Figure 3 | Scientific Reports

Figure 3

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

Figure 3

Probability density functions for the number of large particles in the slurry. (a) Schematically drawn probability density function for the particle number x in 1 ml of the original slurry, where the average number of large particles in the original slurry is \(\lambda _0\). (b) The probability density function for the particle number \(x^\prime \) in \(\beta \)ml of the diluted slurry by a factor of \(\alpha \). (c) The probability density function for the number of particles \(x^{\prime \prime }\) in 1 ml, obtained by multiplying \(\alpha /\beta \) by the measured number \(x^\prime \). (d) The probability for the mean \(\overline{x^{\prime \prime }} = (1/n)\sum _{i=1}^{n} x^{\prime \prime }_i\), where \(x^{\prime \prime }_i\) is a random sample from the distribution shown in (c). (e) The probability density for the standard deviation of n-measurements of \(x^{\prime \prime }_i\).

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