Spectral analysis of the topography parameters for isotropic Gaussian rough surfaces applied to gold coating

In the fabrication of microelectronic devices, sputtering of thin films leads to isotropic rough surfaces described by (i) a Gaussian height distribution and (ii) a constant power spectral density (PSD) up to a roll-off frequency of q0 from which it decays as a power law. This paper introduces a robust approach to estimate the topography parameters such as the density, the mean radius of curvature and the height distribution of summits for isotropic Gaussian rough micro-surfaces. The proposed approach consists of computing the PSD function from the atomic force microscopy measurements, approximating the value of q0 and the magnitude P0 of the plateau by curve fitting algorithms, and analytically deriving the topography parameters using the random process theory. The robustness of the proposed methodology is assessed on a sputtered gold micro-surface. The investigations show that the proposed PSD-based approach reduces the dependence of the topography parameters on the sampling length compared to the deterministic method. Moreover, the PSD-based estimated density of summits is in a good agreement with scanning electron microscopy analysis, in contrast to both deterministic and autocorrelationbased methods. The proposed approach is therefore more suitable to extract topography parameters from measurements of micro-surfaces for the development of contact asperity-based models.

Automated summary

This paper introduces a robust approach for estimating the topography parameters of isotropic Gaussian rough micro-surfaces and evaluates the reliability of the method. The results show that the PSD-based approach reduces the dependence of topography parameters on sampling length and provides more accurate estimations compared to deterministic methods.