Transient two-dimensional 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 singularities and extreme thermo-mechanical stresses. Thus, accurate calculation of the flux field, as well as the temperature field, is essential in transient thermo-mechanical stress analysis. Although the finite element method (FEM) is highly efficient and commonly used, its application with conventional elements suffers from poor accuracy in the prediction of the flux field in these regions. The accuracy of the results from the boundary element method (BEM) formulation, which requires computationally intensive time-integratian 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 responses 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. 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 a chip attached to a substrate with an adhesive and the other is representative of BGA technology. Both are subjected to buoyancy-induced cooling from a uniform temperature.