Transient heat conduction analysis of electronic packages by coupled boundary and finite element methods

Electronic packages experience large temperature excursions during their fabrication and under operational conditions. Inherent to electronic packages are the presence of geometric and material discontinuities. The regions where adhesive bond lines intersect with convective heat loss surfaces are the most critical locations for failure initiation due to heat flux singuhuities and extreme thermo-mechanical stresses. Thus, accurate calculation of the flux field, as well as the temperature field, is essential in transient thennomechanical stress anillysis. Although the finite element method (FEM) is highly efficient and commonly used, its application with conventional elements suffers fiom poor accuracy in the predicrion of the flux field in these regions. The accuracy of the results fiom the boundary element method (BEM) formulation, which requires computationally intensive time-integrabon schemes, is much higher than that of the FEM. However, in this study, a novel boundary element-finite element coupling algorithm is developed to investigate transient thermal response of electronic packages consisting of dissimilar materials. The new algorithm combines the advantages of both methods while not requiring any iterations along the interfaces between BEM and FEM domains. The BEM pafi of the solution captures the singular nature of the flux field arising from geometric and material discontinuities and also provides accurate solutions in a region described by smaller length scales, such as the dieattach or the solder ball, than those of the other components. This type of coupled formulation avoids the fine discretization required by FEM to achieve accurate results in regions with small length scales and geometric and material discontinuities. The capabilities of this new approach are demonstrated by considering two typical electronic packages. One is composed of (3 chip attached to a substrate with an adhesive and the other is representative of BGA technology. Both are subjected to natural cooling from a uniform temperature. The boundary conditions along the interfaces between BEM and FBM domains are matched by satisfying temperature continuity and energy balance. The present algorithm combines the efficiency of FEM and accuracy of BEM and provides a robust method for the solution of timedependent heat conduction problems involving dissimilar materials.