Stability and surface morphology of films obtained by a chemical vapor deposition process

A model is proposed to study the stability of a solid-gas interface under conditions of diffusive transport towards the surface. A dispersion relation is derived which relates the effects of species transport, surface diffusion, surface tension and geometrical factors with the stability of perturbations on the interface. The results indicate that two-dimensional perturbations of the surface are most critical and non-planar growth will be of a three-dimensional nature. The effects of substrate temperature and bulk phase concentration of the reacting species on the critical wavelength are also presented. Depending on the rate-limiting process and the temperature dependence of the transport parameters, the critical wavelength can either decrease or increase with increasing substrate temperature. Finally it is shown that the weakly non-linear form of the model reduces under certain conditions to either the deterministic Kardar-Parisi-Zhang equation or the Kuramoto-Sivashinsky equation.