The paper addresses grain growth in copper interconnects in the presence of thermal expansion mismatch stresses. The evolution of grain structure and texture in copper in the simultaneous presence of two driving forces, curvature and elastic stored energy difference, is modeled by using a hybrid Potts model simulation approach. The elastic stored energy is calculated by using the commercial finite element code ABAQUS, where the effect of elastic anisotropy on the thermal mismatch stress and strain distribution within a polycrystalline grain structure is modeled through a user material (UMAT) interface. Parametric studies on the effect of trench width and the height of the overburden were carried out. The results show that the grain structure and texture evolution are significantly altered by the presence of elastic strain energy.
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Radhakrishnan, B., Sarma, G. Coupled Finite Element–Potts Model Simulations of Grain Growth in Copper Interconnects. MRS Online Proceedings Library 1156, 404 (2008). https://doi.org/10.1557/PROC-1156-D04-04