Calibration of oscillation amplitude in dynamic scanning force microscopy

A method to precisely calibrate the oscillation amplitude in dynamic scanning force microscopy is described. It is shown that the typical electronics used to process the dynamic motion of the cantilever can be adjusted to transfer the thermal noise of the cantilever motion from its resonance frequency to a much lower frequency within the typical bandwidth of the corresponding data acquisition electronics of a scanning force microscopy system. Based on this concept, two procedures for the calibration of the oscillation amplitude are proposed. One is based on a simple calculation of the root mean square deviation measured at the outputs of the electronics used to process the dynamic motion of the cantilever, and the second one is based on analysis of the corresponding spectrum and the calculation of the quality factor, the resonance frequency and the signal strength. We show that the proposed scheme for amplitude calibration using thermal noise is experimentally and theoretically robust, with soft as well as with hard cantilevers. Moreover, it is directly related to well-defined quantities such as the force constant and thermal energy, in contrast to the calibration using amplitude versus distance curves, which requires non-trivial a priori assumptions regarding the amplitude versus distance relation. (paper)