Energetics of Epitaxial Island Arrangements on Substrate Mesas

[+] Author and Article Information
N. D. Machtay

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

R. V. Kukta

Department of Mechanical Engineering, State University of New York, Stony Brook, NY 11794-2300

J. Appl. Mech 73(2), 212-219 (May 14, 2005) (8 pages) doi:10.1115/1.2073327 History: Received February 02, 2005; Revised May 14, 2005

Self-assembly of strained epitaxial deposits (islands) grown on a substrate is a promising route to fabricate nanostructures of significance for electronic and optoelectronic devices. The challenge is to achieve specific island arrangements that are required for device functionality and high performance. This article investigates growth on a topographically patterned substrate as a means to control the arrangement of islands. By taking free energy to consist of elastic energy and surface energy, minimum energy configurations are calculated for islands on a raised substrate mesa. Configurations of one, two, and three islands at different positions on the mesa are considered to determine their relative energies as a function of mesa size, island size, mismatch strain between the island and substrate materials, surface energy, and elastic moduli. Insight is offered on the mechanisms responsible for certain physical observations such as a transition from the formation of multiple islands to a single island as mesa size is reduced.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Geometry of the system under consideration

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Figure 2

The four island configurations considered for the energetic analysis. (a) A single centered island, (b) dual edge mounted islands, (c) three islands, one at each edge and one in the center, and (d) an asymmetric single edge mounted island.

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Figure 3

A typical finite element mesh in the vicinity of an island at the edge of a mesa

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Figure 4

(a) Plot of nondimensional free energy versus aspect ratio for an island on a flat substrate. Solid lines plot curves of fixed L¯∗=0, L¯∗=0.125π, L¯∗=0.25π, L¯∗=0.375π, L¯∗=0.5π, L¯∗=0.625π, L¯∗=0.75π. The dashed line traces energy minima for different values of L¯∗. (b) Aspect ratio of the minimum free energy island plotted versus L¯∗ obtained from the dashed line in (a). Poisson ratio is ν=0.25.

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Figure 5

Dimensionless free energy of two non-interacting islands measured relative to that of a single island of the same total volume plotted versus the normalized characteristic length L¯∗. Poisson ratio is ν=0.25.

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Figure 6

Plots of dimensionless free energy versus aspect ratio for islands on a substrate mesa in the case L¯∗=1, D¯=23.7, H¯=8.4, and ν=0.25. Curves correspond to the configurations shown in Fig. 2.

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Figure 7

Minimum free energy state for each of the configurations in Fig. 2 plotted versus the normalized characteristic length. The geometric parameters are D¯=23.7 and H¯=8.4 and Poisson ratio is ν=0.25. These curves plot the minima of the curves in Fig. 6 and similar plots that are not shown.

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Figure 8

Island aspect ratio α of the minimum energy configurations in Fig. 7 plotted versus normalized characteristic length

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Figure 9

Minimum free energy of each configuration in Fig. 2 plotted versus the normalized characteristic length for the geometric parameters (a) D¯=13.7 and H¯=4.8 and (b) D¯=4.7 and H¯=1.6. These plots are similar to Fig. 7. The Poisson ratio is ν=0.25 in both.

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Figure 10

Plots of chemical potential versus normalized characteristic length for small edge mounted and centered islands. The results apply to systems of sufficiently large D¯ and H¯. Poisson ratio is ν=0.25.



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