We study cracking from the interface of an In60-Pb40 solder joint on a brittle GaAs die when the joint is subjected to a uniform temperature change. Our primary objective is to apply and validate a fracture initiation criterion based on critical values of the stress intensities that arise from an analysis of the asymptotic elastic stress fields at the interface corner. In some regards the approach is similar to interface fracture mechanics; however, it differs in that it is based on a singular field other than that for a crack. We begin by determining the shape that the solder bump will assume after reflow when constrained by a fixed diameter wetting pad on the GaAs. To simplify the interpretation of the results, we focus on a class of solder bumps of various sizes, but with a self-similar shape. The approach, though, can be applied to different size and shape solder bumps. We then compute the asymptotic interface corner fields when the system is subjected to a uniform temperature change. The asymptotic structure (radial and angular dependence) of the elastic fields is computed analytically, and the corresponding stress intensities that describe the scaling of the elastic fields with geometry and loading are computed by axisymmetric finite element analysis. In order to assess the validity of fracture correlation using critical stress intensities, we designed and fabricated a series of test structures consisting of In60-Pb40 solder bumps on a GaAs chip. The test structures were subjected to uniform temperature drops from room temperature to induce cracking at the interface corner. From the tests we determined the relationship between the solder bump size and the temperature change at which cracking occurred. Not unexpectedly, smaller bumps required larger temperature changes to induce cracking. The observed scaling between solder bump size and temperature change is well described by the critical stress intensity failure criterion based on only a single parameter, the critical value of the mode 1 stress intensity, K1crn. Interestingly, this is because over a significant region, the mode 2 and constant terms in the asymptotic expansion cancel each other. This failure criterion provides the necessary machinery to construct failure maps in terms of geometry and thermomechanical loading. We conclude by describing how to apply the approach in more general and more practical settings that are possibly applicable to a wide range of problems in microelectronics, optoelectronics, and microelectromechanical systems packaging.
Boundary Integral Equations for an Anisotropic Bimaterial with Thermally Imperfect Interface and Internal Inhomogeneities