Frequency and force modulation atomic force microscopy: low-impact tapping-mode imaging without bistability

Since the 1980s, atomic force microscopy (AFM) has rapidly developed into a versatile, high-resolution characterization technique, available in a variety of imaging modes. Within intermittent-contact tapping-mode, imaging bistability and sample mechanical damage continue to be two of the most important challenges faced daily by AFM users. Recently, a new double-control-loop tapping-mode imaging algorithm (frequency and amplitude modulation AFM, FAM-AFM) was proposed and evaluated within numerical simulations, demonstrating a reduction in the repulsive tip–sample forces and the absence of bistability. This article presents a much simpler algorithm, frequency and force modulation AFM (FFM-AFM), which requires only a single control loop and offers the same benefits as FAM-AFM. The concept is applied to calculate the cross-sectional scan of a carbon nanotube sample resting on a silicon surface, which is then compared to a previously reported image obtained in conventional amplitude-modulation tapping-mode, shown to be in agreement with the experimental result.