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Equation 1 · Part 3 · Advanced Semiconductor Fabrication in Practice: An Advanced Technical Guide

fraction

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

What this part means

Divide the expression above the line by the one below it.

Its job in the formula

The expression above the fraction bar is divided by the complete expression below it. The denominator must not be zero.

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.

Open the illustrated fractions: division written vertically guide →

Sources cited in the surrounding passage

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