面向近原子尺度制造的光学测量精度极限分析

Analysis of optical measurement precision limit for close-to-atomic scale manufacturing

纳米级乃至更高精度的测量是原子及近原子尺度制造技术发展的基础和保障.光学测量具有精度高、测量范围广、测量直观等优点,其对单个成像光斑中心的定位可达远超衍射极限的精度.但由于光本身散粒噪声、探测器暗电流噪声等随机性的存在,光学测量存在精度极限.本文基于克拉美罗下界理论发展了可适用于任意强度分布像斑的精度极限计算方法,并以典型艾里斑为例,分析了成像过程中反映信噪比、能量集中度、计算方式的参数对定位精度极限的影响规律并给出提高精度的建议和结论.对实验所得像斑进行了精度极限计算,验证了所得结论对类似艾里斑的像斑的适用性.研究为原子及近原子尺度制造过程中光学测量的应用和优化提供了分析方法和理论指导.

Measurement technology with nanometer scale or higher level precision is the basis and guarantee for developing atomic and close-to-atomic scale manufacturing.Optical measurement has the advantages of high precision,wide range and real-time measurement.The precision of localizing a single imaging spot’s center is not limited by the diffraction limit and could reach nanometer scale.However,the shot noise of light and the dark current noise of the detector bring about a precision limit for optical measurement.Based on the Cramer-Rao lower bound theory,a precision limit estimation method for general imaging profiles is developed in this paper.Taking the typical Airy spot for example,the influences of the parameters such as signal-to-noise ratio,energy concentration and processing method on the positioning precision limit are analyzed,and suggestions and conclusions for improving the measurement precision are given.The precision limit of a laboratory imaging spot is calculated,which verifies that the conclusions are also suitable for the imaging profiles similar to the Airy spot.The research provides the analytical method and theoretical guidance for the application and optimization of optical measurement in atomic and close-to-atomic scale manufacturing.