Surface slope distribution with mathematical molding on Au(111) thin film growth

Abstract

In this article, the authors developed a topographic image processing procedure based on polynomial interpolating functions for studying growth of thin films at nanoscale. Using the topographic atomic force microscopy images as input for the proposed procedure, the authors obtained the surface slope distributions at different thicknesses (2–60nm) for evaporated Au(111) films as well as the thickness dependence of the mean slope. The scaling exponents [namely, the growth exponent β=0.70±0.02 and the dynamic one 1∕z=0.004±0.013 that determine the thickness dependence of the roughness (σ) and the size of the surface features (ξ) as σ∼thicknessβ and ξ∼thickness1∕z, respectively] that result from our analysis indicate that the growth front of the Au films is formed by mound-shaped surface features that grow preferentially in height (i.e., without lateral coarsening). These results, together with the evolution of the mean slope toward a saturation value, suggest that the morphology evolution of the Au films corresponds to early stages of a growth regime characterized by the formation of steep mounds with selected slopes. Plausibly, such mounds would be responsible for the columnar structure observed in thicker Au films by microscopy.