As one of the fundamental sources of noise in atomic force microscopy (AFM), thermal fluctuations of the cantilever have been studied for the case of a free tip but not much for cantilevers in contact. In this paper, using the equipartition theorem, we calculated the thermal deflection amplitude for all normal modes of an elastically supported AFM cantilever, including the free cantilever as a special case. With increasing contact stiffness, the mean thermal fluctuation amplitude decreases for all cantilever modes when in the elastic contact. In addition, considering the optical lever detection scheme used in most AFMs, we calculated the corresponding output thermal noise amplitude. The experiments validated our theoretical calculations. Our investigation facilitates a more comprehensive understanding of the thermal noise in AFM. It provides guidance for thermally excited contact-resonance AFM, which is promising for quantitative viscoelastic measurements.

中文翻译：

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接触式原子力显微镜中的热噪声

作为原子力显微镜 (AFM) 中噪声的基本来源之一，悬臂的热波动已针对自由尖端的情况进行了研究，但对于接触的悬臂则研究不多。在本文中，使用均分定理，我们计算了弹性支撑 AFM 悬臂的所有法向模式的热偏转幅度，包括作为特殊情况的自由悬臂。随着接触刚度的增加，弹性接触时所有悬臂模式的平均热波动幅度都会减小。此外，考虑到大多数 AFM 中使用的光学杠杆检测方案，我们计算了相应的输出热噪声幅度。实验验证了我们的理论计算。我们的调查有助于更全面地了解 AFM 中的热噪声。