### Abstract

Starting from a detailed model for the kinetics of a step edge or island boundary, we derive a Gibbs-Thomson-type formula and the associated step stiffness as a function of the step edge orientation angle, Θ. Basic ingredients of the model are (i) the diffusion of point defects ("adatoms") on terraces and along step edges; (ii) the convection of kinks along step edges; and (iii) constitutive laws that relate adatom fluxes, sources for kinks, and the kink velocity with densities via a meanfield approach. This model has a kinetic (nonequilibrium) steady-state solution that corresponds to epitaxial growth through step flow. The step stiffness, β̃(Θ), is determined via perturbations of the kinetic steady state for small edge Péclet number P, which is the ratio of the deposition to the diffusive flux along a step edge. In particular, β̃ is found to satisfy β̃ = O(Θ^{-1}) for O(P ^{1/3}) > Θ ⇒ 1, which is in agreement with independent, equilibrium-based calculations.

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

Pages (from-to) | 242-273 |

Number of pages | 32 |

Journal | Multiscale Modeling and Simulation |

Volume | 7 |

Issue number | 1 |

DOIs | |

State | Published - 2008 |

### Fingerprint

### Keywords

- Adatoms
- Edge-atoms
- Ehrlich-Schwoebel barrier
- Epitaxial growth
- Gibbs-Thomson formula
- Island dynamics
- Kinetic steady state
- Line tension
- Step edge
- Step edge kinetics
- Step permeability
- Step stiffness
- Surface diffusion

### ASJC Scopus subject areas

- Chemistry(all)
- Modeling and Simulation
- Ecological Modeling
- Physics and Astronomy(all)
- Computer Science Applications

### Cite this

*Multiscale Modeling and Simulation*,

*7*(1), 242-273. https://doi.org/10.1137/070690948

**Anisotropic step stiffness from a kinetic model of epitaxial growth.** / Margetis, Dionisios; Caflisch, Russel.

Research output: Contribution to journal › Article

*Multiscale Modeling and Simulation*, vol. 7, no. 1, pp. 242-273. https://doi.org/10.1137/070690948

}

TY - JOUR

T1 - Anisotropic step stiffness from a kinetic model of epitaxial growth

AU - Margetis, Dionisios

AU - Caflisch, Russel

PY - 2008

Y1 - 2008

N2 - Starting from a detailed model for the kinetics of a step edge or island boundary, we derive a Gibbs-Thomson-type formula and the associated step stiffness as a function of the step edge orientation angle, Θ. Basic ingredients of the model are (i) the diffusion of point defects ("adatoms") on terraces and along step edges; (ii) the convection of kinks along step edges; and (iii) constitutive laws that relate adatom fluxes, sources for kinks, and the kink velocity with densities via a meanfield approach. This model has a kinetic (nonequilibrium) steady-state solution that corresponds to epitaxial growth through step flow. The step stiffness, β̃(Θ), is determined via perturbations of the kinetic steady state for small edge Péclet number P, which is the ratio of the deposition to the diffusive flux along a step edge. In particular, β̃ is found to satisfy β̃ = O(Θ-1) for O(P 1/3) > Θ ⇒ 1, which is in agreement with independent, equilibrium-based calculations.

AB - Starting from a detailed model for the kinetics of a step edge or island boundary, we derive a Gibbs-Thomson-type formula and the associated step stiffness as a function of the step edge orientation angle, Θ. Basic ingredients of the model are (i) the diffusion of point defects ("adatoms") on terraces and along step edges; (ii) the convection of kinks along step edges; and (iii) constitutive laws that relate adatom fluxes, sources for kinks, and the kink velocity with densities via a meanfield approach. This model has a kinetic (nonequilibrium) steady-state solution that corresponds to epitaxial growth through step flow. The step stiffness, β̃(Θ), is determined via perturbations of the kinetic steady state for small edge Péclet number P, which is the ratio of the deposition to the diffusive flux along a step edge. In particular, β̃ is found to satisfy β̃ = O(Θ-1) for O(P 1/3) > Θ ⇒ 1, which is in agreement with independent, equilibrium-based calculations.

KW - Adatoms

KW - Edge-atoms

KW - Ehrlich-Schwoebel barrier

KW - Epitaxial growth

KW - Gibbs-Thomson formula

KW - Island dynamics

KW - Kinetic steady state

KW - Line tension

KW - Step edge

KW - Step edge kinetics

KW - Step permeability

KW - Step stiffness

KW - Surface diffusion

UR - http://www.scopus.com/inward/record.url?scp=55149111162&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=55149111162&partnerID=8YFLogxK

U2 - 10.1137/070690948

DO - 10.1137/070690948

M3 - Article

VL - 7

SP - 242

EP - 273

JO - Multiscale Modeling and Simulation

JF - Multiscale Modeling and Simulation

SN - 1540-3459

IS - 1

ER -