Transient two-dimensional thermal analysis of electronic packages by the boundary element method

The fabrication of electronic packages involves heating and then cooling from high processing temperatures. Because these devices consist of bonded materials with different thermal and mechanical properties, high thermomechanical stresses develop due to thermal and stiffness mismatches of bonded materials at regions with geometric and/or material discontinuities. These high stresses may result in crack initiations, leading to delaminations. Therefore, accurate temperature and flux distributions are critical when computing thermomechanical stresses, knowledge of which is essential for reliable designs. This study presents an analysis method based on the boundary element method (BEM) to investigate the transient thermal response of electronic packages consisting of dissimilar materials while subjected to general boundary conditions. In order to demonstrate its capability, a chip on a substrate configuration subject to convective cooling is considered. The boundary conditions across the interfaces between the chip and the adhesive and adhesive and substrate are matched through exact expressions. The results capture the singular flux field arising from the mismatch in the thermal conduction coefficients and geometric discontinuity. The comparison of the results with those obtained from finite element analysis shows that BEM is rather robust and efficient for this class of transient conduction analyses.