Dynamic modeling and sensitivity analysis of dAFM in the transient and steady state motions

Abstract

In this paper, based on the slow time varying function theory, dynamical equations for the amplitude and phase of the dynamic atomic force microscope are derived. Then, the sensitivity of the amplitude and phase to the dissipative and conservative parts of interaction force is investigated. The most advantage of this dynamical model is the ability to simulate and analysis the dynamics behavior of amplitude and phase of the AFM tip motion not only in the steady state but also in the transient regime. Using numerical analysis the transient and steady state behavior of amplitude and phase is studied and the sensitivity of amplitude and phase to the interaction force is analyzed.

Modelling and nanoscale force spectroscopy of frequency modulation atomic force microscopy

“…where 0 is the resonance frequency of cantilever when there is no interaction between tip and sample and is its resonance frequency when the interaction between tip and sample is occurred, the dynamic equations of amplitude and phase are derived as [40]:…”

“…So, for the analysis of the transient motion and simulation of FM-AFM behaviour, the alternative mathematical method for control system is preferred. In this paper, based on the slow time varying function theory [36]- [40], the dynamical equations for the amplitude and phase of AFM is derived and by adding control system to keep the phase at 90 o and amplitude of cantilever oscillation at fixed value, the FM-AFM is modelled. The most advantages of the proposed dynamical model are not only independency of modelling and simulation to the PLL system but also the direct access to the amplitude and phase signals and capability of investigating the transient behaviour of phase and amplitude beside their steady state motion.…”

“…The most advantages of the proposed dynamical model are not only independency of modelling and simulation to the PLL system but also the direct access to the amplitude and phase signals and capability of investigating the transient behaviour of phase and amplitude beside their steady state motion. The study of the amplitude, frequency and phase response in transient regime can be led to the increase of speed and precision of feedback control which has direct influence of the image precision [40]- [45]. This opens the possibility to capture the information conveyed by the sensing tip in a transient motion of cantilever, contrasted to the steady state used in current dynamic techniques [45].…”

Resonance‐Size Parameter Relationship and Dynamics of an AFM Subjected to Multimode Excitation and Based on the Modified Couple Stress Theory

“…In convention, the literatures investigated the steady behavior of AFM probe [2][3][4][5][6][7][8][9]. Definitely, the investigation of the amplitude and phase behavior in the transient regime will increase significantly the speed of imaging and accuracy.…”

“…Chang et al [12] presented a new algorithm for high speed AFM imaging of biopolymers by investigating the transition from transient part to steady state regime. Payam [9] studied the transient behavior of tapping mode-AFM in the mass-spring-damper model. Some literatures [13][14][15][16] investigated the multifrequency excitation of FM-AFM systems in fast force spectroscopy and material characterization at the atomic scale as well.…”