Lateral stiffness of the tip and tip-sample contact in frictional force microscopy

In atomic force and frictional force microscopy, quantitative interpretation of lateral stiffness at the tip-sample contact requires a detailed understanding of all factors contributing to the frictional force as measured in a typical experiment. We used a scanning transmission electron microscope to image and determine the geometry of the tip apex of a variety of atomic force microscope cantilevers. On the basis of this measured structure, we then used finite element analysis to model the lateral stiffness of the tip and found that the tip stiffness is often smaller than the lateral stiffness of the cantilever. Furthermore, we analyzed the stiffness of the tip sample contact and found that for sharp tips the contact stiffness can also be comparable to the lateral stiffness of the cantilever. If these two effects are ignored, significant errors can result in the calculation of lateral forces. We demonstrated the effects of lateral tip and contact stiffness experimentally and used the measurements to calculate the radius of the tip-sample contact.