Thermal Stress and Reliability Analysis of TSV-Based 3-D ICs With a Novel Adaptive Strategy Finite Element Method

Thermomechanical stress is one of the most important issues in performance and reliability analysis of through silicon via-based 3-D integrated circuits (3-D ICs), where an accurate numerical approach is generally needed to produce stress models and identify weak points in the structure. In this paper, we propose a knowledge-oriented nonuniform (KONU) refinement strategy for 3-D IC stress simulation under the framework of a parallel adaptive finite element method (FEM), and apply it in 3-D IC stress and reliability analysis. Parallel adaptive FEM is promising for solving large-scale problems due to its high accuracy and parallel efficiency. It produces refined meshes based on the a posteriori error analysis, which has the quasi-optimal convergence rate for solving the problem. It has high parallel efficiency, which makes it suitable for handling large and complex structures in 3-D ICs. The KONU refinement strategy developed in this paper can efficiently reduce the number of refinement iterations in parallel adaptive FEM for 3-D IC thermomechanical stress simulation and improves the computational efficiency. It is demonstrated in this paper through several examples that parallel adaptive FEM for thermomechanical stress evaluation can be widely applied in 3-D IC reliability analysis, where accurate stress simulation and modeling is exceptionally important to produce accurate results.