0
Research Papers

Mechanics of Quantum-Dot Self-Organization by Epitaxial Growth on Small Areas

[+] Author and Article Information
Robert V. Kukta

Department of Mechanical Engineering, State University of New York, Stony Brook, NY 11794-2300robert.kukta@stonybrook.edu

J. Appl. Mech 77(4), 041001 (Mar 31, 2010) (6 pages) doi:10.1115/1.4000903 History: Received June 24, 2008; Revised October 13, 2009; Published March 31, 2010; Online March 31, 2010

Energetic arguments are used to understand the mechanics of Stranski–Krastanow epitaxial systems constrained to grow on a finite area of a substrate. Examples include selective area epitaxy and growth on patterned substrate features as raised mesa and etched pits. Accounting only for strain energy, (isotropic) surface energy, wetting layer potential energy, and geometric constraints, a rich behavior is obtained, whereby equilibrium configurations consist of a single island, multiple islands, or no islands, depending on the size of the growth area. It is shown that island formation is completely suppressed in the case of growth on a sufficiently small area. These behaviors are in stark contrast to growth on an indefinitely large area, where the same model suggests that the minimum free energy configuration of systems beyond the wetting layer transition thickness is a single island atop a wetting layer. The constraint of growing on a finite area can suppress island coarsening and produce minimum energy configurations with multiple self-organized islands of uniform size and shape.

FIGURES IN THIS ARTICLE
<>
Copyright © 2010 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Plot of the minimum energy configuration as a function of window size and nominal film thickness for the case ν=0.3, l¯=0.1, and γ¯w=0.5. The elastic interaction energy between islands is neglected.

Grahic Jump Location
Figure 2

Plot of the wetting layer thickness and island aspect ratio of the minimum energy configuration versus nominal film thickness for the case of window size (A/Le2)1/2=1000 and the same material constants as in Fig. 1

Grahic Jump Location
Figure 3

Plot of the geometry of the minimum energy configuration versus window size at nominal film thickness H0/Le=0.5 and the same material constants as in Fig. 1. Geometry is represented in terms of the ratio of material volume in the island(s) to the wetting layer nVI/AH and island aspect ratio a.

Grahic Jump Location
Figure 4

Plot of the wetting layer thickness and island aspect ratio of the minimum energy configuration versus nominal film thickness for the case of window size (A/Le2)1/2=20 and the same material constants as in Fig. 1

Grahic Jump Location
Figure 5

Plot of the minimum energy configuration as a function of the window size and nominal film thickness for the case ν=0.3, l¯=0.1, and γ¯w=0.5, and with elastic interaction energy included. Configuration (4) was not considered in the calculation.

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In