A technique to measure the flatness of next-generation 450 mm wafers using a three-point method with an autonomous calibration function

摘要

In this paper, a three-point method with an autonomous calibration function is proposed to measure the flatness of next-generation 450 mm wafers. The measuring method is comprised of the following two processes: (1) the measurement of the flatness of the wafer across the circumference of the circle by three displacement sensors that are built-in to the wafer holder and (2) the measurement along several straight lines that pass through the rotational center point and two points on the circumference of the circle while changing the straight line for measurement by rotating the wafer step by step. Through these two processes, the flatness of the wafer can be determined by the proposed algorithm, which can automatically reduce the influence of motion errors and the zero-difference of the three sensors. The conceptual design and the algorithm utilized in the proposed method are explained using theoretical analyses and numerical calculations. The results of this study are as follows: the expanded uncertainty of wafer flatness is approximately 6.8 and 0.3 (mu)m when the sampling number for the measurement across the circumference of the circle with a radius of 220 mm is 10~(3) and 10~(6), respectively. The measurements were observed under the practical conditions that: (a) the sampling number for the measurement along several straight lines that pass through the rotational center point and two points on the circumference of the circle that has a radius of 220mm is 100, (b) the radius of the circular sensor is 1 mm, (c) the standard deviation of the sensor is 0.1 (mu)m, and (d) the adjacent sensor interval is 30 mm.