EUV Photon Shot Noise Calculator

How it works

A photon of wavelength λ carries energy E = hc / λ With hc = 1239.84 eV·nm, an EUV photon at 13.5 nm carries about 91.8 eV — roughly 14× the energy of a 193 nm DUV photon. Because the energy per photon is fixed, a given exposure dose corresponds to a specific number of photons per unit area:

At 30 mJ/cm² that is only ~20 photons per nm². Multiply by the feature area (and an optional absorbed fraction) to get the mean number of photons N that actually expose the feature. Photon arrivals are independent, so N follows Poisson statistics: the standard deviation is σ = √N and the relative shot noise is 1/√N. Halving the feature area or the dose raises that relative noise by √2 — which is why the smallest features at the lowest doses are where stochastic printing failures first appear.

What the model deliberately ignores

• Resist chemistry. Real exposure adds acid generation, chemical amplification, quencher, and development — each with its own statistics. Photon shot noise is the floor, not the whole story.
• Absorption. The "absorbed fraction" is a single lumped number here. Thin EUV resists absorb only a portion of incident photons (often ~10–40%), and it is the absorbed count that drives stochastics.
• Blur and threshold. Whether a photon-count fluctuation becomes a defect also depends on secondary-electron blur and the development threshold — see the companion blur and defect-probability tools.

Further reading

The stochastic-defect literature around EUV is the place to calibrate intuition — for example the body of work by P. De Bisschop (imec) on stochastic printing failures, and resist-photon-statistics discussions from the SPIE Advanced Lithography community. Treat the numbers here as order-of-magnitude teaching values, not measured defectivity.