Ehsanipour Milad, Damircheli Mehrnoosh, Eslami Babak
Department of Mechanical Engineering, Shahr-e-Qods Branch, Islamic Azad University, Tehran, Iran.
Department of Mechanical Engineering, Widener University, Chester, Pennsylvania.
Microsc Res Tech. 2019 Sep;82(9):1438-1447. doi: 10.1002/jemt.23297. Epub 2019 May 20.
During the past years, different theoretical and experimental works are done to enhance the observables (mostly higher eigenmode's phase contrast) in multifrequency atomic force microscopy methods. In this study, the geometry of rectangular cantilevers is studied and an optimum dimension that can provide maximum phase contrast for a given set of samples is found. The analysis is done both numerically and experimentally. A sensitivity analysis is provided to demonstrate which dimension (length, width, thickness, tip-radius, and cantilever and sample angle) of the cantilever has a higher effect on the results. The effects of geometrical dimensions are categorized into to: (a) effect on dynamics of the cantilever (b) effects on cantilever's specifications (i.e., spring constant and quality factor). Length and width of the cantilever dominates the static behavior of the cantilever. While thickness (for lower values), tip radius, and approach angle mostly affect the dynamic behavior of the cantilever. Theoretically, it is found as the length increases the phase contrast increase. This relationship is opposite for width. It was also observed that the effect of thickness for a specific range on the phase contrast depends on the 1st eigenmode amplitude setpoint. This study shows for having higher contrast, lower tip-radius is needed. The optimum angle between cantilever and sample to enhance bimodal atomic force microscopy imaging is also found. Based on the commercially available cantilevers, the optimum cantilever dimension is provided. Three different cantilevers with similar dimensions are experimentally tested and theoretical results are verified.
在过去几年中，人们开展了不同的理论和实验工作，以提高多频原子力显微镜方法中的可观测值（主要是高阶本征模的相位对比度）。在本研究中，对矩形悬臂梁的几何形状进行了研究，并找到了一组给定样品能提供最大相位对比度的最佳尺寸。分析通过数值计算和实验两种方式进行。提供了敏感性分析，以证明悬臂梁的哪个尺寸（长度、宽度、厚度、尖端半径以及悬臂梁与样品的夹角）对结果有更大影响。几何尺寸的影响可分为两类：(a) 对悬臂梁动力学的影响；(b) 对悬臂梁参数（即弹簧常数和品质因数）的影响。悬臂梁的长度和宽度主导着其静态行为。而厚度（对于较小值）、尖端半径和接近角主要影响悬臂梁的动态行为。理论上发现，随着长度增加，相位对比度增加。宽度的情况则相反。还观察到，特定范围内厚度对相位对比度的影响取决于第一本征模振幅设定值。本研究表明，为了获得更高的对比度，需要更小的尖端半径。还找到了悬臂梁与样品之间用于增强双峰原子力显微镜成像的最佳角度。基于市售悬臂梁，给出了最佳悬臂梁尺寸。对三种尺寸相似的不同悬臂梁进行了实验测试，并验证了理论结果。
