Excitation frequency dependence of noise and minimum detectable force in amplitude-modulation atomic force microscopy
Phys. Rev. Applied 25, 014033 – Published 14 January, 2026
DOI: https://doi.org/10.1103/z1cp-wxbx
Abstract
Atomic force microscopy (AFM) is a versatile nanoscale imaging technique. Since its force detection accuracy and spatiotemporal resolution are fundamentally limited by the minimum detectable force (MDF) arising from system noise, a deep understanding of MDF is essential for both instrumentation and applications. In particular, elucidating the imaging conditions that minimize the MDF is crucial for observing fragile supramolecular complexes. However, the theoretical MDF of amplitude-modulation (AM) AFM has received little attention, and its formulations remain inconsistent. Specifically, although we recently clarified the strong dependence of force sensitivity on the cantilever’s driving frequency, the optimal excitation frequency from the MDF perspective remains unknown. Here, we present an exact solution for the MDF of AM-AFM that accounts for excitation-frequency-dependent noise and force conversion. Our results show that MDF is strongly governed by the driving frequency and the cantilever Q-factor. In the repulsive regime, driving above the resonance peak frequency causes a sharp MDF increase, exceeding that of other dynamic modes by over an order of magnitude, whereas lower-side-slope excitation yields only ∼1.41–1.73 times larger MDF; similar behavior is observed in the attractive regime. These findings resolve a long-standing inconsistency in the MDF of AM-AFM and demonstrate that slope excitation, rather than resonance excitation, enables the detection of several-fold weaker forces, leading to more accurate force estimation and visualization of previously unobservable fragile molecules.
