A Practical Finite Element Approach for Simulating Dynamic Crack Growth in Cu/Ultra Low-k Interconnect Structures

2025-07-31

AI Summary

Simulating dynamic crack propagation in Cu/ultra-low-k interconnect structures remains challenging due to severe mesh distortion and numerical instability in conventional methods. Method: This paper proposes an efficient numerical framework integrating the edge-based smoothed finite element method (ES-FEM) with the crack element method (CEM). An adaptive element-splitting strategy is introduced to precisely track crack paths while preserving mesh quality; additionally, a topology-adaptively updated dynamic fracture energy release rate model is formulated to enhance computational robustness and stability. Contribution/Results: The method demonstrates high accuracy and strong convergence across multiple benchmark problems in dynamic fracture mechanics. It is successfully applied to thermo-mechanically coupled crack evolution analysis of realistic Cu/ultra-low-k interconnects, significantly improving both engineering applicability and computational efficiency for brittle-dielectric fracture simulation in microelectronic packaging.

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• Machine Learning: Learning on the Edge & Model Compression

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Abstract

This work presents a practical finite element modeling strategy, the Crack Element Method (CEM), for simulating the dynamic crack propagation in two-dimensional structures. The method employs an element-splitting algorithm based on the Edge-based Smoothed Finite Element Method (ES-FEM) to capture the element-wise crack growth while reducing the formation of poorly shaped elements that can compromise numerical accuracy and computational performance. A fracture energy release rate formulation is also developed based on the evolving topology of the split elements. The proposed approach is validated through a series of classical benchmark problems, demonstrating its accuracy and robustness in addressing dynamic fracture scenarios. Finally, the applicability of the CEM is illustrated in a case study involving patterned Cu/Ultra Low-k interconnect structures.

Problem

• Simulate dynamic crack growth in Cu/Ultra Low-k interconnects
• Improve numerical accuracy in crack propagation modeling
• Validate method for dynamic fracture scenarios

Innovation

• Crack Element Method for dynamic crack growth
• Edge-based Smoothed Finite Element algorithm
• Fracture energy release rate formulation