Characterization of Intermittent Contact in Tapping-Mode Atomic Force Microscopy (original) (raw)
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Near-grazing dynamics in tapping-mode atomic-force microscopy
International Journal of Non-Linear Mechanics, 2007
In tapping-mode atomic force microscopy, nonlinear e¤ects due to large variations in the force …eld on the probe tip over very small length scales and the intermittency of contact may induce strong dynamical instabilities. In this paper, a discontinuity-mapping-based analysis is employed to investigate the destabilizing e¤ects of low-velocity contact on a lumped-mass model of an oscillating atomic-forcemicroscope cantilever tip interacting with a typical sample surface. As illustrated using two tip-sample force models, the analysis qualitatively captures the potential loss of stability and disappearance of a lowcontact-velocity steady-state response. The quantitative agreement of the predictions of the discontinuitymapping-based analysis with direct numerical simulations, at least for su¢ciently low-velocity contact, supports its use in the passive redesign or active control of the tip-sample mechanism for purposes of preventing such a loss of stability.
Nonlinear dynamics of atomic force microscopy with intermittent contact
Chaos, Solitons & Fractals, 2007
When the atomic force microscopy (AFM) in tapping mode is in intermittent contact with a soft substrate, the contact time can be a significant portion of a cycle, resulting in invalidity of the impact oscillator model, where the contact time is assumed to be infinitely small. Furthermore, we demonstrate that the AFM intermittent contact with soft substrate can induce the motion of higher modes in the AFM dynamic response. Traditional ways of modeling AFM (one degree of freedom (DOF) system or single mode analysis) are shown to have serious mistakes when applied to this kind of problem. A more reasonable displacement criterion on contact is proposed, where the contact time is a function of the mechanical properties of AFM and substrate, driving frequencies/amplitude, initial conditions, etc. Multi-modal analysis is presented and mode coupling is also shown.
Feedback-induced instability in tapping mode atomic force microscopy: theory and experiment
… of the Royal …, 2010
We investigate a mathematical model of tapping mode atomic force microscopy (AFM), which includes surface interaction via both van der Waals and meniscus forces. We also take particular care to include a realistic representation of the integral control inherent to the real microscope. Varying driving amplitude, amplitude setpoint and driving frequency independently shows that the model can capture the qualitative features observed in AFM experiments on a flat sample and a calibration grid. In particular, the model predicts the onset of an instability, even on a flat sample, in which a large-amplitude beating-type motion is observed. Experimental results confirm this onset and also confirm the qualitative features of the dynamics suggested by the simulations. The simulations also suggest the mechanism behind the beating effect; that the control loop over-compensates for sufficiently high gains. The mathematical model is also used to offer recommendations on the effective use of AFMs in order to avoid unwanted artefacts.
Dynamical Study of a Piecewise-Smooth Model in Tapping Mode Atomic Force Microscope
Conferência Brasileira de Dinâmica, Controle e Aplicações, 2011
This paper deals with the dynamics of a piecewise-smooth model used to represents the Tapping Mode Atomic Force Microscope behavior. Created by Binning et al (1986), Atomic Force Microscopy became a powerful tool in scanning probe process. A micro-cantilever vibrates, excited by a piezo electric transducer and this vibration is detected by a photo detector. Working close from its resonance, the micro-cantilever has a nonlinear behavior, due to this, chaotic behavior may occur. Represented by a piecewise SDOF system, the dynamics of the model are investigate via numerical simulations and the study of figures like, phase portrait, FFT, time history and Lyapunov exponents show chaotic behavior in a interval of time. This fact is not a desirable outcome in AFM image achievement.
