Non-contact atomic force microscope: Modeling and simulation using van der Pol averaging method

Topic and aim. One of the tools which are extremely useful and valuable for creating a topography of surfaces, measuring forces, and manipulating material with nano-meter-scale features is the Atomic force microscope (AFM). Since it can create the image of the surface object in different mediums at the nano-scale, AFM can be used in a wide variety of applications and industries. This work aimed at creating the mathematical model of the non-contact atomic force microscope. Models and Methods. The lumped parameter model of the atomic force microscope in the non-contact operation mode is utilized to make the mathematical model of the micro cantilever of the AFM in this article. In this mode, non-contact operation mode, a stiff micro machined cantilever is oscillated by the harmonic external force in the attractive regime, i.e. the sharp tip at the end of the cantilever is quite close to the surface of the specimen but not in contact. In this work, the mathematical model is nonlinear since we use the van der Waals force as the sample-tip interaction. We use the van der Pol average method to find solution of the system and get the frequency response equation. Results. This equation was employed to investigate the effect of non-linearity, excitation amplitude, and damping coefficient on the response of the system. Also, the steady-state motion stability was studied, and state space trajectory and timing response of states were demonstrated.