Influence of thermal noise on measured bond lengths in force measurements using dynamic atomic force microscopy

The use of dynamic methods in atomic force microscopy (AFM) has lead to spectacular advances in force measurements and imaging. There has been a gradual shift to stiffer cantilevers and smaller amplitudes, resulting in higher resolution imaging and three-dimensional force mapping. However, when amplitudes become much smaller than 1 Å, they can approach the same order as the thermal noise of the cantilever. In this article, we explore the effect of thermal noise on force measurements using small-amplitude, dynamic AFM. He restricts himself to off-resonance, amplitude-modulation AFM, as this is easiest to model and analyze. He finds that position and force noise increase roughly with the square root of temperature, as expected from the equipartition theorem; however, a closer look reveals a more complicated behavior due to nonlinearities in the system and the competition of position and force noise in these systems.