Abstract
Many investigations have focused on steady-state nonlinear dynamics of cantilevers in tapping mode atomic force microscopy (TM-AFM). However, a transient dynamic model—which is essential for a model-based control design—is still missing. In this paper, we derive a mathematical model which covers both the transient and steady-state behavior. The steady-state response of the proposed model has been validated with existing theories. Its transient response, however, which is not covered with existing theories, has been successfully verified with experiments. Besides enabling model-based control design for TM-AFM, this model can explain the high-end aspects of AFM such as speed limitation, image quality, and eventual chaotic behavior.
Highlights
Atomic force microscopy (AFM) is a powerful tool for imaging the surface of samples with a sub-nanometer resolution which has many different applications in experimental sciences such as physics and biology [1,2,3,4]
These results show that the static response of the proposed model agrees with the existing models for steadystate response of the AFM cantilever
The results show the practical implications of the transient behavior of the tapping mode AFM (TM-AFM) on the final image quality
Summary
Atomic force microscopy (AFM) is a powerful tool for imaging the surface of samples with a sub-nanometer resolution which has many different applications in experimental sciences such as physics and biology [1,2,3,4]. At the far right-hand side of Fig. 1, where the sample is far from the cantilever, obviously there is no interaction and the amplitude is independent of the distance. The controller fluctuates between the two height values, which causes artifacts on the image Researchers have studied these nonlinear effects, their consequences, and the related problems, extensively [15,16,17]. How fast the amplitude can adjust itself to the variations in the height totally depends on its dynamic trajectory This problem is crucial for high-speed AFM, where the changes of the distance happen in time intervals that are comparable or shorter than the cantilevers response time. The second subsection graphically explains the reason behind the chaotic behavior of TM-AFM as a consequence of high control gains as previously reported in [18]
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
