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

TL;DR

This paper highlights how dark uncertainty can cause significant underestimation of total measurement uncertainty in hybrid metrology for semiconductor manufacturing, risking overconfidence and potential failure.

Contribution

It demonstrates that standard uncertainty models often ignore dark uncertainty, proposing a random effects model to better account for it in linewidth measurements.

Findings

Random effects model estimates total uncertainty at +/- 0.8 nm

Common mean model underestimates uncertainty by up to five times

Dark uncertainty significantly impacts hybrid measurement accuracy

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.