Thermal noise of microcantilevers in viscous fluids

We present a simple theoretical framework to describe the thermal noise of a microscopic mechanical beam in a viscous fluid: we use the Sader approach to describe the effect of the surrounding fluid (added mass and viscous drag) and the fluctuation dissipation theorem for each flexural modes of the system to derive a general expression for the power spectrum density of fluctuations. This prediction is compared with an experimental measurement on a commercial atomic force microscopy cantilever in a frequency range covering the two first resonances. A very good agreement is found on the whole spectrum, with no adjustable parameters but the thickness of the cantilever.