压电响应力显微镜悬臂梁模态振型的原位测量
In-situ Piezoresponse Force Microscopy Cantilever Mode Shape Profiling
摘要：
压电响应力显微镜（PFM）测量中的频率依赖的振幅和相位被证明是用于进行测量的原子力显微镜（AFM）悬臂梁的欧拉-伯努利（EB）动力学的结果。作为边界条件变化的函数的悬臂模态形状的变化决定了悬臂对尖端和样品之间的力的灵敏度。传统的PFM和AFM测量是在一个光束检测器（OBD）光斑位置处测量悬臂的运动。一个单一的OBD点的位置提供了一个有限的图片的总悬臂运动，事实上，实验观察到的悬臂振幅和相位被证明是强烈依赖于OBD点的位置，许多测量。在这项工作中，通常观察到的PFM响应的频率依赖性解释通过实验测量和分析理论EB建模的PFM响应作为一个函数的频率和OBD点的位置上的周期性极化的锂离子电池（PPLN）样品。一个值得注意的结论是，一个共同的选择OBD点的位置，在或附近的悬臂的尖端是特别容易受到频率相关的幅度和相位变化源于悬臂传感器的动态，而不是从样品的压电响应。
英文摘要：
The frequency-dependent amplitude and phase in piezoresponse force microscopy (PFM) measurements are shown to be a consequence of the Euler-Bernoulli (EB) dynamics of atomic force microscope (AFM) cantilever beams used to make the measurements. Changes in the cantilever mode shape as a function of changes in the boundary conditions determine the sensitivity of cantilevers to forces between the tip and the sample. Conventional PFM and AFM measurements are made with the motion of the cantilever measured at one optical beam detector (OBD) spot location. A single OBD spot location provides a limited picture of the total cantilever motion and in fact, experimentally observed cantilever amplitude and phase are shown to be strongly dependent on the OBD spot position for many measurements. In this work, the commonly observed frequency dependence of PFM response is explained through experimental measurements and analytic theoretical EB modeling of the PFM response as a function of both frequency and OBD spot location on a periodically poled lithium niobate (PPLN) sample. One notable conclusion is that a common choice of OBD spot location, at or near the tip of the cantilever is particularly vulnerable to frequency dependent amplitude and phase variations stemming from dynamics of the cantilever sensor rather than from the piezoresponse of the sample.
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