Effect of Additives on Shape Evolution during Electrodeposition: I. Multiscale Simulation with Dynamically Coupled Kinetic Monte Carlo and Moving-Boundry Finite-Volume Codes

Abstract

A multiscale simulation model was developed to simulate shape evolution during copper electrodeposition in the presence of additives. The model dynamically coupled a kinetic Monte Carlo (KMC) model (for surface chemistry and roughness evolution) with a finite volume (FV) model (for transport and chemical reactions in the electrolyte) and a level-set code (for tracking macroscopic movement of the metal/electrolyte interface). The KMC code was coarse-grained and used a multisite mesoparticle approach to account for the adsorption of large molecules. A multilevel grid approach was used to achieve numerical efficiency and accurate interface tracking. The model was demonstrated for an application involving in-fill of two-dimensional trenches by copper electrodeposition with additives [bis(3-sulfopropyl)disulfide], polyethylene glycol, chloride, and l-(2-hydroxyethyl)-2-imidazolidinethione. Demonstration calculations were carried out with use of initial estimates for the physicochemical parameters associated with a proposed reaction mechanism. The approach was found to be feasible for computing stable, dynamic behavior during macroscopic shape evolution over extended periods of time while simultaneously tracking microscopic roughness evolution associated with nearly molecular scale events at the surface. Numerical results include predictions of the surface concentration distributions as a function of time and distance for each reactant, product, and intermediate species associated with the proposed reaction mechanism.