Continuum Modelling of the Growth of Interfaces

A continuum model is presented for studying various growth processes. One of the model equations describes of 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, our model represents a continuum version of Eden growth. The introduction of another field describing the dynamics of the vapor allows for the modelling of phenomena ranging from ballistic deposition to Diffusion -Limited-Aggregation (DLA) within the framework of the same equations. Our equations capture non-local 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 our DLA model lead to patterns significantly 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 the columnar morphology observed in thin films and discuss the extent of their validity.