Coarse-Grained Kinetic Monte Carlo Simulation of Copper Electrodeposition with Additives

Abstract

A (2+1)D kinetic Monte Carlo (KMC) code was developed for coarse-grained as well as atomic-scale simulations that require detailed consideration of complex surface-reaction mechanisms associated with electrodeposition of copper in the presence of additives. The physical system chosen for simulation is similar to that used by the microelectronics industry to fabricate on-chip interconnects, where additives are used to tailor shape evolution. Although economically significant, such systems are often designed in an empirical manner that would be greatly enhanced by improved understanding of the additive mechanism gained through simulations. By comparing simulated results at atomic as well as coarse-grained scales with theoretical results obtained analytically for various limiting cases of behavior, the validity of the KMC code was tested. It was found that the surface roughness at a specified length scale can be accurately simulated by using a coarse-grained KMC code with lattice spacing of 1/10 or smaller than that of the specified length scale—a result that is particularly useful for comparing experimental data on surface roughness with numerical simulations. For second-order homogeneous surface reactions, it is shown that the KMC-simulated surface coverage approaches the analytical surface coverage as surface mixing is increased by increasing the surface diffusion rate. The results verified the numerical accuracy and the reduced computational cost of the coarse-grained KMC approach for simulating complex chemical and electrochemical mechanisms.