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Equation 1 · Part 5 · Advanced Semiconductor Fabrication in Practice: An Advanced Technical Guide

∝

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

What this part means

Proportional to; the scale factor is not shown.

Its job in the formula

Proportional to; the scale factor is not shown.

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 variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the surrounding passage

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