Patterned bilayer plate microstructures subjected to thermal loading: Deformation and stresses

International Journal of Solids and Structures

Volumn 46, Issue 1, 2009, Pages 125-134

  Zhang, Yanhang ^a   Dunn, Martin L ^b  

^a Boston University   (United States)

^b University of Colorado   (United States)

Author keywords

Curvature; Finite element method; Generalized plane strain; Geometric nonlinearity; Micro electro mechanical systems (MEMS); Patterned plate microstructures; Stress; Thermomechanical deformation

Indexed keywords

COMPOSITE MICROMECHANICS; DEFORMATION; LINEWIDTH; MACHINE DESIGN; MECHANICAL ENGINEERING; MECHANICS; MECHATRONICS; MEMS; MICROELECTROMECHANICAL DEVICES; MICROMACHINING; MICROSTRUCTURE; PLATES (STRUCTURAL COMPONENTS); STRESS CONCENTRATION; STRESSES; SUBSTRATES;

CURVATURE; GENERALIZED PLANE STRAIN; GEOMETRIC NONLINEARITY; MICRO-ELECTRO-MECHANICAL SYSTEMS (MEMS); PATTERNED PLATE MICROSTRUCTURES; THERMOMECHANICAL DEFORMATION;

FINITE ELEMENT METHOD;

EID: 55149090069     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2008.08.020     Document Type: Article

References (40)

