Dynamics of damped cantilevers

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.