSN)
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  • 2092-6200(eISSN)
테크노프레스 (Techno-Press)
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Anisotropic, non-uniform misfit strain in a thin film bonded on a plate substrate

  • Huang, Y. (Department of Civil and Environmental Engineering and Department of Mechanical Engineering, Northwestern University) ;
  • Ngo, D. (Department of Mechanical and Industrial Engineering, University of Illinois) ;
  • Feng, X. (Department of Engineering Mechanics, Tsinghua University) ;
  • Rosakis, A.J. (Graduate Aeronautical Laboratory, California Institute of Technology)
  • 투고 : 2007.07.13
  • 심사 : 2007.11.05
  • 발행 : 2008.03.25
⟨ 이전 논문 다음 논문 ⟩

초록

Current methodologies used for the inference of thin film stresses through curvature measurements are strictly restricted to stress and curvature states which are assumed to remain uniform over the entire film/substrate system. These methodologies have recently been extended to non-uniform stress and curvature states for the thin film subject to non-uniform, isotropic misfit strains. In this paper we study the same thin film/substrate system but subject to non-uniform, anisotropic misfit strains. The film stresses and system curvatures are both obtained in terms of the non-uniform, anisotropic misfit strains. For arbitrarily non-uniform, anisotropic misfit strains, it is shown that a direct relation between film stresses and system curvatures cannot be established. However, such a relation exists for uniform or linear anisotropic misfit strains, or for the average film stresses and average system curvatures when the anisotropic misfit strains are arbitrarily non-uniform.

키워드

참고문헌

  1. Brown, M.A., Park, T.S., Rosakis, A.J., Ustundag, E., Huang, Y., Tamura, N. and Valek, B. (2006), "A comparison of X-ray microdiffraction and coherent gradient sensing in measuring discontinuous curvatures in thin film: substrate systems", J. Appl. Mech., 73, 723-729. https://doi.org/10.1115/1.2150500
  2. Brown, M.A., Rosakis, A.J., Feng, X., Huang, Y. and Ustundag, E. (2007), "Thin film/substrate systems featuring arbitrary film thickness and misfit strain distributions: Part II. Experimental validation of the nonlocal stress-curvature relations", Int. J. Solids Struct., 44, 1755-1767. https://doi.org/10.1016/j.ijsolstr.2006.10.015
  3. Feng, X., Huang, Y., Jiang, H., Ngo, D. and Rosakis, A.J. (2006), "The effect of thin film/substrate radii on the Stoney formula for thin film/substrate subjected to non-uniform axisymmetric misfit strain and temperature". J. Mech. Mater. Struct., 1, 1041-1054. https://doi.org/10.2140/jomms.2006.1.1041
  4. Finot, M., Blech, I.A., Suresh, S. and Fijimoto, H. (1997), "Large deformation and geometric instability of substrates with thin-film deposits" J. Appl. Phys., 81, 3457-3464. https://doi.org/10.1063/1.365042
  5. Freund, L.B. (2000), "Substrate curvature due to thin film mismatch strain in the nonlinear deformation range", J. Mech. Phys. Solids., 48, 1159. https://doi.org/10.1016/S0022-5096(99)00070-8
  6. Freund, L.B. and Suresh, S. (2004), Thin Film Materials; Stress, Defect Formation and Surface Evolution. Cambridge University Press, Cambridge, U.K..
  7. Huang, Y. and Rosakis, A.J. (2005), "Extension of Stoney's formula to non-uniform misfit strain distributions in thin film/substrate systems. The case of radial symmetry", J. Mech. Phys. Solids., 53, 2483-2500. https://doi.org/10.1016/j.jmps.2005.06.003
  8. Huang, Y., Ngo, D. and Rosakis, A.J. (2005), "Non-uniform, axisymmetric misfit strain in thin films bonded on plate substrates/substrate systems: The relation between non-uniform film stresses and system curvatures", Acta Mechanica Sinica., 21, 362-370. https://doi.org/10.1007/s10409-005-0051-9
  9. Huang, Y. and Rosakis, A.J. (2007), "Extension of Stoney's formula to arbitrary temperature distributions in thin film/substrate systems", J. Appl. Mech., 74, 1225-1233. https://doi.org/10.1115/1.2744035
  10. Lee, H., Rosakis, A.J. and Freund, L.B. (2001), "Full field optical measurement of curvatures in ultra-thin film/substrate systems in the range of geometrically nonlinear deformations", J. Appl. Phys., 89, 6116-6129 https://doi.org/10.1063/1.1364650
  11. Master, C.B. and Salamon, N.J. (1993), "Geometrically nonlinear stress-deflection relations for thin film/substrate systems", Int. J. Engrg. Sci., 31, 915-925. https://doi.org/10.1016/0020-7225(93)90103-2
  12. Ngo, D., Feng, X., Huang, Y., Rosakis, A.J. and Brown, M.A. (2007), "Thin film/substrate systems featuring arbitrary film thickness and misfit strain distributions: Part I. Analysis for obtaining film stress from nonlocal curvature information", Int. J. Solids Struct., 44, 1745-1754. https://doi.org/10.1016/j.ijsolstr.2006.10.016
  13. Ngo, D., Huang, Y., Rosakis, A.J. and Feng, X. (2006), "Spatially non-uniform, isotropic misfit strain in thin films bonded on plate substrates: the relation between non-uniform stresses and system curvatures", Thin Solid Films., 515, 2220-2229. https://doi.org/10.1016/j.tsf.2006.05.013
  14. Park, T.S. and Suresh, S. (2000), "Effects of line and passivation geometry on curvature evolution during processing and thermal cycling in copper interconnect lines", Acta Materialia., 48, 3169-3175. https://doi.org/10.1016/S1359-6454(00)00114-2
  15. Salamon, N.J. and Masters, C.B. (1995), "Bifurcation in isotropic thin film/substrate plates", Int. J. Solids Struct., 32, 473-481. https://doi.org/10.1016/0020-7683(94)00129-K
  16. Shen, Y.L., Suresh, S. and Blech, I.A. (1996), "Stresses, curvatures, and shape changes arising from patterned lines on silicon wafers", J. Appl. Phys., 80, 1388-1398. https://doi.org/10.1063/1.362938
  17. Stoney, G.G. (1909), "The tension of metallic films deposited by electrolysis", Proc. R. Soc. Lond., A82, 172-175.
  18. Wikstrom, A., Gudmundson, P. and Suresh, S. (1999a), "Thermoelastic analysis of periodic thin lines deposited on a substrate", J. Mech. Phys. Solids., 47, 1113-1130. https://doi.org/10.1016/S0022-5096(98)00092-1
  19. Wikstrom, A., Gudmundson, P. and Suresh, S. (1999b), "Analysis of average thermal stresses in passivated metal interconnects", J. Appl. Phys., 86, 6088-6095. https://doi.org/10.1063/1.371658

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