This study proposes a new structural design and analysis of a metrology reference module for a quasi-Abbé-error-free three-axis measurement platform used in 12-inch wafer inspection, with travel ranges of 300 mm (X/Y) and 5 mm (Z). Based on a prior platform architecture with zero Abbé error in all three axes, this study focuses on optimizing the metrology reference module by integrating three-axis reference mirrors into a monolithic structure. This integration eliminates assembly errors, simplifies construction, and enhances structural performance. Finite element analysis (FEA) was used to optimize stiffness-to-weight ratio and minimize deformation under static loads, which improved interferometric measurement accuracy and reduced errors caused by the effect of structural deformation on the wafer. A prototype was built based on the FEA results and validated through experimental modal testing. The results show a 96.4% decrease in static deformation (from 15.62 µm to 564 nm) and a 45.67% increase in the first natural frequency, indicating significant improvements in both static and dynamic rigidity. The results of the modal testing further validated the strong correlation between experimental measurements and simulation, indicating that the established model accurately captures the dynamic characteristics of the structure. This confirms the high accuracy and reliability of the FEA model for structural performance prediction.

1. [1] Y. Shimizu, L. C. Chen, D. W. Kim, X. Chen, X. Li, and H. Matsukuma, “An insight into optical metrology in manufacturing,” Measurement Science and Technology, Vol.32, No.4, Article No.042003, 2021. https://doi.org/10.1088/1361-6501/abc578
2. [2] Y. B. Huang, K. C. Fan, Z. F. Lou, and W. Sun, “A novel modeling of volumetric errors of three-axis machine tools based on Abbé and Bryan principles,” Int. J. of Machine Tools and Manufacture, Vol.151, Article No.103527, 2020. https://doi.org/10.1016/j.ijmachtools.2020.103527
3. [3] Y. X. He, R. J. Li, J. Li, W. K. Zhao, Z. Y. Cheng, Q. X. Huang, and K. C. Fan, “Novel compensation method of volumetric errors for micro-coordinate measuring machines using Abbé and Bryan principles,” IEEE Trans. on Instrumentation and Measurement, Vol.71, Article No.1004510, 2022. https://doi.org/10.1109/TIM.2022.3183678
4. [4] T. Hausotte, B. Percle, U. Gerhardt, D. Dontsov, E. Manske, and G. Jäger, “Interference signal demodulation for nanopositioning and nanomeasuring machines,” Measurement Science and Technology, Vol.23, No.7, Article No.074004, 2012. https://doi.org/10.1088/0957-0233/23/7/074004
5. [5] I. Ortlepp, “High-precision nanopositioning and nanomeasuring machines for alternative nanofabrication,” Novel Patterning Technologies (SPIE Proc. Vol.12956), Article No.129560D, 2024. https://doi.org/10.1117/12.3010844
6. [6] G. Jäger, E. Manske, T. Hausotte, A. Müller, and F. Balzer, “Nanopositioning and nanomeasuring machine NPMM-200—A new powerful tool for large-range micro-and nanotechnology,” Surface Topography: Metrology and Properties, Vol.4, No.3, Article No.034004, 2016. https://doi.org/10.1088/2051-672X/4/3/034004
7. [7] E. Manske, T. Fröhlich, R. Füßl, I. Ortlepp, R. Mastylo, U. Blumröder, D. Dontsov, M. Kühnel, and P. Köchert, “Progress of nanopositioning and nanomeasuring machines for cross-scale measurement with sub-nanometre precision,” Measurement Science and Technology, Vol.31, No.8, Article No.085005, 2020. https://doi.org/10.1088/1361-6501/ab848c
8. [8] C. Schober, C. Pruss, A. Herkommer, and W. Osten, “The NPMM-200: Large area high resolution for freeform surface measurement,” 7th European Seminar on Precision Optics Manufacturing (SPIE Proc. Vol.11478), pp. 40-46, 2020. https://doi.org/10.1117/12.2564918
9. [9] J. B. Bryan, “The Abbé principle revisited: An updated interpretation,” Precision Engineering, Vol.1, No.3, pp. 129-132, 1979. https://doi.org/10.1016/0141-6359(79)90037-0
10. [10] T. A. M. Ruijl, “Ultra precision coordinate measuring machine: Design, calibration and error compensation,” Ph.D. thesis, Delft University of Technology, 2001.
