Approximate Real-Time Force Spectroscopy Within Amplitude-Modulation Atomic Force Microscopy Topographical Imaging Using Few Harmonics and Fourier Methods

Quantitative measurement of the probe-sample interaction forces as a function of distance and time during imaging has been at the forefront of atomic force microscopy (AFM) research. This type of information is extremely valuable for understanding the material response to a variety of stimuli and interactions, such as mechanical deformations that vary in magnitude and rate of application, chemical interactions, or electromagnetic interactions. A variety of methods for performing such measurements simultaneously with topographical imaging is available, including methods based on Fourier analysis. Within these methods, reconstruction of the tip-sample force curve generally requires measurement of a large number of harmonics of the probe oscillation, which presents challenges such as the need for specialized hardware, low signal-to-noise ratio, and the need for extensive user expertise. In this paper, we present a simple method to perform a Gaussian-model-based fit of the tip-sample force curve across the surface, simultaneously with imaging, which requires measurement of only the first two or three harmonics for elastic materials. While such an approach only offers an approximate representation of the force curve, it can be highly accurate and fast, and has low instrumentation requirements, such that it can be relatively simple to implement on most commercial AFM setups.