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Equation 14 · Part 4 · Patterning at the Limit: What Actually Happens When a Chip Is Manufactured

=

EPE=σoverlay2+σCD2+σLER2,\mathrm{EPE} = \sqrt{\sigma_{\mathrm{overlay}}^{2} + \sigma_{\mathrm{CD}}^{2} + \sigma_{\mathrm{LER}}^{2}},
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What this part means

The expressions on both sides represent the same quantity under the stated assumptions.

Its job in the formula

The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.

The passage around this formula

If the contributing terms were independent and Gaussian, the budget would combine as EPE=σoverlay2+σCD2+σLER2\mathrm{EPE} = \sqrt{\sigma_{\mathrm{overlay}}^{2} + \sigma_{\mathrm{CD}}^{2} + \sigma_{\mathrm{LER}}^{2}}. 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.

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Learn the underlying idea

An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.

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Sources cited in the surrounding passage

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