1. Brown M.A., Rosakis A.J., Feng X., Huang Y., and Ustundag E. 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 (2007) 1745-1754
2. Carter J., Cowen A., Hardy B., Mahadevan R., Stonefield M., and Wilcenski S. Poly MUMPs Design Handbook (2005), MEMSCAP Inc. Available from:
3. De Groot P., and Deck L. Surface profiling by analysis of white-light interferograms in the special frequency domain. J. Modern Opt. 42 (1995) 389-401
4. Dunn M.L., and Cunningham S.J. Thermo- and electromechanical behavior of thin-film micro and nanostructures. In: Bhushan B. (Ed). Chapter 56 in the Handbook of Nanotechnology. 2nd ed. (2006), Springer, Berlin
5. Dunn M.L., Zhang Y., and Bright V.M. Deformation and structural stability of layered plate microstructures subjected to thermal loading. J. Microelectromech. Syst. 11 (2002) 372-384
6. Dunn M.L. Photomechanics of mono- and polydomain liquid crystal elastomer films. J. Appl. Phys. 102 (2007) Art. No. 013506
7. Ege E.S., and Shen Y.L. Thermomechanical response and stress analysis of copper interconnects. J. Electron. Mater. 32 (2003) 1000-1011
8. Fahnline D.E., Masters C.B., and Salamon N.J. Thin film stress from nonspherical substrate bending measurements. J. Vac. Sci. Technol. A 9 (1991) 2483-2487
9. Feng X., Huang Y., and Rosakis A.J. On the stoney formula for a thin film/substrate system with nonuniform substrate thickness. J. Appl. Mech. 74 (2007) 1276-1281
10. Feng X., Huang Y., and Rosakis A.J. Extension of Stoney's formula to arbitrary temperature distributions in thin film/substrate systems. J. Appl. Mech. 74 (2007) 1225-1233
11. Finot M., and Suresh S. Small and large deformation of thick and thin film multilayers: effects of layer geometry, plasticity and compositional gradients. J. Mech. Phys. Solids 44 (1996) 683-721
12. Finot M., Blech I.A., Suresh S., and Fujimoto H. Large deformation and geometric instability of substrates with thin film deposits. J. Appl. Phys. 81 (1997) 3457-3464
13. Freund L.B. The stress distribution and curvature of a general compositionally graded semiconductor layer. J. Crystal Growth 132 (1993) 341-344
14. Freund L.B. Some elementary connections between curvature and mismatch strain in compositionally graded thin films. J. Mech. Phys. Solids 44 (1996) 723-736
15. Freund L.B., Floro J.A., and Chason E. Extension of the Stoney formula for substrate curvature to configurations with thin substrate or large deformations. Appl. Phys. Lett. 74 (1999) 1987-1989
16. Freund L.B. Substrate curvature due to thin film mismatch strain in the nonlinear deformation range. J. Mech. Phys. Solids 48 (2000) 1159-1174
17. Freund L.B., and Suresh S. Thin Film Materials: Stress, Defect Formation and Surface Evolution (2003), Cambridge University Press, Cambridge
18. Gouldstone A., Shen Y.L., Suresh S., and Thompson C.V. Evolution of stresses in passivated and unpassivated metal interconnects. J. Mater. Res. 13 (1998) 1956-1966
19. Hyer M.W. Some observations on the cured shape of thin unsymmetric laminates. J. Compos. Mater. 15 (1981) 175-194
20. Hyer M.W. The room-temperature shape of four-layer unsymmetric cross-ply laminates. J. Compos. Mater. 16 (1982) 318-340
21. Keller R.R., Geiss R.H., Barbosa N., Slifka A.J., and Read D.T. Strain-induced grain growth during rapid thermal cycling of aluminum interconnects. Metall. Mater. Trans. A 38 (2007) 2263-2272
22. Kim J., and Lin L.W. Electrostatic scanning micromirrors using localized plastic deformation of silicon. J. Micromech. Microeng. 15 (2005) 1777-1785
23. King, J.A., 1988. Materials Handbook for Hybrid Microelectronics. Teledyne Microelectronics, Los Angeles, California.
24. Masters C.B., and Salamon N.J. Geometrically nonlinear stress-deflection relations for thin film/substrate systems. Int. J. Eng. Sci. 31 (1993) 915-925
25. Masters C.B., and Salamon N.J. Geometrically nonlinear stress-deflection relations for thin film/substrate systems with a finite element comparison. J. Appl. Mech. 61 (1994) 872-878
26. Ngo D., Huang Y., Rosakis A.J., and Feng X. Spatially nonuniform, isotropic misfit strain in thin films bonded on plate substrates: the relation between nonuniform film stresses and system curvatures. Thin Solid Films 515 (2006) 2220-2229
27. Ngo D., Feng X., Huang Y., Rosakis A.J., and Brown M.A. 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 (2007) 1745-1754
28. Pajot J., Maute K., Zhang Y., and Dunn M.L. Design of patterned multilayer films with eigenstrains by topology optimization. Int. J. Solids Struct. 43 (2006) 1832-1853
29. Park T.S., and Suresh S. Effects of line and passivation geometry on curvature evolution during processing and thermal cycling in copper interconnect lines. Acta Mater. 48 (2000) 3169-3175
30. Park T.S., Suresh S., Rosakis A.J., and Ryu J. Measurement of full-field curvature and geometrical instability of thin film-substrate systems through CGS interferometry. J. Mech. Phys. Solids 51 (2003) 2191-2211
31. Sharpe W.N. Mechanical properties of MEMS materials. In: Gad-el-Hak M. (Ed). A chapter in the MEMS Handbook (2002), CRC Press, Boca Raton, FL
32. Shen Y.L., Suresh S., and Blech I.A. Stress, curvatures, and shape changes arising from patterned lines on silicon wafers. J. Appl. Phys. 80 (1996) 1388-1398
33. Shen Y.L. Local Joule heating and overall resistance increase in void-containing aluminum interconnects. J. Electron. Mater. 30 (2001) 367-371
34. Wikstrom A., Gudmundson P., and Suresh S. Thermoelastic analysis of periodic thin lines deposited on a substrate. J. Mech. Phys. Solids 47 (1999) 1113-1130
35. Wikstrom A., Gudmundson P., and Suresh S. Analysis of average thermal stresses in passivated metal interconnects. J. Appl. Phys. 86 (1999) 6088-6095
36. Wikstrom A., and Gudmundson P. Stresses in passivated lines from curvature measurements. Acta Mater. 48 (2000) 2429-2434
37. Yeo I.S., Ho P.S., and Anderson S.G.H. Characterization of thermal stresses in Al(Cu) fine lines. I. Unpassivated line structures. J. Appl. Phys. 78 (1995) 945-952
38. Yeo I.S., Ho P.S., and Anderson S.G.H. Characterization of thermal stresses in Al(Cu) fine lines. II. Passivated line structures. J. Appl. Phys. 78 (1995) 953-961
39. Zhang Y., and Dunn M.L. Deformation of multilayer thin film microstructures during post-release cyclic thermal loading: implications for MEMS design, packaging, and reliability. J. Microelectromech. Syst. 12 (2003) 788-796
40. Zhang Y., and Dunn M.L. Geometric and material nonlinearity during the deformation of micron-scale thin-film bilayers subject to thermal loading. J. Mech. Phys. Solids 52 (2004) 2101-2126