Unified moving boundary model with fluctuations for unstable diffusive growth

TL;DR

This paper develops a unified moving boundary model for unstable diffusive growth, incorporating fluctuations, and derives effective interface equations that explain different growth regimes and their experimental implications.

Contribution

It introduces a comprehensive moving boundary model with noise for diffusive growth, deriving effective equations that unify different kinetic regimes and explain observed scaling behaviors.

Findings

The model reproduces the Kuramoto-Sivashinsky and KPZ regimes.

Long transient effects can obscure KPZ scaling in experiments.

Numerical simulations support the theoretical predictions.

Abstract

We study a moving boundary model of non-conserved interface growth that implements the interplay between diffusive matter transport and aggregation kinetics at the interface. Conspicuous examples are found in thin film production by chemical vapor deposition and electrochemical deposition. The model also incorporates noise terms that account for fluctuations in the diffusive and in the attachment processes. A small slope approximation allows us to derive effective interface evolution equations (IEE) in which parameters are related to those of the full moving boundary problem. In particular, the form of the linear dispersion relation of the IEE changes drastically for slow or for instantaneous attachment kinetics. In the former case the IEE takes the form of the well-known (noisy) Kuramoto-Sivashinsky equation, showing a morphological instability at short times that evolves into kinetic roughening of the Kardar-Parisi-Zhang class. In the instantaneous kinetics limit, the IEE combines Mullins-Sekerka linear dispersion relation with a KPZ nonlinearity, and we provide a numerical study of the ensuing dynamics. In all cases, the long preasymptotic transients can account for the experimental difficulties to observe KPZ scaling. We also compare our results with relevant data from experiments and discrete models.