Tip Mass Effects on Image Contrast

Modal Flexural Sensitivity of AFM Cantilever

Dec. 05, 2011

Fig. 1: Schematic diagram of the flexural vibration of the AFM micro-cantilever, the contact force between the tip and sample surface is modeled by a linear spring.

Fig. 1: Schematic diagram of the flexural vibration of the AFM micro-cantilever, the contact ... more

When an oscillating AFM cantilever approaches a sample, the tip-sample interaction force influences the cantilever dynamics. The magnitude of the contact interaction force depends on the stiffness of the materials. Stiffness of the material affects sensitivity of different modes differently. This sensitivity controls the image contrast. Here, the effect of tip mass on the modal flexural sensitivity of AFM cantilever to the variations of surface stiffness and image contrast is investigated.

Modal Flexural Sensitivity to the Surface Stiffness Variations

The atomic force microscope is being utilized for imaging surface topography of samples on an atomic scale. The dynamic behavior of the AFM greatly influences the surface imaging process. When the AFM micro-cantilever tip scans the surface of a sample, an interaction force appears between the tip and the sample surface which depends on the tip position relative to the sample surface. This interaction force is attractive or repulsive. One of the important factors in the repulsive regime is the stiffness of the material. It has been shown that the interaction force between tip and sample has a different impact on the dynamic behavior of each vibration mode of the AFM [1]. Thus, each mode shows different sensitivities to variations of surface stiffness. On the other hand, the sensitivity of the AFM micro-cantilever can influence the image contrast [2].

Higher Image Contrast

To achieve a higher image contrast, it is desirable to use the frequency of the highest sensitive mode of AFM micro-cantilever as the excitation frequency. Several researches have been carried out to study the modal sensitivity of AFM micro-cantilever to surface stiffness variations [1]-[6]. The results show that for the materials that are compliant relative to the AFM micro-cantilever, the first mode is the most sensitive mode. Moreover, if the surface stiffness is increased, higher flexural vibration modes are more sensitive than the first mode. So, to achieve a better image contrast on soft materials, the excitation frequency close to the first resonance frequency should be selected, while for stiff materials, the excitation frequency close to higher resonance frequencies is the best choice.

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The tip mass reduces micro-cantilever resonance frequency [7].

Analysis

In this work we analyze the effect of the tip mass on the sensitivity of flexural vibration modes to the surface stiffness variations. The results of our numerical analysis for investigating the effect of tip mass on the sensitivity of first three modes are given in figures 2-4. The parameters of AFM given in [8] are utilized. As seen, for low values of stiffness (soft materials), the micro-cantilever with smaller tip mass has a larger sensitivity. In contrast, for higher values of surface stiffness (stiff materials), the sensitivities of the micro-cantilever with different tip masses are close to each other. Nevertheless, for larger tip masses, the sensitivity increases slightly. In addition, for higher eigenmodes and for soft materials, the effect of tip mass is more pronounced. So, to obtain a better image contrast for soft materials, a lower tip mass is recommended while for stiffer materials, increasing the tip mass should lead to more sensitivity and thus better image contrast.

References
[1] Rabe U. et al.: Appl. Phys. A 66 (1998)
[2] Turner J. A. and Wiehn J. S.: Nanotechlogy 12 (2001)
[3] Chang W. J. et al.: Phys. Lett. A 312 (2003)
[4] Espinoza F. J. et al.: New j. phys. 11 (2009)
[5] Lee H. L. and Chang W. J.: Ultramicroscopy 108 (2008)
[6] Kahrobaiyan M. H. et al.: Int. J. Mech. Sci. 52 (2010)
[7] Farrokh Payam A., et al.: Nanomaterials & Biostructures 4 (3) 2009
[8] Lozano J. R. et al.: Garcia R., Physical review B 79 (2009)

Authors
Dr. Amir Farrokh Payam
Dr. Morteza Fathipour
Department of Electrical & Computer Engineering
Faculty of Engineering
University of Tehran
Tehran, Iran

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Tip Mass Effects on Image Contrast

Modal Flexural Sensitivity of AFM Cantilever

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