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Published equation contexts

EPE=σoverlay2+σCD2+σLER2\mathrm{EPE} = \sqrt{\sigma_{\mathrm{overlay}}^{2} + \sigma_{\mathrm{CD}}^{2} + \sigma_{\mathrm{LER}}^{2}}

Why this formula appears here

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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σoverlay2\sigma_{\mathrm{overlay}}^{2}

Symbol sigma_overlay^2

sigmaoa_overlay2y^2 is one of the signed contributions combined to compute the quantity on the left.

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σCD2\sigma_{\mathrm{CD}}^{2}

Symbol sigma_CD^2

sigmaCa_CD2D^2 is one of the signed contributions combined to compute the quantity on the left.

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σLER2\sigma_{\mathrm{LER}}^{2}

Symbol sigma_LER^2

sigmaLa_LER2R^2 is one of the signed contributions combined to compute the quantity on the left.

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Published contexts (1)

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

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

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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