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We study a moving boundary model of non-conserved interface growth thatimplements the interplay between diffusive matter transport and aggregationkinetics at the interface. Conspicuous examples are found in thin filmproduction by chemical vapor deposition and electrochemical deposition. Themodel also incorporates noise terms that account for fluctuations in thediffusive and in the attachment processes. A small slope approximation allowsus to derive effective interface evolution equations (IEE) in which parametersare related to those of the full moving boundary problem. In particular, theform of the linear dispersion relation of the IEE changes drastically for slowor for instantaneous attachment kinetics. In the former case the IEE takes theform of the well-known (noisy) Kuramoto-Sivashinsky equation, showing amorphological instability at short times that evolves into kinetic rougheningof the Kardar-Parisi-Zhang class. In the instantaneous kinetics limit, the IEEcombines Mullins-Sekerka linear dispersion relation with a KPZ nonlinearity,and we provide a numerical study of the ensuing dynamics. In all cases, thelong preasymptotic transients can account for the experimental difficulties toobserve KPZ scaling. We also compare our results with relevant data fromexperiments and discrete models.

Unified moving boundary model with fluctuations for unstable diffusive growth