Abstract
We apply an efficient and fast algorithm to simulate the atomistic strain model for epitaxial systems, recently introduced by Schindler et al. [Phys. Rev. B 67, 075316 (2003)]. The discrete effects in this lattice statics model are crucial for proper simulation of the influence of strain for thin film epitaxial growth, but the size of the atomistic systems of interest is in general quite large and hence the solution of the discrete elastic equations is a considerable numerical challenge. In this paper, we construct an algebraic multigrid method suitable for efficient solution of the large scale discrete strain model. Using this method, simulations are performed for several representative physical problems, including an infinite periodic step train, a layered nanocrystal, and a system of quantum dots. The results demonstrate the effectiveness and robustness of the method and show that the method attains optimal convergence properties, regardless of the problem size, the geometry and the physical parameters. The effects of substrate depth and of invariance due to traction-free boundary conditions are assessed. For a system of quantum dots, the simulated strain energy density supports the observations that trench formation near the dots provides strain relief. © 2006 Elsevier Inc. All rights reserved.
Original language | English (US) |
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Pages (from-to) | 697-714 |
Number of pages | 18 |
Journal | Journal of Computational Physics |
Volume | 219 |
Issue number | 2 |
DOIs | |
State | Published - Dec 10 2006 |
Externally published | Yes |
Bibliographical note
Generated from Scopus record by KAUST IRTS on 2023-02-15ASJC Scopus subject areas
- Physics and Astronomy (miscellaneous)
- Computer Science Applications