Effect of Component Heterogeneity on Global CTE Mismatch Displacement in Areal-Array Solder Interconnects

An analytical model is developed for the problem of a thermally loaded electronic assembly consisting of a nonhomogeneous component attached to a substrate by means of an areal array of solder joints. The component is heterogeneous in the sense that the interior, or “die”, portion and the exterior, or “carrier”, portion may have different elastic moduli, different coefficients of thermal expansion, and/or different temperature excursions. Analytical results are presented for determining (a) the location of the critical joint(s) in the array, defined as those experiencing the maximum shearing displacement due to global CTE mismatch, and (b) the magnitude of the maximum shearing displacement. The critical joint location and the (dimensionless) peak displacement are shown to depend on only two parameters: one involving the material, geometric, and loading characteristics of the component and substrate, the other being the ratio of the die dimension to the array dimension. The stiffness of the solder array is neglected in the model; thus, the results should be valid for (a) thermal/power cycling of low-modulus solders (relative to component and substrate materials), and (b) high-temperature, low-frequency thermal/power cycling, for which a large degree of stress relaxation occurs in the solder. The results may also provide conservative estimates for situations involving stiffer arrays.