Ahemd ElMelegy, Sarwat Zahwi
（Engineering and Surface Metrology Laboratory, National Institute of Standards (NIS), Giza, 12211, Egypt）
Abstract： Scanning probe microscopy (SPM) is a branch of microscopy that forms images of surfaces using a physical probe that scans the specimen. Atomic force microscopy is one of the SPM family which is considered as a very versatile tool for surface imaging and measurements. A wide range of various samples can be measured regardless of being conductive, no-conductive, in vacuum, in air or in a fluid as a unique feature. One of the most challenges in atomic force microscopes (AFMs) is to evaluate the associated uncertainty during the surface measurements by AFMs. Here, an optical AFM is calibrated through the calibration of XYZ stage. The approach is to overcome difficulties experienced when trying to evaluate some uncertainty components which cannot be experimentally determined i.e. tip surface interaction forces and tip geometry. The Monte Carlo method is then used to determine the associated uncertainties due to such factors by randomly drawing the parameters according to their associated tolerances and their probability density functions (PDFs). The whole process follows supplement 2 to “the guide to the expression of the uncertainty in measurement” (GUM). The approach validated in the paper shows that the evaluated uncertainty in AFM is about 10 nm.
Key words： measurement; Monte Carlo method; atomic force microscope （AFM）; nanometrology
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光学原子力显微镜中的蒙特卡罗方法
Ahmed ElMelegy， Sarwat Zahwi
（国家标准研究所 工程与表面计量实验室， 吉萨 12211， 埃及）
摘要:扫描探针显微镜(Scanning probe microscopy， SPM )是显微镜的一个分支， 它利用物理探针扫描标本形成样本表面图像。 而原子力显微镜( Atomic force microscopy， AFM )是SPM中一种多功能的表面成像和测量工具， 对导电、不导电、真空中、空气中或流体中的各种样本均可测量。 原子力显微镜最面临的最大挑战之一是评估其在表面测量过程中所伴随的不确定度。 本研究通过XYZ Phase的标定， 对一台光学原子力显微镜进行了校准。 该方法旨在克服在评估一些无法实验确定的不确定部件时遇到的困难， 如尖端表面相互作用力和尖端几何。 运用蒙特卡罗方法来确定根据相关容差和概率密度函数(PDFs)随机绘制参数而引起的相关不确定度。 整个过程遵循《测量不确定度表示指南》(GUM)补编2。 经本方法验证， 原子力显微镜的评估不确定度为10 nm左右。
关键词:测量； 蒙特卡罗方法； 原子力显微镜； 纳米气象学
引用格式：Ahmed ElMelegy, Sarwat Zahwi. Monte Carlo method in optical atomic force microscopy. Journal of Measurement Science and Instrumentation, 2021, 12（3）： 267-271. DOI： 10．3969／j．issn．1674-8042．2021．03．003
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