Precise design and control of novel electrodeposition applications require computational algorithms that efficiently and accurately capture details at a large range of length- and time-scales. This work presents the development of the Exact- Lattice-First-Passage-Time (ELFPT) method, an efficient and exact method for the simulation of surface diffusion, nucleation and growth during electrodeposition processes on physical lattices. It is based on the First-Passage-Time approach, replacing the hops of random walks with larger jumps at appropriate times. The method includes a flux of particles onto the deposition surface, surface diffusion of adatoms, nucleation and island growth, edge diffusion of adatoms around islands, multi-layer growth, and the option for heteroepitaxial growth onto foreign sub strates. ELFPT is particularly well suited for simulation of systems with dilute concentrations of diffusing particles.

The ELFPT method was applied to model systems emulating the five important categories of electrodeposition: (1) Homoepitaxy, (2) Heteroepitaxy, (3) Multi-Layer Growth, (4) Growth on Monoatomic Step Terraces, (5) Single Crystal Probability in Confined Areas. The five systems were studied for large ranges of key parameters and empirical scaling properties were discovered for several systems. The method was found to be up to 100x faster than KMC under ideal conditions, while simulations of the more realistic model systems were generally about an order of magnitude faster than KMC. ELFPT retains the resolution and accuracy of KMC simulations, and automatically reverts to KMC when diffusion lengths reach the atomic lattice range.

The numerical results confirm the nearest-neighbor distribution predicted by point-island theory and we found that in heteroepitaxial systems the nearest- neighbor distribution is primarily influenced by the substrate parameters DS and FS, where DS is the diffusivity of adatoms on the substrate, and FS is the flux density of adatoms to the substrate. A time-dependent intensity parameter analysis was used to distinguish between layer-by-layer growth, island growth and quasi-layer-by-layer growth. Nucleation on stepped terraces occurred only when the width of the terrace was large compared to the exclusion zone adjacent to the step edges. An empirical parameter, Lambda = log 10 (D/F)/log10 r2, was found that can estimate the probability of growing a single crystal in a confined area of given size r2.