用于力谱分析的功能化AFM探头：通过热噪声测量进行本征模态形状和刚度校准
Functionalized AFM probes for force spectroscopy: eigenmodes shape and stiffness calibration through thermal noise measurements
摘要：
当必须控制探针和样品之间的几何形状时，特别是在力谱中，用胶体珠对原子力显微镜（AFM）悬臂梁进行功能化是一种广泛使用的技术。但仍存在一些问题：粘在悬臂末端的珠子如何影响其机械响应？更重要的是，对于定量测量，我们还能用传统技术确定AFM探针的刚度吗？在这篇文章中，一个胶体的质量加载的本征模式的形状和谐振频率的影响进行了研究，通过测量的热噪声的矩形AFM微悬臂梁与没有一个珠附加在其末端。实验是在自制的基于微分干涉法的超灵敏原子力显微镜上进行的。来自干涉仪的聚焦光束在不同位置探测悬臂梁，并且在没有外部激励的情况下确定模式的空间形状直到第五共振。结果清楚地表明，第一本征模式几乎不改变质量加载。然而，较高共振的振荡行为呈现出显着的差异：在其末端粘有颗粒的情况下，模式的节点朝向悬臂的自由端移位。这些结果进行了比较的分析模型，考虑到质量和负载的惯性矩在欧拉-伯努利框架，其中的本征模式的归一化明确制定出，以允许定量预测的热噪声幅度的每种模式。实验结果和分析模型之间的一个很好的协议被证明，允许一个干净的探头刚度校准。
英文摘要：
The functionalization of an Atomic Force Microscope (AFM) cantilever with a colloidal bead is a widely used technique when the geometry between the probe and the sample must be controlled, particularly in force spectroscopy. But some questions remain: how does a bead glued at the end of a cantilever influence its mechanical response ? And more important for quantitative measurements, can we still determine the stiffness of the AFM probe with traditional techniques? In this article, the influence of a colloidal mass loading on the eigenmodes shape and resonant frequency is investigated by measuring the thermal noise on rectangular AFM microcantilevers with and without a bead attached at their extremities. The experiments are performed with a home-made ultra-sensitive AFM, based on differential interferometry. The focused beam from the interferometer probes the cantilever at different positions and the spatial shapes of the modes are determined up to the fifth resonance, without external excitation. The results clearly demonstrate that the first eigenmode almost doesn't change by mass loading. However the oscillation behavior of higher resonances present a marked difference: with a particle glued at its extremity, the nodes of the mode are displaced towards the free end of the cantilever. These results are compared to an analytical model taking into account the mass and the inertial moment of the load in an Euler-Bernoulli framework, where the normalization of the eigenmodes is explicitly worked out in order to allow a quantitative prediction of the thermal noise amplitude of each mode. A good agreement between the experimental results and the analytical model is demonstrated, allowing a clean calibration of the probe stiffness.
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