PIRE - mathematics, mechanics, materials science

Science at the triple point between
mathematics, mechanics and materials science

Publication 92

Shapes of Epitaxially Grown Quantum Dots


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

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

Back to Publications