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.