The main objective of the work presented in this thesis is to develop new methods to extend the time and length scales of atomistic kinetic Monte Carlo (KMC) simulations. When all the relevant processes and their activation barriers are known, KMC is an extremely efficient method to carry out atomistic simulations for longer time scales. However, in some cases (ex. low barrier repetitive events) direct KMC simulations may not be sufficient to reach the experimentally relevant length and time scales. Accordingly, we have tested and developed several different parallel KMC algorithms and also developed a dynamic boundary allocation (DBA) method to improve parallel efficiency by reducing number of boundary events. Results for parallel KMC simulations of Ag(111) island coarsening at room temperature carried out using a large database of processes obtained from previous self-learning KMC simulations are also presented. We find that at long times the coarsening behavior corresponds to Ostwald ripening. We also find that the inclusion of concerted small-cluster events has a significant impact on the average island size. In addition, we have also developed a first passage time (FPT) approach to KMC simulations to accelerate KMC simulation of (100) multilayer epitaxial growth with rapid edge diffusion. In our FPT approach, by mapping edge-diffusion to a 1D random walk, numerous diffusive hops are replaced with first-passage time to make one large jump to a new location. As a test, we have applied our method to carry out multilayer growth simulations of three different models. We note that despite the additional overhead, the FPT approach leads to a significant speed-up compared to regular KMC simulations
Finally, we present results obtained from KMC simulations of irreversible submonolayer island growth with strain and rapid island relaxation. Our results indicate that in the presence of large strain there is significant anisotropy in qualitative agreement with experiments on InAs/GaAs and Ge/Si growth. Somewhat surprisingly, we also find that the scaled island-size distribution depends only weakly on the effects of strain. This is in qualitative agreement with recent experimental results for InAs/GaAs(100) submonolayer growth.