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σN=σN\sigma_N = \sigma\sqrt{N}

Why this formula appears here

What a mask count actually costs is not one extra exposure. It is an extra circuit through the entire patterning loop: another resist coat, another exposure, another develop, in most multi-patterning schemes another etch and clean, and another round of the metrology that has to confirm the result before the next layer can be trusted to sit on top of it. If a critical layer’s target pitch is split across N separately printable exposures — as litho-etch-litho-etch and self-aligned multiple patterning both do, in different ways — and each exposure contributes an independent, zero-mean placement error of standard deviation σ\sigma , the layer’s overlay-driven placement uncertainty combines in…

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σN\sigma_N

Symbol sigma_N

sigmaNa_N is part of the quantity the equation computes from the expression on the right.

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Published contexts (1)

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σN=σN.\sigma_N = \sigma\sqrt{N}.

Equation 3 · AI Hardware & Semiconductors

Comparing the Main Approaches to Advanced Semiconductor Fabrication

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

What a mask count actually costs is not one extra exposure. It is an extra circuit through the entire patterning loop: another resist coat, another exposure, another develop, in most multi-patterning schemes another etch and clean, and another round of the metrology that has to confirm the result before the next layer can be trusted to sit on top of it. If a critical layer’s target pitch is split across N separately printable exposures — as litho-etch-litho-etch and self-aligned multiple patterning both do, in different ways — and each exposure contributes an independent, zero-mean placement error of standard deviation σ\sigma , the layer’s overlay-driven placement uncertainty combines in…

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