[论文解读] Titanic overconfidence -- dark uncertainty can sink hybrid metrology for semiconductor manufacturing

Adam L. Pintar, Adam Pintar+5 more|arXiv (Cornell University)|Feb 26, 2026

Industrial Vision Systems and Defect Detection被引用 0

一句话总结

这篇论文表明，暗不确定性会导致混合计量低估总线宽不确定性；随机效应模型在95%覆盖下显示 +/- 0.8 nm，远大于标准均值模型估计。

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.

研究动机与目标

• 需要解决半导体制造中混合计量的暗不确定性问题的动机。
• 评估标准不确定性评估方法在处理暗不确定性时与鲁棒替代方案的差异。
• 量化暗不确定性对成像和散射方法测量线宽的影响。
• 提供降低暗不确定性、改进不定一致结果组合的指南。

提出的方法

• 应用随机效应模型来组合来自成像和散射方法的不一致线宽结果。
• 与假设结果一致的常见均值模型进行比较。
• 在两种模型下以95%覆盖估计总不确定性。
• 强调暗不确定性通过模型选择如何影响汇总不确定性。
• 说明计量集成和决策实践中的潜在作用。

实验结果

研究问题

• RQ1 暗不确定性如何影响混合计量中总线宽不确定性的估计？
• RQ2 在组合不一致结果时，随机效应模型与均值模型方法在总不确定性估计上的差异？
• RQ3 我们能否提供实际指南以降低暗不确定性并改善半导体计量中的不定一致结果的组合？
• RQ4 使用不同模型时线宽不确定性的覆盖率（如95%）有何影响？
• RQ5 为避免对混合计量集合过度自信的推荐做法有哪些？

主要发现

• 随机效应模型在95%覆盖下给出总线宽不确定性为 +/- 0.8 nm。
• 当存在暗不确定性时，常见均值模型在总不确定性上的低估可达到五倍之多。
• 标准不确定性评估方法未能考虑暗不确定性和不一致结果。
• 暗不确定性若未被正确建模，可能削弱混合计量的可靠性。
• 论文提出了减少暗不确定性并引导不定一致结果结合的良好实践。