Geometric Evolution Laws for Thin Crystalline Films: Modeling and Numerics
Bo Li 1, John Lowengrub 2, Andreas Ratz 3, Axel Voigt 4*1 Department of Mathematics and Center for Theoretical Biological Physics, University of California at San Diego, La Jolla, CA 92093-0112, USA.
2 Department of Mathematics, University of California at Irvine, Irvine, CA 92697-3875, USA.
3 Institut fur Wissenschaftliches Rechnen, Technische Universitat Dresden, 01062 Dresden, Germany.
4 Department of Mathematics, University of California at Irvine, Irvine, CA 92697-3875, USA; Institut fur Wissenschaftliches Rechnen, Technische Universitat Dresden, 01062 Dresden, Germany; and Department of Physics, Technical University of Helsinki, 02015 Espoo, Finland.
Received 7 October 2008; Accepted (in revised version) 22 January 2009
Available online 6 February 2009
Geometrical evolution laws are widely used in continuum modeling of surface and interface motion in materials science. In this article, we first give a brief review of various kinds of geometrical evolution laws and their variational derivations, with an emphasis on strong anisotropy. We then survey some of the finite element based numerical methods for simulating the motion of interfaces focusing on the field of thin film growth. We discuss the finite element method applied to front-tracking, phase-field and level-set methods. We describe various applications of these geometrical evolution laws to materials science problems, and in particular, the growth and morphologies of thin crystalline films.
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PACS: 05.70.Np, 02.60.Cb, 02.70.Bf, 02.70.Dh, 81.15.Aa
Key words: Interface problems, geometric evolution laws, anisotropy, kinetics, front tracking, level-set, phase-field, chemical vapor deposition, molecular beam epitaxy, liquid phase epitaxy, electrodeposition.
Email: firstname.lastname@example.org (B. Li), email@example.com (J. Lowengrub), firstname.lastname@example.org (A. Ratz), email@example.com (A. Voigt)