Atomistic Modeling of the Fracture Toughness of a Copper Composite with Parallel Carbon Nanotubes for Through Silicon Via Application

Recently, due to the need for a three-dimensional structure in the semiconductor industry, design using copper/carbon nanotube composites is being attempted. To contribute to the reliable design, tensile tests of copper/carbon nanotube composites with half-crack were performed using atomistic simulations that were easy to track the motion of atoms. The two parallel carbon nanotubes present in the composite were shorter than the substrate height, resulting in the nonelongation of the nanotubes during tensile tests. The tensile stress curves of the copper composites were analyzed with validation for failure strength and strain enhancement. Depending on the length of the carbon nanotubes, the failure mechanisms of the copper composites were different from rapid fracture to failure prevention. The fracture toughness of copper composites was measured using the Griffith criteria and the two-specimen method. In this study, a modified two-specimen method was proposed to elaborately measure the critical energy release rate near the carbon nanotubes. The thickness term in the two-specimen method equation was defined as a function through a modeling approach considering the circular shapes of the carbon nanotubes and holes in the composite. Crack growth resistance curves were obtained with critical energy release rate values through the modified two-specimen method. The average error rate of the critical energy release rate values through the modified two-specimen method was found to be reduced.