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Overlay and edge placement error (EPE) budget calculator

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KEY POINTS

Independent error contributors combine as a root sum of squares (RSS), so trimming the largest contributor a little beats cutting a small one a lot. Mask registration error shrinks to one-quarter on the wafer with a 4× reticle. At leading-edge nodes, connections between layers are managed with edge placement error (EPE), overlay plus CD variation, and the budget is only a few nanometers.

Overlay error contributors (3σ, nm)

Scanner contribution (nm)Process contribution (nm)Mask registration error (on the mask) (nm)Reduction ratio (×)Metrology uncertainty (nm)Other (nm)

Total overlay (RSS)2.16nm

(Worst case with all terms aligned, simple sum)4.35nm

Largest contributorScanner (matching, lens, stage) (48.3 %)

Edge placement error (EPE)

Lower layer CD uniformity CDU (3σ) (nm)Upper layer CD uniformity CDU (3σ) (nm)Local CD uniformity LCDU (3σ) (nm)Allowed edge shift in the design (nm)

EPE (3σ)2.61nm

Remaining margin2.39nm

Overlay share of EPE68.7 %

RSS combination assuming each contributor is independent and normally distributed. If contributors are correlated (same tool, same correction model), the total will be larger than the RSS value.

Error breakdown

Overlay shares are relative to total overlay; EPE shares are relative to EPE.
Contributor	3σ (nm)	Share of squares
Scanner (matching, lens, stage)	1.50	48.3 %
Process (wafer bow and distortion, CMP)	1.20	30.9 %
Mask registration error (at wafer scale)	0.75	12.1 %
Metrology uncertainty	0.40	3.4 %
Other (drift, temperature, etc.)	0.50	5.4 %
EPE: Lower layer CDU / 2	0.75	8.3 %
EPE: Upper layer CDU / 2	0.75	8.3 %
EPE: Local CD uniformity LCDU / 2	1.00	14.7 %

From overlay control to EPE control

An error budget allocates the total allowed error among contributors such as the scanner, mask, process and metrology. Independent errors combine as a root sum of squares, so trimming the largest contributor a little does more than cutting a small one a lot. It is not unusual for one of five contributors to account for half the total.

With multiple patterning and EUV, where a pattern edge lands depends not only on placement (overlay) but also on line width variation (CDU) and local variation from stochastic resist effects (LCDU). Edge placement error (EPE), which combines them, has become the main way to control connections and shorts between layers. EPE budgets at leading-edge nodes are a few nanometers, only tens of atoms wide.

FAQ

Why combine errors by root sum of squares?

Independent, normally distributed errors rarely reach their extremes at the same time, so their combined spread is the square root of the sum of their variances.

Why does CD variation count at half its value in EPE?

A line width change moves both edges, so each edge shifts by half of the CD change.

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Last updated: October 23, 2026