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Bimodal amplitude modulation atomic force microscopy (AM-AFM) is widely used in nanoscale topography and mechanical property imaging for a variety of materials. In this paper, the stability of the amplitude/phase spectroscopy curves and the imaging contrast in bimodal AM-AFM for different mode combinations are investigated computationally in ambient air. The results show that with the second mode amplitude used for topography feedback on a stiff material, the amplitude/phase spectroscopy would probably undergo volatile fluctuation, leading to unstable imaging. With the third mode amplitude set for topography imaging, it would be difficult for the feedback to maintain the prescribed amplitude since a large cantilever position variation is required for different sample moduli. With the first mode amplitude set for topography feedback, the amplitude and the phase of the second mode vary monotonically with sample modulus or viscosity in comparison with the third or the fourth mode, which is suitable for compositional contrast imaging. These results would provide useful guidelines for optimum imaging in bimodal AFM measurements.

Bimodal amplitude modulation atomic force microscopy (AM-AFM) is an emerging technique for compositional imaging in liquids. In this work, we investigate the power transfer in bimodal AM-AFM in liquids by a numerical analysis. Power items are calculated by direct numerical integral and the corresponding amplitude and phase response is presented. Results show power balance is satisfied for each mode. The power transfer in each mode is significantly small compared to the external input power and most of the power is dissipated into the surrounding medium, especially for a large setpoint or cantilever-sample separation. The power transfer among different modes is complex and strongly depends on the cantilever and imaging parameters. Power transfer between different modes goes up with increasing free amplitude of the second mode. In addition, a stiffer sample will produce a more complex force spectra, which perturbs the cantilever oscillation more heavily compared to a compliant sample. Besides, the non-driven higher mode of a softer cantilever is more likely to be momentarily excited. The power items and cantilever response during imaging are also provided, revealing the phases in bimodal AFM in liquids may not be utilized to characterize the sample elasticity due to the non-monotonic trends. Instead, the amplitude of the second mode could be used to characterize the elasticity of the sample with moderate to high moduli.

In this work, amplitude modulation atomic force microscopy (AM-AFM) based on the higher flexural modes of the microcantilever is investigated by a numerical approach. The amplitude-distance and phase-distance curves for the first four flexural modes are obtained and compared. The dependence of phase on elastic modulus and viscosity of the sample is analyzed. Results show that a higher flexural mode yields a larger amplitude and phase in the repulsive regime and reduces the bistability, but causes a larger sample deformation and peak repulsive force. Compared to that of a lower flexural mode, the phase of a higher flexural mode provides higher sensitivity to viscosity variation for relatively large moduli.

A theoretical model for calculating the Young’s modulus of multi-layer microcantilevers with a coating is proposed, and validated by a three-dimensional (3D) finite element (FE) model using ANSYS parametric design language (APDL) and atomic force microscopy (AFM) characterization. Compared with typical theoretical models (Rayleigh-Ritz model, Euler-Bernoulli (E-B) beam model and spring mass model), the proposed theoretical model can obtain Young’s modulus of multi-layer microcantilevers more precisely. Also, the influences of coating’s geometric dimensions on Young’s modulus and resonant frequency of microcantilevers are discussed. The thickness of coating has a great influence on Young’s modulus and resonant frequency of multi-layer microcantilevers, and the coating should be considered to calculate Young’s modulus more precisely, especially when fairly thicker coating is employed.