Emergence of step flow from an atomistic scheme of epitaxial growth in1+1dimensions

Abstract

The Burton-Cabrera-Frank (BCF) model for the flow of line defects (steps) on crystal surfaces has offered useful insights into nanostructure evolution. This model has rested on phenomenological grounds. Our goal is to show via scaling arguments the emergence of the BCF theory for noninteracting steps from a stochastic atomistic scheme of a kinetic restricted solid-on-solid model in one spatial dimension. Our main assumptions are: adsorbed atoms (adatoms) form a dilute system, and elastic effects of the crystal lattice are absent. The step edge is treated as a front that propagates via probabilistic rules for atom attachment and detachment at the step. We formally derive a quasistatic step flow description by averaging out the stochastic scheme when terrace diffusion, adatom desorption, and deposition from above are present.

Steric Hindrance of Crystal Growth: Nonlinear Step Flow in 1+1 Dimensions

“…This theme bears resemblance to the main objectives of [5][6][7][8]. However, in these works [5][6][7][8] the authors' attention focuses on near-equilibrium processes, whereas in the present paper we study the kinetic regime in which external material deposition tends to drive the system away from equilibrium. A similar task is undertaken in [13], albeit via a (coarse-grained) "terrace-step-kink" model.…”

“…Our analysis, which focuses on averages of microscopic variables such as the number of adatoms per lattice site, leaves unexplored the issue of stochastic fluctuations in step motion [6].…”

“…By the usual notion of macroscopic diffusion, it is natural to set D := Da 2 = O(1), the surface diffusivity; and F := F (N −1)a , the deposition flux per unit length [6,7]. Thus, the first two lines of (33), with (52), imply…”

Signature of microscale kinetics in mesoscale description of epitaxial growth

“…The present work forms an extension of recent studies in the atomistic origin of crystal growth, e.g., [9][10][11][12][13][14][15][16][17]. Our specific objectives, however, are different from those of past works.…”

“…Our analysis prioritizes kinetic corrections to the 1D BCF model, when the system is not at equilibrium, and thus complements [9,10,[13][14][15], which focus on the derivation of the standard BCF model (near equilibrium). Our goals resemble those of [16,17], in which corrections to the BCF model due to nucleation are considered.…”