Small fluctuations in epitaxial growth via conservative noise

Title of Thesis: SMALL FLUCTUATIONS IN EPITAXIAL GROWTH VIA CONSERVATIVE NOISE Paul Patrone, Masters Degree, 2012 Thesis directed by: Professor Dionisios Margetis Department of Math 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 simplified 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-fluxinduced asymmetric attachment and detachment of atoms at step edges. We discuss implications of our analysis, particularly the narrowing of the TWD with the deposition 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. SMALL FLUCTUATIONS IN EPITAXIAL GROWTH VIA CONSERVATIVE NOISE