0
TECHNICAL PAPERS

Effect of Nonlinear Elastic Behavior on Bilayer Decohesion of Thin Metal Films From Nonmetal Substrates

[+] Author and Article Information
S. P. Baker

Department of Materials Science and Engineering, Cornell University, Bard Hall, Ithaca, NY 14853 e-mail: shefford.baker@cornell.edu

X. Wang

Alventive, Inc., Galeria Parkway, Suite 400, Atlanta, GA 30339e-mail: xwang@alventive.com

C.-Y. Hui

Department of Theoretical and Applied Mechanics, Cornell University, Kimball Hall, Ithaca, NY 14853e-mail: ch45@cornell.edu

J. Appl. Mech 69(4), 407-414 (Jun 20, 2002) (8 pages) doi:10.1115/1.1468998 History: Received March 15, 2001; Revised December 15, 2001; Online June 20, 2002
Copyright © 2002 by ASME
Your Session has timed out. Please sign back in to continue.

References

Hu,  M. S., Thouless,  M. D., and Evans,  A. G., 1988, “The Decohesion of Thin Films From Brittle Substrates,” Acta Metall., 36, pp. 1301–1307.
Drory,  M. D., Thouless,  M. D., and Evans,  A. G., 1988, “On the Decohesion of Residually Stressed Thin Films,” Acta Metall., 36, pp. 2019–2028.
Suo,  Z., and Hutchinson,  J. W., 1989, “Steady-State Cracking in Brittle Substrates Beneath Adherent Films,” Int. J. Solids Struct., 25, pp. 1337–1353.
Evans,  A. G., and Dalgleish,  B. J., 1992, “The Fracture Resistance of Metal-Ceramic Interfaces,” Acta Metall. Mater., 40, pp. S295–S305.
Bagchi,  A., Lucas,  G. E., Suo,  Z., and Evans,  A. G., 1994, “A New Procedure for Measuring the Decohesion Energy for Thin Ductile Films on Substrates,” J. Mater. Res., 9, pp. 1734–1741.
Kriese,  M. D., Gerberich,  W. W., and Moody,  N. R., 1999, “Quantitative Adhesion Measures of Multilayer Films: Part II. Indentation of W/Cu, W/W, Cr/W,” J. Mater. Res., 14, pp. 3019–3026.
Lane,  M., and Dauskardt,  R. H., 2000, “Adhesion and Reliability of Copper Interconnects With Ta and TaN Barrier Layers,” J. Mater. Res., 15, pp. 203–211.
Baker, S. P., Keller, R.-M., and Arzt, E., 1998, “Energy Storage and Recovery in Thin Metal Films on Substrates,” Proceedings, Thin Films: Stresses and Mechanical Properties VII, R. C. Cammarata et al. eds., Materials Research Society, Warrendale PA, pp. 605–610.
Shu, J., Clyburn, S., Mates, T., and Baker, S. P., 1999, “Effects of Thickness and Oxygen Content on Thermomechanical Behavior of Thin Cu Gilms Passivated With AlN,” Proceedings, Materials Reliability in Microelectronics IX, D. D. Brown, et al., eds., Materials Research Society, Pittsburgh, PA, pp. 707–712.
Keller,  R.-M., Baker,  S. P., and Arzt,  E., 1998, “Quantitative Analysis of Strengthening Mechanisms in Thin Cu films: Effects of Film Thickness, Grain Size and Passivation,” J. Mater. Res., 13, pp. 1307–1317.
Wang, X., 2000, “Bilayer Modeling and Measurements of Adhesion of Copper Thin Films to Glass,” M.S. thesis, Cornell University, Ithaca, NY.

