Multiscale simulations of copper electrodeposition onto a resistive substrate

Abstract

During the initial stages of copper electrodeposition onto a thin seed layer, a nonuniform potential distribution arises, resulting in local variations in growth rate and deposit morphology. Early stages of morphology evolution during copper electrodeposition are of practical importance but have not been well studied. Here, a new multiscale approach is developed for numerical simulation of the effect of a macroscopic potential distribution along a seed layer on microscopic local roughness evolution. The key contribution is a generic method for coupling multiple computer codes, and the demonstration of its use. The macroscopic code passes the local potential at ten points along the seed layer to ten kinetic Monte Carlo codes, each of which simulates additive-free copper electrodeposition and roughness evolution on an initially flat surface. Periodically, each Monte Carlo code computes the local film thickness and passes it back to the resistance code, which updates the potential distribution for the next iteration. Results are obtained for a wide range of parameter space including both constant-potential and constant-current operation. A confirmation procedure was developed to verify that the multiscale approach (using small Monte Carlo simulation domains with periodic boundary conditions) does not significantly alter the physical accuracy of the simulations.