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Equation 3 · Part 2 · Comparing the Main Approaches to Advanced Semiconductor Fabrication

Symbol σ

σN=σN.\sigma_N = \sigma\sqrt{N}.
σ\sigma

What this part means

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

Its job in the formula

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

The passage around this formula

…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 quadrature: σN=σN\sigma_N = \sigma\sqrt{N}. Treat this as a simplified budgeting device rather than a physical law; real exposures on the same scanner and same reticle stage are not fully independent, and correlated error can be partly…

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