Titanic overconfidence -- dark uncertainty can sink hybrid metrology for semiconductor manufacturing

2026-02-26

AI Summary

This study addresses a critical yet overlooked issue in semiconductor metrology: the severe underestimation of total measurement uncertainty in hybrid metrology due to the unaccounted “dark uncertainty” arising from inconsistent assumptions across multiple data sources. By integrating imaging and scatterometry techniques, the work systematically reveals the potentially detrimental impact of this oversight. At a 95% confidence level, a random-effects model yields a realistic uncertainty estimate of ±0.8 nm for critical linewidth measurements, whereas the conventional common-mean model underestimates uncertainty by a factor of five, exposing significant overconfidence. The study advocates adopting the random-effects model for handling inconsistent datasets and proposes best practices to mitigate dark uncertainty, thereby establishing a more robust uncertainty evaluation framework aligned with IEEE roadmap objectives.

Technology Category

Machine Learning: Calibration & Uncertainty QuantificationReasoning under Uncertainty: Uncertainty RepresentationsPlanning, Routing, and Scheduling: Scheduling under Uncertainty

Application Category

Security and Privacy: Large-scale security measurementsWeb Mining and Content Analysis: Web measurementsSearch and Retrieval-Augmented AI: Web evaluation methodologies and metrics

Abstract

Hybrid metrology for semiconductor manufacturing is on a collision course with dark uncertainty. An IEEE technology roadmap for this venture has targeted a linewidth uncertainty of +/- 0.17 nm at 95 % coverage and advised the hybridization of results from different measurement methods to hit this target. Related studies have applied statistical models that require consistent results to compel a lower uncertainty, whereas inconsistent results are prevalent. We illuminate this lurking issue, studying how standard methods of uncertainty evaluation fail to account for the causes and effects of dark uncertainty. We revisit a comparison of imaging and scattering methods to measure linewidths of approximately 13 nm, applying contrasting statistical models to highlight the potential effect of dark uncertainty on hybrid metrology. A random effects model allows the combination of inconsistent results, accounting for dark uncertainty and estimating a total uncertainty of +/- 0.8 nm at 95 % coverage. In contrast, a common mean model requires consistent results for combination, ignoring dark uncertainty and underestimating the total uncertainty by as much as a factor of five. To avoid such titanic overconfidence, which can sink a venture, we outline good practices to reduce dark uncertainty and guide the combination of indeterminately consistent results.

Problem

• hybrid metrology
• dark uncertainty
• semiconductor manufacturing
• linewidth measurement
• uncertainty evaluation

Innovation

• dark uncertainty
• hybrid metrology
• random effects model
• linewidth measurement
• uncertainty evaluation