Refined BCF-type boundary conditions for mesoscale surface step dynamics

Deposition on a vicinal surface with alternating rough and smooth steps is described by a solid-on-solid model with anisotropic interactions. Kinetic Monte Carlo (KMC) simulations of the model reveal step pairing in the absence of any additional step attachment barriers. We explore the description of this behavior within an analytic Burton-Cabrera-Frank (BCF)-type step dynamics treatment. Without attachment barriers, conventional kinetic coefficients for the rough and smooth steps are identical, as are the predicted step velocities for a vicinal surface with equal terrace widths. However, we determine refined kinetic coefficients from a two-dimensional discrete deposition-diffusion equation formalism which accounts for step structure. These coefficients are generally higher for rough steps than for smooth steps, reflecting a higher propensity for capture of diffusing terrace adatoms due to a higher kink density. Such refined coefficients also depend on the local environment of the step and can even become negative (corresponding to net detachment despite an excess adatom density) for a smooth step in close proximity to a rough step. Our key observation is that incorporation of these refined kinetic coefficients into a BCF-type step dynamics treatment recovers quantitatively the mesoscale step-pairing behavior observed in the KMC simulations. Disciplines Astrophysics and Astronomy | Mathematics | Physics Comments This article is from Physical Review B 91 (2015): 235441, doi: 10.1103/PhysRevB.91.235441. Posted with permission. This article is available at Iowa State University Digital Repository: http://lib.dr.iastate.edu/physastro_pubs/178 PHYSICAL REVIEW B 91, 235441 (2015) Refined BCF-type boundary conditions for mesoscale surface step dynamics Renjie Zhao,1,2 David M. Ackerman,1 and James W. Evans1,2,3 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 (Received 16 April 2015; published 24 June 2015) Deposition on a vicinal surface with alternating rough and smooth steps is described by a solid-on-solid model with anisotropic interactions. Kinetic Monte Carlo (KMC) simulations of the model reveal step pairing in the absence of any additional step attachment barriers. We explore the description of this behavior within an analytic Burton-Cabrera-Frank (BCF)-type step dynamics treatment. Without attachment barriers, conventional kinetic coefficients for the rough and smooth steps are identical, as are the predicted step velocities for a vicinal surface with equal terrace widths. However, we determine refined kinetic coefficients from a two-dimensional discrete deposition-diffusion equation formalism which accounts for step structure. These coefficients are generally higher for rough steps than for smooth steps, reflecting a higher propensity for capture of diffusing terrace adatoms due to a higher kink density. Such refined coefficients also depend on the local environment of the step and can even become negative (corresponding to net detachment despite an excess adatom density) for a smooth step in close proximity to a rough step. Our key observation is that incorporation of these refined kinetic coefficients into a BCF-type step dynamics treatment recovers quantitatively the mesoscale step-pairing behavior observed in the