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Measurement of cantilever spring constant using an electrostatic sensing and actuating force measurement system

We report the measurement of the spring constant of a cantilever using an electrostatic sensing and actuating force measurement system. The force measurement system consists of three main parts: a monolithic flexure stage, a three-electrode capacitor, and a digital controller. The most important feature of the system is the utilization of the three-electrode capacitor simultaneously as a position sensor and an electrostatic force generator. This allows us to constantly adjust and maintain gap distances between three electrodes, which is critical for this design to generate precise electrostatic compensation force. The force measurement system was partly upgraded and its performance was improved. The uncertainty estimation for the upgraded force measurement system is given. By measuring the spring constant of a commercially available cantilever force sensor, we demonstrate that the force measurement system is capable of calibrating the cantilever spring constant. The spring constant of the cantilever force sensor was measured to be (2227 ± 63) mN m−1 (coverage factor k = 2), corresponding to a relative expanded uncertainty of 2.8%.