Excitation frequency dependence of noise and minimum detectable force in amplitude-modulation atomic force microscopy

Abstract

Atomic force microscopy (AFM) is a versatile nanoscale imaging technique. Since its spatiotemporal resolution is fundamentally limited by the minimum detectable force (MDF) arising from system noise, a deep understanding of MDF is essential for improving instrumentation. However, the theoretical MDF of amplitude-modulation (AM) AFM has long remained inconsistent, with three reported expressions yielding conflicting coefficients: 1.84, 1.41, and 0.71 times those of other dynamic modes. Moreover, although we recently clarified the strong dependence of force sensitivity on the cantilever's driving frequency, previous theories overlooked this effect. Here, we present an exact solution for the MDF of AM-AFM that accounts for noise frequency dependence, excitation efficiency, and arbitrary cantilever Q-factors. Our results clarify that the coefficient strongly depends on the driving frequency and Q-factor. Notably, when driven at the resonance slope, it stays within 1 and 1.41, thus resolving this long-standing inconsistency. Our findings provide essential guidance for improving instrumentation to visualize previously inaccessible phenomena.