Scaling Behavior of Cyclical Surface Growth

TL;DR

This paper investigates the scaling behavior of cyclical surface growth, revealing how surface roughness evolves with cycles and how primary process effects influence the asymptotic behavior, supported by simulations and experiments.

Contribution

It introduces a scaling framework for cyclical surface growth, analyzing the influence of linear and non-linear primary processes on surface roughness evolution.

Findings

Surface roughness follows a power-law with the number of cycles.

Asymptotic exponents are inherited from the dominant process.

Experimental data confirms the power-law scaling in electrodeposition/dissolution.

Abstract

The scaling behavior of cyclical surface growth (e.g. deposition/desorption), with the number of cycles n, is investigated. The roughness of surfaces grown by two linear primary processes follows a scaling behavior with asymptotic exponents inherited from the dominant process while the effective amplitudes are determined by both. Relevant non-linear effects in the primary processes may remain so or be rendered irrelevant. Numerical simulations for several pairs of generic primary processes confirm these conclusions. Experimental results for the surface roughness during cyclical electrodeposition/dissolution of silver show a power-law dependence on n, consistent with the scaling description.