Effect of cantilever geometry on the optical lever sensitivities and thermal noise method of the atomic force microscope.

Calibration of the optical lever sensitivities of atomic force microscope (AFM) cantilevers is especially important for determining the force in AFM measurements. These sensitivities depend critically on the cantilever mode used and are known to differ for static and dynamic measurements. Here, we calculate the ratio of the dynamic and static sensitivities for several common AFM cantilevers, whose shapes vary considerably, and experimentally verify these results. The dynamic-to-static optical lever sensitivity ratio is found to range from 1.09 to 1.41 for the cantilevers studied - in stark contrast to the constant value of 1.09 used widely in current calibration studies. This analysis shows that accuracy of the thermal noise method for the static spring constant is strongly dependent on cantilever geometry - neglect of these dynamic-to-static factors can induce errors exceeding 100%. We also discuss a simple experimental approach to non-invasively and simultaneously determine the dynamic and static spring constants and optical lever sensitivities of cantilevers of arbitrary shape, which is applicable to all AFM platforms that have the thermal noise method for spring constant calibration.