### Abstract

A kinetic theory is formulated for the velocity of a step edge in epitaxial growth. The formulation involves kinetic, mean-field equations for the density of kinks and “edge adatoms” along the step edge. Equilibrium and kinetic steady states, corresponding to zero and nonzero deposition flux, respectively, are derived for a periodic sequence of step edges. The theoretical results are compared to results from kinetic Monte Carlo (KMC) simulations of a simple solid-on-solid model, and excellent agreement is obtained. This theory provides a starting point for modeling the growth of two-dimensional islands in molecular-beam epitaxy through motion of their boundaries, as an alternative to KMC simulations.

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

Pages (from-to) | 6879-6887 |

Number of pages | 9 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 59 |

Issue number | 6 |

DOIs | |

State | Published - 1999 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

### Cite this

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*59*(6), 6879-6887. https://doi.org/10.1103/PhysRevE.59.6879

**Kinetic model for a step edge in epitaxial growth.** / Caflisch, Russel; Weinan, W. E.; Gyure, Mark F.; Merriman, Barry; Ratsch, Christian.

Research output: Contribution to journal › Article

*Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 59, no. 6, pp. 6879-6887. https://doi.org/10.1103/PhysRevE.59.6879

}

TY - JOUR

T1 - Kinetic model for a step edge in epitaxial growth

AU - Caflisch, Russel

AU - Weinan, W. E.

AU - Gyure, Mark F.

AU - Merriman, Barry

AU - Ratsch, Christian

PY - 1999

Y1 - 1999

N2 - A kinetic theory is formulated for the velocity of a step edge in epitaxial growth. The formulation involves kinetic, mean-field equations for the density of kinks and “edge adatoms” along the step edge. Equilibrium and kinetic steady states, corresponding to zero and nonzero deposition flux, respectively, are derived for a periodic sequence of step edges. The theoretical results are compared to results from kinetic Monte Carlo (KMC) simulations of a simple solid-on-solid model, and excellent agreement is obtained. This theory provides a starting point for modeling the growth of two-dimensional islands in molecular-beam epitaxy through motion of their boundaries, as an alternative to KMC simulations.

AB - A kinetic theory is formulated for the velocity of a step edge in epitaxial growth. The formulation involves kinetic, mean-field equations for the density of kinks and “edge adatoms” along the step edge. Equilibrium and kinetic steady states, corresponding to zero and nonzero deposition flux, respectively, are derived for a periodic sequence of step edges. The theoretical results are compared to results from kinetic Monte Carlo (KMC) simulations of a simple solid-on-solid model, and excellent agreement is obtained. This theory provides a starting point for modeling the growth of two-dimensional islands in molecular-beam epitaxy through motion of their boundaries, as an alternative to KMC simulations.

UR - http://www.scopus.com/inward/record.url?scp=0000791278&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000791278&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.59.6879

DO - 10.1103/PhysRevE.59.6879

M3 - Article

C2 - 11969675

AN - SCOPUS:0000791278

VL - 59

SP - 6879

EP - 6887

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 6

ER -