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In the chemical mechanical polishing process of semiconductor manufacturing, the concentration of ‘large’ particles (   \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$\ge $$\end{document}   ≥0.5 μm) in the slurry, which is considerably larger in size than the main abrasives (   \documentclass[12pt]{minimal} 				\usepackage{amsmath} 				\usepackage{wasysym}  				\usepackage{amsfonts}  				\usepackage{amssymb}  				\usepackage{amsbsy} 				\usepackage{mathrsfs} 				\usepackage{upgreek} 				\setlength{\oddsidemargin}{-69pt} 				\begin{document}$$\approx $$\end{document}   ≈0.1 μm), is a critical parameter that strongly influences manufacturing defects, yields, and reliabilities of large-scale-integrated circuits. Various instruments, so-called particle counters, based on light scattering, light extinction, and holography techniques have been developed to measure and monitor the large particle concentration in semiconductor fabs in real time. However, sizeable fluctuation in the measured particle concentration complicates the statistical process control in the fabs worldwide. Here, we show that an inherent fluctuation exists in the counting of large particles, which is universal, independent of instrument type, and quantitatively determined by the instrument’s operation parameters. We analytically derive a statistical theory of the fluctuation based on Poisson statistics and validate the theory through experiments and Monte-Carlo simulation. Furthermore, we provide a strategy to enhance the measurement accuracy by statistically adjusting the instrumental parameters commonly involved in the particle counters. The present results and analyses could be useful for statistical process control in semiconductor fabs to prevent large particle-induced defects such as micro-scratches and pits on wafers.

Universal inherent fluctuations in statistical counting of large particles in slurry used for semiconductor manufacturing