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]
An Analytical Model for Time-Dependent Shearing Deformation in Area-Array Interconnects
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.
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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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