Two-Dimensional Thermal-Induced Warpage Prediction for Multi-Chiplet Heterogeneous Integration System in Advanced Packaging

Thermal-induced warpage is a bottleneck problem in advanced packaging technology. In this paper, a new way of predicting the warpage deformation is proposed for multi-chiplet heterogeneous integration system, where the system deformations are considered as the combined actions of several asymmetric trimaterial assemblies based on the superposition principle. Firstly, an analytical model for an asymmetric tri-material assembly is derived by the beam theory. The rotation and rigid translation behaviors are investigated for the asymmetrical structures, which are determined by both the geometrical structures and the material properties. Secondly, the finite element method (FEM) is adopted to validate the analytical model and obtain the sample data. Then, the unknown parameters in the analytical model are extracted by the random forest algorithm (RF). Finally, a data-driven scale factor is introduced to modify the analytical model and improve its accuracy. The superposition warpage deformation of a heterogeneous integration system with 14 chiplets predicted by the present analytical model shows a good agreement with the FEM results with high efficiency. Therefore, the new thermal-induced warpage prediction method has a good potential of executing warpage analysis and package design of the multi-chiplet heterogeneous integration system in advanced packaging.