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Equation 1 · Part 7 · Advanced Semiconductor Fabrication in Practice: An Advanced Technical Guide

Numerator: 1

σdose∝1Nphotons\sigma_{\text{dose}} \propto \frac{1}{\sqrt{N_{\text{photons}}}}
11

What this part means

The complete quantity above the fraction bar.

Its job in the formula

1 occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

Frederick Chen’s analysis of a real 3-nanometer via layer measured this directly: at typical exposure conditions (roughly 60–89 mJ/cm² depending on resist chemistry), the observed missing-via rate came in at the parts-per-million level — “many orders of magnitude higher than expected from basic estimates” that treat each pixel’s exposure as statistically independent [ 3 ] . The gap between the naive estimate and the measured rate is explained by correlation between neighboring exposed pixels: a defect does not need every pixel in a feature to fail independently, it needs a contiguous cluster of neighboring pixels to under- or over-expose together, which happens far more often than…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.