Characterization of Probe Dynamic Behaviors in Critical Dimension Atomic Force Microscopy
Journal of Research of the National Institute of Standards and Technology, 2009
This paper describes a detailed computational model of the interaction between an atomic force microscope probe tip and a sample surface. The model provides analyses of dynamic behaviors of the tip to estimate the probe deflections due to surface intermittent contact and the resulting dimensional biases and uncertainties. Probe tip and cantilever beam responses to intermittent contact between the probe tip and sample surface are computed using the finite element method. Intermittent contacts with a wall and a horizontal surface are computed and modeled, respectively. Using a 75 nm Critical Dimension (CD) tip as an example, the responses of the probe to interaction forces between the sample surface and the probe tip are shown in both time and frequency domains. In particular, interactions between the tip and both a vertical wall and a horizontal surface of a silicon sample are modeled using Lennard-Jones theory. The Snap-in and snap-out of the probe tip in surface scanning are calculated and shown in the time domain. The calculation includes the compliance of the probe, the sample-tip interaction force model, and dynamic forces generated by vibration. Cantilever and probe tip deflections versus interaction forces in the time domain can be derived for both vertical contact with a plateau and horizontal contact with a side wall. Dynamic analysis using the finite element method and Lennard-Jones model provide a unique means to analyze the interaction of the probe and sample, including calculation of the deflection and the gap between the probe tip and the measured sample surface.
Microcantilever dynamics in tapping mode atomic force microscopy via higher eigenmodes analysis
Journal of Applied Physics, 2013
Microcantilever dynamics in tapping mode atomic force microscopy (AFM) is addressed via a multimode approximation, which allows to consider external excitation at primary or secondary resonance and to highlight the effect of higher order eigenmodes. Upon presenting the AFM model and its multimode discretization, the dynamic response is investigated via numerical simulation of single-and three-mode models by considering different bifurcation parameters. Typical features of tapping mode AFM response as nonlinear hysteresis, bistability, higher harmonics contribution, impact velocity, and contact force are addressed. The analysis is conducted by evaluating damping of higher modes according to the Rayleigh criterion, which basically accounts for structural damping representative of the behavior of AFMs in air. Nominal damping situations more typical of AFMs in liquids are also investigated, by considering sets of modal Q-factors with different patterns and ranges of values. Variable attractive-repulsive effects are highlighted, along with the possible presence of a coexisting multi-periodic orbit when the system is excited at second resonance. V C 2013 AIP Publishing LLC. [http://dx.
Applied Physics Letters, 2001
We present a mechanical model for the atomic force microscope tip tapping on a sample. The model treats the tip as a forced oscillator and the sample as an elastic material with adhesive properties. It is possible to transform the model into an electrical circuit, which offers a way of simulating the problem with an electrical circuit simulator. Also, the model predicts the energy dissipation during the tip-sample interaction. We briefly discuss the model and give some simulation results to promote an understanding of energy dissipation in a tapping mode.
An atomic force microscope tip designed to measure time-varying nanomechanical forces
Nature Nanotechnology, 2007
Tapping-mode atomic force microscopy (AFM), in which the vibrating tip periodically approaches, interacts and retracts from the sample surface, is the most common AFM imaging method. The tip experiences attractive and repulsive forces that depend on the chemical and mechanical properties of the sample, yet conventional AFM tips are limited in their ability to resolve these time-varying forces. We have created a specially designed cantilever tip that allows these interaction forces to be measured with good (sub-microsecond) temporal resolution and material properties to be determined and mapped in detail with nanoscale spatial resolution. Mechanical measurements based on these force waveforms are provided at a rate of 4 kHz. The forces and contact areas encountered in these measurements are orders of magnitude smaller than conventional indentation and AFM-based indentation techniques that typically provide data rates around 1 Hz. We use this tool to quantify and map nanomechanical changes in a binary polymer blend in the vicinity of its glass transition.
Journal of Applied Physics, 2010
There is great interest in using proximal probe techniques to simultaneously image and measure physical properties of surfaces with nanoscale spatial resolution. In this regard, there have been recent innovations in generating time-resolved force interaction between the tip and surface during regular operation of tapping mode atomic force microscopy ͑TMAFM͒. These tip/sample forces can be used to measure physical material properties of surface in an analogous fashion to the well-established static force curve experiment. Since its inception, it has been recognized that operation of TMAFM in fluids differs significantly from that in air, with one of the major differences manifested in the quality factor ͑Q͒ of the cantilever. In air, Q is normally on the order of 200-400, whereas in fluids, it is of the order of approximately 1-5. In this study, we explore the impact of imaging parameters, i.e., set point ratio and free cantilever oscillation amplitude, on time varying tip-sample force interactions in fluid TMAFM via simulation and experiment. The numerical AFM model contains a feedback loop, allowing for the simulation of the entire scanning process. In this way, we explore the impact of varying the Young's modulus of the surface on the maximum tapping force.