Thermally induced deformations in die-substrate assembly

The work focuses on the thermally induced deformations caused by the processing of Flip Chip Ball Grid Arrays (FCBGA). Analytical expressions for substrate displacements are derived based on the Plate Theory and Suhir's solution for stresses in tri-material assembly. The validity of the model is established by comparing the analytical solution to the numerical finite element results as well as to the experimental data. The benefits of the proposed model are twofold: 1) it provides a tool for fundamental understanding of the deformation process of interest, and 2) has a predictive capability. More specifically, an analysis is presented on the nature and degree of influence that different geometric and material parameters have on the substrate deflections, as well as a "Warpage Contour Plot", proposed as a tool for warpage prediction that can be easily utilized in the early stages of the design process