Multi-layer thin films/substrate system subjected to non-uniform misfit strains

International Journal of Solids and Structures

Volumn 45, Issue 13, 2008, Pages 3688-3698

  Feng, X ^a   Huang, Y ^b   Rosakis, A J ^c  

^a TSINGHUA UNIVERSITY   (China)

^b NORTHWESTERN UNIVERSITY   (United States)

^c CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

Author keywords

Interfacial shears; Multi layer thin films; Non local stress curvature relations; Non uniform misfit strain; Non uniform wafer curvatures

Indexed keywords

DEPOSITION; STRAIN MEASUREMENT; SUBSTRATES;

INTERFACIAL SHEARS; MULTI-LAYER THIN FILMS; NON-UNIFORM WAFER CURVATURES;

MULTILAYERS;

EID: 42649136246     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2007.09.012     Document Type: Article

References (19)

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 non-local stress-curvature relations. Int. J. Solids Struct. 44 (2007) 1755-1767
2. Feng X., Huang Y., Jiang H., Ngo D., and Rosakis A.J. 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 (2006) 1041-1054
3. Finot M., Blech I.A., Suresh S., and Fijimoto H. Large deformation and geometric instability of substrates with thin-film deposits. J. Appl. Phys. 81 (1997) 3457-3464
4. Freund L.B. Substrate curvature due to thin film mismatch strain in the nonlinear deformation range. J. Mech. Phys. Solids 48 (2000) 1159
5. Freund L.B., and Suresh S. Thin Film Materials; Stress, Defect Formation and Surface Evolution (2004), Cambridge University Press, Cambridge, UK
6. Huang Y., Ngo D., and Rosakis A.J. 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 Mech. Sin. 21 (2005) 362-370
7. Huang, Y., Rosakis, A.J., in press. Extension of Stoney's formula to arbitrary temperature distributions in thin film/substrate systems. J. Appl. Mech. (ASME Trans.).
8. Huang Y., and Rosakis A.J. Extension of Stoney's formula to non-uniform temperature distributions in thin film/substrate systems. The case of radial symmetry. J. Mech. Phys. Solids 53 (2005) 2483-2500
9. Lee H., Rosakis A.J., and Freund L.B. Full field optical measurement of curvatures in ultra-thin film/substrate systems in the range of geometrically nonlinear deformations. J. Appl. Phys. 89 (2001) 6116-6129
10. 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
11. Ngo D., Huang Y., Rosakis A.J., and Feng X. 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 (2006) 2220-2229
12. 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
13. 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
14. 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
15. Salamon N.J., and Masters C.B. Bifurcation in isotropic thin film/substrate plates. Int. J. Solids Struct. 32 (1995) 473-481
16. Shen Y.L., Suresh S., and Blech I.A. Stresses, curvatures, and shape changes arising from patterned lines on silicon wafers. J. Appl. Phys. 80 (1996) 1388-1398
17. Stoney G.G. The tension of metallic films deposited by electrolysis. Proc. R. Soc. Lond. A82 (1909) 172-175
18. 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
19. Wikstrom A., Gudmundson P., and Suresh S. Analysis of average thermal stresses in passivated metal interconnects. J. Appl. Phys. 86 (1999) 6088-6095