Sensitivity of vibration modes of atomic force microscope cantilevers in continuous surface contact

The sensitivity of flexural vibration modes for the rectangular cantilever of an atomic force microscope (AFM) has been derived by taking into account the cantilever slope, and a closed-form expression is obtained. As expected, the results show that each mode has a different sensitivity and that the first mode is the most sensitive mode for the AFM cantilever. The sensitivity of flexural modes is greater for a lower normal contact stiffness between the material surface and the cantilever tip. The high-order flexural modes are more sensitive than the low-order modes as the contact stiffness increases. The sensitivities of the first four vibration modes for a sloped cantilever have been compared to those of a level cantilever. The effects of various cantilever slopes on the sensitivity have also been compared. Increasing the cantilever slope apparently decreases the sensitivity as the contact stiffness becomes small. As the contact stiffness becomes large, the increasing tip length increases the sensitivity of the vibration modes.