Generalized model for solid-on-solid interface growth

Abstract

We present a probabilistic cellular automaton (PCA) model to study solid-on-solid interface growth in which the transition rules depend on the local morphology of the profile obtained from the interface representation of the PCA. We show that the model is able to reproduce a wide range of patterns whose critical roughening exponents are associated to different universality classes, including random deposition, Edwards-Wilkinson, and Kardar-Parisi-Zhang. By means of the growth exponent method, we consider a particular set of the model parameters to build the two-dimensional phase diagram corresponding to a planar cut of the higher dimensional parameter space. A strong indication of phase transition between different universality classes can be observed, evincing different regimes of deposition, from layer-by-layer to Volmer-Weber and Stransk-Krastanov-like modes. We expect that this model can be useful to predict the morphological properties of interfaces obtained at different surface deposition problems, since it allows us to simulate several experimental situations by setting the values of the specific transition probabilities in a very simple and direct way.