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Publication 12-CNA-007

Analytical Validation of a Continuum Model for Epitaxial Growth with Elasticity on Vicinal Surfaces

G. Dal Maso 
SISSA, Trieste, Italy 
dalmaso@sissa.it

Irene Fonseca
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213
fonseca@andrew.cmu.edu

Giovanni Leoni 
Department of Mathematical Sciences 
Carnegie Mellon University 
Pittsburgh, PA 15213 
giovanni@andrew.cmu.edu

Abstract: In this paper it is shown existence of weak solutions of a variational inequality derived from the continuum model introduced by Xiang [7, formula (3.62)] (see also the work of Xiang and E [8] and Xu and Xiang [9]) to describe the self-organization of terraces and steps driven by misfit elasticity between a film and a substrate in heteroepitaxial growth. This model is obtained as a continuum limit of discrete theories of Duport, Politi, and Villain [3] and Tersoff, Phang, Zhang, and Lagally[6].

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