AFM Nanomanipulation Using Nonlinear Calibration of Optical Levers

Abstract—The atomic force microscope (AFM) has been widely used as a nano-effector with a function of force sensing to detect in-teraction forces between an AFM tip and a sample, thereby control-ling the process of the nanomanipulation. However, both the extent and accuracy of force application are significantly limited by the nonlinearity of the commonly used optical lever with a nonlinear position-sensitive detector (PSD). In order to compensate the non-linearity of the optical lever, a nonlinear calibration method is pre-sented. This method applies the nonlinear curve fit to a full-range position-voltage response of the photodiode, obtaining a contin-uous function of its voltage-related sensitivity. Thus, interaction forces can be defined as integrals of this sensitivity function be-tween any two responses of photodiode voltage outputs, instead of rough transformation with a single conversion factor. The lat-eral position-voltage response of the photodiode, a universally ac-knowledged puzzle, was directly characterized by an accurately calibrated force sensor composed of a tippless piezoresistive micro-cantilever and corresponding electronics, regardless of any knowl-edge of the cantilevers and laser measuring system. Experiments using a rectangular cantilever (normal spring constant 0.24 N/m) demonstrated that the proposed nonlinear calibration method re-strained the sensitivity error of normal position-voltage responses to 3.6 % and extended the force application range. Index Terms—Atomic force microscope (AFM), force calibra-tion, nanomanipulation, nonlinearity compensation, optical lever