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 autocorrelation-based 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.

在微电子器件的制造中，溅射的薄膜导致通过（i）的高斯高度分布和（ii）恒定功率谱密度（PSD）向上描述了各向同性粗糙表面的滚降频率q ₀从它作为幂律衰减。本文介绍了一种可靠的方法来估计各向同性高斯粗糙微表面的密度、平均曲率半径和峰顶高度分布等地形参数。所提出的方法包括根据原子力显微镜测量值计算 PSD 函数，逼近q ₀的值和幅度P ₀通过曲线拟合算法对高原进行分析，并使用随机过程理论分析推导地形参数。在溅射的金微表面上评估了所提出方法的稳健性。调查表明，与确定性方法相比，所提出的基于 PSD 的方法减少了地形参数对采样长度的依赖性。此外，与确定性和基于自相关的方法相比，基于 PSD 的峰顶估计密度与扫描电子显微镜分析非常一致。因此，所提出的方法更适合从微表面的测量中提取地形参数，以开发基于接触粗糙的模型。