Abstract
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%.
Highlights
The Atomic Force Microscope (AFM) is a typical surface imaging instrument for micro- or nano-scale specimens
As the deflection of the cantilever was quite small in our calibration, the position sensitive detector (PSD) output signals and the deflection of the cantilever should conform to a linear relationship
Our calibration results of seven cantilevers fall into the distribution range of spring constant given by the manufacturer in
Summary
The Atomic Force Microscope (AFM) is a typical surface imaging instrument for micro- or nano-scale specimens. Researchers have adopted it to measure force down to picoNewton (pN) scale in biophysics and nanomechanical fields [1,2]. Such applications need to measure or control the force between the force sensor (the AFM cantilever probe) and the sample surface. The force measurements rely on cantilevers with a known spring constant. As current micromachining process cannot precisely control the dimensions (especially the thickness) and material properties of each cantilever, probe manufacturers usually give a nominal spring constant with a wide range for each cantilever model. In precision force metrology, the spring constant of each cantilever must be calibrated properly [3]
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