Research on Error Compensation and Fitting Algorithms of Wafer Alignment Calibrator
LIU Tundong1,CHEN Zengyan1,WANG Ruoyu1,TANG Zhichen1,ZHENG Peng2
1. Pen-Tung Sah Institute of Micro-Nano Science and Technology, Xiamen University, Xiamen, Fujian 361102, China
2. Xiamen Institute of Measurement and Testing, Xiamen, Fujian 361004, China
Abstract Wafer alignment calibrator plays a crucial role in semiconductor manufacturing and inspection processes. However, the accuracy of wafer center positioning can be affected by measurement errors. Consequently, the development of error compensation algorithms is paramount to refining the accuracy of wafer alignment calibrator. To address the impact of wafer carrier surface tilt on sampling accuracy, a physical model of a tilted wafer and its elliptical projection on the horizontal plane is established. An analytical relationship between the ellipse and the wafer center is derived from this model. Subsequently, an elliptical equation is employed for fitting purposes. To further enhance compensation and fitting accuracy, an extended Kalman filter-based ellipse fitting algorithm with a forgetting factor is proposed. This algorithm employs density-based spatial clustering of applications with noise for data preprocessing, coupled with improved progressive consistent sampling to improve the distribution of sample points. Additionally, an iterative reweighted least squares method is applied for ellipse fitting, resulting in high-precision estimation of the wafer center. Experimental results demonstrate that the proposed method achieves a fitting accuracy of 99.95% after error compensation, thus validating its effectiveness.
LIU Tundong,CHEN Zengyan,WANG Ruoyu, et al. Research on Error Compensation and Fitting Algorithms of Wafer Alignment Calibrator[J]. Acta Metrologica Sinica, 2024, 45(8): 1115-1124.
LIANG J, LI P, ZHOU D, et al. Robust Ellipse Fitting via Alternating Direction Method of Multipliers［J］. Signal Processing, 2019, 164: 30-40.
ZHANG G K. Analysis and Research on Transforming Differential Circle Projection into a Deformed Ellipse［J］. Science of Surveying and Mapping, 2004(3): 14-15.
LI G Q, ZHANG L L, CHEN Y. Study on the Laser Marking Process of Silicon Wafer［J］. Applied Laser, 2023, 43(4): 80-86.
QUAN Y, LING Q. Ellipse Fitting Algorithm Based on Geometric Symmetry［J］. Automation & Instrumentation, 2020, 35(5): 51-55.
［8］
FORNACIARI M, PRATI A, CUCCHIARA R. A fast and effective ellipse detector for embedded vision applications［J］. Pattern Recognition, 2014, 47(11): 3693-3708.
［10］
LIANG J, LI P, ZHOU D, et al. Robust ellipse fitting via alternating direction method of multipliers［J］. Signal processing, 2019(164): 30-40.
BING M, CAN Y, AIHUA L, et al. A Faster DBSCAN Algorithm Based on Self-Adaptive Determination of Parameters［J］. Procedia Computer Science, 2023(221): 113-120.
［4］
FOKKINGA M. The Hough transform［J］. Journal of Functional Programming, 2017, 21(2): 129-133.
GUO S Y, WU Y D. Improved Ellipse Fitting Algorithm with Outlier Remova［J］. Computer Science, 2022, 49(4): 188-194.
XU J, HU H, LEI Y, et al. A Wafer Prealignment Algorithm Based on Fourier Transform and Least Square Regression［J］. IEEE Transactions on Automation Science and Engineering, 2017: 1771-1777.
［5］
NGUYEN T, AHUJA S, WU Q. A real-time ellipse detection based on edge grouping［C］//2009 IEEE International Conference on Systems, Man and Cybernetics. San Antonio, TX, USA, 2009.
［9］
DONG H, SUN G, PANG W, et al. Fast ellipse detection via gradient information for robotic manipulation of cylindrical objects［J］. IEEE Robotics and Automation Letters, 2018, 3(4): 2754-2761.
［11］
LIANG J, WANG Y, ZENG X. Robust Ellipse Fitting via Half-Quadratic and Semidefinite Relaxation Optimization［J］. IEEE Transactions on Image Processing, 2015, 24(11): 4276-4286.
DOBAKHSHARI A S, ABDOLMALEKI M, TERZI J V, et al. Robust Hybrid Linear State Estimator Utilizing SCADA and PMU Measurements［J］. IEEE Transactions on Power Systems, 2021, 36(2): 1264-1273.
WANG Q Y, QIAN Z H, HE G L, et al. Dynamic Weighing System of Pneumatic Conveying Based on ExtendedKalman Filter Algorithm ［J］. Acta Metrologica Sinica, 2022, 43(5): 624-628.
2024, Vol. 45 
