An analytical model is developed for predicting the time-dependent shearing displacement in area-array solder interconnects due to global CTE mismatch under thermal cycling. As a first step toward incorporating the creep deformation of the solder, the material is modeled as viscoelastic and temperature-independent. This permits one to invoke the correspondence principle of viscoelasticity to map the authors’ previously derived, closed-form solution for an elastic nonprismatic (concave, convex, or cylindrical) Timoshenko beam under shear loading into the associated viscoelastic solution. This leads to general analytical results for the frequency-dependent shear displacement amplitude in the critical joint. The results are expressed conveniently in terms of a “full-creep correction factor” and a “frequency correction factor,” which explicitly show the effects of the following parameters on the joint deformation: joint shape; array population; array, component, and substrate dimensions; viscoelastic material properties of the interconnect material; elastic properties of the component and substrate materials; and loading frequency. To demonstrate the technique for a particular viscoelastic constitutive law, the solder is assumed to behave elastically under hydrostatic loads and as a viscoelastic Kelvin solid under deviatoric conditions. For this special case the creep portion of the deformation is shown to be dependent upon only two dimensionless parameters: a dimensionless loading frequency and a material- and shape-dependent joint parameter. The results of the study may be useful in identifying design and process modifications that may improve the thermal fatigue life of area arrays. [S1043-7398(00)00404-7]
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e-mail: stephen.heinrich@marquette.edu
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December 2000
Technical Papers
An Analytical Model for Time-Dependent Shearing Deformation in Area-Array Interconnects
S. M. Heinrich,
e-mail: stephen.heinrich@marquette.edu
S. M. Heinrich
Department of Civil and Environmental Engineering, Marquette University, P.O. Box 1881, Milwaukee, WI 53201-1881
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S. Shakya,
S. Shakya
Department of Civil and Environmental Engineering, Marquette University, P.O. Box 1881, Milwaukee, WI 53201-1881
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J. Liang,
J. Liang
EMC Corporation, Hopkinton, MA 01748
11
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P. S. Lee
P. S. Lee
Rockwell Automation, 1201 S. Second Street, Milwaukee, WI 53204
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S. M. Heinrich
Department of Civil and Environmental Engineering, Marquette University, P.O. Box 1881, Milwaukee, WI 53201-1881
e-mail: stephen.heinrich@marquette.edu
S. Shakya
Department of Civil and Environmental Engineering, Marquette University, P.O. Box 1881, Milwaukee, WI 53201-1881
J. Liang
11
EMC Corporation, Hopkinton, MA 01748
P. S. Lee
Rockwell Automation, 1201 S. Second Street, Milwaukee, WI 53204
Contributed by the Electrical and Electronic Packaging Division for publication in the JOURNAL OF ELECTRONIC PACKAGING. Manuscript received by the EEPD August, 1999; revised manuscript received January 28, 2000. Associate Technical Editor: M. Shiratori.
J. Electron. Packag. Dec 2000, 122(4): 328-334 (7 pages)
Published Online: January 28, 2000
Article history
Received:
August 1, 1999
Revised:
January 28, 2000
Citation
Heinrich, S. M., Shakya, S., Liang, J., and Lee, P. S. (January 28, 2000). "An Analytical Model for Time-Dependent Shearing Deformation in Area-Array Interconnects ." ASME. J. Electron. Packag. December 2000; 122(4): 328–334. https://doi.org/10.1115/1.1289631
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