Commun. Comput. Phys., 6 (2009), pp. 553-564.


Inverted List Kinetic Monte Carlo with Rejection Applied to Directed Self-Assembly of Epitaxial Growth

Michael A. Saum 1, Tim P. Schulze 1*, Christian Ratsch 2

1 Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996, USA.
2 Department of Mathematics and Institute for Pure and Applied Mathematics, University of California in Los Angeles, Los Angeles, California 90095, USA.

Received 19 August 2008; Accepted (in revised version) 11 November 2008
Available online 6 February 2009

Abstract

We study the growth of epitaxial thin films on pre-patterned substrates that influence the surface diffusion of subsequently deposited material using a kinetic Monte Carlo algorithm that combines the use of inverted lists with rejection. The resulting algorithm is well adapted to systems with spatially heterogeneous hopping rates. To evaluate the algorithm's performance we compare it with an efficient, binary-tree based algorithm. A key finding is that the relative performance of the inverted list algorithm improves with increasing system size.

AMS subject classifications: 82B80, 82B21, 82D25, 65C05
PACS: 68.43.Hn, 68.55.J-
Key words: Epitaxial growth, kinetic Monte Carlo, binary-tree search.

*Corresponding author.
Email: msaum@math.utk.edu (M. A. Saum), schulze@math.utk.edu (T. P. Schulze), cratsch@math.ucla.edu (C. Ratsch)
 

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