First-passage time approach to kinetic Monte Carlo simulations of metal (100) growth

A first-passage-time FPT approach to accelerate kinetic Monte Carlo KMC simulations of metal 100 epitaxial growth with fast edge diffusion is described. In our approach, the process of singly-bonded edge diffusion is replaced by a calculation of the first-passage time for an edge diffuser to be absorbed either by corner rounding or kink attachment, while the remaining activated processes are treated with regular KMC. To calculate the FPT two different methods were used. In the first more computationally efficient method, the mean FPT was calculated using an analytical expression, which takes into account the difference between the hopping rate for an atom along the edge and at a corner site. In the second method, the full FPT distribution is numerically calculated based on the eigenvectors and eigenvalues of the corresponding transition matrix. As a test of this approach we have studied three different models of multilayer growth, including two irreversible growth models as well as an effective-medium theory model of Cu/Cu 100 growth. By taking into account the interactions of edge diffusers with other atoms we have obtained very good agreement using both methods between our FPT KMC and regular KMC simulations. In addition, we find that our FPT approach can lead to a significant speed-up compared to regular KMC simulations.