CMU Campus
Center for                           Nonlinear Analysis
CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups CNA Comments Form Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses SIAM Chapter Seminar Positions Contact
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
fonseca@andrew.cmu.edu

Aldo Pratelli
Dipartimento di Matematica "F. Casorati"
Pavia, Italy
aldo.pratelli@unipv.it

Barbara Zwicknagl
University of Bonn
Hausdorff Center for Mathematics
Bonn, Germany
zwicknagl@iam.uni-bonn.de

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 as

Back to CNA Publications