### Abstract

We introduce a numerical method based on the level-set technique to compute capture numbers used in mean-field rate equations that describe epitaxial growth. In our level-set approach, islands grow with a velocity that is computed from solving the diffusion equation for the adatom concentration. The capture number for each island is then calculated by integrating the growth velocity of an island around the island boundary. Thus, our method by construction includes all spatial correlations between islands. The functional form of the capture numbers σ_{s} is, to first approximation, affinely dependent on the island sizes. Integration of a completely deterministic set of mean-field rate equations for the first time properly reproduces the correct island densities and cluster size distribution.

Original language | English (US) |
---|---|

Article number | 115401 |

Pages (from-to) | 1154011-1154014 |

Number of pages | 4 |

Journal | Physical Review B - Condensed Matter and Materials Physics |

Volume | 63 |

Issue number | 11 |

State | Published - 2001 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physical Review B - Condensed Matter and Materials Physics*,

*63*(11), 1154011-1154014. [115401].

**Rate equations and capture numbers with implicit islands correlations.** / Gibou, F. G.; Ratsch, C.; Gyure, M. F.; Chen, S.; Caflisch, Russel.

Research output: Contribution to journal › Article

*Physical Review B - Condensed Matter and Materials Physics*, vol. 63, no. 11, 115401, pp. 1154011-1154014.

}

TY - JOUR

T1 - Rate equations and capture numbers with implicit islands correlations

AU - Gibou, F. G.

AU - Ratsch, C.

AU - Gyure, M. F.

AU - Chen, S.

AU - Caflisch, Russel

PY - 2001

Y1 - 2001

N2 - We introduce a numerical method based on the level-set technique to compute capture numbers used in mean-field rate equations that describe epitaxial growth. In our level-set approach, islands grow with a velocity that is computed from solving the diffusion equation for the adatom concentration. The capture number for each island is then calculated by integrating the growth velocity of an island around the island boundary. Thus, our method by construction includes all spatial correlations between islands. The functional form of the capture numbers σs is, to first approximation, affinely dependent on the island sizes. Integration of a completely deterministic set of mean-field rate equations for the first time properly reproduces the correct island densities and cluster size distribution.

AB - We introduce a numerical method based on the level-set technique to compute capture numbers used in mean-field rate equations that describe epitaxial growth. In our level-set approach, islands grow with a velocity that is computed from solving the diffusion equation for the adatom concentration. The capture number for each island is then calculated by integrating the growth velocity of an island around the island boundary. Thus, our method by construction includes all spatial correlations between islands. The functional form of the capture numbers σs is, to first approximation, affinely dependent on the island sizes. Integration of a completely deterministic set of mean-field rate equations for the first time properly reproduces the correct island densities and cluster size distribution.

UR - http://www.scopus.com/inward/record.url?scp=0034905927&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0034905927&partnerID=8YFLogxK

M3 - Article

VL - 63

SP - 1154011

EP - 1154014

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 1098-0121

IS - 11

M1 - 115401

ER -