A Wafer Pre-Alignment Algorithm Based on Weighted Fourier Series Fitting of Circles and Least Squares Fitting of Circles

Abstract

The wafer pre-aligner is a crucial component in the lithography process to correct the wafer center and notch orientation. To improve the precision and the efficiency of pre-alignment, a new method to calibrate the center and the orientation of a wafer based on the weighted Fourier series fitting of circles (WFC) method and the least squares fitting of circles (LSC) method, respectively, is proposed. The WFC method effectively suppressed the influence of the outliers and had high stability compared with the LSC method when fitted to the center of the circle. While the weight matrix degenerated to the identity matrix, the WFC method degenerated into the Fourier series fitting of circles (FC) method. The fitting efficiency of the FC method is 28% higher than that of the LSC method, and the fitting accuracy of the center of the FC method is the same as that of the LSC method. In addition, the WFC method and the FC method perform better than the LSC method in radius fitting. The pre-alignment simulation results showed that the absolute position accuracy of the wafer was ±2 µm, the absolute direction accuracy was 0.01°, and the total calculation time was less than 3.3 s in our platform.