Numerical Methods for the simulation of epitaxial growth and their application in the study of a meander instability

Abstract

The surface morphology of thin crystalline films grown by molecular beam epitaxy (MBE), a technique to produce high-quality, almost defect-free crystals, is strongly influenced by kinetic processes on an atomistic scale. To incorporate these effects in a continuum model requires some care. Here we use a step flow model, which is a free boundary problem for the position of atomic height steps on the crystalline surface.We present two complementary approaches to derive a numerical method for solving this problem: a front tracking ansatz and a diffuse interface approximation. The numerical methods are used to study the nonlinear regime of a step meandering instability. © 2008 Springer-Verlag.