Permeability and kinetic coefficients for mesoscale BCF surface step dynamics: Discrete two-dimensional deposition-diffusion equation analysis
Abstract
Here, a discrete version of deposition-diffusion equations appropriate for description of step flow on a vicinal surface is analyzed for a two-dimensional grid of adsorption sites representing the stepped surface and explicitly incorporating kinks along the step edges. Model energetics and kinetics appropriately account for binding of adatoms at steps and kinks, distinct terrace and edge diffusion rates, and possible additional barriers for attachment to steps. Analysis of adatom attachment fluxes as well as limiting values of adatom densities at step edges for nonuniform deposition scenarios allows determination of both permeability and kinetic coefficients. Behavior of these quantities is assessed as a function of key system parameters including kink density, step attachment barriers, and the step edge diffusion rate.
- Authors:
-
- Ames Lab. and Iowa State Univ., Ames, IA (United States)
- Ames Lab. and Iowa State Univ., Ames, IA (United States); Univ. Federal de Vicosa, Minas Gerais (Brazil)
- Publication Date:
- Research Org.:
- Ames Lab., Ames, IA (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1254314
- Alternate Identifier(s):
- OSTI ID: 1246514
- Report Number(s):
- IS-J-8980
Journal ID: ISSN 2469-9950; PRBMDO
- Grant/Contract Number:
- AC02-07CH11358
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Physical Review B
- Additional Journal Information:
- Journal Volume: 93; Journal Issue: 16; Journal ID: ISSN 2469-9950
- Publisher:
- American Physical Society (APS)
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
Citation Formats
Zhao, Renjie, Evans, James W., and Oliveira, Tiago J.. Permeability and kinetic coefficients for mesoscale BCF surface step dynamics: Discrete two-dimensional deposition-diffusion equation analysis. United States: N. p., 2016.
Web. doi:10.1103/PhysRevB.93.165411.
Zhao, Renjie, Evans, James W., & Oliveira, Tiago J.. Permeability and kinetic coefficients for mesoscale BCF surface step dynamics: Discrete two-dimensional deposition-diffusion equation analysis. United States. https://doi.org/10.1103/PhysRevB.93.165411
Zhao, Renjie, Evans, James W., and Oliveira, Tiago J.. Fri .
"Permeability and kinetic coefficients for mesoscale BCF surface step dynamics: Discrete two-dimensional deposition-diffusion equation analysis". United States. https://doi.org/10.1103/PhysRevB.93.165411. https://www.osti.gov/servlets/purl/1254314.
@article{osti_1254314,
title = {Permeability and kinetic coefficients for mesoscale BCF surface step dynamics: Discrete two-dimensional deposition-diffusion equation analysis},
author = {Zhao, Renjie and Evans, James W. and Oliveira, Tiago J.},
abstractNote = {Here, a discrete version of deposition-diffusion equations appropriate for description of step flow on a vicinal surface is analyzed for a two-dimensional grid of adsorption sites representing the stepped surface and explicitly incorporating kinks along the step edges. Model energetics and kinetics appropriately account for binding of adatoms at steps and kinks, distinct terrace and edge diffusion rates, and possible additional barriers for attachment to steps. Analysis of adatom attachment fluxes as well as limiting values of adatom densities at step edges for nonuniform deposition scenarios allows determination of both permeability and kinetic coefficients. Behavior of these quantities is assessed as a function of key system parameters including kink density, step attachment barriers, and the step edge diffusion rate.},
doi = {10.1103/PhysRevB.93.165411},
journal = {Physical Review B},
number = 16,
volume = 93,
place = {United States},
year = {Fri Apr 08 00:00:00 EDT 2016},
month = {Fri Apr 08 00:00:00 EDT 2016}
}
Web of Science
Works referenced in this record:
The Growth of Crystals and the Equilibrium Structure of their Surfaces
journal, June 1951
- Burton, W. K.; Cabrera, N.; Frank, F. C.
- Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, Vol. 243, Issue 866
Steps on surfaces: experiment and theory
journal, September 1999
- Jeong, Hyeong-Chai; Williams, Ellen D.
- Surface Science Reports, Vol. 34, Issue 6-8
Crystal surfaces in and out of equilibrium: A modern view
journal, March 2010
- Misbah, Chaouqi; Pierre-Louis, Olivier; Saito, Yukio
- Reviews of Modern Physics, Vol. 82, Issue 1
Morphological evolution during epitaxial thin film growth: Formation of 2D islands and 3D mounds
journal, April 2006
- Evans, J. W.; Thiel, P. A.; Bartelt, M. C.
