Kinetics of surface steps in the presence of impurities: Patterns and instabilities.

Abstract

We consider the flow of atomic steps on a crystal surface in the presence of impurities. A mesoscopic model of the effect is proposed and studied by numerical simulations. In the smal line tension limit complex highly connected step patterns are formed that exhibit distinct repeating features. To explain these features we make the ansatz that the system is locally close to weakly unstable steady states. Using a differential equation approach we calculate these steady-state configurations analytically, and verify the ansatz; the analytical predictions are in agreement with numerical simulations. We also predict that the typical length scale of the patterns should grow with time as \ensuremath{\surd}t . This coarsening law is consistent with numerical simulations of the mesoscopic model.