Small fluctuations in epitaxial growth via conservative noise
Abstract
We study the combined effect of growth (material deposition from above) and
nearest-neighbor entropic and force-dipole interactions in a stochastically perturbed
system of N line defects (steps) on a vicinal crystal surface in 1+1 dimensions.
First, we formulate a general model of conservative white noise, and we derive sim-
plified formulas for the terrace width distribution (TWD) and pair correlations,
particularly the covariance matrix of terrace widths, in the limit N → ∞ for small
step fluctuations. Second, we apply our formalism to two specific noise models
which stem, respectively, from: (i) the fluctuation-dissipation theorem for diffusion
of adsorbed atoms; and (ii) the phenomenological consideration of deposition-flux-
induced asymmetric attachment and detachment of atoms at step edges. We discuss
implications of our analysis, particularly the narrowing of the TWD with the de-
position flux, connection of noise structure to terrace width correlations, behavior
of these correlations in the macroscopic limit, and comparison of our perturbation
results to a known mean field approach.