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Research Papers

Effect of Microstructure on Electromigration-Induced Stress

[+] Author and Article Information
Antoinette M. Maniatty

Professor
Fellow ASME
Department of Mechanical,
Aerospace, and Nuclear Engineering,
Rensselaer Polytechnic Institute,
110 8th Street,
Troy, NY 12180
e-mail: maniaa@rpi.edu

Jiamin Ni

Department of Mechanical, Aerospace,
and Nuclear Engineering,
Rensselaer Polytechnic Institute,
110 8th Street,
Troy, NY 12180
e-mail: nij4@rpi.edu

Yong Liu

Distinguished Member of Technical Staff
Fairchild Semiconductor,
82 Running Hill Road,
South Portland, ME 04106
e-mail: yong.liu@fairchildsemi.com

Hongqing Zhang

Semiconductor Packaging Analysis,
IBM Microelectronics,
2070 Route 52,
Hopewell Junction, NY 12533
e-mail: zhangh@us.ibm.com

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received July 20, 2015; final manuscript received October 15, 2015; published online November 9, 2015. Assoc. Editor: Harold S. Park.

J. Appl. Mech 83(1), 011010 (Nov 09, 2015) (9 pages) Paper No: JAM-15-1376; doi: 10.1115/1.4031837 History: Received July 20, 2015; Revised October 15, 2015

In this paper, a finite element based simulation approach for predicting the effect of microstructure on the stresses resulting from electromigration-induced diffusion is described. The electromigration and stress-driven diffusion equation is solved coupled to the mechanical equilibrium and elastic constitutive equation, where a diffusional inelastic strain is introduced. Here, the focus is on the steady state, infinite life case, when the current-driven diffusion is balanced by the resulting stress gradient. The effect of the crystal orientation in Sn-based solder joints on the limiting current density for an infinite life is investigated and compared to experimental observations in the literature. The effect of the grain structure for Al interconnect lines on the dominant diffusion path and estimates for the effective charge number for two different diffusion paths in Al interconnects determined by matching simulations to experimental measurements of elastic strain components in the literature are also presented.

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References

Figures

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Fig. 1

Cross-sectional diagrams of Al interconnect lines from the experiments by (a) Wang et al. [8] and (b) Zhang et al. [9]

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Fig. 2

Comparison of the measured normal elastic strain ε33e as a function of distance from the cathode end, normalized by the line length L, for Al conductor lines in Wang et al. [8] and Zhang et al. [9]

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Fig. 3

(a) Cu–solder–Cu structure as in Ref. [37] and (b) model mesh

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Fig. 4

The predicted Blech limit, threshold value of jL for which the solder is predicted to have an infinite life, as a function of the angle that the crystal c-axis deviates from the direction of the applied electric field, i.e., the x3-axis

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Fig. 5

(a) Linear fit to the data in Wang et al. [8] used to define the measured elastic strain ε33e(m) to match using the algorithm in Sec. 3.2 and (b) resulting electromigration dilatational strain γ assuming grain boundary diffusion

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Fig. 6

Fit to the data in Zhang et al. [9] used to define the measured elastic strain ε33e(m) to match using the algorithm in Sec. 3.2

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Fig. 7

Comparison of the measured and computed deviatoric elastic strain components for two different sets of values for a1, a2, and a3 associated with different diffusion paths: (a) ε22e′ and (b) ε33e′

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