Fractal topography of surfaces exposed to gas-cluster ion beams and modeling simulations

Surface topography measured by atomic force microscope is reported before and after various gas-cluster ion beam (GCIB) treatments along with modeling simulations of topography changes. Height correlation and spectral distributions of these surfaces show characteristics of random fractals with Hurst exponent H typically 0.5<H<1.0 and correlation lengths from ∼10 to over 500 nm. The roughness increases or decreases depending on the initial surface and the nature of the GCIB. The power spectral density distributions observed have a broad power-law roll off from a low-frequency plateau to a high-frequency one. This occurs over an approximate range of spatial frequencies from 5×10−3 to 5×10−1 nm−1. Data from several example surfaces are given. Roughening is shown to be a statistical accumulation of individual cluster impacts and the process is modeled by Monte Carlo simulations resulting in fractal surfaces. A continuum model that incorporates surface mobility is used to simulate the smoothing, and methods to combine this with the Monte Carlo model are presented. The behavior of surfaces under exposure to GCIB is satisfactorily simulated by this combined model. Accurate simulation of the surface smoothing requires that the surface-mobility model be independent of the spatial frequency over the bandwidth of observation, unlike Fick’s law of diffusion. The nonphysical prediction of previous simulations that the topography trends toward the complete absence of roughness is also corrected.