11. [11] I. Widdershoven, R. L. Donker, and H. A. M. Spaan, “Realization and calibration of the ‘Isara 400’ ultra-precision CMM,” J. of Physics: Conf. Series, Vol.311, Article No.012002, 2011. https://doi.org/10.1088/1742-6596/311/1/012002
12. [12] H. A. M. Spaan and I. Widdershoven, “Isara 400 ultra-precision CMM,” Optical Fabrication, Testing, and Metrology IV (SPIE Proc. Vol.8169), Article No.81690T, 2011. https://doi.org/10.1117/12.902237
13. [13] R. Donker, I. Widdershoven, and H. A. M. Spaan, “ISARA 400: Enabling ultra-precision coordinate metrology for large parts,” Proc. of the 10th Int. Euspen Conf., 2010.
14. [14] E. Bos, T. Moers, and M. van Riel, “Design and verification of an ultra-precision 3D-coordinate measuring machine with parallel drives,” Measurement Science and Technology, Vol.26, No.8, Article No.085904, 2015. https://doi.org/10.1088/0957-0233/26/8/085904
15. [15] A. J. M. Moers, M. C. J. M. van Riel, and E. J. C. Bos, “Design and verification of the TriNano ultra precision CMM,” Innovation in Mechanical Engineering – Shaping the Future: Proc., Vol.56, 2011.
16. [16] Z. Zhang, Q. Huang, G. Wang, H. Li, L. Zhang, R. Cheng, R. Li, and Q. Pan, “Design method and error analysis of 3D measurement system in accordance with the Abbé principle,” Measurement, Vol.252, Article No.117369, 2025. https://doi.org/10.1016/j.measurement.2025.117369
17. [17] Z. Zhang, Q. Huang, J. Lu, H. Li, R. Cheng, and L. Zhang, “On-machine separation and compensation of target mirror’s surface shape errors in multidimensional interferometric measurement system,” Review of Scientific Instruments, Vol.96, Issue 1, Article No.015105, 2025. https://doi.org/10.1063/5.0232489
18. [18] T. Hirschmann, G. Schindler, I. Greisberger, M. Braun, and D. Radonic, “Closed-loop XY-stage control with yaw rotation tracking,” Application Note: Motion & Sensing, Vol.37, 2021.
19. [19] W. Land, “Test & measurement: Machine positioning uncertainty with laser interferometer feedback,” Laser Focus World, Vol.52, No.5, pp. 55-60, 2016.
20. [20] A. Okyay, K. Erkorkmaz, and M. B. Khamesee, “Modal analysis, metrology, and error budgeting of a precision motion stage,” J. of Manufacturing and Materials Processing, Vol.2, Issue 1, Article No.8, 2018. https://doi.org/10.3390/jmmp2010008
21. [21] M. Torralba, J. A. Yagüe-Fabra, J. A. Albajez, M. Valenzuela, R. Acero, and J. J. Aguilar, “A three-layer and two-stage platform for positioning with nanometer resolution and submicrometer accuracy,” Proc. 11th Int. Symp. on Measurement and Quality Control (ISMQC’2013), 2013.
