Analytical Approach for Preliminary Deformation Investigation

The objective of this study is to compare the results from experiment and modeling on simplified models with those from analytical solution. The target is to understand if simple analytical models or tools can be used for fast indication and preliminary evaluation of material behavior. Simple samples and respective models will be built and evaluated for warpage at temperatures of interest, namely room temperature and reflow temperature. Following this an analytical approach using Timoshenko beam formula will be evaluated and results compared with the experimental and modeling results. Finally, it will be decided if and how a simplified tool can be developed for fast and preliminary results for material comparison basis as a means of eliminating material that will not reach the desired performance prior to building more elaborate models or samples. The analysis focuses on bi-material structures for the time being and hence is more suited as a rough estimate for frame based packages, though an example for a Ball Grid Array (BGA) package is also presented. The assumptions and limitations of this methodology will be outlined. Keywords—packaging, thermo-mechanical modeling, Timoshenko equation, warpage, finite element analysis (FEA), package design, analytics (key words)