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

Abstract

An improved time-dependent analytical model is developed for predicting the maximum shearing displacement in an area-array electronic assembly under global thermal mismatch loading. The thermal loads are assumed to be uniform within the component and substrate, with both step-function and sinusoidal temperature histories being considered. The time-dependent effects in the array’s shear deformation are introduced in an approximate manner by modeling the interconnect material (solder) as a temperature-independent linear viscoelastic material. The viscoelastic constitutive law used for the solder is that of a three-parameter viscoelastic standard solid in distortion and an elastic solid in the hydrostatic mode. In the authors’ previous work the steady-state shear force in the joints was assumed to vary sinusoidally with a frequency-independent amplitude. This assumption has been relaxed in the present study, leading to improved accuracy. All results have been derived as closed-form correction factors to be applied to the easily calculated unconstrained shear displacement to obtain the maximum shear displacement. All the correction factors depend on prescribed geometric and material parameters of the component, substrate, and joints. The results have been presented in the form of dimensionless plots to aid in the analysis or design process, thereby providing convenient alternatives or supplements to time-consuming and expensive finite element analyses of entire assemblies.