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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

Fiks, V. B. , 1959, “ On Mechanism of Mobility of Ions in Metals,” Sov. Phys. Solid State, 1, pp. 14–28.
Huntington, H. B. , and Grone, A. R. , 1961, “ Current-Induced Marker Motion in Gold Wires,” J. Phys. Chem. Solids, 20, pp. 76–87. [CrossRef]
Black, J. R. , 1969, “ Electromigration—A Brief Survey and Some Recent Results,” IEEE Trans. Electron. Dev., 16(4), pp. 338–347. [CrossRef]
Blech, I. A. , and Tai, K. L. , 1977, “ Measurement of Stress Gradients Generated by Electromigration,” Appl. Phys. Lett., 30(8), pp. 387–389. [CrossRef]
Blech, I. A. , 1976, “ Electromigration in Thin Aluminum Films on Titanium Nitride,” J. Appl. Phys., 47(4), pp. 1203–1208. [CrossRef]
Blech, I. A. , and Herring, C. , 1976, “ Stress Generation by Electromigration,” Appl. Phys. Lett., 29(3), pp. 131–133. [CrossRef]
Hau-Riege, S. P. , and Thompson, C. V. , 2000, “ The Effect of the Mechanical Properties of the Confinement Material on EM in Metallic Interconnects,” J. Mater. Res., 15(8), pp. 1797–1802. [CrossRef]
Wang, P.-C. , Cargill, G. S., III , Noyan, I. C. , and Hu, C.-K. , 1998, “ Electromigration-Induced Stress in Aluminum Conductor Lines Measured by X-Ray Microdiffraction,” Appl. Phys. Lett., 72(11), pp. 1296–1298. [CrossRef]
Zhang, H. , Cargill, G. S., III , Ge, Y. , Maniatty, A. M. , and Liu, W. , 2008, “ Strain Evolution in Al Conductor Lines During Electromigration,” J. Appl. Phys., 104(12), p. 123533. [CrossRef]
Tu, K. N. , 1994, “ Irreversible Processes of Spontaneous Whisker Growth in Bimetallic Cu–Sn Thin-Film Reactions,” Phys. Rev. B Condens. Matter, 49(3), pp. 2030–2034. [CrossRef] [PubMed]
Li, S. , and Basaran, C. , 2009, “ Effective Diffusivity of Lead Free Solder Alloys,” Comput. Mater. Sci., 47(1), pp. 71–78. [CrossRef]
Wang, Y. , Lu, K. H. , Gupta, V. , Stiborek, L. , Shirley, D. , Chae, S.-H. , Im, J. , and Ho, P. S. , 2012, “ Effects of Sn Grain Structure on the Electromigration of Sn–Ag Solder Joints,” J. Mater. Res., 27(08), pp. 1131–1141. [CrossRef]
Tasooji, A. , Lara, L. , and Lee, K. , 2014, “ Effect of Grain Boundary Misorientation on Electromigration in Lead-Free Solder Joints,” J. Electron. Mater., 43(12), pp. 4386–4394. [CrossRef]
Lee, K. , Kim, K.-S. , Tsukada, Y. , Suganuma, K. , Yamanaka, K. , Kuritani, S. , and Ueshima, M. , 2011, “ Influence of Crystallographic Orientation of Sn–Ag–Cu on Electromigration in Flip-Chip Joint,” Microelectron. Reliab., 51(12), pp. 2290–2297. [CrossRef]
Dyson, B. F. , Anthony, T. R. , and Turnbull, D. , 1967, “ Interstitial Diffusion of Copper in Tin,” J. Appl. Phys., 38(8), p. 3408. [CrossRef]
Wu, A. T. , and Hsieh, Y. C. , 2008, “ Electromigration-Induced Grain Rotation in Anisotropic Conducting Beta Tin,” Appl. Phys. Lett., 92(12), p. 121921. [CrossRef]
Lu, M. , Shih, D.-Y. , Lauro, P. , Goldsmith, C. , and Henderson, D. W. , 2008, “ Effect of Sn Grain Orientation on Electromigration Degradation Mechanism in High Sn-Based Pb-Free Solders,” Appl. Phys. Lett., 92(21), p. 211909. [CrossRef]
Korhonen, M. A. , Borgesen, P. , Tu, K. N. , and Li, C. Y. , 1993, “ Stress Evolution Due to Electromigration in Confined Metal Lines,” J. Appl. Phys., 73(8), pp. 3790–3799. [CrossRef]
Ye, H. , Basaran, C. , and Hopkins, D. , 2004, “ Deformation of Solder Joint Under Current Stressing and Numerical Simulation—I,” Int. J. Solids Struct., 41(18–19), pp. 4939–4958. [CrossRef]
Ye, H. , Basaran, C. , and Hopkins, D. , 2004, “ Deformation of Solder Joint Under Current Stressing and Numerical Simulation—II,” Int. J. Solids Struct., 41(18–19), pp. 4959–4973. [CrossRef]
Li, S. , Abdulhamid, M. F. , and Basaran, C. , 2009, “ Damage Mechanics of Low Temperature Electromigration and Thermomigration,” IEEE Trans. Adv. Packag., 32, pp. 478–485.
Singh, N. , Bower, A. F. , and Shankar, S. , 2010, “ A Three-Dimensional Model of Electromigration and Stress Induced Void Nucleation in Interconnect Structures,” Modell. Simul. Mater. Sci. Eng., 18(6), p. 065006. [CrossRef]
Liu, S. , and Liu, Y. , 2011, Modeling and Simulation for Packaging Assembly: Manufacturing, Reliability and Testing, Wiley, Singapore.
