Growth and Pattern Formation for Thin Films

Epitaxy is the growth of a thin film by attachment to an existing substrate in which the crystalline properties of the film are determined by those of the substrate. In heteroepitaxy, the substrate and film are of different materials, and the resulting mismatch between lattice constants can introduce stress into the system. We have developed an island dynamics model for epitaxial growth that is solved using a level set method. This model uses both atomistic and continuum scaling, since it includes island boundaries that are of atomistic height, but describes these boundaries as smooth curves. The strain in the system is computed using an atomistic strain model that is solved using an algebraic multigrid method and an artificial boundary condition. Using the growth model together with the strain model, we simulate pattern formation on an epitaxial surface.