Efficient High-Fidelity Two-Dimensional Warpage Modeling for Advanced Packaging Analysis

The mismatch of thermal expansion coefficients between different materials incurs nonuniform deformation in a package called warpage. The warpage effect has evolved into a crucial reliability concern that demands careful management in advanced packaging. Considering the severe impact of the effect, we develop an efficient, high-fidelity warpage modeling of preprocessing followed by matrix calculation to address the issue by transforming a three-dimensional packaging structure to a two-dimensional thermo-solid coupling problem. The transformation provides an efficient measure to reduce the complexity of the packaging analysis. We then apply formal numerical methods to this model for a better trade-off between accuracy and efficiency. Experimental results show that our model averagely achieves respective speedups of 11.0X and 12130X in preprocessing and matrix calculation and an overall speedup of 233.9X with only 1.0% error over the Ansys commercial analysis tool. In particular, such high efficiency and accuracy enable our model for large-scale optimization, simulation, and modeling applications.