A Level-Set Method for Epitaxial Growth and Self-Organization of Quantum Dots

Christian Ratsch

We have developed an island dynamics model that employs the level-set technique to describe epitaxial growth. The motion of the island boundaries is described by the evolution of a continuous level-set function. Islands are nucleated on the surface and their boundaries are moved at rates that are determined by the adatom density, which is obtained from solving the diffusion equation. Thus, the individual islands on the surface are resolved, while the adatoms are treated in a mean-field picture. The typical simulation timestep can be chosen much larger than in an atomistic simulation, even when several microscopic processes with vastly different rates are relevant. This is the case for example when there is high reversibility, and results for the scaled island size distribution during submonolayer epitaxy will be shown. Our method is ideally suited to study the formation and self-organization of quantum dots, which is a strain driven phenomena. We will discuss how the large timesteps make it feasible to solve the elastic equations at every timestep, and couple the solution of the elastic equations to the microscopic parameters of our model. In this case, diffusion and attachment and detachment are spatially varying. Our results indicate that in a system with spatially varying diffusion rates one obtains regions of high and low island densities, and in particular regions with high island ordering.

Presentation (PowerPoint File)

Back to Workshop II: Multiscale Modeling in Condensed Matter and Materials Sciences, including Mini-Workshop: Time Acceleration Methods in Atomistic Simulations