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A continuum model of kinetic roughening and coarsening in thin films

Ortiz, M. and Repetto, E. A. and Si, H. (1999) A continuum model of kinetic roughening and coarsening in thin films. Journal of the Mechanics and Physics of Solids, 47 (4). pp. 697-730. ISSN 0022-5096. doi:10.1016/S0022-5096(98)00102-1.

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We present a phenomenological continuum model of film growth based on a series expansion of the deposition flux in powers of the profile gradient, consideration of the energetics of the film–substrate interface and the enforcement of Onsagers reciprocity relations. The interfacial term, which operates at very small thicknesses, is nonconservative and breaks the ±h symmetry of the remaining terms in the kinetic equation. By virtue of this term, very thin flat films are predicted to be stable within an appropriate range of parameters, and to loose stability and become rough at a well-defined critical thickness. This instability effectively provides an island nucleation mechanism. For thick films, the rate processes envisioned in the model favor a characteristic slope for the film profile, a feature which is in keeping with observation for a number of systems including YBCO films. The enforcement of reciprocity ensures the existance of a kinetic potential and enables the use of direct methods of the calculus of variations. Within this framework, we provide an explicit construction for the coarsening of the film profile based on a sharp interface approximation. The construction predicts characteristic exponents for the evolution of grain size and film roughness which are in close agreement with the observational evidence for YBCO. The predictions of the construction are also born out by numerical tests.

Item Type:Article
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Ortiz, M.0000-0001-5877-4824
Additional Information:© 1999 Elsevier. Received 1 June 1998, Revised 28 September 1998. We are grateful to H. Atwater, K. Bhattacharya, D. Goodwin, R.V. Kohn and T. Schulze for helpful suggestions and discussions. Support from the National Science Foundation and the Defense Advanced Research Projects Agency under the initiative Modeling and Simulation of Advanced Materials Processes: Virtual Integrated Prototyping Initiative for Thin Films is gratefully acknowledged.
Funding AgencyGrant Number
Defense Advanced Research Projects Agency (DARPA)UNSPECIFIED
Subject Keywords:A Diffusion; A Surface; B Superconducting material; B Thin films; C Variational calculus
Issue or Number:4
Record Number:CaltechAUTHORS:20171213-091830314
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Official Citation:M. Ortiz, E.A. Repetto, H. Si, A continuum model of kinetic roughening and coarsening in thin films, In Journal of the Mechanics and Physics of Solids, Volume 47, Issue 4, 1999, Pages 697-730, ISSN 0022-5096, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:83862
Deposited By: Lydia Suarez
Deposited On:13 Dec 2017 22:52
Last Modified:15 Nov 2021 20:14

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