Micro contact and stick-slip number between AFM probe tip and sample surface

Abstract

In an atomic force microscope (AFM), the cantilever probe, probe tip and sample surface form a micro system in which micro contact, elastic deformation, relative sliding and friction occur during scanning with the contact mode. In this paper, the energy conversion and dissipation during scanning process in the micro system is investigated based on the Mauges-Daules contact model. A dimensionless stick-slip number $\eta = \sqrt {{{8U_1 h^2 } \mathord{\left/ {\vphantom {{8U_1 h^2 } {\left( {k_\theta R_s^2 } \right)}}} \right. \kern-\nulldelimiterspace} {\left( {k_\theta R_s^2 } \right)}}}$ is defined to describe the micro stick-slip behavior under AFM. Through numerical simulation of the dynamics of the probe tip, it is shown that AFM lateral force is dependent on the defined stick-slip number. If η<1, lateral force is weak and stick-slip phenomenon disappears. When η=1, the probe tip jumps between the asperities on sample surface, showing stick-slip behavior but without energy dissipation. In the case of η>1, the tip moves off the sticking points with an adhesion hysteresis, resulting in an energy dissipation. Therefore, the stick-slip number can serve as a characteristic parameter. Numerical simulation of AFM lateral force with different stick-slip numbers is in agreement with experimental results. Finally a method to extract frictional force from the AFM lateral force signal is proposed.