The role of the transition function in a continuum model for kinetic roughening and coarsening in thin films
Abstract. In a recently suggested model for kinetic roughening and coarsening in high-temperature super-conducting thin films, a transition function is used which takes the energetics of the boundary layer at the film/substrate interface into account. Apart from having some basic properties, this function can be chosen quite arbitrarily.
We show that certain decay and concavity properties of this function have a major impact on the film growth. In particular, a modified decay can circumvent the occurrence of negative film heights which is predicted in the original model, and a change in curvature alters stability properties of the film. These observations do not only underscore the importance of the transition function in the model, but they also suggest to estimate the actual transition function from experimental data or from atomistic simulation.