Analysis and control of micro-cantilever in dynamic mode AFM

Korayem, Moharam Habibnejad; Zafari, S.; Amanati, A.; Damircheli, Mehrnoosh; Ebrahimi, N.

doi:10.1007/s00170-010-2588-4

Cited by 15 publications

(9 citation statements)

References 22 publications

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“…The procedure mentioned above is also related to the Riemann function method for integrating partial differential equations. Dynamic responses have been considered in the field of control of distributed systems and in elastodynamics in connection with vibrations and cracking problems [23][24][25][26].…”

Section: Advances In Mathematical Physicsmentioning

confidence: 99%

“…There, the Green function was obtained by working with a solution basis that considers hyperbolic and trigonometric functions in the general solution. These functions depend upon simple roots of a complete quadratic polynomial due to the inclusion of a second derivative spatial term in (24). When the axial load is removed, the solution basis reduces to the one considered for particular cases of vibrating beams.…”

Section: Closed Form Of the Transfer Function For A Multispanmentioning

confidence: 99%

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Nanobeams and AFM Subject to Piezoelectric and Surface Scale Effects

Claeyssen

Copetti

Tonetto

et al. 2018

Advances in Mathematical Physics

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Vibration dynamics of elastic beams that are used in nanotechnology, such as atomic force microscope modeling and carbon nanotubes, are considered in terms of a fundamental response within a matrix framework. The modeling equations with piezoelectric and surface scale effects are written as a matrix differential equation subject to tip-sample general boundary conditions and to compatibility conditions for the case of multispan beams. We considered a quadratic and a cubic eigenvalue problem related to the inclusion of smart materials and surface effects. Simulations were performed for a two stepped beam with a piezoelectric patch subject to pulse forcing terms. Results with Timoshenko models that include surface effects are presented for micro- and nanoscale. It was observed that the effects are significant just in nanoscale. We also simulate the frequency effects of a double-span beam in which one segment includes rotatory inertia and shear deformation and the other one neglects both phenomena. The proposed analytical methodology can be useful in the design of micro- and nanoresonator structures that involve deformable flexural models for detecting and imaging of physical and biochemical quantities.

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Section: Advances In Mathematical Physicsmentioning

confidence: 99%

Section: Closed Form Of the Transfer Function For A Multispanmentioning

confidence: 99%

Nanobeams and AFM Subject to Piezoelectric and Surface Scale Effects

Claeyssen

Copetti

Tonetto

et al. 2018

Advances in Mathematical Physics

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“…Atomic Force Microscopy (AFM) plays an important role in studying the surface topography of materials and measuring intermolecular forces [1][2][3]. Tapping Mode Atomic Force Microscopy (TMAFM) reduces sample destruction, in comparison to contact mode, and, as a result, is widely used for studying compliant materials such as polymers, biomaterials and semiconductors [2,4].…”

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of tapping-mode AFM considering capillary force interactions

2011

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The Atomic Force Microscope (AFM) scans the topography of a sample surface using a microsized flexible cantilever. In tapping-mode AFM, the tip-surface interactions are strongly nonlinear, rapidly changing and hysteretic. This paper explores, numerically, a flexible beam model that includes attractive, adhesive and repulsive contributions, as well as the interaction of the capillary fluid layers that cover both the tip and the sample in ambient conditions common in experiments. Forward-time simulation has been applied with an event handling numerical technique for dynamic analysis, and the Amplitude-Phase-Distance (APD) curves have been extracted. The branches of periodic solutions are found to end precisely where the cantilever comes into grazing contact with event surfaces in state space, corresponding to the onset of capillary interactions and the onset of repulsive forces associated with surface contact. The dissipated power, in the presence of conservative tip-sample interaction forces where the source of hysteresis is the formation and rupture of a liquid bridge between the tip and the sample, has been measured too. This simulation provides a more accurate way to validate the design of a new AFM probe and AFM controller than simulations which use the lumped-mass model.

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“…Atomic force microscopy (AFM), which has a cantilever with a sharp pyramidal or conical tip at the free end, is now widely used as a powerful technique for studying surface topography on an atomic scale (Chang et al, ; Korayem et al, ; Mazeran and Loubet, ). When a tip scans across a sample surface, it induces a dynamic interaction force between the tip and the sample surface.…”

Section: Introductionmentioning

confidence: 99%

Study of the sensitivity and resonant frequency of the torsional modes of an AFM cantilever with a sidewall probe based on a nonlocal elasticity theory

Abbasi

Mohammadi

2015

Microscopy Res & Technique

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A relationship based on a nonlocal elasticity theory is developed to investigate the torsional sensitivity and resonant frequency of an atomic force microscope (AFM) with assembled cantilever probe (ACP). This ACP comprises a horizontal cantilever and a vertical extension, and a tip located at the free end of the extension, which makes the AFM capable of topography at sidewalls of microstructures. First, the governing differential equations of motion and boundary conditions for dynamic analysis are obtained by a combination of the basic equations of nonlocal elasticity theory and Hamilton's principle. Afterward, a closed-form expression for the sensitivity of vibration modes has been obtained using the relationship between the resonant frequency and contact stiffness of cantilever and sample. These analysis accounts for a better representation of the torsional behavior of an AFM with sidewall probe where the small-scale effect are significant. The results of the proposed model are compared with those of classical beam theory. The results show that the sensitivities and resonant frequencies of ACP predicted by the nonlocal elasticity theory are smaller than those obtained by the classical beam theory.

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Analysis and control of micro-cantilever in dynamic mode AFM

Cited by 15 publications

References 22 publications

Nanobeams and AFM Subject to Piezoelectric and Surface Scale Effects

Nanobeams and AFM Subject to Piezoelectric and Surface Scale Effects

Dynamic analysis of tapping-mode AFM considering capillary force interactions

Study of the sensitivity and resonant frequency of the torsional modes of an AFM cantilever with a sidewall probe based on a nonlocal elasticity theory

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