Dynamics Of Atomic Force Microscope Research Articles

The improvement of the accuracy of electromagnetic actuator based atomic force microscope operating in contact mode and the development of a new methodology for the estimation of control parameters and the achievement of superior image quality

The dynamics of atomic force microscope (AFM) acting in contact mode is crucial for correct interpretation of AFM images and especially for the identification of artefacts and the determination of their sources. This paper presents a methodology for the interpretation and improvement of the AFM image quality. The developed AFM dynamic model has been applied for the control of scanning parameters to achieve superior image quality. The model provides possibility to tune AFM parameters, such as tip-surface interaction force and scanning speed in respect of the sample’s material and cantilever’s tip geometry. This methodology allows us to ensure the ideal imaging conditions, to evaluate AFM images and to produce a superior picture quality. Using this model, we can also analyze experimental data and simulate the experimental results.

In-situ piezoresponse force microscopy cantilever mode shape profiling

The frequency-dependent amplitude and phase in piezoresponse force microscopy (PFM) measurements are shown to be a consequence of the Euler-Bernoulli (EB) dynamics of atomic force microscope (AFM) cantilever beams used to make the measurements. Changes in the cantilever mode shape as a function of changes in the boundary conditions determine the sensitivity of cantilevers to forces between the tip and the sample. Conventional PFM and AFM measurements are made with the motion of the cantilever measured at one optical beam detector (OBD) spot location. A single OBD spot location provides a limited picture of the total cantilever motion, and in fact, experimentally observed cantilever amplitude and phase are shown to be strongly dependent on the OBD spot position for many measurements. In this work, the commonly observed frequency dependence of PFM response is explained through experimental measurements and analytic theoretical EB modeling of the PFM response as a function of both frequency and OBD spot location on a periodically poled lithium niobate sample. One notable conclusion is that a common choice of OBD spot location—at or near the tip of the cantilever—is particularly vulnerable to frequency dependent amplitude and phase variations stemming from dynamics of the cantilever sensor rather than from the piezoresponse of the sample.

Multi-modal analysis on the intermittent contact dynamics of atomic force microscope

A multi-modal analysis on the intermittent contact between an atomic force microscope (AFM) with a soft sample is presented. The intermittent contact induces the participation of the higher modes into the motion and various subharmonic motions are shown. The AFM tip mass enhances the coupling of different modes. The AFM tip mass is modeled by the Dirac delta function and the coupling effects are analyzed via the Galerkin method. The necessity of applying multi-modal analysis to the intermittent contact problem is demonstrated. Unlike the impact oscillator model which assumes the impact/contact time is infinitesimal, the contact time can be a significant fractional portion in each cycle, especially for the soft sample case and thus results in different dynamic behavior from that of an impact oscillator.

Event-driven feedback tracking and control of tapping-mode atomic force microscopy

This paper presents an event-driven, discrete-in-time feedback strategy for tracking and stabilizing naturally occurring periodic oscillations in the probe-tip dynamics of atomic force microscope (AFM) cantilevers in tapping-mode operation. Specifically, robust dynamic tracking and stabilization is achieved by the imposition of discrete changes in the vertical offset between the cantilever support and the sample surface based on an estimated linearization of the system dynamics about a dynamically generated reference trajectory. Here, use is made not only of the oscillation amplitude, as is typical in commercial control implementations for AFMs, but also of the instantaneous phase information. It is shown that stabilization and desirable performance during surface scanning is possible, even in the presence of uncertainty and limited state access. In particular, the methodology enables robust tracking and use of low-contact-velocity periodic system responses that are unstable in the absence of control.

Dynamics of tapping mode atomic force microscopy in liquids: Theory and experiments

A mathematical model is presented to predict the oscillating dynamics of atomic force microscope cantilevers with nanoscale tips tapping on elastic samples in liquid environments. Theoretical simulations and experiments performed in liquids using low stiffness probes on hard and soft samples reveal that, unlike in air, the second flexural mode of the probe is momentarily excited near times of tip-sample contact. The model also predicts closely the tip amplitude and phase of the tip at different set points.

Nonlinear dynamics of atomic force microscope with PI feedback

Frequency modulation of an atomic force microscope is based on a PI control law, which keeps the amplitude equal to a desired value. This paper analyses the stability and performance of the closed-loop nonlinear dynamics of AFM. Numerical results are presented to corroborate the validity of theoretical analysis.