A physics engine, and a verification tool enforced on top of it. PhysWall inverts a closed, published, non-linear physical law at a single measurement point — and refuses when the inverse is not unique. Seven laws, one engine, and the same refusal in all of them.
A physical-logic engine that decomposes a measurement gap along four axes — the machine, the law, the object, and which definition — and runs every domain through one structure.
RF matching, PCB loss, orbital conversion, photonic scattering, stream gauges, ocean waves, basketball. Same engine, same refusal: when the measurement cannot carry a conclusion, it says so instead of answering.
Defect density doubled this week. What changed?
A question from chip manufacturing, which is not a field anybody here works in. It is here because the answer needs nothing but published numbers and one habit: ask what the measurement can distinguish before asking what it says.
Patterning at the smallest nodes is limited by counting statistics. The exposure delivers a finite number of photons per feature, and a feature either prints or it does not. A published simulation study — Park et al., Scientific Reports 15, 43476 (2025) — gives simulated defect count against trench CD at 36 nm pitch, as a figure.
A separate analysis by Frederick Chen converts that figure to defect density, fits a curve, and derives a crossover dose of 31 mJ/cm² at which a 0.4% change in dose corresponds to twice the defect density.
dose drift 0.2% → defects ×1.4 to ×1.5
0.4% → defects ×2.0 ← the derived point
0.6% → defects ×2.0 to ×2.8
1.0% → defects ×2.4 to ×5.7
⚠ This page said "a Samsung study reports that a 0.4% change doubles the defect density" until an outside reviewer traced the chain. It does not. The study publishes a figure; the 0.4% is a third party's inference from it, and the analyst says so himself: he assumed a parabolic fit and writes that “we can get different fits to the data points which can lead to much lower crossovers”.
⚠ Which is worse than the caveat that was already here. The table was widened because the shape ABOVE the crossover is not published. It turns out the crossover itself moves with the choice of fit — so the anchor is not fixed either, and the range above is narrower than the evidence supports.
Nothing, on its own. A doubling is exactly what four-tenths of one percent of dose drift produces. The measurement cannot separate a process that changed from a dose that moved within a fraction of its own tolerance.
⚠ And the 1% dose-control figure often quoted alongside this is not from a datasheet either. It traces to a van Schoot (ASML) presentation at the 2021 EUVL Workshop, and it is for High-NA rather than the NXE tools. A conference slide is not a specification, and the distinction matters when the whole question is what the number can carry.
And better defect counting will not fix it. The ambiguity is in the relationship, not in the count — which makes this the case where more measurement effort is wasted effort, and knowing that in advance is worth more than the effort.
No verdict. And the reason, stated: the dose at the same point in time is not in the measurement. Until it is, a doubling is consistent with both answers.
If defects rose six-fold, dose drift would have to be at least a full percent — and that is the most generous of the three shapes. On a straight-line reading it takes two percent; on a saturating one, no dose drift reaches six-fold at all. The conclusion survives the uncertainty about shape, which the doubling did not.
A dose excursion of that size is far larger than this class of tool is normally operated to hold. That one is a process change, and the same relationship that refused the first question answers the second.
A tool that only ever refuses is useless. The value is that one relationship does both, and says which is which.
The gap is well documented. The trade-off between yield and throughput was written down plainly by Chris Mack, CTO of Fractilia, in Semiconductor Digest in March 2022: stochastics force fabs to choose between reducing scanner throughput by raising dose, or buying another scanner. Measurement of these defects has improved enormously, and there are companies whose entire business is making that measurement trustworthy.
What we did not find is anyone stating that a doubling does not distinguish the two answers. That is a claim someone can refute by sending us a reference, which is the point of putting it this way — an earlier draft of this page said "only we can do this", and that is not a claim anybody can check.
⚠ Every figure here is from published literature. None of this is our field, and that is deliberate: a decomposition that only works where its author is expert is not a decomposition.
PhysWall was developed and architected by Gadi Zion.
Built on PhysWall — the same engine reads antenna bandwidth, conductor loss, bit erasure and heat limits. It answers what the measurement implies, and refuses when the measurement cannot say.⚠ Check this instead of believing it. Every number here reproduces from a source that is named, and the claims that turned out wrong are still printed next to what replaced them. The same engine runs all of these — it asks how much a measurement allows you to conclude, and refuses the same way in every field. The same engine runs all of these — it asks how much a measurement allows you to conclude, and refuses the same way in every field. How to check each one →