Permeability and kinetic coefficients for mesoscale BCF surface step dynamics: Discrete two-dimensional deposition-diffusion equation analysis

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. Disciplines Condensed Matter Physics | Physics Comments This article is published as Zhao, Renjie, James W. Evans, and Tiago J. Oliveira. "Permeability and kinetic coefficients for mesoscale BCF surface step dynamics: Discrete two-dimensional deposition-diffusion equation analysis." Physical Review B 93, no. 16 (2016): 165411, doi:10.1103/PhysRevB.93.165411. Posted with permission. This article is available at Iowa State University Digital Repository: http://lib.dr.iastate.edu/physastro_pubs/449 PHYSICAL REVIEW B 93, 165411 (2016) Permeability and kinetic coefficients for mesoscale BCF surface step dynamics: Discrete two-dimensional deposition-diffusion equation analysis Renjie Zhao,1,2 James W. Evans,1,2,3,* and Tiago J. Oliveira1,2,4 1Ames Laboratory, USDOE, Iowa State University, Ames, Iowa 50011, USA 2Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50011, USA 3Department of Mathematics, Iowa State University, Ames, Iowa 50011, USA 4Departamento de Fı́sica, Universidade Federal de Viçosa, 36570-900, Viçosa, Minas Gerais, Brazil (Received 15 December 2015; revised manuscript received 15 March 2016; published 8 April 2016) 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