Coupling of conservative and dissipative forces in frequency-modulation atomic force microscopy

Abstract

Frequency modulation atomic force microscopy (FM-AFM) utilizes the principle of self-excitation to ensure the cantilever probe vibrates at its resonant frequency, regardless of the tip-sample interaction. Practically, this is achieved by fixing the phase difference between tip deflection and driving force at precisely 90°. This, in turn, decouples the frequency shift and excitation amplitude signals, enabling quantitative interpretation in terms of conservative and dissipative tip-sample interaction forces. In this article, we theoretically investigate the effect of phase detuning in the self-excitation mechanism on the coupling between conservative and dissipative forces in FM-AFM. We find that this coupling depends only on the relative difference in the drive and resonant frequencies far from the surface, and is thus very weakly dependent on the actual phase error particularly for high quality factors. This establishes that FM-AFM is highly robust with respect to phase detuning, and enables quantitative interpretation of the measured frequency shift and excitation amplitude, even while operating away from the resonant frequency with the use of appropriate replacements in the existing formalism. We also examine the calibration of phase shifts in FM-AFM measurements and demonstrate that the commonly used approach of minimizing the excitation amplitude can lead to significant phase detuning, particularly in liquid environments.

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