Figures

Grahic Jump Location
Thermomechanical behavior of a 1-μm thick Cu film encapsulated between Si3N4 layers on a Si substrate (10). The solid line indicates the expected thermoelastic behavior of the film. The data deviate upward from the thermoelastic line beginning at about 150°C during initial heating indicating the onset of compressive plastic yielding although the film is still in tension. This nonlinear unloading behavior is included in the subsequent decohesion modeling.
Grahic Jump Location
Schematic of the bilayer adhesion problem. (a) The strain energy release rate can be obtained by comparing the strain energy in the film far ahead of and far behind the decohesion crack front. (b) Far ahead of the crack, the strain energy is just that arising from the initial stresses in the two layers. We then imagine (c) releasing the films from the substrate and (d) applying edge forces S and moments M to ensure that the two layers have the same length and curvature along the interface. When these two conditions are met, the layers can be joined, and have the configuration of the bilayer behind the crack. The strain energy can be calculated from S and M and the properties of the layers.
Grahic Jump Location
The linearization of the Cu film unloading problem is accomplished by approximating substrate curvature σ–T data with straight lines during heating
Grahic Jump Location
The σ–ε behavior corresponding to the approximation of the σ–T data in Fig. 3 along the path ABCDE obtained using the temperature-dependent thermal expansion coefficients of Cu and Si 11
Grahic Jump Location
Schematic of the bilayer decohesion problem when layer 2 is the driver and layer 1 is the target. For this configuration, Eqs. (123456789101112131415161718) still hold and the solution can still be used. Only the range of validity of the solutions (Sections 2.1.3 and 2.2) changes.
Grahic Jump Location
Normalized strain energy release rates G (lower surface) and G* (upper surface) as defined in Eq. (21) for linear and nonlinear bilayers, respectively, with σ1o=1280,σ2o=400, and σ2*=150 as a function of the stiffness ratios ω (Eq. 7(b)) and ω* (Eq. 14(b)) at a thickness ratio of δ=1 (Eq 7(a)). The bilayer curves up as shown in Fig. 2. As ω→0,G→0 and G*→constant.G* increases with increasing ω*.
Grahic Jump Location
Fractional difference in strain energy release rate, F (Eq. (22)), as a function of the elastic stiffness ratios ω and ω* corresponding to the data shown in Fig. 6(δ=1). The difference is zero along the line ω=ω* and increases rapidly as ω decreases and ω* increases. The point marked with a cross indicates the stiffness ratios for the case of a Cr/Cu bilayer. The strain energy release rate is about 5% higher for nonlinear than for linear unloading (branches BH and BF, respectively, in Fig 4) at this point. Note that the scale and perspective are different from Fig. 6.
Grahic Jump Location
Normalized strain energy release rates G (lower surface) and G* (upper surface) as defined in Eq. (21) for linear and nonlinear bilayers, respectively, with σ1o=1280,σ2o=400, and σ2*=150 as a function of the stiffness ratio ω* (Eq. (14b)) and the thickness ratio δ (Eq. (7a)) for ω=1 (Eq. (7b)). The bilayer curves up as shown in Fig. 2. Both G and G* go to zero as δ goes to zero and increase as δ increases.
Grahic Jump Location
Fractional difference in strain energy release rate, F (Eq. (22)), as a function of the elastic stiffness ratio ω* and the thickness ratio δ corresponding to the data shown in Fig. 8(ω=1). The difference is zero along the line log(ω*)=0 and increases as ω* increases. F increases as δ increases and the upper linear layer dominates. As δ decreases, F approaches a constant that depends on ω*. The dark line indicates the stiffness ratios for the case of a Cr/Cu bilayer. The difference in strain energy release rate reaches a maximum of about 24% at about log(δ)=−1.2. Note that the scale and perspective are different from Fig. 8.
Grahic Jump Location
Normalized strain energy release rates G (lower surface) and G* (upper surface) as defined in Eq. (21) for linear and nonlinear bilayers, respectively, with σ1o=0,σ2o=400, and σ2*=150 as a function of the stiffness ratios ω (Eq. (7b)) and ω* (Eq. (14b)) at a thickness ratio of δ=1 (Eq. (7a)). The bilayer curves down as shown in Fig. 5. As ω→0,G→0 and G*→constant.G* increases with increasing ω*.
Grahic Jump Location
Fractional difference in strain energy release rate, F (Eq. (22)), as a function of the elastic stiffness ratios ω and ω* corresponding to the data shown in Fig. 10(δ=1). The difference increases rapidly as ω decreases and ω* increases. The point marked with a cross indicates the stiffness ratios for the case of a Cu/glass bilayer. The strain energy release rate is about 15% higher for nonlinear than for linear unloading (branches BH and BF, respectively, in Fig 4) at this point. Note that the scale and perspective are different from Fig. 10.
Grahic Jump Location
Normalized strain energy release rates G (lower surface) and G* (upper surface) as defined in Eq. (21) for linear and nonlinear bilayers, respectively, with σ1o=0,σ2o=400, and σ2*=150 as a function of the stiffness ratio ω* (Eq. (14b)) and the thickness ratio δ (Eq. (7a)) for ω=0.3 (Eq. (7b)). The bilayer curves down as shown in Fig. 5. Both G and G* go to zero as δ goes to zero and increase as δ increases.
Grahic Jump Location
Fractional difference in strain energy release rate, F (Eq. (22)), as a function of the elastic stiffness ratio ω* and the thickness ratio δ corresponding to the data shown in Fig. 12(ω=0.3). The difference is zero along the line log(ω*)=0 and increases as ω* increases. F increases as δ increases and the upper linear layer dominates. As δ decreases, F approaches a constant that depends on ω*. The dark line indicates the stiffness ratios for the case of a Cu/glass bilayer. The difference in strain energy release rate reaches a maximum of about 17% as δ→0. Note that the scale and perspective are different from Fig. 12.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In