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Accurate Calibration and Uncertainty Estimation of the Normal Spring Constant of Various AFM Cantilevers

机译：各种AFM悬臂的正常弹簧常数的精确校准和不确定度估计

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摘要

Measurement of force on a micro- or nano-Newton scale is important when exploring the mechanical properties of materials in the biophysics and nanomechanical fields. The atomic force microscope (AFM) is widely used in microforce measurement. The cantilever probe works as an AFM force sensor, and the spring constant of the cantilever is of great significance to the accuracy of the measurement results. This paper presents a normal spring constant calibration method with the combined use of an electromagnetic balance and a homemade AFM head. When the cantilever presses the balance, its deflection is detected through an optical lever integrated in the AFM head. Meanwhile, the corresponding bending force is recorded by the balance. Then the spring constant can be simply calculated using Hooke’s law. During the calibration, a feedback loop is applied to control the deflection of the cantilever. Errors that may affect the stability of the cantilever could be compensated rapidly. Five types of commercial cantilevers with different shapes, stiffness, and operating modes were chosen to evaluate the performance of our system. Based on the uncertainty analysis, the expanded relative standard uncertainties of the normal spring constant of most measured cantilevers are believed to be better than 2%.
机译：在探索生物物理和纳米机械领域中材料的机械性能时，以微米或纳米牛顿为单位的力测量非常重要。原子力显微镜（AFM）广泛用于微力测量。悬臂探针用作AFM力传感器，并且悬臂的弹簧常数对测量结果的准确性具有重要意义。本文提出了一种常规的弹簧常数校准方法，该方法结合了电磁天平和自制的AFM头。当悬臂按下天平时，将通过集成在AFM头中的光学杆检测其挠度。同时，通过天平记录相应的弯曲力。然后，可以使用胡克定律简单地计算弹簧常数。在校准过程中，将应用反馈环路来控制悬臂的偏转。可能影响悬臂稳定性的错误可以迅速得到补偿。选择了五种类型的商业悬臂，它们具有不同的形状，刚度和操作模式，以评估我们系统的性能。根据不确定性分析，大多数测得的悬臂梁的正常弹簧常数的扩展相对标准不确定度被认为优于2％。

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