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

Document Type




Format of Original

6 p.

Publication Date



American Society of Mechanical Engineers

Source Publication

Journal of Electronic Packaging

Source ISSN


Original Item ID

doi: 10.1115/1.1289631


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 ‘‘fullcreep 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.


Journal of Electronic Packaging, Vol. 122, No. 4 (December 2000): 328-334. DOI.