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Published December 2003 | public
Journal Article

A Continuum Theory of Multispecies Thin Solid Film Growth by Chemical Vapor Deposition


A continuum theory for the chemical vapor deposition of thin solid films is proposed, in which a flowing, chemically reacting, gaseous mixture is coupled to the bulk of a growing thin film via the equations that govern the morphological evolution of the interface separating them. The vapor-film interface is viewed as a surface of zero thickness capable of sustaining mass and endowed with thermodynamic variables that account for its distinct structure. We consider situations in which species diffusion and heat conduction occur in all three phases (vapor, bulk and surface), with the former mechanism augmented by the convective transport of particles in the gas. Special attention is given to the chemical reactions that occur both in the vapor and on the film surface. Ours is a conceptual framework based on conservation laws for chemical species, momentum and energy, together with a separate balance of configurational forces. These balances are supplemented by an appropriate version of the second law which is used to develop suitable constitutive relations for each of the phases. In particular, we investigate the case of an elastic film, deposited on a rigid substrate and in contact with a reacting, multispecies, ideal vapor, whose surface behaves like an anisotropic, chemically reactive, multicomponent, ideal lattice gas. In addition to recovering the standard equations that describe the behavior of the gas and film phases, we derive the coupled PDE's that govern the interfacial morphological, chemical, and thermal evolution. In particular, the constitutively augmented interfacial configurational force balance provides a "kinetic relation" linking the thermodynamic "driving force" at the film surface to the growth rate. The special cases of (i) negligible interfacial species densities, and (ii) local (mechanical) equilibrium of both multi- and single-species films are investigated.

Additional Information

© 2004 Kluwer Academic Publishers. Received 16 September 2002; in revised form 3 February 2004. A portion of the work presented here was conducted while M.E.J. was a Ph.D. student at Caltech and, later, a postdoctoral associate at Carnegie Mellon University. The authors would like to thank Paolo Cermelli, Roger Fosdick, Dave Goodwin, Mort Gurtin, Jim Knowles, Bob Kohn, and Tom Pence for numerous valuable discussions and comments. Various useful suggestions made by the anonymous reviewers have also been of significant help to us. Finally, 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.

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