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 derive simplified formulas for the terrace width distribution and terrace width correlations in the limit N → ∞ for small step fluctuations. Our general result expresses terrace width correlations as an interplay of noise covariance and step interaction strength. 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. In both cases of noise, we find that terrace width correlations decay exponentially with the step number difference; this behavior leads to vanishing correlations in the macroscopic limit. Our analysis may be used to (i) determine the noise in quasi-one-dimensional surfaces and (ii) assess the validity of previous mean field approximations.