Calibration and Nonlinearity Compensation for Force Application in AFM based Nanomanipulation

Abstract — Both the extent and accuracy of force application in atomic force microscope (AFM) nanomanipulation are significantly limited by the nonlinearity of the commonly used optical lever with a nonlinear position-sensitive detector (PSD). In order to compensate the nonlinearity of the optical lever, a nonlinear calibration method is presented. This method applies the nonlinear curve fit to a full-range position-voltage response of the photodiode, obtaining a continuous function of its voltagerelated sensitivity. Thus, Interaction forces can be defined as integrals of this sensitivity function between any two responses of photodiode voltage outputs, instead of rough transformation with a single conversion factor. The lateral position-voltage response of the photodiode, a universally acknowledged puzzle, was directly characterized by an accurately calibrated force sensor composed of a tippless piezoresistive force sensor, regardless of any knowledge of the cantilevers and laser measuring system. Experiments using a rectangular cantilever (normal force constant 0.24 N/m) demonstrated that the proposed nonlinear calibration method restrained the sensitivity error of normal position-voltage responses to 3.6 % and extended the force application range. Index Terms — Atomic force microscope, nanomanipulation, force calibration, nonlinearity compensation. I