Harmonic and power balance tools for tapping-mode atomic force microscope

Abstract

The atomic force microscope(AFM) is a powerful tool for investigating surfaces at atomic scales. Harmonic balance and power balance techniques are introduced to analyze the tapping-mode dynamics of the atomic force microscope. The harmonic balance perspective explains observations hitherto unexplained in the AFM literature. A nonconservative model for the cantilever-sample interaction is developed. The energy dissipation in the sample is studied and the resulting power balance equations combined with the harmonic balance equations are used to estimate the model parameters. Experimental results confirm that the harmonic and power balance tools can be used effectively to predict the behavior of the tapping cantilever. Keywords Atomic force microscopes, Surface dynamics Disciplines Electrical and Computer Engineering CommentsThe following article appeared in Journal of Applied Physics 89, 6473 (2001) The atomic force microscope ͑AFM͒ is a powerful tool for investigating surfaces at atomic scales. Harmonic balance and power balance techniques are introduced to analyze the tapping-mode dynamics of the atomic force microscope. The harmonic balance perspective explains observations hitherto unexplained in the AFM literature. A nonconservative model for the cantilever-sample interaction is developed. The energy dissipation in the sample is studied and the resulting power balance equations combined with the harmonic balance equations are used to estimate the model parameters. Experimental results confirm that the harmonic and power balance tools can be used effectively to predict the behavior of the tapping cantilever.

Quantitative Analysis of Scanning Force Microscopy Data Using Harmonic Models

“…Such a resonant system with a high quality factor behaves like a filter which strongly limits excitations at higher harmonics of the fundamental (typically below 1% of the amplitude). 24,25 This allows to construct a meaningful harmonic solution of eq 3, even if F ts depends in a nonlinear way on z. Correspondingly, the lock-in amplifier in an atomic force microscope usually only measures the parameters of the first harmonic.…”

Probing attractive forces at the nanoscale using higher-harmonic dynamic force microscopy

“…Specifically our discussion follows along the lines of prior studies that have dealt with single-degree-of-freedom models oscillating in a nonquadratic potential well. 7,[26][27][28]30,35,[38][39][40] We consider the case where the only force present is due to the van der Waals interaction between the tip and sample. We also use a more general interaction force law valid for large tip-substrate separations.…”

“…[26][27][28][29][30][31][32][33][34] Because the tipsample interaction forces are inherently nonlinear they modify both the amplitude and phase of the approaching resonating cantilever. In addition, they also generate higher harmonics in the vibration spectrum of the SFM cantilever.…”

Channel modeling and detector design for dynamic mode high density probe storage

“…Such a dependence is well characterized by the Lennard-Jones like force that is typically characterized by weak longrange attractive forces and strong short range repulsive forces (see Figure 1(d)). Thus the probe based data storage system can be viewed as an interconnection of a linear cantilever system G with the nonlinear tip-media interaction forces in feedback (see Figure 1(b) and note that p = G(h + η + g) with h = φ(p)); see [11]). …”