We report on the derivation of an stochastic differential equation that describes the growth dynamics of solid surfaces growing from a vapor phase, such as the surfaces of aggregates grown by Electrochemical Deposition (ECD), or of those produced by Chemical Vapor Deposition (CVD). We formulate an unified moving boundary problem that is relevant both to ECD and CVD experiments, into which we allow for fluctuations in the various processes leading to growth: surface diffusion, attachment/detachment events, and surface kinetics. By means of perturbative techniques we are able to derive a closed stochastic nonlinear differential equation for the surface profile. The equation has the form of the stochastic Kuramoto-Sivashinsky equation and generalizations thereof. As a function of surface kinetics, the dispersion relation is modified, in such a way that the interface properties (roughness, etc.) change. Moreover, our results allow to interpret the lack of universal properties for the surface fluctuations found in many experiments as originated in the (diffusive) instabilities existing in the system prior to chieving its asymptotic state.
Keywords: Moving boundary problems, fluctuations, Electrochemical Deposition, Chemical Vapor Deposition, diffusional instabilities, surface/aggregate growth
European Congress on Computational Methods in Applied Sciences and Engineering - ECCOMAS 2004
Publication date: July 2004.
R. Cuerno, M. Castro, Stochastic differential equation for surface growth from a vapor phase: a moving boundary problem with fluctuations, European Congress on Computational Methods in Applied Sciences and Engineering - ECCOMAS 2004. Jyväskylä, Finland, 24-28 July 2004