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Publication 92

Shapes of Epitaxially Grown Quantum Dots

Authors:

CMUIrene Fonseca
Department of Mathematical Sciences
Carnegie Mellon University
Pittsburgh, PA 15213


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.
Get the paper in its entirety
14-CNA-009.pdf

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