| As the demand for faster electronic devices increases, the spacing between interconnect wiring lines within integrated circuits decreases. In this work, an algorithm which couples the level set method with the extended finite element method is presented, and the combined methods are used to investigate the effects of the proximity of multiple interconnect lines in integrated circuits on the growth of cracks due to fatigue from thermal cycling. The level set method is used to represent the crack and track crack growth. The extended finite element method is used to determine the rate of crack growth. The combined method requires no remeshing and allows cracks to pass arbitrarily through elements, while the discontinuities across the crack faces are handled by enrichment functions. It is shown that the level set method and the extended finite element method work well in conjunction, providing an efficient algorithm for crack growth in two dimensions. In addition, an extension of the level set algorithm into three dimensions is presented.; In the framework of a two-dimensional model where interconnect lines are represented by material inclusions, it is shown that the proximity of inclusions has a large effect on fatigue crack growth. Furthermore, crack paths are also affected by the configuration of initial cracks. Single cracks in the presence of two closely spaced inclusions tend to get very long. For certain initial configurations, two cracks emanating from each of two inclusions show a potential for connecting. The numerical investigation presented here indicates that if the spacing between interconnect lines decreases to a significant degree, the integrity of the integrated circuit will be compromised. |
