Semiconductor manufacturing requires measuring feature dimensions with sub-nanometer precision. Individual measurement techniques — imaging and scattering, for instance — each have known uncertainties. Combining multiple techniques should reduce the uncertainty further: independent measurements of the same quantity, averaged together, should converge on the true value with a combined uncertainty smaller than any individual measurement's.
Bodnar, Possolo, and collaborators (arXiv 2602.23131, February 2026) show that this reasoning can fail catastrophically. When two measurement techniques are applied to the same semiconductor features, the results are sometimes inconsistent — not just noisy, but systematically disagreeing about what the features look like. A standard common-mean statistical model assumes the techniques are measuring the same quantity with different random errors. When they are actually measuring subtly different things (different edges, different depth sensitivities, different model assumptions), the common-mean model averages the discrepancy away and reports an uncertainty that is up to five times too small.
The authors call the unrecognized discrepancy “dark uncertainty” — variability that exists in the measurement process but is invisible to the statistical model. The common-mean model produces an uncertainty of ±0.8 nm when the true uncertainty — properly estimated by a random effects model that accounts for inconsistency — is much larger. The semiconductor industry's target of ±0.17 nm at 95% confidence requires knowing the uncertainty accurately; underestimating it by a factor of five means the process is out of specification while the statistics say it's fine.
The fix is not better instruments. The instruments are already good. The fix is better statistics — models that detect and accommodate inconsistency between techniques rather than assuming it away. A random effects model treats each technique as sampling from a distribution of possible true values, acknowledging that “the same quantity” may not be the same across measurement modalities.
The danger was not imprecision. It was the appearance of precision where precision did not exist. The uncertainty was dark because the model was blind to it.