Island Dynamics and Level Set Methods for Continuum Modeling of Epitaxial Growth

Molecular Beam Epitaxy is a method for growing atomically thin films of material. During epitaxial growth, atoms are deposited on a surface, where they hop randomly until attaching at the edges of partially completed atomic monolayers. This process has practical application to the fabrication of high speed semiconductor electronic devices. We have formulated a new model for epitaxial growth, the “Island Dynamics Model”, in which the growth is described by the motion of the partial monolayer (“island”) boundaries, coupled to diffusive transport of the deposited atoms. This provides a continuum description in the lateral surface directions, but atomic scale discreteness in the surface height, which is well suited to the regime of practical interest. Level set methods are employed for computations based on this model. In this paper we give some elementary background on epitaxial growth, outline the Island Dynamics Model, review the Level Set Method, and discuss the novel level set techniques required in this application. We also present comparisons with two traditional models for epitaxial growth, Kinetic Monte Carlo simulations and Rate Equations.