Calibration of the Effective Spring Constant of Ultra-Short Cantilevers for a High-Speed Atomic Force Microscope

Abstract

Ultra-short cantilevers are a new type of cantilever designed for the next generation of high-speed atomic force microscope (HS-AFM). Ultra-short cantilevers have smaller dimensions and higher resonant frequency than conventional AFM cantilevers. Moreover, their geometry may also be different from the conventional beam-shape or V-shape. These changes increase the difficulty of determining the spring constant for ultra-short cantilevers, and hence limit the accuracy and precision of force measurement based on a HS-AFM. This paper presents an experimental method to calibrate the effective spring constant of ultra-short cantilevers. By using a home-made AFM head, the cantilever is bent against an electromagnetic compensation balance under servo control. Meanwhile the bending force and the cantilever deflection are synchronously measured by the balance and the optical lever in the AFM head, respectively. Then the effective spring constant is simply determined as the ratio of the force to the corresponding deflection. Four ultra-short trapezoid shape cantilevers were calibrated using this method. A quantitative uncertainty analysis showed that the combined relative standard uncertainty of the calibration result is less than 2%, which is better than the uncertainty of any previously reported techniques.