← All parts of this equation

Equation 14 · Part 2 · Patterning at the Limit: What Actually Happens When a Chip Is Manufactured

Symbol sigma_CD^2

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

What this part means

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

Its job in the formula

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

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.

Read this part in the article →

Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

See this notation across published equations →

Sources cited in the surrounding passage

These citations provide research context; check each source for the exact claim it supports.