Hao, J. , Liu, Y. , Rioux, M. , and Zhang, A. L. L. , 2011, “ Electromigration Prediction and Test for 0.18 μm Power Technology in Wafer Level Reliability,” IEEE Electronic Components and Technology Conference (ECTC), Lake Buena Vista, FL, May 31–June 3, pp. 1934–1938.
Liu, Y. , Zhang, Y. , and Liang, L. , 2010, “ Prediction of Electromigration Induced Voids and Time to Failure or Solder Joint of a Wafer Level Chip Scale Package,” IEEE Trans. Comput. Packag. Technol., 33, pp. 544–552. [CrossRef]
Dandu, P. , Fan, X. J. , Liu, Y. , and Diao, C. , 2010, “ Finite Element Modelling on Electromigration of Solder Joints in Wafer Level Packaging,” Microelectron. Reliab., 50(4), pp. 547–555. [CrossRef]
Liu, Y. , Luk, T. , and Irving, S. , 2009, “ Parameter Modeling for Wafer Probe Test,” IEEE Electron. Packag. Manuf., 32, pp. 81–88. [CrossRef]
Liu, Y. , Liang, L. , Irving, S. , and Luk, T. , 2008, “ 3D Modeling of Electromigration Combined With Thermal–Mechanical Effect for IC Device and Package,” Microelectron. Reliab., 48(6), pp. 811–824. [CrossRef]
Gleixner, R. J. , and Nix, W. D. , 1999, “ A Physically Based Model of Electromigration and Stress-Induced Void Formation in Microelectronic Interconnects,” J. Appl. Phys., 86(4), pp. 1932–1944. [CrossRef]
Povirk, G. L. , 1997, “ Numerical Simulations of Electromigration and Stress-Driven Diffusion in Polycrystalline Interconnects,” Mater. Res. Soc. Symp. Proc., 473, pp. 337–342. [CrossRef]
Bower, A. , and Freund, L. , 1993, “ Analysis of Stress-Induced Void Growth Mechanisms in Passivated Interconnect Lines,” J. Appl. Phys., 74(6), pp. 3855–3868. [CrossRef]
Bower, A. , and Craft, D. , 1998, “ Analysis of Failure Mechanisms in the Interconnect Lines of Microelectronic Circuits,” Fatigue Fract. Eng. Mater. Struct., 21, pp. 611–630. [CrossRef]
Buchovecky, E. , Jadhav, N. , Bower, A. F. , and Chason, E. , 2009, “ Finite Element Modeling of Stress Evolution in Sn Films Due to Growth of the Cu6Sn5 Intermetallic Compound,” J. Electron. Mater., 38(12), pp. 2676–2684. [CrossRef]
Wilkening, J. , Borucki, L. , and Sethian, J. A. , 2004, “ Analysis of Stress-Driven Grain Boundary Diffusion. Part II: Degeneracy,” SIAM J. Appl. Math., 64, pp. 1864–1886. [CrossRef]
Sarychev, M. E. , Zhitnikov, Y. V. , Borucki, L. , Liu, C.-L. , and Makhviladze, T. , 2000, “ A New, General Model for Mechanical Stress Evolution During Electromigration,” Thin Solid Films, 365(2), pp. 211–218. [CrossRef]
Maniatty, A. , Liu, Y. , Klaas, O. , and Shephard, M. , 2002, “ Higher Order Stabilized Finite Element Method for Hyperelastic Finite Deformation,” Comput. Methods Appl. Mech. Eng., 191, pp. 1491–1503. [CrossRef]
Lu, M. , Shih, D.-Y. , Lauro, P. , and Goldsmith, C. , 2009, “ Blech Effect in Pb-Free Flip Chip Solder Joint,” Appl. Phys. Lett., 94(1), p. 011912. [CrossRef]
Huntington, H. B. , 1975, “ Effect of Driving Forces on Atom Motion,” Thin Solid Films, 25(2), pp. 265–280. [CrossRef]
Puttlitz, K. J. , and Stalter, K. A. , 2004, Handbook of Lead-Free Solder Technology for Microelectronic Assemblies, Marcel Dekker, New York.
Rayne, J. A. , and Chandrasekhar, B. S. , 1960, “ Elastic Constants of β Tin From 4.2 K to 300 K,” Phys. Rev., 120(5), pp. 1658–1663. [CrossRef]
Zhou, B. , Bieler, T. R. , Lee, T.-K. , and Liu, K.-C. , 2009, “ Methodology for Analyzing Slip Behavior in Ball Grid Array Lead-Free Solder Joints After Simple Shear,” J. Electron. Mater., 38(12), pp. 2702–2711. [CrossRef]
Vellinga, W. P. , Martin, M. A. , and Geers, M. G. D. , 2006, “ Microstructure Evolution in a Pb-Free Solder Alloy During Mechanical Fatigue,” Mater. Sci. Eng. A, 431(1–2), pp. 166–174.

Figures

Grahic Jump Location
Fig. 1

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

Grahic Jump Location
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]

Grahic Jump Location
Fig. 3

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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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

Grahic Jump Location
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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