Equation 14 · Patterning at the Limit: What Actually Happens When a Chip Is Manufactured
What does this equation mean?
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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol sigma_overlay^2
sigmverla is one of the signed contributions combined to compute the quantity on the left.
Symbol sigma_CD^2
sigm is one of the signed contributions combined to compute the quantity on the left.
Symbol sigma_LER^2
sigmE is one of the signed contributions combined to compute the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →subscript
The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.
superscript
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
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What the article says around this equation
If the contributing terms were independent and Gaussian, the budget would combine as . and the largest term would dominate. That independence assumption is exactly what makes the model useful and exactly where it is weakest: overlay and local variability share common causes through the same exposure, the same etch and the same stack. Treat the expression as a budgeting device, not a physical law. The roadmap cites published numerical simulations estimating that overlay takes about 40 per cent of the edge placement error budget and line-edge roughness about 25 per cent [ 1 ] . On that split, placement — not printing — is the single largest contributor.
Sources cited in the surrounding passage
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