Commun. Comput. Phys., 10 (2011), pp. 1089-1112.

Simulation of Three-Dimensional Strained Heteroepitaxial Growth Using Kinetic Monte Carlo

Tim P. Schulze 1*, Peter Smereka 2

1 Department of Mathematics, University of Tennessee, Knoxville, TN 37996, USA.
2 Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA.

Received 10 December 2010; Accepted (in revised version) 24 December 2010
Available online 2 August 2011


Efficient algorithms for the simulation of strained heteroepitaxial growth with intermixing in 2+1 dimensions are presented. The first of these algorithms is an extension of the energy localization method [T. P. Schulze and P. Smereka, An energy localization principle and its application to fast kinetic Monte Carlo simulation of heteroepitaxial growth, J. Mech. Phys. Sol., 3 (2009), 521-538] from 1+1 to 2+1 dimensions. Two approximations of this basic algorithm are then introduced, one of which treats adatoms in a more efficient manner, while the other makes use of an approximation of the change in elastic energy in terms of local elastic energy density. In both cases, it is demonstrated that a reasonable level of fidelity is achieved. Results are presented showing how the film morphology is affected by misfit and deposition rate. In addition, simulations of stacked quantum dots are also presented.

AMS subject classifications: 82B80, 82B21, 82D25, 65C05

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Key words: Heteroepitaxy, strained thin film, kinetic Monte Carlo.

*Corresponding author.
Email: (T. P. Schulze), (P. Smereka)

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