Continuum model for the growth of interfaces

A continuum model is presented for studying various growth processes. One of the model equations is used to define a growing interface with an arbitrary topology and captures the intrinsic dynamics of the aggregate with surface diffusion incorporated in a natural manner. With an appropriate local growth mechanism, this model represents a continuum version of the Eden growth model. The introduction of another field describing the dynamics of the vapor enables the modeling of phenomena ranging from ballistic deposition to diffusion-limited aggregation (DLA) within the framework of the same equations. Our equations capture nonlocal effects, such as shadowing or screening in a local. way, and permit the monitoring of the interior structure of the growing film. Our results are benchmarked against those of experiments on sputter deposited films. Simple modifications of the model lead to patterns that are different from standard DLA structures but similar to those observed in electrochemical deposition. We also examine models that use the no-overhang approximation in the description of columnar morphology observed in thin films and discuss their validity in comparison with our model.