SI-traceable determination of spring constants of various atomic force microscope cantilevers with a small uncertainty of 1%

Abstract

We have demonstrated the feasibility of using the nano force calibrator (NFC), consisting of a microbalance and a nano-stage, as a calibration device, which can accurately determine normal spring constants (k) of various atomic force microscope (AFM) cantilevers with traceability to the Système International d'Unités (SI units). From very compliant (k < 0.1 N m−1) to stiff (k > 10 N m−1) cantilevers, three types of commercial levers with different shapes (beam and V) and operating modes (contact and tapping) were chosen to test NFC calibration performances. We have found that all types of levers could be well characterized by the NFC even when a small force (approximately 500 nN) was used to calibrate a soft cantilever (k < 0.1 N m−1). We declared the relative standard uncertainty of the spring constant calibration of our method to be better than 1%, based on calibration results and uncertainty analysis. Because of its small calibration uncertainty, the NFC is recommendable for accurate calibration of AFM cantilevers and as a reference method for assessing other popularly used calibration methods.