Nonlinear tip-sample interactions affecting frequency responses of microcantilevers in tapping mode atomic force microscopy

Abstract

Tapping mode atomic force microscopy is receiving a great deal of interest because of its ability to image compliant materials as well as to overcome adhesion forces. In this operation mode, the vibration amplitude of the cantilever is much higher than the equilibrium separation between tip and sample. For our experiments, a silicon microcantilever and a freshly cleaved mica sample were used. Frequency responses were measured for different values of equilibrium separation distance. Experimental results revealed a drastic decrease in vibration amplitude and a large shift of resonant frequency to higher values. This frequency shift and amplitude damping depend drastically on the equilibrium position with respect to the free oscillation amplitude of the cantilever. A model taking into account the attractive Van der Waals force as well as repulsive contact force was used. Parameters such as position of the tip, force acting during intermittent contact and frequency responses have been calculated. Good agreement is obtained and the relevant parameters involved in tapping mode are discussed.Since its invention, atomic force microscopy (AFM) [1] has been a promising tool for investigating many kinds of surfaces of conductive and nonconductive materials. During the last few years, different operating principles have been developed especially for investigating compliant materials such as biological cells [2] and polymers [3] for which acting forces should be controlled in order to avoid sample distortion and damage. For these kinds of materials contact mode has some drawbacks; in addition to possible sample damage, other forces such as adhesion force, shear force during scanning, and capillary force can act at the same time. All these factors have led to development of other operation modes such as non-contact mode AFM and recently the tapping mode [4][5][6].to detect long-range interaction [7]. Good resolution can be obtained when the rest position of the cantilever is close to the sample and the vibration amplitude is small enough. In ambient environment, some parasitic interactions can be observed, for example hydrodynamic interaction, capillary force, or sticking effect [8].In tapping operation mode, the vibration amplitude is large enough (in the range of 100 nm). Equilibrium separation between tip and sample is much smaller than the free cantilever vibration amplitude allowing for an intermittent tip/sample contact once per cycle. Large amplitudes combined with large repulsive contact forces, provide the cantilever with enough energy to overcome capillary and adhesion forces. Also, intermittent short contact can be compliant enough to avoid possible damage to the sample.The mechanisms involved in tapping operation mode have been investigate recently [9][10][11][12]. During a vibration cycle, the tip is subject to attractive and repulsive forces acting at different tip/sample positions. The attractive force is quite weak in comparison to the stronger repulsive force, which can increase the cantilever resonance freque...

Simulations of switching vibrating cantilever in atomic force microscopy

“…The derivatives are taken with respect to time; z r is the rest position of the tip above the sample; z t and z s are the positions of the tip and sample, respectively. Interaction force, f ts , can be approximated as a function of tip-to-sample distance, d, by [8] d 0 s 30 where H, R, s, E i , and n i are the Hamaker constant, radius of the tip, interatomic distance, Young's modulus, and Poisson coef®cient, respectively. The mechanical model is depicted in Fig.…”

Scanning Probe Microscopy

“…Several works describing the fundamentals of dynamic imaging were recently published ( − ). Correlations between amplitude, frequency and phase with tip sharpness, viscoelasticity, and sample mechanical properties have been reported ( − ). Especially noteworthy was Sader's () examination of the frequency response of cantilevers in fluids.…”

Models for quantitative charge imaging by atomic force microscopy

“…[15][16][17][18][19][20] Much work has been done in modeling of the tip-sample interaction in atomic-force microscopy. [21][22][23][24][25][26][27][28][29] In this article, we combine both electrostatic and AFM modeling to interpret AFM images of charge. We describe two models for quantitative charge imaging, one appropriate for noncontact mode imaging, the second for intermittent contact ͑tapping͒ mode imaging.…”