Dynamics of damped cantilevers

Abstract

In atomic force microscopy cantilevers are used to detect forces caused by interactions between probing tip and sample. The minimum forces which can be detected with commercial sensors are typically in the range of 10−12 N. In the future, the aim will be to construct sensors with improved sensitivities to detect forces in the range of 10−18 N. These sensors could be used for mass spectroscopy or magnetic resonance force microscopy. Achieving this goal requires smaller sensors and increased quality factor Q. In this article we describe a model to characterize the dynamics of cantilevers of each eigenmode. In contrast to previous models, the damping is treated rigorously in the calculations.

A local sensor for joint temperature and velocity measurements in turbulent flows

“…Additionally, the frequency response of the cantilever may be lowered further in fluids. The two main reasons are the effect of the fluid added mass, and the damping due to viscosity [30,31]. The frequency shift for cantilever resonance caused by viscous effects have been extensively studied as it impacts the cantilever thermal noise power spectrum [32,33,34].…”

Amplitude dependence of image quality in atomically-resolved bimodal atomic force microscopy

“…7 Theoretically, the effective stiffness of the second flexural mode is about 40 times higher than in the first flexural mode, and the resonance frequency is about 6.2 times higher. 8,9 This can be implemented with bimodal AFM, 10,11 in which the first flexural mode is excited at a large amplitude and the second flexural mode at a small amplitude to detect short range interactions.…”

“…These amplitudes were calibrated with a thermal spectrum and the ratio of the deflection sensitivity of two flexural modes. 8,23,26,27 The frequency shifts of the first flexural mode, Df 1 , and of the second flexural mode, Df 2 , were recorded in quasi-constant height mode using low gain integral feedback to compensate for thermal drift. This observation mode was chosen to show the short-range force contribution to Df 1 and Df 2 independently.…”

Special cantilever geometry for the access of higher oscillation modes in atomic force microscopy

“…The quality factor might also be influenced by the larger area of the cantilever end anchored to the chip. This could affect the minimum detectable force F n min = ͱ 2k B D n T⌬ / Q n , 15 which depends on Q ͑k B -Boltzmann constant, T-temperature, D n -spring constant of the nth eigenmode, and n -frequency of the nth eigenmode͒.…”