An Analytical Model for Time-Dependent Shearing Deformation in Area-Array Interconnects
Author:
Heinrich S. M.1, Shakya S.1, Liang J.2, Lee P. S.3
Affiliation:
1. Department of Civil and Environmental Engineering, Marquette University, P.O. Box 1881, Milwaukee, WI 53201-1881 2. EMC Corporation, Hopkinton, MA 01748 3. Rockwell Automation, 1201 S. Second Street, Milwaukee, WI 53204
Abstract
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]
Publisher
ASME International
Subject
Electrical and Electronic Engineering,Computer Science Applications,Mechanics of Materials,Electronic, Optical and Magnetic Materials
Reference24 articles.
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