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

TL;DR

This paper introduces a practical finite element method, CEM, for simulating dynamic crack growth in interconnect structures, combining element-splitting with ES-FEM to improve accuracy and efficiency.

Contribution

The paper develops the Crack Element Method (CEM), integrating element-splitting and ES-FEM, to accurately simulate dynamic crack propagation in complex interconnect structures.

Findings

CEM accurately predicts crack growth in benchmark tests.

The method reduces poorly shaped elements, improving numerical stability.

CEM effectively models crack behavior in Cu/Ultra Low-k interconnects.

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.