The Island Dynamics Model for Epitaxial Growth using the Level Set Method
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Results for irreversible aggregation
Results for reversible aggregation
More recent results
Ostwald ripening
Nucleation and growth on surfaces with defects
Effects of a spatially varying potential energy surface (that results from inhomogeneous strain)
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Epitaxial growth is the deposition of a metarial on top of a substrate, where the material deposited is in registry
with the substrate. We have developed an island dynamics model for the simulation of thin film growth that employs
the level set method. A level-set model for the simulation of epitaxial growth is described. In this model, the
motion of island boundaries of discrete atomic layers is determined by the time evolution of a continuous level-set
function F. The adatom concentration is treated in
a mean field manner. It is obtained by solving the diffusion equation. A typical result for the level set function
and the adatom concentration is shown in the figure below:
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Level Set Function |
Surface Morphology |
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Results for irreversible aggregation
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We have used this model to systematically examine the importance of various fluctuations in the submonolayer and
multilayer regimes. We find that, in the submonolayer regime for large values of D/F and irreversible aggregation,
the dominant fluctuations are associated with the spatial seeding of islands.
The location of a an island that is seeded on the surface has to be chosen with a probability that is weighted by the local value of square of the local adatom concentration. The the island density and island size distribution that is obtained with this model is in excellent agreement with kinetic Monte Carlo simulations and experiments. The latter is shown in the following figure:
| No additional information or approximation is needed to simulate growth of several layers.
The movie on the right shows a typical levelset simulation out to 10 atomic layers. Note that the surface roughens
(as is evident from the fact that the number of exposed layers increases with time) and coarsens (as it is evident
from the fact that the islands get bigger in higher layers). To play movie again, right click in this frame and select "Reload". |
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Results for reversible aggregation
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Detachment of adatoms from island boundaries can easily be included in our model. The details of this are described
in M. Peterson et. al, submitted to Phys. Rev. E. (PDF) One of the main accomplishments of this approach is that frequent detachment and re-attachment
of atoms does not need to be resolved explicitly, and thus the computational effort is essentially unchanged when
detachment is allowed. The figure of merrit is again the scaling of the island size distribution. The excellent
agreement of the scaling of the island size distribution in comparison with KMC simulations and experimental data
is shown the the following figure:
The fact that detachment can be simulated without any additional computational cost allows us to use this method
to look at problems that where difficult to address with conventionel atomistic (or continuum) methods. We are
currently in the process of implementing strain in the model.
Relevant Publications
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C. Ratsch, C. Anderson, R.E. Caflisch, L. Feigenbaum, D. Shaevitz, M. Sheffler, and C. Tiee, "Multiple Domain
Dynamics Simulated with Coupled Level Sets, submitted to Appl. Math. Lett.. PDF
M. Petersen, A. Zangwill, and C. Ratsch, "Homoepitaxial Ostwald Ripening", submitted to Surf. Science. PDF
C. Ratsch, M.F. Gyure, R.E. Caflisch, F. Gibou, M. Petersen, M. Kang, J.R. Garcia, and D.D. Vvedensky, "Level-Set Method for Island Dynamics in Epitaxial Growth", Phys. Rev. B 65, 195403 (2002). PDF or Link to journal
C. Ratsch, M. Kang, And R.E. Caflisch, Atomic size effects in continuum modeling, Phys. Rev. E 64, 020601 (2001). PDF or Link to journal
S. Chen, M.Kang, B. Merriman, R.E. Caflisch, C. Ratsch, R. Fedkiw, M.F. Gyure, and S. Osher, "Level Set Method for Thin Film Epitaxial Growth," J. Comp. Phys.167, 475 (2001). PDF
C. Ratsch, M.F. Gyure, S. Chen, M. Kang, and D.D. Vvedensky, Fluctuation and Scaling in Aggregation Phenomena, Phys. Rev. B 61, R10598 (2000). PDF or Link to journal
R.E. Caflisch, M.F. Gyure, B. Merriman, S. Osher, C. Ratsch, D.D. Vvedensky and J. J. Zinck, "Island Dynamics and the Level Set Method for Epitaxial Growth," Appl. Math Lett. 12, 13 (1999). Link to journal
M.F. Gyure, C. Ratsch, B. Merriman, R.E. Caflisch, S. Osher, J. J. Zinck and D.D. Vvedensky, "Level Set Methods for the Simulation of Epitaxial Phenomena," Phys. Rev E 58, R6927 (1998).PDFor Link to journal