22. [22] M. Torralba, M. Valenzuela, J. A. Yagüe-Fabra, J. A. Albajez, and J. J. Aguilar, “Large range nanopositioning stage design: A three-layer and two-stage platform,” Measurement, Vol.89, pp. 55-71, 2016. https://doi.org/10.1016/j.measurement.2016.03.075
23. [23] S. Hesse, C. Schäffel, H. U. Mohr, M. Katzschmann, and H. J. Büchner, “Design and performance evaluation of an interferometric controlled planar nanopositioning system,” Measurement Science and Technology, Vol.23, No.7, Article No.074011, 2012. https://doi.org/10.1088/0957-0233/23/7/074011
24. [24] T. T. Chung, T. H. Tseng, and C. S. L. Chan, “Design and analysis of an Abbé free coplanar stage,” MATEC Web of Conf., Vol.95, Article No.07017, 2017. https://doi.org/10.1051/matecconf/20179507017
25. [25] C. Y. Liao, Y. Hung, F. S. Yang, and L. C. Chen, “Development of a novel multifunctional Abbé-free 12”-wafer measuring stage for semiconductor manufacturing,” Proc. of the 9th Int. Conf. of Asian Society for Precision Engineering and Nanotechnology, 2022.
26. [26] K. C. Fan, C. L. Liu, P. T. Wu, Y. C. Chen, and W. L. Wang, “The structure design of a micro-precision CMM with Abbé principle,” Proc. of the 35th Int. MATADOR Conf., pp. 297-300, 2007. https://doi.org/10.1007/978-1-84628-988-0_67
27. [27] K. C. Fan, F. Cheng, H. Y. Wang, and J. K. Ye, “The system and the mechatronics of a pagoda type micro-CMM,” Int. J. of Nanomanufacturing, Vol.8, Nos.1-2, pp. 67-86, 2012. https://doi.org/10.1504/IJNM.2012.044656
28. [28] W. Gao, S. Dejima, H. Yanai, K. Katakura, S. Kiyono, and Y. Tomita, “A surface motor-driven planar motion stage integrated with an XYθ_Z surface encoder for precision positioning,” Precision Engineering, Vol.28, pp. 329-337, 2004. https://doi.org/10.1016/j.precisioneng.2003.12.003
29. [29] F. Fern, R. Füßl, G. Eichfelder, E. Manske, and M. Kühnel, “Coordinate transformation and its uncertainty under consideration of a non-orthogonal coordinate base,” Measurement Science and Technology, Vol.32, Issue 4, Article No.045001, 2021. https://doi.org/10.1088/1361-6501/aba3f5
30. [30] U. Griesmann, Q. Wang, and T. D. Raymond. “Optical flatness metrology for 300 mm silicon wafers,” American Institute of Physics Proc. of the 2005 Conf. on Characterization and Metrology for ULSI Technology, Vol.788, pp. 599-603, 2005.
31. [31] K. T. Turner, S. Veeraraghavan, and J. K. Sinha, “Predicting distortions and overlay errors due to wafer deformation during chucking on lithography scanners,” J. of Micro/Nanopatterning, Materials, and Metrology, Vol.8, Issue 4, Article No.043015, 2009. https://doi.org/10.1117/1.3247857
32. [32] R. Ding, H. Luo, Z. Li, Z. Zhou, D. Qu, and W. Xiong, “Structural design and simulation of a multi-channel and dual working condition wafer defect inspection prototype,” Micromachines, Vol.14, Issue 8, Article No.1568, 2023. https://doi.org/10.3390/mi14081568
33. [33] G. Kalkowski, T. Peschel, G. Hassall, H. Alves, and S. Risse, “Investigations into an electrostatic chuck design for 450mm Si wafer,” Metrology, Inspection, and Process Control for Microlithography XXVI, Vol.8324, Article No.83242Z, 2012. https://doi.org/10.1117/12.916380
34. [34] R. Müller, K. Afanasiev, M. Ziemann, and V. Schmidt, “Super-flat wafer chucks: from simulation and testing to a complete 300mm wafer chuck with low wafer deformation between pins,” Extreme Ultraviolet (EUV) Lithography V, Vol.9048, Article No.90482E, 2014. https://doi.org/10.1117/12.2046209
35. [35] B. J. Schwarz and M. H. Richardson, “Experimental modal analysis,” CSI Reliability Week, Vol.35, No.1, pp. 1-12, 1999.