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Publication 14-CNA-009

Shapes of Epitaxially Grown Quantum Dots

Irene Fonseca
Center for Nonlinear Analysis
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh PA 15213-3890 USA

Aldo Pratelli
Dipartimento di Matematica "F. Casorati"
Pavia, Italy

Barbara Zwicknagl
University of Bonn
Hausdorff Center for Mathematics
Bonn, Germany

Abstract: A variational model introduced by Spencer and Tersoff (Appl. Phys. Lett. 96:073114, 2010) to describe optimal faceted shapes of epitaxially deposited lms is studied analytically in the case in which there are a non-vanishing crystallographic miscut and a lattice incompatibility between the lm and the substrate. Existence of faceted minimizers for every volume of the deposited film is established. In particular, it is shown that there is no wetting effect for small volumes. Geometric properties including a faceted version of the zero contact angle are derived, and the explicit shapes of minimizers for small volumes are identified.

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