Modeling the Influence of Grains and Material Interfaces on Electromigration

We present an efficient approach to properly treat grain boundaries and material interfaces when modeling electromigration in copper nano-interconnects. Our approach uses several spatial material parameters to identify the locations of the grain boundaries and material interfaces during simulation, thereby not requiring the definition of multiple materials or complex meshes and geometrical interfaces. Using this method even very coarse meshes, with a grid spacing twice the size of the thinnest element (the grain boundary thickness), were able to reasonably reproduce the vacancy concentration of thin copper interconnects, including the microstructure. However, using a grid spacing greater than one half the grain boundary thickness resulted in underestimates of the induced stress.