Simulation of Kinetically Limited Nucleation and Growth at Monatomic Step Edges

Abstract

A kinetic Monte Carlo ͑KMC͒ numerical approach was used to investigate initial stages of kinetically controlled nucleation and growth on electrodes. Deposition, surface diffusion, nucleation, and growth were simulated for a pristine system consisting of metal ions in solution adjacent to a face-centered-cubic ͑fcc͒ surface that is initially configured with a series of parallel, monatomic step edges. Simulations were carried out with an atomic-scale, solid-on-solid KMC algorithm, in which the deposited atoms occupied the sites of a fcc lattice. One series of simulations was carried out for metal deposition onto a substrate of the same metal. The results were characterized according to a dimensionless quantity, ⌳, that represented the ratio of the rate of surface diffusion to the rate of deposition. It was found for large values of ⌳ that the deposit grew at the monatomic step edges, whereas for small values of ⌳ the step edges played no role in the nucleation of islands. A second series of simulations was carried out for deposition onto a foreign substrate. The growth modes associated with various combinations of system parameters was explored.Electrochemical deposition of metal in small-scale surface features, an established technology for on-chip interconnects used by semiconductor devices, may also be of growing importance for novel applications associated with nanotechnology. As the discovery of new molecular-scale structures moves toward technological applications, the ability to produce well-engineered products will depend on having precise quantitative understanding of the small-scale phenomena that affect the quality control of each step of the manufacturing processes. Therefore, interest arises in using stochastic methods to simulate electrodeposition events at the small scale to augment traditional engineering methods which are based on continuum approaches. The present work uses a kinetic Monte Carlo ͑KMC͒ method to simulate the first stages of nucleation and growth at defect sites ͑monatomic step edges͒ on otherwise pristine metal electrodes.The experimental electrodeposition literature is extensive and has led to numerous theoretical treatments of electrocrystallization phenomena. 1-3 In these, models for the electrode kinetics have been proposed to describe bulk metal growth, and atomistic approaches have been taken by formulating rate expressions for the attachment and detachment of single atoms to the electrode surface. Attachment rate expressions have been accompanied by surface diffusion models, which take into account the surface energetic parameters which govern the movement of adatoms on the electrode surface. The attachment/detachment kinetics, combined with thermodynamic considerations, have been used to develop theoretical predictions of nucleation rate. In addition, the effect of solution-phase mass transport limitations on nucleation kinetics has been investigated. 4 The theory of metal growth on crystalline faces has been developed for many cases among which are two-dimensional ͑2-D͒ and...

An exact and efficient first passage time algorithm for reaction–diffusion processes on a 2D-lattice

“…particles are more likely to attach to the edge, which is in agreement with the larger islands seen in the first experiment. Nonetheless, all ratios of D/F exhibit an exclusion zone, confirming physical observations [18,19] and previous calculations [30].…”

“…It is of practical interest to know how far the influence of the edge extends into the domain. Stephens et al predicted regimes at which particles are very unlikely to nucleate between step-edges [30]. We are interested in statistical results for those predictions to quantify the probability of particles nucleating at a given distance from the advancing step-edge.…”

“…This method has been shown to be applicable for complex systems including electrodeposition with additives [30,31]. The accuracy and efficiency of the original method have been enhanced by using adaptive grids for the level set function [20], or by combining the island dynamics method with KMC simulations at the edge of islands [33].…”

Structural effects on trends in the deposition and dissolution of metal-supported metal adstructures

“…In other studies, detailed Monte Carlo and kinetic Monte Carlo-based models have been developed to provide atomistic insight into these phenomena (see, e.g., Refs. [2,[23][24][25][26][27]); such * Tel. : +1 630 252 4711; fax: +1 630 252 4646.…”

Kinetic Monte Carlo simulation of electrodeposition using the embedded-atom method

“…Hybrid multiscale simulation methods that blend the SOS technique (KMC) and continuum mechanics have been applied to model copper electrodeposition in trenches [16,17]. The SOS method has been applied to polycrystalline growth [18,19], facet growth [20] and twodimensional growth [21][22][23]. However, a main drawback of the SOS model is that it does not accurately describe the metal crystalline microstructure, as is possible via MD using EAM potentials.…”