A Level-Set Method for Simulating Island Coarsening

Abstract

Modeling of microstructural evolution during thin-film deposition requires a knowledge of several key activation energies (surface diffusion, island edge atom diffusion, adatom migration over descending step edges, etc.). These and other parameters must be known as a function of crystal orientation. In order to generate values for these parameters, we have developed a numerical simulation in tandem with physical experiments. By tuning the simulation to the results from experiments we can extract and verify approximate values for these parameters. The numerical method we use is based upon the level set method. Our model is a continuum model in directions parallel to the crystal facet, and resolves each discrete atomic layer in the normal direction. The model includes surface diffusion, step edge dynamics, and attachment/detachment rates all of which may depend upon the local geometry of the step edge. The velocity field for advancing the island edges in the level set framework is generated by computing the equilibrium adatom density on the flat terraces resulting in Laplace's equation with mixed boundary conditions at the step edges. We have turned to the finite element method for solving this equation, which results in very good agreement with analytically known solutions and with experiment.