Frequency dependence of viscous and viscoelastic dissipation in coated micro-cantilevers from noise measurement.

We measure the mechanical thermal noise of soft silicon atomic force microscope cantilevers. Using an interferometric setup, we obtain a resolution down to 10(-14) m Hz(-1/2) on a wide spectral range (3-10(5) Hz). The low frequency behavior depends dramatically on the presence of a reflective coating: almost flat spectra for uncoated cantilevers versus a 1/f like trend for coated ones. The addition of a viscoelastic term in models of the mechanical system can account for this observation. Use of Kramers-Kronig relations validate this approach with a complete determination of the response of the cantilever: a power law with a small coefficient is found for the frequency dependence of viscoelasticity due to the coating, whereas the viscous damping due to the surrounding atmosphere is accurately described by the Sader model.