Efficient High-Fidelity Warpage Modeling for Advanced Packaging Analysis

The mismatch in thermal expansion coefficients among different materials leads to nonuniform deformation in a package, known as warpage. The warpage has become a significant reliability issue in advanced packaging that requires careful management. To address the issue, we have developed a high-fidelity warpage modeling approach that contains preprocessing followed by matrix calculations. This method transforms a three-dimensional packaging structure into a two-dimensional thermo-mechanical coupling problem, simplifying the packaging analysis. We apply finite element methods to the model and obtain the balance between accuracy and efficiency. Experimental results show that our model offers superior accuracy compared to the widely used Suhir’s model, achieving average speedups of 11.0X in preprocessing and 12130X in matrix calculations, with an overall speedup of 233.9X and only 1.0% error compared to the Ansys commercial analysis tool. This high efficiency and accuracy make our model suitable for large-scale optimization, package simulation, and modeling applications.