EUV Lithography Photon Shot Noise Calculator

Extreme ultraviolet lithography & nanometer patterning: Model stochastic photon shot noise, Poisson photon count variance, line edge roughness (LER), and contact hole yield.

EUV Exposure & Feature Scale

Exposure Dose D (mJ/cm²): Wafer incident EUV dose

Feature Critical Dimension CD (nm): Contact hole diameter or line width

Feature Geometry: Patterning topology

Resist EUV Absorption Fraction A (%): Photons absorbed in resist film (typical 15-30%)

Quantum Yield / Acid Multiplication: Acids generated per absorbed EUV photon

Stochastic Failure Criterion (k·σ): Defect cutoff tail in standard deviations

Stochastic Shot Noise Analysis

Incident EUV Photons / Feature

Shot Noise Uncertainty (σ / N)

1 / √N_absorbed

Photogenerated Acids / Hole

N_abs · Quantum Yield

Estimated LWR / LER (3σ)

Line width roughness estimate

Stochastic Failure Rate (ppm)

Missing/bridging contacts

Total Photons per Billion Contacts

Fab-scale exposure density

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Frequently Asked Questions

What are EUV stochastic defects?

Stochastic defects are random, non-repeating printing failures caused by local statistical variations in photon absorption and chemical acid generation. They manifest as stochastic micro-bridges (unintended short circuits) in dense lines or missing/closed vias (open circuits) in contact arrays.

Why are Metal Oxide Resists (MOR) used for EUV?

Traditional Chemically Amplified Resists (CAR) are made of organic polymers with low EUV photon absorption (10% to 20%). Metal oxide resists (e.g. tin-oxide nanoparticles) possess heavy elements that absorb 2 to 4 times more EUV energy per nanometer of film, quadrupling the absorbed photon count and slashing stochastic shot noise.

How does scanner source power relate to stochastic defects?

To overcome photon shot noise without reducing scanner throughput, high-power CO2-driven laser produced plasma (LPP) sources (producing 300W to 500W of EUV) are required to deliver high doses (45 - 70 mJ/cm²) within the brief exposure scan duration.