- Surface Science Reports, Vol. 61, Issue 1-2
The Spiral Growth of Crystals
journal, January 1961
- Chernov, A. A.
- Soviet Physics Uspekhi, Vol. 4, Issue 1
Morphological equilibration of a facetted crystal
journal, February 1992
- Ozdemir, M.; Zangwill, A.
- Physical Review B, Vol. 45, Issue 7
Critical terrace width for step flow growth: Effect of attachment-detachment asymmetry and step permeability
journal, June 2007
- Ranguelov, Bogdan; Altman, M. S.; Markov, Ivan
- Physical Review B, Vol. 75, Issue 24
Step bunching with general step kinetics: stability analysis and macroscopic models
journal, April 2003
- Pierre-Louis, O.
- Surface Science, Vol. 529, Issue 1-2
Phase field models for step flow
journal, August 2003
- Pierre-Louis, O.
- Physical Review E, Vol. 68, Issue 2
Effect of step permeability on step instabilities due to alternation of kinetic coefficients on a growing vicinal face
journal, October 2007
- Sato, M.
- The European Physical Journal B, Vol. 59, Issue 3
Statistics of second layer nucleation in heteroepitaxial growth
journal, June 2002
- Filimonov, S. N.; Hervieu, Yu. Yu.
- Surface Science, Vol. 507-510
Kinetics of second layer nucleation with permeable steps
journal, October 2014
- Hervieu, Yu. Yu.; Markov, Ivan
- Surface Science, Vol. 628
Slope selection of mounds with permeable steps in homoepitaxy
journal, February 2013
- Korutcheva, Elka; Koroutchev, Kostadin; Markov, Ivan
- The European Physical Journal B, Vol. 86, Issue 2
Macroscopic view of crystal-step transparency
journal, October 2008
- Quah, John; Young, Jerrod; Margetis, Dionisios
- Physical Review E, Vol. 78, Issue 4
Step Permeability and the Relaxation of Biperiodic Gratings on Si(001)
journal, April 1997
- Tanaka, S.; Bartelt, N. C.; Umbach, C. C.
- Physical Review Letters, Vol. 78, Issue 17
Kinetic length, step permeability, and kinetic coefficient asymmetry on the Si(111) (7×7) surface
journal, August 2002
- Chung, W. F.; Altman, M. S.
- Physical Review B, Vol. 66, Issue 7
Boundary Conditions for Burton–Cabrera–Frank Type Step-Flow Models: Coarse-Graining of Discrete 2D Deposition-Diffusion Equations
journal, January 2011
- Ackerman, David M.; Evans, J. W.
- Multiscale Modeling & Simulation, Vol. 9, Issue 1
From discrete hopping to continuum modeling on vicinal surfaces with applications to Si(001) electromigration
journal, April 2005
- Zhao, Tong; Weeks, John D.; Kandel, Daniel
- Physical Review B, Vol. 71, Issue 15
Refined BCF-type boundary conditions for mesoscale surface step dynamics
journal, June 2015
- Zhao, Renjie; Ackerman, David M.; Evans, James W.
- Physical Review B, Vol. 91, Issue 23
Terrace-edge-kink model of atomic processes at the permeable steps
journal, March 2004
- Filimonov, S. N.; Hervieu, Yu. Yu.
- Surface Science, Vol. 553, Issue 1-3
Anisotropic Step Stiffness from a Kinetic Model of Epitaxial Growth
journal, January 2008
- Margetis, Dionisios; Caflisch, Russel E.
- Multiscale Modeling & Simulation, Vol. 7, Issue 1
Transition from Island Growth to Step-Flow Growth for Si/Si(100) Epitaxy
journal, March 1997
- Voigtländer, Bert; Weber, Thomas; Šmilauer, Pavel
- Physical Review Letters, Vol. 78, Issue 11
Fundamental processes in Si/Si and Ge/Si epitaxy studied by scanning tunneling microscopy during growth
journal, September 2001
- Voigtländer, Bert
- Surface Science Reports, Vol. 43, Issue 5-8
Anisotropic coarsening: One-dimensional decay of Ag islands on Ag(110)
journal, April 2013
- Han, Yong; Russell, Selena M.; Layson, Anthony R.
- Physical Review B, Vol. 87, Issue 15
Analytic formulations for one-dimensional decay of rectangular homoepitaxial islands during coarsening on anisotropic fcc (110) surfaces
journal, October 2013
- Wang, Chi-Jen; Han, Yong; Walen, Holly
- Physical Review B, Vol. 88, Issue 15