EUV Dose–Defect Calculator
The core process-window trade-off: more dose means more photons and fewer stochastic defects, but slower, costlier exposure. Sweep the dose, watch the defect tail fall across orders of magnitude, and read off the dose needed to hit a target defect rate.
How it works
Dose sets the mean number of absorbed photons in a feature, μ = photons/nm² × area × absorbed fraction, and a feature is modelled as defective if it absorbs fewer than N min photons. Because the count is Poisson, the defect probability is the lower tail P(N < N min) — computed here with the regularized incomplete gamma function. Sweeping dose from 15 to 60 mJ/cm² traces the classic dose-response curve: as μ rises, the fixed threshold sits further into the safe part of the distribution and the failure tail collapses roughly exponentially.
The tool then inverts that curve. Given a target defect rate, it solves for the dose that reaches it — the practical question a process engineer actually asks. If the target can't be reached even at 150 mJ/cm², dose isn't the right lever: the feature is too small, absorbs too little, or the threshold is set too high.
Connection to SECD-CRF
This is the dimension the Stage 1 Monte-Carlo engine explores in run_dose_sensitivity_study() — sweeping dose and measuring how defect probability responds. The repo validates that the trend is monotonic (more dose → fewer defects) against known EUV physics. This calculator is the fast, closed-form cousin of that study for a single feature. The full, layout-aware version is the SECD-CRF project.
What the model deliberately ignores
- One feature, no layout. A real chip has billions of features with different geometries; yield depends on the whole distribution, not one contact.
- Assumed threshold.
N minlumps development, blur, and chemistry into a single clip level — it is not measured. - Dose isn't free. The model shows defects falling with dose but not the throughput, heating, and cost that rise with it — those set the real ceiling.
Method & numerics
For each dose D, μ(D) = photons_per_nm²(D, 13.5 nm) × area × absorbed and P(D) = P(N < N min) = Q(N min, μ) via regularized upper incomplete gamma (validated against direct summation to 1e-6). The dose-to-target is found by bisection on the monotonic P(D) over 5–150 mJ/cm². The chart plots log₁₀ P vs dose so the many-orders-of-magnitude tail stays readable; the violet line is your working dose and the red dashed line is your target.