Research on PPB-Level Ultra-Low Linear Expansion Coefficient Measurement Based on Fizeau Interference and Dynamic Refractive Index Compensation
Abstract
As extreme ultraviolet (EUV) lithography enters the sub-nanometer precision era, the demand for characterizing ultra-low expansion materials has reached the 10-9 (PPB) level. At this resolution, even minute airflow disturbances or transient temperature gradients become dominant noise sources. To mitigate these effects, this study employs a high-vacuum thermal control chamber to maintain pressure below 100Pa and limits temperature fluctuations to within 0.1℃. We further enhanced the Fizeau interferometry system by developing a dynamic compensation model based on optical path drift. The model captures real-time atmospheric pressure and thermal field conditions via a sensor array in a vacuum chamber. And after integrating Ciddor's semi-empirical air refractive index formula, we precisely invert the optical path length change caused by residual air. Experimental results show that this compensation model significantly improves isothermal phase repeatability to 0.3nm. Based on this precision compensation system, we measured a microcrystalline sample over a 5-50℃ range, obtaining a CTE of 4.72*10-9/℃. Following the integrated evaluation, the system's expanded uncertainty was significantly reduced to 1.01*10-9. This achievement enables reliable characterization of ultra-low CTE materials at the PPB level, significantly enhancing the system's ability to suppress interference from complex thermal vacuum environments. This provides high-precision metrology support for material selection and validation in the next generation of high-end semiconductor lithography equipment.
View attachment 173814